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Title: SOLID state
Description: Easy understanding and applied solid state book written by Smart and Moore
Description: Easy understanding and applied solid state book written by Smart and Moore
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Third Edition
SOLID STATE CHEMISTRY
An Introduction
Third Edition
SOLID STATE CHEMISTRY
An Introduction
Lesley E
...
Moore
Taylor & Francis
Taylor & Francis Group
Boca Raton London New York Singapore
A CRC title, part of the Taylor & Francis imprint, a member of the Taylor & Francis
Group, the academic division of T&F Informa plc
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Reprinted
material is quoted with permission, and sources are indicated
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Reasonable efforts have been made to publish reliable data and information, but the author
and the publisher cannot assume responsibility for the validity of all materials or for the
consequences of their use
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For permission to photocopy or use material electronically from this work, please access
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Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and
are used only for identification and explanation without intent to infringe
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Solid state chemistry: an introduction/Lesley Smart and Elaine Moore
...
p
...
Includes bibliographical references and index
...
paper) 1
...
I
...
) II
...
QD478
...
0421–dc22
2004058533
Taylor & Francis Group is the Academic Division of T&F Informa plc
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taylorandfrancis
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crcpress
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A few
changes of emphasis have been made along the way
...
Chapter 5 now contains a section
on fuel cells and electrochromic materials
...
Chapter 7 now covers mesoporous solids and ALPOs,
and Chapter 8 includes a section on photonics
...
Chapter 11 is new, and looks at the solid state chemical
aspects of nanoscience
...
As ever, we thank our friends in the Chemistry Department at the OU, who have been
such a pleasure to work with over the years, and have made enterprises such as this
possible
...
When we
tried to decide on the changes (apart from updating) to be made, the advice from our
editor was “if it ain’t broke, don’t fix it
...
The main changes from the first edition are two new chapters: Chapter 2 on X-ray
diffraction and Chapter 3 on preparative methods
...
Other additions include an introduction to
ALPOs and to clay minerals in Chapter 7 and to ferroelectrics in Chapter 9
...
We hope that
the book now covers most of the basic undergraduate teaching material on solid state
chemistry
...
Our thanks are also due to Dr
...
As always, we thank our colleagues at the Open University for all their support and
especially the members of the lunch club, who not only keep us sane, but also keep us
laughing
...
Lesley E
...
Moore
Open University, Walton Hall, Milton Keynes
Preface to the First Edition
The idea for this book originated with our involvement in an Open University inorganic
chemistry course (S343: Inorganic Chemistry)
...
It was also apparent that this area was playing a
larger role in the undergraduate syllabus at many universities, due to the exciting new
developments in the field
...
Of those that did most, if not all, were aimed at final year
undergraduates and postgraduates
...
This book is an attempt to provide such a text
...
Examples of solid state
devices are used throughout the book to show how the choice of a particular solid for a
particular device is determined by the properties of that solid
...
It introduces
many of the crystal structures that appear in later chapters and discusses the concepts of
ionic radii and lattice energies
...
Chapter 2 introduces the band theory of solids
...
Physicists more often develop the band model via the free electron theory, which is
included here for completeness
...
Chapter 3 discusses solids that are not perfect
...
Defects lead to
interesting and exploitable properties and several examples of this appear in this chapter,
including photography and solid state batteries
...
Chapter 4
covers low-dimensional solids, the properties of which are not isotropic
...
Chapter 6 deals with
optical properties and Chapter 7 with magnetic properties of solids
...
The approach adopted is deliberately nonmathematical, and assumes only the chemical
ideas that a first-year undergraduate would have
...
As this book originated with an Open University text, it is only right that we should
acknowledge the help and support of our colleagues on the Course Team, in particular
Dr
...
Kiki Warr
...
Joan Mason who read
and commented on much of the script, and to the anonymous reviewer to whom
Chapman & Hall sent the original manuscript and who provided very thorough and useful
comments
...
We hope that some of this transmits itself to the
student
...
Smart and Elaine A
...
Smart studied chemistry at Southampton University
...
D
...
After returning to the United Kingdom, she took an SRC Fellowship
to Bristol University to work on X-ray crystallography for 3 years
...
At the Open University, she has been involved in the production of
undergraduate courses in inorganic and physical chemistry
...
She was also an author on two of these, The Third
Dimension and Separation, Purification and Identification
...
Solid State Chemistry was first produced in 1992
...
Elaine A
...
Phil, in theoretical chemistry with Peter Atkins
...
She has
produced OU teaching texts in chemistry for courses at levels 1, 2, and 3 and has written
texts in astronomy at level 2
...
She oversaw the introduction of
multimedia into chemistry courses and designed multimedia material for levels 1 and 2
...
Rob Janes of the Open University, of Metal-Ligand Bonding,
which is part of a level 3 Course in Inorganic Chemistry and copublished with the Royal
Society of Chemistry
...
She is author or coauthor on over 40 papers in scientific journals
...
BASIC SI UNITS
Physical quantity (and symbol)
Name of SI unit
Length (l)
Metre
m
Mass (m)
Kilogram
kg
Time (t)
Second
s
Electric current (I)
Ampere
A
Thermodynamic temperature (T)
Kelvin
K
Amount of substance (n)
Mole
Luminous intensity (Iv)
Candela
Symbol for unit
mol
cd
DERIVED SI UNITS
Physical quantity (and
symbol)
Name of SI
unit
Symbol for SI derived unit and
definition of unit
Frequency (v)
Hertz
Hz (=s−1)
Energy (U), enthalpy (H)
Joule
J (=kg m2 s−2)
Force
Newton
N (=kg m s−2=J m−1)
Power
Watt
W (=kg m2 s−3=J s−1)
Pressure (p)
Pascal
Pa (=kg m−1 s−2=N m−2=J m−3)
Electric charge (Q)
Coulomb
C (=A s)
Electric potential difference (V) Volt
V(=kg m2 s−3 A−1=J A−1 s−1)
Capacitance (c)
Farad
F (=A2 s4 kg−1 m−2=A s V−1= A2 s2 J−1)
Resistance (R)
Ohm
Ω (=V A−1)
Conductance (G)
Siemen
S (=A V−1)
Magnetic flux density (B)
Tesla
T (=V s m−2=J C−1 s m−2)
SI PREFIXES
10–18
10–15
10–12
10–9
10–6
10–3
10–2
10–1
alto
femto
pico
nano
micro
milli
centi
deci kilo
a
f
p
n
µ
m
c
d
103
k
106
109
1012 1015 1018
mega
giga
tera
peta
exa
M
G
T
P
E
FUNDAMENTAL CONSTANTS
Constant
Symbol
Value
Speed of light in a vacuum
c
2
...
602189×10–19 C
Charge of a proton
e
Charge of an electron
−e
Avogadro constant
NA
6
...
380662×10–23 J K−1
Gas constant
R=NAk
8
...
648456×104 mol−1
Planck constant
h
6
...
05457×10–34 J s
Vacuum permittivity
ε0
8
...
27402×10–24 J T−1
Electron g value
ge
2
...
We have
seen immense strides in the development and understanding of nano-technology, microand meso-porous solids, fuel cells, and the giant magnetoresistance effect, to mention but
a few areas
...
All substances, except helium, if cooled sufficiently form a solid phase; the vast
majority form one or more crystalline phases, where the atoms, molecules, or ions pack
together to form a regular repeating array
...
We look at the structure and bonding in these solids, how the properties of a solid
depend on its structure, and how the properties can be modified by changes to the
structure
...
1 INTRODUCTION
To understand the solid state, we need to have some insight into the structure of simple
crystals and the forces that hold them together, so it is here that we start this book
...
This technique relies on the fact that the distances between atoms in crystals are of the
same order of magnitude as the wavelength of X-rays (of the order of 1 Å or 100 pm): a
crystal thus acts as a three-dimensional diffraction grating to a beam of X-rays
...
(Some of the
principles underlying this technique are discussed in Chapter 2, where we review the
physical methods available for characterizing solids
...
The structures of many inorganic crystal structures can be discussed in terms of the
simple packing of spheres, so we will consider this first, before moving on to the more
formal classification of crystals
...
2 CLOSE-PACKING
Think for the moment of an atom as a small hard sphere
...
1 shows two possible
arrangements for a layer of such identical atoms
...
1 (a), the spheres would move to the positions in Figure 1
...
The layer in Figure 1
...
To build up a
close-packed structure in three-dimensions we must now add a second layer (layer B)
...
The layer B in Figure 1
...
When we
add a third layer, there are two possible positions where it can go
...
This is known as
hexagonal close-packing (hcp) (Figure 1
...
In this structure, the hollows marked
with a dot are never occupied by spheres, leaving very small channels through the layers
(Figure 1
...
Second, the third layer could be positioned over those hollows marked with a dot
...
This is known as
cubic close-packing (ccp) (Figure 1
...
(The names hexagonal and cubic for these
structures arise from the resulting symmetry of the structure—this will be discussed more
fully later on
...
Each sphere in the structure is surrounded by twelve equidistant neighbours—six in
the same layer, three in the layer above and three in the layer below: the coordination
number of an atom in a close-packed structure is thus 12
...
Two different types of space are
contained within a close-packed structure: the first we will consider is called an
octahedral hole
...
5(a) shows two close-packed layers again but now with the
octahedral holes shaded
...
The centres of these spheres lay at the corners
An introduction to crystal structures
3
FIGURE 1
...
Solid state chemistry
4
FIGURE 1
...
An introduction to crystal structures
5
FIGURE 1
...
of an octahedron, hence the name (Figure 1
...
If n spheres are in the array, then there
are also n octahedral holes
...
6(a) shows two close-packed layers, now with the second type of
space, tetrahedral holes, shaded
...
6(b))
...
The octahedral holes in a close-packed structure are much bigger than the tetrahedral
holes—they are surrounded by six atoms instead of four
...
4 Three ccp layers
...
5 (a) Two layers of closepacked spheres with the enclosed
octahedral holes shaded; (b) a
computer representation of an
octahedral hole
...
414r
...
225r (Figure 1
...
Of course, innumerable stacking sequences are possible when repeating close-packed
layers; however, the hexagonal close-packed and cubic close-packed are those of
An introduction to crystal structures
7
maximum simplicity and are most commonly encountered in the crystal structures of the
noble gases and of the metallic elements
...
FIGURE 1
...
Solid state chemistry
8
FIGURE 1
...
414r fitting into an octahedral hole;
(b) a sphere of radius 0
...
1
...
8
...
6
...
) In this structure an atom in the middle of a
cube is surrounded by eight identical and equidistant atoms at the corners of the cube—
An introduction to crystal structures
9
the coordination number has dropped from twelve to eight and the packing efficiency is
now 68%, compared with 74% for close-packing
...
This is built by
placing square layers like the one shown in Figure 1
...
Figure 1
...
9(b) that each atom sits at the
corner of a cube
...
The
majority of metals have one of the three basic structures: hcp, ccp, or bcc
...
The distribution of the packing types among the
most stable forms of the metals at 298 K is shown in Figure 1
...
As we noted earlier, a
very few metals have a mixed hcp/ccp structure of a more complex type
...
FIGURE 1
...
Solid state chemistry
10
FIGURE 1
...
FIGURE 1
...
An introduction to crystal structures
11
1
...
The concept of symmetry is an extremely useful one
when it comes to describing the shapes of both individual molecules and regular
repeating structures, as it provides a way of describing similar features in different
structures so that they become unifying features
...
Take some simple examples illustrated in Figure 1
...
If you imagine a
mirror dividing the spoon in half along the plane indicated, then you can see that
Solid state chemistry
12
FIGURE 1
...
one-half of the spoon is a mirror image or reflection of the other
...
Objects can also possess rotational symmetry
...
11(c) imagine an axle
passing through the centre of the snowflake; in the same way as a wheel rotates about an
An introduction to crystal structures
axle, if the snowflake is rotated through
13
of a revolution, then the new position is
indistinguishable from the old
...
11(d), rotating the 50p coin by of
a revolution brings us to the same position as we started (ignoring the pattern on the
surface)
...
Actions such as rotating a molecule are called symmetry operations, and the
rotational axes and mirror planes possessed by objects are examples of symmetry
elements
...
As chemists, you will come
across both
...
The Hermann-Mauguin notation
can be used to describe the point symmetry of individual molecules but in addition can
also describe the relationship of different molecules to one another in space—their socalled space-symmetry—and so is the form most commonly met in crystallography and
the solid state
...
1
...
1 AXES OF SYMMETRY
As discussed previously for the snowflake and the 50p coin, molecules and crystals can
also possess rotational symmetry
...
12 illustrates this for several molecules
...
12(a) the rotational axis is shown as a vertical line through the O atom in
OF2; rotation about this line by 180° in the direction of the arrow, produces an identical
looking molecule
...
Axes of symmetry are denoted by the symbol n (Cn), where n is the order of the axis
...
The BF3 molecule in Figure 1
...
In the same way, the XeF4 molecule in
(c) has a fourfold axis, 4 (C4), and four quarter turns are necessary to bring it back to the
beginning
...
The smallest rotation possible is 1/∞, and so the axis is an infinite-order axis of
symmetry
...
4
...
In a structure, such a mirror
Solid state chemistry
14
FIGURE 1
...
FIGURE 1
...
plane is known as a plane of symmetry and is given the symbol m (σ)
...
13 illustrate some
examples
...
13(a)), one is
the plane of the molecule, and the other is at right angles to this
...
The diagrams for BF3 and XeF4 (also
planar molecules) only show the planes of symmetry which are perpendicular to the plane
of the molecule
...
4
...
In this operation you have to imagine a
line drawn from any atom in the molecule, through the centre of symmetry and then
continued for the same distance the other side; if for every atom, this meets with an
identical atom on the other side, then the molecule has a centre of symmetry
...
12, XeF4 and BeF2 both have a centre of symmetry, and BF3 and
OF2 do not
...
4
...
The
Hermann-Mauguin inversion axis is a combination of rotation and inversion and is given
the symbol
The symmetry element consists of a rotation by 1/n of a revolution about
the axis, followed by inversion through the centre of symmetry
...
14 for a tetrahedral molecule such as CF4
...
14 The (S4) inversion
(improper) axis of symmetry in the
tetrahedral CF4 molecule
...
Rotation about the axis through 90° takes F1 to the position shown as
a dotted F; inversion through the centre then takes this atom to the F3 position
...
The symmetry element
consists of a rotation by 1/n of a revolution about the axis, followed by reflection through
a plane at right angles to the axis
...
14 thus presents an S4 axis, where the F1
rotates to the dotted position and then reflects to F2
...
1
...
4
...
However, in the solid state, we are interested in regular arrays of
TABLE 1
...
Figure 1
...
In
(a), two OF2 molecules are related to one another by a plane of symmetry; in (b), three
OF2 molecules are related to one another by a threefold axis of symmetry; in (c), two OF2
molecules are related by a centre of inversion
...
Solid state chemistry
18
FIGURE 1
...
1
...
It was first noted by
Robert Hooke in 1664 that the regularity of their external appearance is a reflection of a
high degree of internal order
...
Steno observed in 1671 that this is not because their internal structure
varies but because some faces develop more than others do
...
The constancy of the
interfacial angles reflects the internal order within the crystals
...
This building block is known as the unit cell
...
This is achieved by
defining the shape and symmetry of each unit cell as well as its size and the positions of
the atoms within it
...
5
...
16(a)
...
16(b))
...
This is the only example of a one-dimensional lattice and it
can vary only in the spacing a
...
1
...
2 ONE- AND TWO-DIMENSIONAL UNIT CELLS
The unit cell for the one-dimensional lattice in Figure 1
...
If we took this unit cell and repeated it over again, we would reproduce the
original array
...
16 A one-dimensional
lattice (a,b) and the choice of unit cells
(c)
...
17 Choice of unit cell in a
square two-dimensional lattice
...
In Figure 1
...
There is never one unique
unit cell that is ‘correct
...
This is equally true in two and three dimensions
...
e
...
In
Figure 1
...
All of
these, if repeated, would reproduce the array: it is conventional to choose the smallest cell
that fully represents the symmetry of the structure
...
Figure 1
...
It is always
possible to define a non-centred oblique unit cell, but doing so may lose information
about the symmetry of the lattice
...
17 and (b) in Figure 1
...
However, they each contain one lattice point because four adjacent
unit cells share each lattice point
...
The unit cell marked (a) in Figure 1
...
18 Choice of unit cell in a
centred-rectangular lattice
...
19 An a glide
perpendicular to b
...
This cell is said to be centred and is given the symbol C
...
5
...
4 introduced the idea of symmetry, both in individual molecules and for
extended arrays of molecules, such as are found in crystals
...
The glide plane combines translation with reflection
...
19 is an example of
this symmetry element
...
The +
sign next to the circle indicates that the molecule lies above the plane of the page in the z
direction
...
The symmetry element consists of reflection through this
plane of symmetry, followed by translation
...
In the example illustrated, the translation takes place in
the x direction
...
You will notice two
things about the molecule generated by this symmetry element: first, it still has a + sign
against it, because the reflection in the plane leaves the z coordinate the same and second,
it now has a comma on it
...
The screw axis combines translation with rotation
...
e
...
), and the
translation distance is given by the ratio i/n
...
20 illustrates a 21 screw axis
...
20 A 21 screw axis along z
...
Notice that in this
case the molecule starts above the plane of the paper (indicated by the + sign) but the
effect of a twofold rotation is to take it below the plane of the paper (− sign)
...
21
probably illustrates this more clearly, and shows the different effects that rotational and
screw axes of the same order have on a repeating structure
...
All other symmetry elements—
glide plane, mirror plane, inversion centre, and inversion axis—produce a mirror image
of the original
...
5
...
22
...
e
...
All the possible unit cell shapes that can fulfill this
criterion are illustrated in Figure 1
...
2
...
These unit cell shapes are
determined by minimum symmetry requirements which are also detailed in Table 1
...
The three-dimensional unit cell includes four different types (see Figure 1
...
The primitive unit cell—symbol P—has a lattice point at each corner
...
The body-centred unit cell—symbol I—has a lattice point at each corner and one at
the centre of the cell
...
The face-centred unit cell—symbol F—has a lattice point at each corner and one in
the centre of each face
...
The face-centred unit cell—symbol A, B, or C—has a lattice point at each corner, and
one in the centres of one pair of opposite faces (e
...
, an A-centred cell has lattice
points in the centres of the bc faces)
...
21 Comparison of the
effects of twofold and threefold
rotation axes and screw axes
...
3) are produced
...
2
...
)
FIGURE 1
...
An introduction to crystal structures
25
FIGURE 1
...
The symmetry of a crystal is a point group taken from a point at the centre of a perfect
crystal
...
Combining this with planes of symmetry and centres
of symmetry, we find 32 point groups that can describe the shapes of perfect crystals
...
e
...
2 The seven crystal systems
System
Unit cell
Minimum symmetry requirements
Triclinic
α≠β≠γ≠90° None
a≠b≠c
Monoclinic
α=γ=90°
β≠90°
a≠b≠c
Orthorhombic
α=β=γ=90° Any combination of three mutually perpendicular twofold
a≠b≠c
axes or planes of symmetry
One twofold axis or one symmetry plane
Trigonal/rhombohedral α=β=γ≠90° One threefold axis
a=b=c
Hexagonal
α=β=90°
γ=120°
a=b≠c
Tetragonal
α=β=γ=90° One fourfold axis or one fourfold improper axis
a=b≠c
Cubic
α=β=γ=90° Four threefold axes at 109° 28′ to each other
a=b=c
One sixfold axis or one sixfold improper axis
different space-filling patterns)! These are all documented in the International Tables for
Crystallography (see Bibliography at end of the book)
...
In a real crystal, an atom, a complex ion, a
molecule, or even a group of molecules could occupy a lattice point
...
It is instructive to note how much of a structure these various types of unit cell
represent
...
We can work out similar occupancies for the three-dimensional case
...
A corner site is
shared by eight unit cells, an edge site by four, a face site by two and a molecule at the
body-centre is not shared by any other unit cell (Figure 1
...
Using these figures, we can
work out the number of molecules in each of the four types of cell in Figure 1
...
The results are listed in Table
1
...
An introduction to crystal structures
27
FIGURE 1
...
5
...
It is useful to be able to refer to both crystal faces and to the planes
in the crystal in some way—to give them a name—and this is usually done by using
Miller indices
...
Figure 1
...
A set of parallel lines is defined by two indices, h and k, where h and k are the
number of parts into which a and b, the unit cell edges, are divided by the lines
...
Start by
finding a line next to the one passing through the origin, In the set of lines marked A, the
line next to the one passing through the origin
TABLE 1
...
TABLE 1
...
If the set of lines lies parallel to one of the axes then there is no intercept
and the index becomes zero
...
g
...
Notice
that if we had selected the line on the other side of the origin in A we would have indexed
no difference exists between the two pairs of indices and always the
the lines as the
lines are the same set of lines
...
Notice
hk and the
also, in Figure 1
...
The Miller indices for planes in three-dimensional lattices are given by hkl, where l is
now the index for the z-axis
...
Thus a plane is indexed hkl
when it makes intercepts
and with the unit cell edges a, b, and c
...
27
depicts some cubic lattices with various planes shaded
...
25 Unit cells showing a
molecule on (a) a face, (b) an edge,
and (c) a corner
...
26 A rectangular net
showing five sets of lines, A–E, with
unit cells marked
...
28
...
27(a), the
shaded planes lie parallel to y and z, but leave the unit cell edge a undivided; the Miller
planes are the
indices of these planes are thus 100
...
1
...
6 INTERPLANAR SPACINGS
It is sometimes useful to be able to calculate the perpendicular distance dhkl between
parallel planes (Miller indices hkl)
...
5
...
5
...
These projections are called packing
diagrams because they are particularly useful in molecular structures
Solid state chemistry
32
FIGURE 1
...
An introduction to crystal structures
33
FIGURE 1
...
for showing how the molecules pack together in the crystal, and thus the intermolecular
interactions
...
It has the
simplicity of a universal system which enables unit cell positions to be compared from
structure to structure regardless of variation in unit cell size
...
5 d-spacings in different crystal
systems
Crystal system
Cubic
Tetragonal
Orthorhombic
Hexagonal
dhkl, as a function of Miller indices and lattice parameters
Solid state chemistry
34
Monoclinic
FIGURE 1
...
To take a simple example, in a cubic unit cell with a=1000 pm, an atom with an x
coordinate of 500 pm has a fractional coordinate in the x direction of
Similarly, in the y and z directions, the fractional coordinates are given by and
respectively
...
29 for the body-centred unit cell of Figure
1
...
The projection is shown on the yx plane (i
...
, we are looking at the unit cell straight
down the z-axis)
...
Any z-coordinate that is not 0 or 1
is marked on the diagram in a convenient place
...
1
...
Ions tend to
be formed by the elements in the Groups at the far left and far right of the Periodic Table
...
Cations can also be formed by some of
the Group III(13) elements, such as aluminium, Al3+, by some of the low oxidation state
transition metals and even occasionally by the high atomic number elements in Group
IV(14), such as tin and lead, giving Sn4+ and Pb4+
...
An ionic bond is formed between two oppositely charged ions because of the
electrostatic attraction between them
...
Ionic crystals are therefore
composed of infinite arrays of ions which have packed together in such a way as to
maximize the coulombic attraction between oppositely charged ions and to minimize the
repulsions between ions of the same charge
...
However, just because it is possible to form a particular ion, does not mean that this
ion will always exist whatever the circumstances
...
This is particularly true for the elements in the centre of the Periodic Table
...
6
...
Two later sections (1
...
5 and 1
...
6) look at the crystalline structures of covalently
bonded species
...
Second, we look at molecular crystals, which
are formed from small, individual, covalently-bonded molecules
...
These forces arise due to interactions between dipole moments in the molecules
...
Molecules that do not possess a
dipole also interact with each other because ‘transient dipoles’ arise due to the movement
of electrons, and these in turn induce dipoles in adjacent molecules
...
Finally, in this section, we take a very brief look at the structures of some silicates—
the compounds that largely form the earth’s crust
...
6
...
30
...
30 The CsCl unit cell
...
ions, Cl−, at the corners
...
Note the similarity of this unit cell to the bodycentred cubic structure adopted by some of the elemental metals such as the Group I
(alkali) metals
...
e
...
and at the body-centre
)
...
The unit cell contains one formula unit of CsCl,
with the eight corner chlorines each being shared by eight unit cells
...
Caesium is a large ion (ionic radii are discussed in detail later in Section 1
...
4) and so
is able to coordinate eight chloride ions around it
...
The Sodium Chloride (or Rock Salt) Structure (NaCl)
Common salt, or sodium chloride, is also known as rock salt
...
A unit cell of the sodium chloride structure is illustrated in Figure
1
...
The unit cell is cubic and the structure consists of two interpenetrating face-centred
arrays, one of Na+ and the other of Cl− ions
...
31 The NaCl unit cell
...
FIGURE 1
...
Na, blue spheres; Cl,
grey spheres
...
An alternative way of viewing this structure is to think of it as a cubic close-packed
array of chloride ions with sodium ions filling all the octahedral holes
...
32)
...
31
...
As you might expect from their relative positions in Group I, a sodium ion is smaller
than a caesium ion and so it is now only possible to pack six chlorides around it and not
eight as in caesium chloride
...
If you find this
difficult to see, work it out for yourself by counting the numbers of ions in the different
sites and applying the information given in Table 1
...
Table 1
...
TABLE 1
...
33 (a) An [MX6]
octahedron, (b) a solid octahedron, and
(c) plan of an octahedron with
contours
...
33(a) and Figure 1
...
These can also be depicted
An introduction to crystal structures
39
as viewed from above with contours marked, as in Figure 1
...
Octahedra can link
together via corners, edges, and faces, as seen in Figure 1
...
The
FIGURE 1
...
Solid state chemistry
40
FIGURE 1
...
linking of octahedra by different methods effectively eliminates atoms because some of
the atoms are now shared between them: two MO6 octahedra linked through a vertex has
the formula, M2O11; two MO6 octahedra linked through an edge has the formula, M2O10;
two MO6 octahedra linked through a face has the formula, M2O9
...
An
octahedron has 12 edges, and each one is shared by two octahedra in the NaCl structure
...
35, which shows a NaCl unit cell with three NaCl6
octahedra shown in outline, and one of the resulting tetrahedral spaces is depicted by
shading
...
It can be described as an hcp array of arsenic atoms with nickel
atoms occupying the octahedral holes
...
This is not the case for arsenic: each arsenic atom sits in the centre of a
trigonal prism of six nickel atoms (Figure 1
...
An introduction to crystal structures
41
The Zinc Blende (or Sphalerite) and Wurtzite Structures (ZnS)
Unit cells of these two structures are shown in Figure 1
...
38, respectively
...
Zinc blende is often contaminated by iron, making it very dark in colour and thus lending
it the name of ‘Black Jack’
...
FIGURE 1
...
(For undistorted
hcp c/a=1
...
) Ni, blue spheres;
As, grey spheres, (b) The trigonal
prismatic coordination of arsenic in
NiAs
...
37 The crystal structure of
zinc blende or sphalerite, ZnS
...
FIGURE 1
...
Zn, blue spheres; S,
grey spheres
...
Each zinc ion is thus
tetrahedrally coordinated by four sulfides and vice versa
...
Notice that if all the
atoms were identical, the structure would be the same as that of a diamond (see Section
1
...
5)
...
The wurtzite structure is composed of an hcp array of sulfide ions with alternate
tetrahedral holes occupied by zinc ions
...
Compounds adopting the structure include BeO, ZnO, and
NH4F
...
The coordination number for close-packing, where all the atoms are identical, is
twelve
...
Generally, the larger a cation is, the more anions it can pack around
itself (see Section 1
...
4)
...
6
...
K
...
The structure is illustrated
in Figure 1
...
It can be described as related to a ccp array of calcium ions with fluorides
occupying all of the tetrahedral holes
...
Nevertheless, it gives an exact description of the relative positions of the ions
...
39(a) depicts the fourfold tetrahedral coordination
Solid state chemistry
44
FIGURE 1
...
(a) Computer generated
unit cell as a ccp array of cations: Ca,
An introduction to crystal structures
45
blue spheres; grey spheres, (b) and (c)
The same structure redrawn as a
primitive cubic array of anions
...
of the fluoride ions very clearly
...
39(a)
...
By drawing cubes with fluoride ions at each corner as has been done in Figure 1
...
Indeed, it
is possible to move the origin and redraw the unit cell so that this feature can be seen
more clearly as has been done in Figure 1
...
The unit cell is now divided into eight
smaller cubes called octants, with each alternate octant occupied by a calcium cation
...
In the example with the biggest anion
and smallest cation, Li2Te, the telluriums are approximately close-packed (even though
there is a considerable amount of covalent bonding)
...
However, the anions
could not be described as close-packed because they are not touching
...
These are the only structures where 8:4 coordination is found
...
4)
...
In both structures, the cations occupy all the
octahedral holes in every other anion layer, giving an overall layer structure with 6:3
coordination
...
The
cadmium iodide structure is shown in Figure 1
...
e
...
This is evidence that the bonding in some of these
structures is not entirely ionic, as we have tended to imply so far
...
6
...
Solid state chemistry
46
The Rutile Structure
The rutile structure is named after one mineral form of titanium oxide (TiO2)
...
A unit cell is illustrated in Figure
1
...
The unit cell is tetragonal and the structure again demonstrates 6:3
FIGURE 1
...
Cd, blue
spheres; I, grey spheres
...
It is not geometrically possible for the coordination around Ti to be a perfect
octahedron and for the coordination around O to be a perfect equilateral triangle
...
41(b)
...
41(c) shows a plan of the unit cell looking down
the chains of octahedra so that they are seen in projection
...
Solid state chemistry
48
FIGURE 1
...
(a) Unit cell, (b) parts of
two chains of linked [TiO6] octahedra,
and (c) projection of structure on base
An introduction to crystal structures
49
of unit cell
...
The β-cristobalite Structure
The β-cristobalite structure is named after one mineral form of silicon dioxide, SiO2
...
6
...
The only metal halide adopting this structure is
beryllium fluoride, BeF2, and it is characterized by 4:2 coordination
...
6
...
Many thousands of inorganic crystal structures exist
...
The Bismuth Triiodide Structure (BiI3)
This structure is based on an hcp array of iodides with the bismuths occupying one-third
of the octahedral holes
...
Corundum α-Al2O3
This mineral is the basis for ruby and sapphire gemstones, their colour depending on the
impurities
...
This structure may be described as
an hcp array of oxygen atoms with two-thirds of the octahedral holes occupied by
aluminium atoms
...
However, it is suggested that this structure is adopted in preference to other possible ones
because the four aluminiums surrounding an oxygen approximate most closely to a
regular tetrahedron
...
The Rhenium Trioxide Structure (ReO3)
This structure (also called the aluminium fluoride structure) is adopted by the fluorides of
Al, Sc, Fe, Co, Rh, and Pd; also by the oxides WO3 (at high temperature) and ReO3 (see
Chapter 5, Section 5
...
1)
...
Part of the structure is given in Figure 1
...
Solid state chemistry
50
...
42 (a) Part of the ReO3
structure, (b) ReO3 structure showing
the linking of [ReO6] octahedra, and
An introduction to crystal structures
51
(c) unit cell
...
Mixed Oxide Structures
Three important mixed oxide structures exist: spinel, perovskite, and ilmenite
The Spinel and Inverse-spinel Structures
The spinels have the general formula AB2O4, taking their name from the mineral spinel
MgAl2O4: generally, A is a divalent ion, A2+, and B is trivalent, B3+
...
43 The spinel structure,
CuAl2O4 (AB2O4)
...
Cu, blue spheres;
Al, pink spheres; O, red spheres
...
A spinel crystal containing n AB2O4 formula units has 8n tetrahedral holes and 4n
octahedral holes; accordingly, one-eighth of the tetrahedral holes are occupied by A2+
ions and one-half of the octahedral holes by the B3+ ions
...
43
...
The B ions occupy octahedral sites
...
When compounds of general formula AB2O4 adopt the inverse-spinel structure, the
formula is better written as B(AB)O4, because this indicates that half of the B3+ ions now
occupy tetrahedral sites, and the remaining half, together with the A2+ ions, occupy the
Solid state chemistry
52
octahedral sites
...
7) Fe(MgFe)O4, and Fe(ZnFe)O4
...
A unit cell is shown in Figure 1
...
The central Ca (A) atom is
coordinated to 8 Ti atoms (B) at the corners and to 12 oxygens (X) at the midpoints of the
cell edges
...
First, it can be
described as a ccp array of A and X atoms with the B atoms occupying the octahedral
holes (compare with the unit cell of NaCl in Figure 1
...
Second, perovskite has the same octahedral framework as ReO3 based on BX6 octahedra
with an A atom added in at the centre of the cell (Figure 1
...
Compounds adopting
this structure include SrTiO3, SrZrO3, SrHfO3, SrSnO3, and BaSnO3
...
3
...
FIGURE 1
...
See colour insert following
page 196
...
The Ilmenite Structure
The ilmenite structure is adopted by oxides of formula ABO3 when A and B are similar in
size and their total charge adds up to +6
...
The structures related to close-packing are summarized in Table 1
...
1
...
4 IONIC RADII
We know from quantum mechanics that atoms and ions do not have precisely defined
radii
...
It is a
very useful concept, therefore, particularly for those structures based on close-packing, to
think of ions as hard spheres, each with a particular radius
...
Table 1
...
From Table 1
...
We can see, however, that the picture is not precisely true, neither would we
expect it to be, because atoms and ions are squashable entities and their
TABLE 1
...
Nevertheless, it is a useful concept to
develop a bit further as it enables us to describe some of the ionic crystal structures in a
simple pictorial way
...
Each set is named after the
person(s) who originated the method of determining the radii
...
It is most
important to remember that you must not mix radii from more than one set of values
...
e
...
8 Interatomic distances of some alkali
halides, rM-x/pm
F−
Cl−
Br−
I−
Li+
201
30
56
257
24
18
275
23
27
302
21
Na+
231
35
50
281
33
17
298
31
25
323
30
K+
266
16
48
314
14
15
329
14
24
353
13
Rb+
282
46
328
15
343
23
366
of values, you will obtain an approximately correct internuclear distance as determined
from the crystal structure)
...
In order to
obtain values for individual ionic radii from these, the value of one radius needs to be
fixed by some method
...
Once the iodide radius is
known then the radii of the metal cations can be found from the structures of the metal
iodides—and so on
...
It is very difficult to come up with a consistent set of values for the ionic
radii, because of course the ions are not hard spheres, they are somewhat elastic, and the
radii are affected by their environment such as the nature of the oppositely charged ligand
and the coordination number
...
Pauling’s method was to
take a series of alkali halides with isoelectronic cations and anions and assume that they
are in contact: if you then assume that each radius is inversely proportional to the
effective nuclear charge felt by the outer electrons of the ion, a radius for each ion can be
calculated from the internuclear distance
...
With
some refinements this method gave a consistent set of values that was widely used for
many years; they are usually known as effective ionic radii
...
Such a map is shown for NaCl and LiF in Figure
1
...
The electron density contours fall to a minimum—although not to zero—in between
the nuclei and it is suggested that this minimum position should be taken as the radius
position for each ion
...
The most comprehensive set of
radii has been compiled by
FIGURE 1
...
Solid state chemistry
56
Shannon and Prewitt using data from almost a thousand crystal structure determinations
and based on conventional values of 126 pm and 119 pm for the radii of the O2− and F−
ions, respectively
...
A selection of this data is shown in Table 1
...
Several important trends in the sizes of ions can be noted from the data in Table 1
...
The radii of ions within a Group of the Periodic Table, such as the alkali metals,
increase with atomic number, Z: as you go down a Group, more electrons are present,
and the outer ones are further from the nucleus
...
In a series of isoelectronic cations, such as Na+, Mg2+, and Al3+, the radius decreases
rapidly with increasing positive charge
...
3
...
g
...
4
...
g
...
In this case, the nuclear charge stays the same, but the
number of electrons that it acts on decreases
...
As you move across the Periodic Table for a series of similar ions, such as the first row
transition metal divalent ions, M2+, there is an overall decrease in radius
...
A similar effect is observed for the
M3+ ions of the lanthanides and this is known as the lanthanide contraction
...
D
...
, A32 (1976), 751
...
6
...
7
...
9
...
The picture of ions as hard spheres works best for fluorides and oxides, both of which are
small and somewhat uncompressable ions
...
When we were discussing particular crystal structures in the previous section we noted
that a larger cation such as Cs+, was able to pack eight chloride ions around it, whereas
the smaller Na+ only accommodated six
...
The lattice would not be stable in this state because the negative charges
would be too close together for comfort and we would predict that the structure would
change to one of lower coordination, allowing the anions to move further apart
...
e
...
46
...
46(a) and the limiting case for stability, when the
anions are touching, in Figure 1
...
The anion radius, r− in Figure 1
...
From the geometry of the right-angled triangle we can
see
that
The
radius
ratio,
is
given
by
Using similar calculations it is
possible to calculate limiting ratios for the other geometries: Table 1
...
On this basis, we would expect to be able to use the ratio of ionic radii to predict
possible crystal structures for a given substance
...
This is because the model is too
Solid state chemistry
58
simplistic—ions are not hard spheres, but are polarized under the influence of other ions
instead
...
The ability of an ion to distort an electron cloud—its polarizing power—
is greater for small ions with high charge; the distortion of the electron cloud means that
the bonding between two such ions becomes more directional in character
...
The higher the formal charge on a metal ion, the greater will be the
proportion of covalent
FIGURE 1
...
bonding between the metal and its ligands
...
It also seems that there is
little energy difference between the six-coordinate and eight-coordinate structures, and
the six-coordinate structure is usually preferred—eight-coordinate structures are rarely
found, for instance, no eight-coordinate oxides exist
...
In this structure, the three orthogonal p orbitals lie in the same direction as
the vectors joining the cation to the surrounding six anions
...
10 Limiting radius ratios for different
coordination numbers
Coordination number
Geometry
Limiting radius ratio
Possible structures
0
...
414
6
Octahedral
Rock-salt, rutile
0
...
00
σ bonding to take place
...
1
...
5 EXTENDED COVALENT ARRAYS
The last section noted that many ‘ionic’ compounds in fact possess some degree of
covalency in their bonding
...
Indeed, some of
these elements themselves are covalently bonded solids at room temperature
...
Take, for instance, one of the forms of carbon: diamond
...
47); the positions of the atomic
Solid state chemistry
60
FIGURE 1
...
centres are the same as in the zinc blende structure, with carbon now occupying both the
zinc and the sulfur positions
...
It is interesting to note how the
different type of bonding has affected the coordination: here we have identical atoms all
the same size but the coordination number is now restricted to four because this is the
maximum number of covalent bonds that carbon can form
...
The covalent bonds in
diamond are strong, and the rigid three-dimensional network of atoms makes diamond
the hardest substance known; it also has a high melting temperature (m
...
) (3773 K)
...
Silica (SiO2) gives us other examples of giant molecular structures
...
Each of these
also exists in low and high temperature forms, α- and β-, respectively
...
6
...
Quartz
is commonly encountered in nature: the structure of β-quartz is illustrated in Figure 1
...
Notice how once again the
covalency of each atom dictates the coordination around itself, silicon having four bonds
and oxygen two, rather than the larger coordination numbers that are found for metallic
and some ionic structures
...
An introduction to crystal structures
61
For our final example in this section, we will look at the structure of another
polymorph of carbon
...
49
...
48 The β-quartz structure
...
49 SThe crystal structure
of graphite
...
) The structure of normal graphite consists of
two-dimensional layers of carbon atoms joined together in a hexagonal array
...
This
carbon-carbon distance is rather shorter than the one observed in diamond, due to the
Solid state chemistry
62
presence of some double bonding
...
7 pm
...
Graphite is a soft grey solid with a high m
...
and
low density; its softness is attributed to the weak bonding between the layers which
allows them to slide over one another
...
In addition, graphite crystals shear easily
parallel to the layers
...
In fact, its lubricant properties are dependent on an adsorbed
layer of nitrogen, and when this is lost under extreme conditions such as low pressure or
high temperature, then the lubricant properties are also lost
...
The electrons in
the delocalised π-orbital are mobile, and so graphite is electrically conducting in the
layers like a two-dimensional metal, but is a poor conductor perpendicular to the layers
...
6
...
In
Section 1
...
In Section 1
...
In the graphite structure we see covalently bonded layers of carbon atoms held
together by weak van der Waals forces, and will meet this again, together with hydrogen
bonding in the next section on molecular crystal structures
...
These electrons occupy the space between the cations, binding them together, but are able
to move under the influence of an external field, thus accounting for the electrical
conductivity of metals
...
The attractive force, F, is given by Coulomb’s Law:
where q1 and q2 are the charges on the two ions, and r is the distance between
them
...
Ionic
bonds are strong and nondirectional; the energy of the interaction is given by
force×distance, and is inversely proportional to the separation of the charges, r
...
Ions
An introduction to crystal structures
63
pack together in regular arrays in ionic crystals, in such a way as to maximize Coulombic
attraction, and minimize repulsions
...
Covalent bonds are strong and directional
...
The separation of
negative and positive charge creates an electric dipole, and the molecule can align itself
in an electric field
...
The partial electric charges on
polar molecules can attract one another in a dipole-dipole interaction
...
The movement of the valence electrons creates ‘transient dipoles’, and
these in turn induce dipole moments in adjacent molecules
...
These dispersion forces drop off rapidly with distance, decreasing as a function of
The weak nonbonded interactions that occur between molecules are often referred to
collectively as van der Waals forces
...
Where hydrogen is
bonded to a very electronegative element such as oxygen or fluorine, there is a partial
negative charge, δ−, on the electronegative element, and an equal and opposite δ+ charge
on the hydrogen
...
A network of alternating
Solid state chemistry
64
weak and strong bonds is built up, and examples can be seen in water (H2O) and in
hydrogen fluoride (HF)
...
1
...
7 ATOMIC RADII
An atom in a covalently bonded molecule can be assigned a covalent radius, rc and a
non-bonded radius, known as the van der Waals radius
...
For diatomic molecules such as F2, this is no problem, but for other
elements, such as carbon, which do not have a diatomic molecule, an average value is
calculated from a range of compounds that contain a C–C single bond
...
Again, these are average values compiled
from many crystal structures
...
11 Single-bond covalent radii and van
der Waals radii (in parentheses) for the typical
elements/pm
Group
I
Group
II
Group
III
Group
IV
Group
V
Group
VI
Group
VII
H
Group
VIII
He
37 (120)
−(140)
Li
Be
B
C
N
O
F
Ne
135
90
80
77 (170)
74 (155)
73 (152)
71 (147)
−(154)
Na
Mg
Al
Si
P
S
Cl
Ar
154
130
125
117 (210)
110 (180) 104 (180)
99 (175)
−(188)
K
Ca
Ga
Ge
As
Br
Kr
200
174
126
122
121 (185) 117 (190)
114 (185)
−(202)
Rb
Sr
In
Sn
Sb
Te
I
Xe
211
192
141
137
141
137 (206)
133 (198)
−(216)
Cs
Ba
T1
Pb
Bi
Po
At
Rn
225
198
171
175
170
140
–
–
Se
then it is assumed that there is some bonding between them
...
11 gives the
covalent and van der Waals radii for the typical elements
...
6
...
The example of graphite in the previous section in a way forms a bridge between these
structures and the structures with infinite three-dimensional arrays
...
Examples of molecular crystals are found throughout organic, organometallic, and
inorganic chemistry
...
We
will look at just two examples, carbon dioxide and water (ice), both familiar, small,
covalently bonded molecules
...
50
...
The structure of one form of ice (crystalline water) is depicted in Figure 1
...
Each
H2O molecule is tetrahedrally surrounded by four others
...
This open hydrogen-bonded network of water molecules makes ice less dense
than water, so that it floats on the surface of water
...
12, relating
the type of structure to its physical properties
...
50 (a) The crystal structure
of CO2, (b) packing diagram of the unit
cell of CO2 projected on to the xy
plane
...
C, blue spheres; O, grey spheres
...
An introduction to crystal structures
67
1
...
9 SILICATES
The silicates form a large group of crystalline compounds with rather complex but
interesting structures
...
Silicon itself crystallizes with the same structure as diamond
...
5
...
51 The crystal structure of
ice
...
(Section 1
...
5)
...
The silicon atom in all these structures is tetrahedrally coordinated
...
12 Classification of crystal structures
Type
Structural
unit
Bonding
Characteristics
Examples
Ionic
Cations and
anions
Electrostatic, nondirectional
Hard, brittle, crystals of high
m
...
; moderate insulators;
melts are conducting
Alkali metal
halides
Extended
covalent
array
Atoms
Mainly covalent
Strong hard crystals of high
m
...
; insulators
Diamond,
silica
Molecular
Molecules
Mainly covalent
between atoms in
molecule, van der
Waals or hydrogen
bonding between
Soft crystals of low m
...
and
Ice, organic
large coefficient of expansion; compounds
insulators
Solid state chemistry
68
molecules
Metallic
Metal atoms Band model (see
Chapter 4)
Single crystals are soft;
Iron,
strength depends on structural aluminium,
defects and grain; good
sodium
conductors; m
...
s vary but
tend to be high
FIGURE 1
...
The silicate structures are most conveniently discussed in terms of the SiO44− unit
...
52(a)
...
Some minerals, such as olivines (Figure 1
...
These compounds do not contain Si—O—Si—O—Si—…chains, but there is
considerable covalent character in the metal-silicate bonds
...
The structure of olivine itself, (Mg,Fe)2SiO4, which can be described as an assembly of
SiO44− ions and Mg2+ (or Fe2+) ions, appears earlier in Table 1
...
In most silicates, however, the SiO44− tetrahedra are linked by oxygen sharing through
a vertex, such as is illustrated in Figure 1
...
Notice that each terminal oxygen confers a negative charge on the
FIGURE 1
...
See colour insert following page 196
...
anion and the shared oxygen is neutral
...
52, omit these charges as they can
be readily calculated
...
The negative charges
on the silicate framework are balanced by metal cations in the lattice
...
Solid state chemistry
70
Discrete SiO44− Units
Examples are found in: olivine (Table 1
...
53) an important constituent of
basalt; garnets, M3IIM2III(SiO4)3 (where MII can be Ca2+, Mg2+, or Fe2+, and MIII can be
Al3+, Cr3+, or Fe3+) and the framework of which is composed of MIIIO6 octahedra which
are joined to six others via vertex-sharing SiO4 tetrahedra—the MII ions are coordinated
by eight oxygens in dodecahedral interstices; Ca2SiO4, found in mortars and Portland
cement; and zircon, ZrSiO4, which has eight-coordinate Zr
...
52(b)) are not common but occur in thortveitite,
Sc2Si2O7, and hemimorphite, Zn4(OH)2Si2O7
...
52(c))
...
Minerals with this structure are called pyroxenes (e
...
, diopside (CaMg(SiO3)2)
and enstatite (MgSiO3))
...
FIGURE 1
...
See colour insert following
page 196
...
Double Chains
Here alternate tetrahedra share two and three oxygen atoms, respectively, as in Figure
1
...
This class of minerals is known as the amphiboles (Figure 1
...
Most of the asbestos minerals fall in this
class
...
An introduction to crystal structures
71
Infinite Layers
The tetrahedra all share three oxygen atoms (Figure 1
...
The repeat unit is Si4O104−
...
g
...
55) and talc (Mg3(OH)2Si4O10) are members, and
contains a sandwich of two layers with octahedrally coordinated cations between the
layers and clay minerals such as kaolin, Al4(OH)8Si4O10
...
Figure 1
...
52(g)
show three and six tetrahedra linked together; these have the general formula [SiO3]n−2n;
rings also may be made from four tetrahedra
...
Other
examples include dioptase (Cu6Si6O18
...
Three-dimensional Structures
4−
If SiO4 tetrahedra share all four oxygens, then the structure of silica, SiO2 is produced
...
e
...
Such minerals include the feldspars (general
formula, M(Al,Si)4O8) the most abundant of the rock-forming minerals; the zeolites,
which are used as ion exchangers, molecular sieves, and catalysts (these are discussed in
detail in Chapter 7); the ultramarines, which are
Solid state chemistry
72
FIGURE 1
...
See colour insert following page 196
...
coloured silicates manufactured for use as pigments, lapis lazuli being a naturally
occurring mineral of this type
...
For instance, cement contains
discrete SiO44− units and is soft and crumbly; asbestos minerals contain double chains of
SiO44− units and are characteristically fibrous; mica contains infinite layers of SiO44−
units, the weak bonding between the layers is easily broken, and micas show cleavage
parallel to the layers; and granite contains feldspars that are based on three-dimensional
SiO44− frameworks and are very hard
...
7 LATTICE ENERGY
The lattice energy, L, of a crystal is the standard enthalpy change when one mole of the
solid is formed from the gaseous ions (e
...
, for NaCl,
for the reaction in
Equation (1
...
An introduction to crystal structures
73
Na+(g)+Cl−(g)=NaCl(s)
(1
...
7
...
FIGURE 1
...
1
...
1 THE BORN-HABER CYCLE
A Born-Haber cycle is the application of Hess’s Law to the enthalpy of formation of an
ionic solid at 298 K
...
A Born-Haber cycle for a metal chloride
(MCl) is depicted in Figure 1
...
From Hess’s law, the sum of the enthalpy changes for each step around
the cycle can be equated with the standard enthalpy of formation, and we get that:
(1
...
The
terms in the Born-Haber cycle are defined in Table 1
...
Notice that the way in which we have defined lattice energy gives negative values; you
may find Equation (1
...
Notice also that electron affinity is defined as the heat
evolved when an electron is added to an atom; as an enthalpy change refers to the heat
absorbed, the electron affinity and the enthalpy change for that process, will have
opposite signs
...
The difficulty in these cycles
sometimes comes in the determination of values for the electron affinity, E
...
3)
This can be broken down into two stages:
e−(g)+O(g)=O−(g)
(1
...
13 Terms in the Born-Haber cycle
NaCl/ kJ
mol−1
AgCl/ kJ
mol−1
107
...
6
M(g)=M+(g)+e−(g)
First ionization energy of metal M
494
732
122
122
−349
−349
−411
...
1
Half the dissociation energy of Cl2
−E(Cl)
Cl(g)+e−(g)=Cl−(g)
The enthalpy change of this reaction is defined as
minus the electron affinity of chlorine
L(MCl,s)
M+(g)+Cl−(g)=MCl(s)
Lattice energy of MCl(s)
Standard enthalpy of formation of MCl(s)
−
e (g)+O(g)=O−(g)
(1
...
5)
experimentally, and so this value can only be found if the lattice energy is known—a
Catch-22 situation! To overcome problems such as this, methods of calculating (instead
of measuring) the lattice energy have been devised and they are described in the next
section
...
7
...
The energy of an ion pair, M+, X− (assuming they are point
charges), separated by distance, r, is given by Coulomb’s Law:
An introduction to crystal structures
75
(1
...
7)
FIGURE 1
...
(e is the electronic charge, 1
...
854×10–
F m−1)
...
The
series will include terms due to the attraction of the opposite charges on cations and
anions and repulsion terms due to cation/cation and anion/anion interactions
...
57
depicts some of these interactions for the NaCl structure
...
The
of
coulombic energy of interaction is given by the summation of all these interactions:
Solid state chemistry
76
or
(1
...
The series is slow to converge, but values of the Madelung constant have
been computed, not only for NaCl, but also for most of the simple ionic structures
...
9)
TABLE 1
...
763
2
0
...
748
2
0
...
519
3
0
...
638
2
0
...
641
2
0
...
172
5
0
...
408
3
0
...
022×1023 mol−1
...
14
...
At small distances, these electron clouds repel each other,
and this too needs to be taken into account when calculating the lattice energy of the
crystal
...
Max Born suggested that the form of this
repulsive interaction could be expressed by:
An introduction to crystal structures
77
(1
...
We can now write an expression for the lattice energy in terms of the energies of the
interactions that we have considered:
(1
...
e
...
If we minimize the lattice energy
(see Box), we get:
(1
...
The other
terms in the equation are well-known constants, and when values for these are
substituted, we get:
(1
...
Derivation of the Born-Landé Equation
We can minimize the lattice energy function by using the standard mathematical
technique of differentiating with respect to r and then equating to zero:
Solid state chemistry
78
(1
...
The values of these constants are given in Table 1
...
For
example, n for rubidium chloride, RbCl, is 9
...
33 (the average of 9, 9, and 10)
...
A structure containing one doubly charged ion has a factor of two in the equation
(Z+Z−=2), whereas one containing two doubly charged ions is multiplied by a factor of
four (Z+Z_=4)
...
TABLE 1
...
F
...
14) varying only
between approximately 0
...
80
...
We can now set up a general equation and use the resulting equation to
calculate the lattice energy of an unknown structure
...
12) with value from the NaCl structure, 0
...
14)
If n is assigned an average value of 9, we arrive at:
(1
...
Some lattice energy values that have been calculated by various methods are shown in
Table 1
...
Remarkably good agreement is achieved, considering all the
approximations involved
...
The equations can be
improved to help with these discrepancies by including the effect of van der Waals
forces, zero point energy (the energy due to the vibration of the ions at 0 K), and heat
capacity
...
It is important to note that the good agreement achieved between the Born-Haber and
calculated values for lattice energy, do not in any way prove that the ionic model is valid
...
TABLE 1
...
12b
calculationc
Equation 1
...
A
...
b
D
...
Morris (1957) J
...
Nucl
...
, 4, 8
...
Cubiociotti (1961) J
...
Phys
...
E
...
B
...
Phys
...
, 69, 3611; H
...
B
...
F
...
Roy
...
, (A) 356, 115
...
As we end this section, let us reconsider ionic radii briefly
...
Clearly, it is going to be extremely difficult to
measure the radii of ions such as ammonium, NH4+, or carbonate, CO32−, for instance
...
Such values are called thermochemical radii, and Table 1
...
1
...
3 CALCULATIONS USING THERMOCHEMICAL CYCLES
AND LATTICE ENERGIES
It is not yet possible to measure lattice energy directly, which is why the best
experimental values for the alkali halides, as listed in Table 1
...
This in itself is not always easy for compounds other than the
alkali halides because, as we noted before, not all of the data is necessarily available
...
17 Thermochemical radii of
polyatomic ionsa
Ion
pm
+
NH4
Ion
pm
−
151
Me4N
+
ClO4
215
+
−
171
PH4
−
AlCl4
281
BF4
−
BH4−
CN
−
CNS
2−
CO3
Ion
pm
2−
226
MnO4
215
177
2−
144
−
119
2−
282
2−
199
164
O2
OH
PtF6
218
−
CH3COO
ClO3
PtCl6
299
N3−
181
PtBr62−
328
140
BrO3
−
108
179
−
IO3
−
148
157
−
NCO
−
NO2
NO3
−
189
178
165
2−
328
2−
244
PtI6
SO4
SeO4
2−
235
a
J
...
Huheey (1983) Inorganic Chemistry, 3rd edn, Harper & Row, New York; based on data from
H
...
B
...
P
...
Chem
...
, 56, 576
...
16):
2e−(g)+S(g)=S2−(g)
(1
...
This is where
lattice energy calculations come into their own because we can use one of the methods
discussed previously to calculate a value of L for the appropriate sulfide and then plug it
into the thermochemical cycle to calculate the enthalpy change of Equation (1
...
Proton affinities can be found in a similar way: a proton affinity is defined as the
enthalpy change of the reaction shown in Equation (1
...
AH+(g)=A(g)+H+(g)
(1
...
Take as an example the formation of the ammonium ion, NH4+(g):
NH3(g)+H+(g)=NH4+(g)
(1
...
18) is minus the proton affinity of
ammonia, −P(NH3,g)
...
58, provided the lattice energy of ammonium chloride is known
...
For instance, we can use arguments to determine whether it is
possible to prepare a compound of sodium in a higher oxidation state
FIGURE 1
...
than normal, NaCl2
...
59
...
The summation becomes:
(1
...
18 lists the relevant values
...
Why? A glance at the figures in Table 1
...
Therefore, NaCl2
does not exist because the extra stabilization of the lattice due to a doubly charged ion is
not enough to compensate for the large second ionization energy
...
59 Born-Haber cycle for a
metal dichloride, MCl2
...
18 Values of the Born-Haber cycle
terms for NaCl2 and MgCl2/kJ mol−1
Na
Mg
108
148
494
736
I1
4565
1452
D(Cl-Cl)
244
244
−2E(Cl)
−698
−698
L(MCl2,s)
−2523
−2523
I1
a
2190
a
641
+
The second ionization energy, I2, refers to the energy change of the reaction: M (g)−e (g)=M2+(g)
...
Interestingly, it was arguments and calculations of this sort that led Neil Bartlett to the
discovery of the first noble gas compound, XePtF6
...
He realised that the ionization energies of
oxygen and xenon are very similar and that although the radius of the Xe+ ion is slightly
different, because the PtF6− anion is very large the lattice energy of [Xe+][PtF6−] should
be very similar to that of the dioxygenyl complex and therefore should exist!
Solid state chemistry
84
Accordingly, he mixed xenon and PtF6 and obtained the orange-yellow solid of xenon
hexafluoroplatinate—the first noble gas compound
...
)
Several examples of problems involving these types of calculation are included in the
questions at the end of the chapter
...
8 CONCLUSION
This opening chapter has introduced many of the principles and ideas that lie behind a
discussion of the crystalline solid state
...
Taking these ideas
further, we have investigated the size of these ions in terms of their radii, and
FIGURE 1
...
thence the energy involved in forming a lattice with ionic bonding
...
QUESTIONS*
1
...
60 depicts several molecules
...
An introduction to crystal structures
85
2
...
14 possess a centre of inversion? What other
rotation axis is coincident with the
3
...
17?
4
...
Index the sets of lines in Figure 1
...
6
...
27(b), (c), and (d)
...
Figure 1
...
If a single atom is
placed at each lattice point then this becomes the unit cell of the ccp (cubic close-packed)
structure
...
(Hint: Calculate the area of each plane assuming a cell
length a
...
)
8
...
30, 1
...
37 together with models if necessary, draw unit cell
projections for (a) CsCl, (b) NaCl, and (c) ZnS (zinc blende)
...
How many formula units, ZnS, are there in the zinc blende unit cell?
10
...
e
...
11
...
*Answers to even-numbered questions are found in the Solutions Manual
...
19 Values of the Born-Haber cycle
terms for CaCl2/kJ mol−1
Term
Value
178
I1
590
I2
1146
D(Cl−Cl)
244
−2E(Cl)
−698
−795
...
A compound AgX has the same crystal structure as NaCl, a density of 6477 kg
m−3, and a unit cell dimension of 577
...
Identify X
...
Estimate a value for the radius of the iodide ion
...
14
...
8 for NaI and NaF
...
15
...
47
...
(See Question 7
...
Use the Born-Haber cycle in Figure 1
...
19 to calculate the
lattice energy of solid calcium chloride, CaCl2:
17
...
61
...
Assume that no ions exist other than
those shown in the figure, and that the charges on the cations and anion are +1 and −1,
respectively
...
Calculate a value for the lattice energy of potassium chloride using Equation
(1
...
Compare this with the value you calculate from the thermodynamic data in Table
1
...
FIGURE 1
...
All bond lengths are equal and
bond angles are 90°
An introduction to crystal structures
87
TABLE 1
...
1
I1
418
122
−E(Cl)
−349
−436
...
21 Values of the Born-Haber cycle
terms for FeS/kJ mol−1
Term
Value
416
...
8
−100
...
22 Values of the Born-Haber cycle
terms for MgO/kJ mol−1
Term
Value
147
...
7
E(O)
141
Solid state chemistry
88
TABLE 1
...
0
−314
...
Calculate a value for the electron affinity of sulfur for two electrons
...
Use the data given in Table 1
...
20
...
Take
magnesium oxide, MgO, as a model and devise a suitable cycle
...
22
...
Calculate a value for the proton affinity of ammonia using the cycle in Figure 1
...
23
...
Compounds of aluminium and magnesium in the lower oxidation states, Al(I) and
Mg(I), do not exist under normal conditions
...
Use this information in a Born-Haber cycle to calculate
a value of the enthalpy of formation,
for AlCl(s) and MgCl(s), using the data in
Table 1
...
TABLE 1
...
1 INTRODUCTION
A vast array of physical methods are used to investigate the structures of solids, each
technique with its own strengths and weaknesses—some techniques are able to
investigate the local coordination around a particular atom or its electronic properties,
whereas others are suited to elucidating the long-range order of the structure
...
We start with X-ray diffraction by powders and single
crystals
...
It gives an overall, average picture of a long-range ordered
structure, but is less suited to giving information on the structural positions of defects,
dopants, and non-stoichiometric regions
...
Powder X-ray diffraction is
probably the most commonly employed technique in solid state inorganic chemistry and
has many uses from analysis and assessing phase purity to determining structure
...
2
...
2
...
The benefits of his
discovery in terms of medical diagnosis and treatment, and in investigating molecular and
atomic structure are immeasurable, and yet Röntgen was a man of such integrity that he
refused to make any financial gain out of his discovery, believing that scientific research
should be made freely available
...
1 (a))
...
Solid state chemistry
92
FIGURE 2
...
peaks (Kα, Kβ) as depicted in Figure 2
...
The frequencies of the Kα and Kβ lines are
characteristic of the anode metal; the target metals most commonly used in X-ray
crystallographic studies are copper and molybdenum, which have Kα lines at 154
...
07 pm, respectively
...
The decrease in energy appears
Physical methods for characterizing solids
93
as radiation; electrons descending from the L shell (n=2) give the Kα lines and electrons
from the M shell (n=3) give the Kβ lines
...
) As the atomic
number, Z, of the target increases, the lines shift to shorter wavelength
...
Usually the Kα line is selected and the Kβ line
is filtered out by using a filter made of a thin metal foil of the element adjacent (Z−1) in
the Periodic Table; thus, nickel effectively filters out the Kβ line of copper, and niobium
is used for molybdenum
...
2
...
2 DIFFRACTION OF X-RAYS
By 1912, the nature of X-rays—whether they were particles or waves—was still
unresolved; a demonstration of X-ray diffraction effects was needed to demonstrate their
wave nature
...
Crystalline solids consist of regular arrays of atoms, ions or molecules with
interatomic spacings of the order of 100 pm
...
Because of the periodic nature of the internal structure, it is possible for crystals
to act as a three-dimensional diffraction grating to light of a suitable wavelength: a Laue
photograph is pictured in Figure 2
...
FIGURE 2
...
Solid state chemistry
94
(From W
...
Moore (1972) Physical
Chemistry, 5th edn, Longman,
London
...
3 Bragg reflection from a
set of crystal planes with a spacing dhkl
...
H
...
L
...
In 1913 they first determined the crystal structure of NaCl, and they went
on to determine many structures including those of KCl, ZnS, CaF2, CaCO3, and
diamond
...
L
...
It is
not like the reflection of light from a mirror, as this requires that the angle of incidence
equals the angle of reflection, and this is possible for all angles
...
Figure 2
...
The
array of black points in the diagram represents a section through a crystal and the lines
joining the dots mark a set of parallel planes with Miller indices hkl and interplanar
spacing dhkl
...
The ray A is scattered by the atom at B and the ray D is scattered by the atom
at F
...
This is known as constructive
interference, and for constructive interference to take place, the path lengths of the
interfering beams must differ by an integral number of wavelengths
...
1)
This must be equal to an integral number, n, of wavelengths
...
2)
This is known as the Bragg equation, and it relates the spacing between the crystal
planes, dhkl, to the particular Bragg angle, θhkl at which reflections from these planes are
observed (mostly the subscript hkl is dropped from the Bragg angle θ without any
ambiguity as the angle is unique for each set of planes)
...
However, the Bragg equation for a second order reflection from a
set of planes hkl is
2λ=2dhklsinθ
which can be rewritten as
(2
...
3 represents a first order reflection from a set of planes with interplanar
The set of planes with interplanar spacing
has Miller indices 2h 2k 2l
...
4)
2
...
3
...
If such a sample is placed in
the path of a monochromatic X-ray beam, diffraction will occur from planes in those
crystallites which happen to be oriented at the correct angle to fulfill the Bragg condition
...
Because the
crystallites can lie in all directions while still maintaining the Bragg condition, the
reflections lie on the surface of cones whose semi-apex angles
FIGURE 2
...
are equal to the deflection angle 2θ (Figure 2
...
In the Debye-Scherrer photographic
method, a strip of film was wrapped around the inside of a X-ray camera (Figure 2
...
The sample was rotated to bring as many planes as possible into the
diffracting condition, and the cones were recorded as arcs on the film
...
Collection of powder diffraction
patterns is now almost always performed by automatic diffractometers (Figure 2
...
5(b))
...
The data, both position and intensity, are readily measured
and stored on a computer for analysis
...
e
...
Although this is often possible for simple compounds in high
Physical methods for characterizing solids
97
symmetry systems, as we shall explain in Section 2
...
3, it is extremely difficult to do for
many larger and/or less symmetrical systems
...
3
...
From equation 2
...
In
the primitive cubic system the 100 planes have the largest separation
Solid state chemistry
98
FIGURE 2
...
and thus give rise to this reflection, and as a=b=c in a cubic system the 010 and the 001
also reflect at this position
...
4
(2
...
5)
For the primitive cubic class all integral values of the indices h, k, and l are possible
...
1 lists the values of hkl in order of increasing value of (h2+k2+ l2) and therefore
of increasing sinθ values
...
Other higher missing values exist where (h2+k2+l2) cannot be an integer:
15, 23, 28, etc
...
Taking Equation 2
...
, missing
...
The cubic unit cell dimension a can be determined from any of the indexed reflections
using Equation 2
...
The experimental error in measuring the Bragg angle is constant for
all angles, so to minimize error, either, the reflection with the largest Bragg angle is
chosen, or more usually, a least squares refinement to all the data is used
...
The differences
arise because the centring leads to destructive interference for some reflections and these
extra missing reflections are known as systematic absences
...
1 Values of (h2+k2+l2)
100
hkl
2
2
2
(h +k +l )
110
111
200
210
211
220
300=221
1
2
3
4
5
6
8
9
Solid state chemistry
100
FIGURE 2
...
Consider the 200 planes that are shaded in the F face-centred cubic unit cells depicted in
Figure 2
...
6; if a is the cell dimension, they have a spacing
reflections from four consecutive planes in this structure
...
Throughout the crystal, equal
numbers of the two types of planes exist, with the result that complete destructive
interference occurs and no 100 reflection is observed
...
Physical methods for characterizing solids
101
FIGURE 2
...
TABLE 2
...
It is possible to characterize the type of Bravais lattice present by the pattern of
systematic absences
...
3
at the end of the next section
...
2 for
each of the cubic lattices
...
5), we can see that if the observed
sin2θ values for a pattern are in the ratio 1:2:3:4:5:6:8…, then the unit cell is likely to be
primitive cubic, and the common factor is
A face-centred cubic unit cell can also be recognized: if the first two lines have a
common factor, A, then dividing all the observed sin2θ values by A gives a series of
numbers, 3, 4, 8, 11, 12, 16…, and A is equal to
A body-centred cubic system gives the values of sin2θ in the ratio 1:2:3:4
:5:6:7:8…with the values 7 and 15 apparently not missing, but now the common factor is
TABLE 2
...
3
...
Figure 1
...
21 illustrate how a twofold screw (21) along z introduces a plane of atoms
exactly halfway between the 001 planes: reflections from these planes will destructively
interfere with reflections from the 001 planes and the 001 reflection will be absent, as
will any reflection for which l is odd
...
19) is to
introduce a plane of atoms halfway along the unit cell in the direction of the glide
...
Systematic absences are summarized in
Table 2
...
Fairly powerful computer programmes for indexing are now in existence, and powder
diffraction patterns can be indexed readily for the high symmetry crystal classes such as
cubic, tetragonal, and hexagonal
...
From the cubic unit cell dimension a, we can calculate the volume of the unit cell, V If
the density, ρ, of the crystals are known, then the mass of the contents of the unit cell, M,
can also be calculated
Solid state chemistry
104
(2
...
Examples of these calculations are in the questions at the end of the
chapter
...
The density of the liquid can be determined in the
traditional way using a density bottle
...
3
...
It is usefully used
as a fingerprint method for detecting the presence of a known compound or phase in a
product
...
When the powder diffraction
pattern of your sample has been measured and both the dhkl spacings and intensity of the
lines recorded, these can be matched against the patterns of known compounds in the
files
...
8)
...
It also gives a rough
check of the purity of a sample—but note that powder diffraction does not detect
amorphous products or impurities of less than about 5%
...
Physical methods for characterizing solids
105
FIGURE 2
...
The peaks
demonstrate zircon to be the main
product containing traces of all the
starting materials
...
To either side
of the Bragg angle, the diffracted beam will destructively interfere and we expect to see a
sharp peak
...
In small crystallites not enough
planes exist to produce complete destructive interference, and so we see a broadened
peak
...
7)
where T is the crystallite thickness, λ the wavelength of the X-rays (T and λ have the
same units), θ the Bragg angle, and B is the full-width at half-maximum (FWHM) of the
peak (radians) corrected for instrumental broadening
...
A highly crystalline sample with a diffraction
peak in a similar position to the sample is chosen and this gives the measure of the
broadening due to instrumental effects
...
g
...
It is a common feature of solid state reactions that reaction mixtures become more
crystalline on heating as is evidenced by the X-ray diffraction pattern becoming sharper
...
9 Powder XRD patterns
illustrate the phase changes in
ferrosilicon with time, when heated at
600°C
...
J
...
)
Following Reactions and Phase Diagrams
Powder X-ray diffraction is also a useful method for following the progress of a solid
state reaction and determining mechanisms, and for determining phase diagrams
...
Figure
2
...
77–0
...
In Figure 2
...
Sodium
halides are used to bring the reaction temperature down, and ferrrous sulfate was the
Physical methods for characterizing solids
107
source of iron; as the temperature of the reaction mixture is increased, the peaks due to
zirconia and silica decrease while those of zircon increase, until at 1060°C, this is the
major component
...
A careful comparison of the intensities of particular lines using standards, not only
enable the different phases be identified but also the proportions of different phases to be
determined so that a phase diagram can be constructed
...
It is then possible to measure their position
and intensity with accuracy, and by the methods we described earlier, index
FIGURE 2
...
the reflections and solve the structure
...
A method known as Rietveld analysis has been developed for solving crystal
structures from powder diffraction data
...
Rietveld formulated a method of assigning
each peak a gaussian shape and then allowing the gaussians to overlap so that an overall
Solid state chemistry
108
line profile could be calculated
...
In favourable cases, the Rietveld method can be used to solve a structure from
the powder diffraction data
...
The trial
structure can then be gradually modified by changing the atomic positions and refined
until a best-fit match with the measured pattern is obtained
...
The method tends to work best if a good trial structure is already
known, for instance if the unknown structure is a slight modification of a known
structure, with perhaps one metal changed for another (Figure 2
...
2
...
In most cases, this can be done with
speed and accuracy, and it is one of the most powerful structural techniques available to a
chemist
...
11 Rietveld analysis of
perovskite with partial substitution of
Ti with Ca
...
)
Physical methods for characterizing solids
109
2
...
1 THE IMPORTANCE OF INTENSITIES
So far, we have only discussed the effects of using crystals as three-dimensional
diffraction gratings for X-rays
...
If we want to magnify an object to see its structure in more detail, why not use a
lens system as in a microscope or a camera? Here a lens system focuses the light that is
scattered from an object (which, if left alone, would form a diffraction pattern) and forms
an image
...
Much of this information is contained in the intensity
of each beam, but as always, there is a snag! The recording methods do not record all of
the information in the beam because they only record the intensity and are insensitive to
the phase
...
Unfortunately, it is this information which derives from the
atomic positions in a structure
...
So far, we have seen that if we measure the Bragg angle of the reflections and
successfully index them, then we get information on the size of the unit cell and, if it
possesses any translational symmetry elements, also on the symmetry
...
In
early photographic work, the relative intensities of the spots on the film were assessed by
eye with reference to a standard, and later a scanning microdensitometer was used
...
FIGURE 2
...
The interaction which takes place between X-rays and a crystal involves the electrons in
the crystal: the more electrons an atom possesses, the more strongly will it scatter the X-
Solid state chemistry
110
rays
...
The scattering factor depends not only on the
atomic number, but also on the Bragg angle θ and the wavelength of the X-radiation: as
the Bragg angle increases, the scattering power drops off
...
13a)
...
We know
that the heavier an atom is, the better it is at scattering X-rays
...
While this is true, the overall picture is more complicated than that because there are
interactions with the reflected beams from other planes to take into account, which may
produce destructive interference
...
12)
...
The unit cell depicted in
the figure has close-packed layers of Cl− ions that lie parallel to a body diagonal, with
indices 111
...
Because a chloride
ion has 18 electrons it scatters the X-rays more strongly than a sodium ion with 10
electrons, the reflections partially cancel and the intensity of the 111 reflection will be
weak
...
When
we come to look at the equivalent situation in KCl, the reflection from the 111 layers
containing K+ ions is exactly out of phase with the reflection from the Cl− close-packed
layers
...
Similarly, this means that the first observed reflection in
the diffraction pattern from KCl is the 200 and it would be very easy to make the mistake
that this was the 100 reflection from a primitive cubic cell with a unit cell length half that
of the real face-centred cell
...
It is given by the general expression for j
atoms in a unit cell
(2
...
Series such as this can also be expressed in terms of sines and cosines, more obviously
reflecting the periodic nature of the wave; they are known as Fourier series
...
8) simplifies to
Physical methods for characterizing solids
111
(2
...
10)
where ρ(x,y,z) is the electron density at a position x y z in the unit cell and V is the volume
of the unit cell
...
8) and
Equation (2
...
In mathematical terms, the electron density is said to be the Fourier
transform of the structure factors and vice versa
...
The intensity of the hkl reflections, Ihkl, are measured as described previously and form
the data set for a particular crystal
...
11)
Taking the square root of the intensity gives a value for the magnitude of the structure
factor (mathematically this is known as the modulus of the structure factor denoted by the
vertical bars either side)
...
12)
Before this information can be used, the data set has to undergo some routine corrections,
this process is known as data reduction
...
Corrections can also be made for anomalous dispersion, which affects the scattering
power of an atom when the wavelength of the incident X-ray is close to its absorption
edge
...
The structure factor (and thus the intensity of a reflection) is dependent on both the
position of each atom and its scattering factor
...
8) or Equation (2
...
It is the great problem of X-ray crystallography that we need to
be able to do the reverse of this calculation—we have the measured magnitudes of the
structure factors, and from them we want to calculate the atomic positions
...
When we take the
square root of the intensity, we only obtain the modulus of the structure factor, and so we
only know its magnitude and not its sign
...
Solid state chemistry
112
2
...
2 SOLVING SINGLE CRYSTAL STRUCTURES
It would seem to be an unresolvable problem—to calculate the structure factors we need
the atomic positions and to find the atomic positions we need both the amplitude and the
phase of the resultant waves, and we only have the amplitude
...
Single crystal X-ray diffraction data is nowadays collected using a computer
controlled diffractometer, which measures the Bragg angle θ and the intensity I for each
hkl reflection
...
A full data set, which
can be thousands of reflections, can be accumulated in hours rather than the days or
weeks of earlier times
...
• The reflections are indexed, and from the systematic absences the Bravais lattice and
the translational symmetry elements of the structure determined: this information often
determines the space group unequivocally, or narrows the possibilities down to a
choice of two or three
...
• Correction factors are applied to the raw intensity data
...
These are known as Fobs or Fo
...
Crystal structures are solved by creating a set of trial phases for the structure factors
...
The first is known as the Patterson method, and it
relies on the presence of at least one (but not many) heavy atoms in the unit cell and so is
useful for solving many inorganic molecular structures
...
Direct methods calculate mathematical probabilities for the phase values and
hence an electron density map of the unit cell; theoreticians have produced packages of
accessible computer programs for solving and refining structures
...
In practice, atoms vibrate about their equilibrium positions; this is
often called thermal motion, although it depends not only on the temperature, but also
on the mass of the atom and the strengths of the bonds holding it
...
Part of the refinement procedure is to allow the electron density of each
atom to refine in a sphere around the nucleus
...
The electron density of each atom can also be refined
within an ellipsoid around its nucleus, when an anisotropic displacement parameter
correction is applied which has six adjustable parameters
...
It is defined as
(2
...
In general, the
lower the R value, the better the structure determination
...
No hard and fast rules exist for the
expected value of R, and interpreting them is very much a matter of experience
...
1, anything above should be
viewed with some degree of suspicion
...
05 and often to below R 0
...
A good structure determination, as well as having a low R value, will also have low
standard deviations on both the atomic positions and the bond lengths calculated from
these positions
...
When a single crystal of a solid can be produced, X-ray diffraction provides an
accurate, definitive structure, with bond lengths determined to tenths of a picometre
...
2
...
However, it is also possible to use neutron diffraction for
crystallographic studies
...
It does have advantages for certain structures, however
...
14)
where λ is the wavelength, ρ is the momentum of the particles (ρ=mv, mass× velocity),
and h is Planck’s constant
...
The
neutrons generated in a nuclear reactor can be slowed using heavy water so that they have
a wavelength of about 100 pm and are thus suitable for structural diffraction experiments
...
Structural studies need a high flux of neutrons and this
usually means that the only appropriate source is a high-flux nuclear reactor such as at
Brookhaven and Oak Ridge in the United States, and Grenoble in France
...
The diffraction experiments we have seen so far are set up with Xrays of a single wavelength λ, so that in order to collect all the diffracted beams, the
Bragg angle θ is varied (Bragg equation λ=2d sinθ)
...
(If we
substitute v=D/t [velocity=distance÷time] in the de Broglie relationship, we see that the
...
The difference between the X-ray and neutron diffraction techniques lies in the
scattering process: X-rays are scattered by the electrons around the nucleus, whereas
neutrons are scattered by the nucleus
...
However, because of the size of the atoms relative to the
wavelength of the X-rays, the scattering from different parts of the cloud is not always in
phase, so the scattering factor decreases with sinθ/λ due to the destructive interference
(Figure 2
...
Because the nucleus is very small, neutron scattering factors do not
decrease with sinθ/λ; and because nuclei are similar in size they are all similar in value
(hydrogen is anomalously large due to the nuclear spin)
...
This means that neutron scattering factors cannot be predicted
but have to be determined experimentally and they vary for different atoms and indeed
for different isotopes (Figure 2
...
Note that because of the different scattering mechanisms, the bond lengths determined
by X-ray and neutron studies will be different
...
2
...
1 USES OF NEUTRON DIFFRACTION
Locating Light Atoms
The fact that neutron scattering factors are similar for all elements means that light atoms
scatter neutrons as effectively as heavy atoms and can therefore be located in the crystal
structure; for example the X-ray scattering factors for deuterium and tungsten are 1 and
74, respectively, whereas the equivalent neutron values are 0
...
486
...
Accordingly, many neutron studies in the
literature have been done with the express purpose of locating hydrogen atoms, or of
exploring hydrogen bonding
...
Similar Atomic Numbers and Isotopes
Atoms near each other in the Periodic Table have very similar X-ray scattering factors
and cannot always be distinguished in an X-ray structure determination,
Solid state chemistry
116
FIGURE 2
...
Physical methods for characterizing solids
117
oxygen and fluorine for instance, or similar metals in an alloy
...
Magnetic Properties
As well as the scattering of the neutrons by the nuclei, there is additional magnetic
scattering of the neutrons from paramagnetic atoms
...
The atomic magnetic moment is due to the alignment of the
FIGURE 2
...
The Ni planes only are
pictured, and alternate close-packed
layers have opposing magnetic
moments
...
electron spins, and so this interaction, like the scattering of X-rays, falls off with
increasing Bragg angle due to the size of the electron cloud
...
In ferromagnetic substances, the magnetic
moments are arranged so that they all point in the same direction and so reinforce one
another; in antiferromagnetic substances, the magnetic moments are ordered so that they
completely cancel one another out, and in ferrimagnetic substances the ordering leads to a
Solid state chemistry
118
partial cancellation of magnetic moments
...
For
instance, the structure of NiO, as determined by X-ray diffraction is the same as NaCl
...
This arises (Figure 2
...
Rietveld Analysis
The technique of Rietveld profile analysis has already been mentioned in the context of
X-ray powder diffraction, but it was with neutron powder diffraction that this technique
originated
...
Single Crystal Studies
The flux of a monochromatic source of neutrons is small, and this necessitates the use of
large single crystals and long counting times for the experiment, in order to get sufficient
intensity
...
However,
new high energy neutron sources are becoming available, such as the one at Grenoble,
and the need for these large single crystals in neutron studies is receding
...
6 ELECTRON MICROSCOPY
Optical microscopy has the advantages of cheapness and ease of sample preparation
...
However, a new technique known as near-field scanning
optical microscopy (NSOM) uses a sub-wavelength-sized aperture rather than a lens to
direct the light on to the sample
...
This technique, still in its infancy, has been used successfully to
study optical and optoelectronic properties of biological and nanometre scale materials
...
An electron microscope is similar in principle to an optical microscope
...
The very short wavelength of the electrons allows resolution
down to 0
...
Physical methods for characterizing solids
119
2
...
1 SCANNING ELECTRON MICROSCOPY (SEM)
In this technique, the electrons from a finely focused beam are rastered across the surface
of the sample
...
It is useful for looking at particle size, crystal
morphology, magnetic domains, and surface defects (Figure 2
...
A wide range of
magnification can be used, the best achievable being about 2 nm
...
2
...
2 TRANSMISSION ELECTRON MICROSCOPY (TEM)
In TEM, a thin sample (200 nm) is used and subjected to a high energy, high intensity
beam of electrons; those which pass through the sample are detected forming a twodimensional projection of the sample (Figure 2
...
The electrons may be elastically or
inelastically scattered
...
15 SEM illustrating
crystals of VSbO4 growing out of βSb2O4 following reaction with V2O5
...
)
beam (bright field image) or the diffracted beam (dark field image)
...
Because the electrons pass through the sample,
TEM/HREM images the bulk structure, and so can detect crystal defects such as phase
boundaries, shear planes, and so on (Figure 2
...
Depending on the instrument,
resolution of 0
...
2
...
3 SCANNING TRANSMISSION ELECTRON MICROSCOPY
(STEM)
These instruments combine the scanning ability of SEM with the high resolution
achieved in TEM, a much smaller probe is used (10–15 nm) which scans across the
sample
...
6
...
2
...
In electron microscopy, the elements
present in the sample also emit characteristic X-rays
...
16 (a) TEM image of a
supported Pt/Cr bimetallic catalyst on
Solid state chemistry
122
C; (b) analysis of the metal particle
sizes of this catalyst
...
18)
...
17 HREM image showing
the atomic sites on the 111 plane of a
Si crystal
...
-Ing
...
)
2
...
7
...
When the electrons are accelerated to kinetic energies above the MeV
range, they are travelling close to the speed of light and they emit so-called synchrotron
radiation (Figure 2
...
For an accelerator in the GeV range (the synchrotron at
Daresbury, United Kingdom, operates at 2 GeV, and its successor, DIAMOND at the
Rutherford Laboratory at 3 GeV) the peak power is radiated at about 1018 Hz
(approximately 10 keV and 1 Å) in the X-ray region of the electromagnetic spectrum
...
20)
...
In an EXAFS experiment, the X-radiation is absorbed by a bound electron in a core
shell (usually the K shell) and ejected as a photoelectron
...
21)
...
The
appropriate frequency X-radiation from the continuous synchrotron radiation is selected
by using the Bragg reflection from a
Solid state chemistry
124
FIGURE 2
...
FIGURE 2
...
Physical methods for characterizing solids
125
FIGURE 2
...
single plane of a carefully cut crystal such as Si (220); often, two crystals are used, as
illustrated in the schematic diagram of a double crystal monochromator in Figure 2
...
By changing the Bragg angle of reflection, the frequency of the X-rays selected may be
changed, and thus the absorption edges of a wide range of elements can be studied
...
21 The Rh absorption edge
and EXAFS
...
22 Bragg reflections from
a double-crystal monochromator
...
Physical methods for characterizing solids
127
Two crystals are used to make the exit
beam parallel to the entrance beam
...
The waves of the ejected photoelectron from the K shell can be thought of as a spherical
wave emanating from the nucleus of the absorbing atom; this encounters neighbouring
atoms and is partially scattered by them producing a phase shift (Figure 2
...
Depending
on the phase shift experienced by the electron, the reflected waves can then interfere
constructively or destructively with the outgoing wave, producing a net interference
pattern at the nucleus of the original atom
...
21) extending out to several hundred eV after the edge
...
23 The EXAFS process:
(a) the photoelectron is ejected by Xray absorption, (b) the outgoing
photoelectron wave (solid line) is
backscattered constructively by the
surrounding atoms (dashed line), and
(c) destructive interference between
the outgoing and the backscattered
wave
...
The interference pattern making up the EXAFS thus
depends on the number, and the type of neighbouring atoms, and their distance from the
absorbing atom
...
A Fourier transform of the EXAFS data gives a
radial distribution function which shows the distribution of the neighbouring atoms as a
function of internuclear distance from the absorbing atom
...
Finally, the radial distribution
function is fitted to a series of trial structural models until a structure which best fits the
Solid state chemistry
128
data is obtained, and the data is refined as a series of coordination shells surrounding the
absorbing atom
...
It is difficult to differentiate atoms of similar atomic
number, and important to note that EXAFS only gives data on distance—no angular
information is available
...
In the example in Figure 2
...
The EXAFS data in Figure
2
...
49 Å, corresponding well to the tetrahedral
coordination found in the X-ray crystal structure
...
92 Å and two
Br atoms at a distance of 2
...
We saw earlier (Figure 2
...
25 presents the corresponding iron K-edge
EXAFS analysis for the same ferrosilicon sample
...
34 Å is found to surround Fe in
both forms, but the beta form is found to have only two Fe atoms coordinated to Fe (2
...
4 Fe atoms at 2
...
X-rays are very penetrating, so EXAFS, like X-ray crystallography, examines the
structure of the bulk of a solid
...
Not only
that, but by using different absorption edges, it can investigate the coordination around
more than one type of atom in the sample
...
7
...
21) can
give information on the oxidation state of the atom and on its chemical environment
...
26 depicts XANES spectra for manganese in different oxidation
states
...
24 EXAFS data for (a)
(NH4+)2MnBr42−: (upper) extracted
EXAFS data; (lower) the radial
distribution function, solid line
experimental, dotted line calculated
...
8 SOLID STATE NUCLEAR MAGNETIC RESONANCE
SPECTROSCOPY (MAS NMR)
In solution NMR spectroscopy, dipolar interactions and anisotropic effects are averaged
out by the molecular motion, but this is not so in the solid state, and the NMR spectra of
solids tend to be broadened by three main effects:
1
...
Physical methods for characterizing solids
131
EXAFS data for (b) the intercalation of MnBr42− in a layered double
hydroxide clay: (upper) extracted EXAFS data; (lower) the radial
distribution function, solid line experimental, dotted line calculated
...
Isotopes in low abundance have long spin-lattice relaxation times which give rise to
poor signal-to-noise ratios
...
3
...
In a solid this gives a range of values, an effect known as the chemical
shielding anisotropy, which broadens the band
...
25 EXAFS patterns as a
function of time illustrating the phase
evolution of beta ferrosilicon from the
alpha form when heated at 600°C
...
J
...
)
Solid state chemistry
132
FIGURE 2
...
The vertical dashed line is the position
of the metal edge
...
(Courtesy of Dr
...
)
The line broadening is due to anisotropic interactions, all of which contain a
(3cos2θ−1) term
...
e
...
Magic angle spinning spectroscopy (MAS NMR) spins the sample
about an axis inclined at this so-called magic angle to the direction of the
magnetic field and eliminates these sources of broadening, improving the
resolution in chemical shift of the spectra
...
MAS NMR is often used nowadays as an umbrella term to imply the application of any
or all of these techniques in obtaining a solid state NMR spectrum
...
MAS NMR has proved very
successful in elucidating zeolite structures
...
Because Al
and Si are next to each other in the Periodic Table they have similar X-ray atomic
scattering factors, and consequently are virtually indistinguishable based on X-ray
crystallographic data
...
29
Si has a nuclear spin I=½ and so gives sharp spectral lines with no quadrupole
broadening or asymmetry; the sensitivity is quite high and 29Si has a natural abundance of
4
...
Pioneering work using MAS NMR on zeolites was carried by E
...
Engelhardt in the late 1970s
...
Each Si is coordinated by four oxygen atoms, but
each oxygen can then be attached either to a Si or to an Al atom giving the five
possibilities: Si(OAl)4, Si(OAl)3(OSi), Si(OAl)2(OSi)2, Si(OAl)(OSi)3, and Si(OSi)4
...
These ranges could then be used in further
structural investigations of other zeolites (Figure 2
...
A MAS NMR spectrum of the
zeolite known as analcite is depicted in Figure 2
...
Analcite has all five possible
environments
...
27
Al has a 100% natural abundance and a nuclear spin
resulting in a strong
resonance which is broadened and rendered asymmetric by second-order quadrupolar
effects
...
Solid state chemistry
134
FIGURE 2
...
The inner boxes
represent the 29Si shift ranges
suggested in the earlier literature
...
2
...
They are useful for investigating phase changes, decomposition, loss of
water or oxygen, and for constructing phase diagrams
...
9
...
The sample is
placed in one chamber, and a solid that will not change phase over the temperature range
of the experiment in the other
...
Any reaction in the sample will be represented as a peak in the plot of
differential temperature; exothermic reactions give an increase in temperature, and
endothermic a decrease, so the peaks appear in opposite directions
...
29 depicts
three exotherms in the DTA of KNO3, due to (i) a phase change from tetragonal to
trigonal at 129°C, (ii) melting at 334°C, and (iii) decomposition above 550°C
...
28 29Si MAS NMR
spectrum at 79
...
9
...
The loss of water of crystallization
or volatiles such as oxygen shows up as a weight loss, as does decomposition
...
The TGA plot for KNO3 in Figure 2
...
2
...
3 DIFFERENTIAL SCANNING CALORIMETRY (DSC)
DSC measures the amount of heat released by a sample as the temperature is increased or
decreased at a controlled uniform rate, and so can investigate chemical reactions and
measure heats of reaction for phase changes (Figure 2
...
FIGURE 2
...
Physical methods for characterizing solids
137
2
...
5–1 nm) that their electron-wave functions can
overlap and electrons tunnel between the two
...
The magnitude of the current is very sensitive to the size
of the gap, changing by a factor of 10 when the distance changes by 100 pm
...
The image is
usually formed by keeping a constant tunnelling current and measuring the distance, thus
creating contours of constant density of states on the surface
...
The map thus illustrates features due to both the topography
and to the electronic structure, and can illustrate the positions of individual atoms (Figure
2
...
FIGURE 2
...
(Courtesy of
Dr
...
, Northeastern
University, Boston, Massachusetts
...
31(b–d))
...
The technique produces atomic scale maps of the
surface
...
31 (a) STM image of a
periodic array of C atoms on HOPG
...
R
...
) (b) Diagram of
AFM
...
11 TEMPERATURE PROGRAMMED REDUCTION (TPR)
Temperature programmed reduction measures the reaction of hydrogen with a sample at
various temperatures
...
Therefore, these results can give
information on the presence of different oxidation states or the effect of a dopant in a
lattice
...
The sample is heated over time in a furnace under a flowing gas mixture, typically 10%
H2 in N2
...
This change is
measured by a thermal conductivity cell (katharometer) and is recorded against either
time or temperature
...
32) measure the temperature at which various
reduction steps take place
...
In the example, we see two peaks, indicating that the reduction of Fe2O3
takes place in two stages, first to Fe3O4 and then to metallic Fe
...
Solid state chemistry
140
(c) AFM diamond tip on a silicon cantilever, and (d) AFM image of
gold cluster on an oxidized surface
...
R
...
)
2
...
We have
therefore concentrated on those which are most widely available, and on those which
examine bulk material rather than surfaces
...
We have also not covered vibrational spectroscopy (IR and
FIGURE 2
...
Raman) as good treatments of this subject are to be found in most undergraduate physical
chemistry texts
...
What are the spacings of the 100, 110, and 111 planes in a cubic crystal system of
unit cell dimension a? In what sequence would you expect to find these reflections in a
powder diffraction photograph?
2
...
Nickel crystallizes in a cubic crystal system
...
What is the Bravais lattice?
4
...
4 for the observed reflections
...
2 pm
...
4 sin2θ values for Cs2TeBr6
sin2θ
...
0199
...
0547
...
0799
...
5 θ values for NaCl
θhkl
13°41′
15°51′
22°44′
26°56′
28° 14′
33°7′
36°32′
37°39′
42°0′
45°13′
50°36′
53°54′
55°2′
59°45′
5
...
5
...
6
...
Physical methods for characterizing solids
143
7
...
1 pm and the density of NaCl is measured to
be 2
...
(The atomic
masses of sodium and chlorine are 22
...
45, respectively
...
A powder diffraction pattern establishes that silver crystallizes in a face-centred
cubic unit cell
...
1°, using Cu-Kα radiation
...
If the density of silver is 10
...
(The atomic mass of silver is 107
...
)
9
...
35×103 kg m−3: calculate a value for Z
...
08 and
15
...
)
10
...
0
pm, b=761
...
4 pm and a density ρ=8
...
(Atomic
masses of Th and Se are 232
...
96, respectively
...
Cu crystallizes with a cubic close-packed structure
...
6° and
25
...
Calculate the unit cell length a, and estimate a radius for the Cu atom
...
Arrange the following atoms in order of their ability to scatter X-rays: Na, Co, Cd,
H, T1, Pt, Cl, F, O
...
33 Co edge EXAFS radial
distribution function for Co(CO)4
...
In a cubic crystal we observe the 111 and 222 reflections, but not 001
...
Interpret the EXAFS radial distribution function for Co(CO)4 shown in Figure
2
...
Solid state chemistry
144
15
...
34 illustrates the 79Si MAS NMR spectrum of the zeolite faujasite
...
16
...
35 illustrates the 29Si spectrum of the same sample of faujasite as Figure
2
...
What has happened to it?
17
...
36)
...
FIGURE 2
...
6 MHz of faujasite of
Si/Al=2
...
FIGURE 2
...
6 MHz of faujasite of
Si/Al=2
...
FIGURE 2
...
2 MHz obtained on
faujasite samples at various stages of
the SiCl4 dealumination procedure: (a)
starting faujasite sample, (b) intact
sample after reaction with SiCl4 before
washing, (c) sample (b) after washing
with distilled water, and (d) after
several washings
...
37 DTA and TGA traces
for ferrous sulfate heptahydrate
...
A TGA trace for 25 mg of a hydrate of manganese oxalate, MnC2O4
...
What was the composition of the hydrate? A
further weight loss occurs at 250°C, but then a weight gain at 900°C
...
Figure 2
...
Describe what processes are taking place
...
1 INTRODUCTION
The interest in the properties of solids and the development of new materials has given
rise to the development of a huge variety of methods for preparing them
...
For example, silica glass for fibre optics needs
to be much freer of impurities than silica glass used to make laboratory equipment
...
Other methods may be chosen because they favour the formation of unusual
oxidation states, for example, the preparation of chromium dioxide by the hydrothermal
method, or because they promote the production of fine powders or, by contrast, large
single crystals
...
In the preparation of solids, care usually has to be taken to use stoichiometric
quantities, pure starting materials, and to ensure that the reaction has gone to completion
because it is usually not possible to purify a solid once it has formed
...
The preparation of organic solid state compounds and polymers is not covered
because, generally, it involves organic synthesis techniques which is a whole field in
itself, and is covered in many organic textbooks
...
The chapter begins by
considering the most basic, and most commonly used, method of preparing solids, the
ceramic method: this grand title disguises the fact that it simply means grinding up the
reactant solids and heating them hard until they react! We then go on to look at
refinements of this method, and ways of improving the uniformity of the reaction and
reducing the reaction temperature
...
Later
sections concentrate on less well-known methods of preparing inorganic solids, such as
using high pressures and gas-phase reactions
...
Preparative methods
149
3
...
2
...
This method is used widely both industrially and in the laboratory, and can be
used to synthesize a whole range of materials such as mixed metal oxides, sulfides,
nitrides, aluminosilicates and many others—the first high-temperature superconductors
were made by a ceramic method
...
It is made by the direct
reaction of zirconia, ZrO2, and silica, SiO2 at 1300°C:
ZrO2(s)+SiO2(s)=ZrSiO4(s)
The procedure is to take stoichiometric amounts of the binary oxides, grind them in a
pestle and mortar to give a uniform small particle size, and then heat in a furnace for
several hours in an alumina crucible (Figure 3
...
Despite its widespread use, the simple ceramic method has several disadvantages
...
This is because the coordination numbers in these ionic
binary compounds are high, varying from 4 to 12 depending on the size and charge of the
ion, and it takes a lot of energy to overcome the lattice energy so that a cation can leave
its position in the lattice and diffuse to a different site
...
Reactions
such as this can be very slow; increasing the temperature speeds up the reaction as it
increases the diffusion rate of the ions
...
Solid state reactions
can only take place at the interface of the two solids and once the surface layer has
reacted, reaction continues as the reactants diffuse from the bulk to the interface
...
Even so, diffusion is often the limiting step
...
To achieve a homogeneous mix of small particles it is necessary to be very thorough
in grinding the reactants
...
Commonly the reaction mixture is removed during the heating process and reground to
bring fresh surfaces in contact and so speed up the reaction
...
The product is
FIGURE 3
...
often not homogeneous in composition, this is because as the reaction proceeds a layer of
the ternary oxide is produced at the interface of the two crystals, and so ions now need to
diffuse through this before they react
...
Trial and error usually
has to be used to find out the best reaction conditions, with samples tested by powder Xray diffraction to determine the phase purity
...
converted to heat, as in an electric fire
...
Higher temperatures in samples
can be achieved by directing an electric arc at the reaction mixture (to 3300 K), and for
very high temperatures, a carbon dioxide laser (with output in the infrared) can give
temperatures up to 4300 K
...
If any of the reactants are volatile or air sensitive, then this simple method of heating
in the open atmosphere is no longer appropriate, and a sealed tube method will be
needed
...
An example of the use of this method is the preparation of samarium sulfide
...
The preparation of samarium sulphide, SmS, is of interest because it contains
samarium (a lanthanide element) in an unusual oxidation state +2 instead of the more
common state +3
...
2 Reacting solids under a
special gas atmosphere
...
(Depending on the temperature of reaction, pyrex or silica are the
common choices for these reaction tubes, as they are fairly inert, and can be sealed on to
a pyrex vacuum system for easy handling
...
The pressures obtained in sealed reaction tubes can be very high,
and it is not unknown for tubes to explode however carefully they are made; it is thus
very important to take safety precautions, such as surrounding the tube with a protective
metal container, and using safety screens
...
Preparative methods
153
Experiments of this type (Figure 3
...
The gas is passed over the
reactants for a time to expel all the air from the apparatus, and then flows over the
reactants during the heating and cooling cycles, exiting through a bubbler to maintain a
positive pressure and prevent the ingress of air by back diffusion
...
3
...
2 REDUCING THE PARTICLE SIZE AND LOWERING THE
TEMPERATURE
In a poly crystalline mixture of solid reactants, we might expect the particle size to be of
the order of 10 µm; even careful and persistent grinding will only reduce the particle size
to around 0
...
Diffusion during a ceramic reaction is therefore taking place across
anywhere between 100 and 10,000 unit cells
...
Spray-Drying
The reactants are dissolved in a suitable solvent and sprayed as fine droplets into a hot
chamber
...
Freeze-Drying
The reactants are dissolved in a suitable solvent and frozen to liquid nitrogen
temperatures (77 K)
...
The Co-Precipitation and Precursor Methods
At a simple level, precursors such as nitrates and carbonates can be used as starting
materials instead of oxides: they decompose to the oxides on heating at relatively low
temperatures, losing gaseous species, and leaving behind fine, more reactive powders
...
A stoichiometric mixture of soluble salts of the metal ions is
dissolved and then precipitated as hydroxides, citrates, oxalates, or formates
...
The precursor method achieves mixing at the atomic level by forming a solid
compound, the precursor, in which the metals of the desired compound are present in the
correct stoichiometry
...
The
precursor is then heated to decompose it to the required product
...
A disadvantage is that it is not always possible
to find a suitable precursor, but the preparation of barium titanate gives a good
illustration of this method
...
It was initially prepared by heating
barium carbonate and titanium dioxide at high temperature
...
(Another way is the solgel method which has also been applied to this material
...
The first step in the preparation is to prepare an oxo-oxalate of titanium
...
Ti(OBu)4(aq)+4H2O(l)=Ti(OH)4(s)+4BuOH(aq)
Ti(OH)4(s)+(COO)22−(aq)=TiO(COO)2(aq)+2OH−(aq)+H2O(l)
Barium chloride solution is then added and barium titanyl oxalate precipitates
...
The temperature used for this final heating is 920
K
...
The products of the precursor method are usually crystalline solids, often containing
small particles of large surface area
...
The Sol-Gel Method
The precipitation methods always have the disadvantage that the stoichiometry of the
precipitate(s) may not be exact if one or more ions are left in solution
...
First, a concentrated solution
or colloidal suspension of the reactants, the ‘sol’, is prepared, which is then concentrated
or matured to form the ‘gel’
...
The main steps in the sol-gel process are outlined in Figure 3
...
The first investigation of a sol-gel process for synthesis was made in the mid-19th
century
...
Unfortunately, to prevent the product cracking and
forming a fine powder, an aging period of a year or more was required! The sol-gel
method was further developed in the 1950s and 1960s after it was realised
Preparative methods
155
FIGURE 3
...
that colloids, which contain small particles (1–1000 nm in diameter), could be highly
chemically homogeneous
...
A gel is a semi-rigid solid
in which the solvent is contained in a framework of material which is either colloidal
(essentially a concentrated sol) or polymeric
...
Sol preparation can be either simply the dispersal of an insoluble solid or
addition of a precursor which reacts with the solvent to form a colloidal product
...
A
typical example of the second method is the addition of metal alkoxides to water; the
alkoxides are hydrolysed giving the oxide as a colloidal product
...
To obtain the final product, the gel is heated
...
Both the time and the temperature needed for reaction in
sol-gel processes can reduced from those in the direct ceramic method; in favourable
cases, the time from days to hours, and the temperature by several hundred degrees
...
Many other materials have been prepared by the sol-gel method, and other sol-gel
preparations have been employed for the materials chosen
...
Lithium Niobate, LiNbO3
Lithium niobate is a ferroelectric material used as an optical switch
...
Several sol-gel preparations have been described, their
advantage being the lower temperature required for the preparation and the greater
homogeneity of the product
...
Each ethoxide was dissolved in absolute
ethanol and the two solutions mixed
...
Lithium niobate is then formed when the gel is heated
...
The remaining ethyl groups are
pyrolysed (i
...
, oxidised to carbon dioxide and water) leaving the oxides
...
One use of doped
tin dioxide is to form a transparent electrode
...
Sol-gel methods have
proved suitable for the preparation of such coatings because gels can be sliced finely
...
2H2O) in absolute ethanol
...
The sol was left in an
open container for five days during which time it formed a gel
...
Finally, it was heated to around 600
K for 10 minutes to produce a layer of tin dioxide doped with Ti4+ ions
...
The sol-gel process
is one way of forming fibres of sufficient purity (chemical vapour deposition, Section 3
...
These processes use volatile compounds of silicon which are more easily
purified, for example by fractional distillation, than silica
...
Liquid silicon alkoxide (Si(OR)4), where
R is methyl, ethyl, or propyl, is hydrolysed by mixing with water
...
Gradually, more and more
SiO4 tetrahedra are linked eventually forming SiO2
...
The
resulting sol is cast into a mould where further cross-linking results in gel formation
...
Condensation continues as the gel ages
...
The gel is porous, and the alcohol and water
produced by hydrolysis and condensation is trapped in the pores
...
It is at this
stage that cracking occurs, but if fibres are drawn with a diameter of less than about 1 cm,
then the stresses produced by drying are reduced and cracking is not a problem
...
Finally, the
silica is heated to around 1300 K to increase the density of the glass
...
A
biosensor uses a substance of biological origin, often an enzyme, to detect the presence
of a molecule
...
Biological materials such as enzymes are potentially extremely useful as sensors
because they can be very specific; for example, where a chemical test may be positive for
any oxidising gas, an enzyme may only give a positive test for oxygen
...
One way around this problem is to trap the enzyme
with its microenvironment in a silica gel
...
In a typical sol-gel
synthesis, this compound would be dissolved in methanol, but in this case, methanol was
avoided because alcohols denature proteins and so the solvent used was water
...
As the sol
formed a gel by condensing, the enzyme was trapped in cavities in the gel surrounded by
an aqueous medium of the correct pH
...
Thus the sol-gel method improves the homogeneity of the product
but reaction times are still long (note the five day gelling time in the tin dioxide
synthesis) and high temperatures (1300 K for silica) are still needed
...
3
...
Recently this method has been used to synthesize solid state
materials such as mixed oxides
...
We
shall briefly consider how microwaves heat solids and liquids because this gives us
insight into which reactions will be good candidates for this method
...
In a solid or liquid the alternating electric field of the
microwave radiation can act in two ways
...
Resistance to their movement causes energy to
be transferred to the surroundings as heat
...
If no particles are
present that can move freely, but molecules or units with dipole moments are present,
then the electric field acts to align the dipole moments
...
The electric field of microwave radiation,
like that of all electromagnetic radiation, is oscillating at the frequency of the radiation
...
If the oscillating electric field changes its direction slowly so that
the time between changes is much greater than τ then the dipoles can follow the changes
...
If the electric field of the radiation
oscillates very rapidly, the dipoles cannot respond fast enough and do not realign
...
Under these conditions the dipole realignment
lags slightly behind the change of electric field and the solid absorbs microwave
radiation
...
The quantities governing this
process are the dielectric constant (see Chapter 9), which determines the extent of dipole
alignment, and the dielectric loss, which governs how efficiently the absorbed radiation is
converted to heat
...
The speed of the reaction process is
then increased by both increasing the rate of the solid state reaction and by increasing the
rate of diffusion, which, as we mentioned earlier, is often the rate-limiting step
...
3
...
The synthesis however takes 24 hours to complete
...
A stoichiometric
mixture of copper(II) oxide, CuO, barium nitrate, Ba(NO3)2, and yttrium oxide, Y2O3,
was placed in a microwave oven which had been modified to allow safe removal of the
nitrogen oxides formed during the reaction
...
Finally, the mixture was ground again and exposed to
microwave radiation for an additional 25 minutes
...
This is one of a range of oxides, mostly nonstoichiometric, which are efficiently heated by microwave radiation
...
Other oxides which strongly absorb microwave
radiation include ZnO, V2O5, MnO2, PbO2, Co2O3, Fe3O4, NiO, and WO3
...
By contrast, a 5 to 6 g sample of calcium oxide,
CaO, exposed to 500 watts microwave radiation only attained a temperature of 356 K
after half an hour
...
Although microwave synthesis dramatically decreases reaction time, it does not solve
the problem of chemical inhomogeneity, and temperatures in the reaction are high
...
One advantage is that less problems occur
with cracking because the heating is from inside, and not absorbed from outside
...
5
...
3
...
Combustion synthesis uses highly exothermic
(∆H<−170 kJ mol−1) and even explosive reactions to maintain a self-propagating high
reaction temperature and has been used to prepare many refractory materials including
borides, nitrides, oxides, silicides, intermetallics, and ceramics
...
Once ignited the reaction propagates as a wave, the synthesis wave, through
the pellet, and the reaction must lose less heat than it generates or it will quench;
temperatures up to 3000 K are maintained during the fast reactions
...
4 depicts the
synthesis wave moving through a mixture of MgO, Fe, Fe2O3, and NaClO4, the images
were captured by a thermal imaging camera
...
The method is now used
commercially in Russia, Spain, and Korea because it is fast, economical, and gives high
purity products
...
Examples of other
useful products of these reactions are:
• Hydrides (e
...
, MgH2) for hydrogen storage
• Borides (e
...
, TiB2) for abrasives and cutting tools
• Carbides (e
...
, SiC and TiC) for abrasives and cutting tools
FIGURE 3
...
Each image is of dimension 3×2 mm
...
06 s
intervals
...
See colour
insert following page 196
...
)
• Nitrides (e
...
, Si3N4) for high strength, heat resistant ceramics
• Oxides (e
...
, cuprates) for high temperature superconductors
• Silicides (e
...
, MoSi2) for high temperature heating elements
• Composites (e
...
, the thermite reaction, 3Fe3O4+8A1=4A12O3+9Fe) have been used to
coat the inside of steel pipes with an inner layer of Fe, and a surface layer of Al2O3,
using a centrifugal process
...
5 HIGH PRESSURE METHODS
High pressure methods fall into three main categories: (i) high solvent pressures in an
autoclave—the hydrothermal method; (ii) using a high pressure of a reactive gas; and (iii)
directly applied hydrostatic pressure on solids
...
3
...
1 HYDROTHERMAL METHODS
The original hydrothermal method involves heating the reactants in a closed vessel, an
autoclave, with water (Figure 3
...
An autoclave is usually constructed from thick
stainless steel to withstand the high pressures, and is fitted with safety valves; it may be
lined with non-reactive materials such as teflon
...
These conditions, in which the pressure is raised above
atmospheric pressure and the temperature is raised above the boiling temperature of water
(but not to as high a temperature as used in the
FIGURE 3
...
Solid state chemistry
162
methods described previously), are known as hydrothermal conditions
...
Synthetic emeralds are also made under hydrothermal
conditions
...
The lower temperatures used are one of the advantages of this method
...
It is useful in metal oxide systems
where the oxides are not soluble in water at atmospheric pressure but dissolve in the
super-heated water of the hydrothermal set up
...
The examples
discussed next are chosen to illustrate these advantages and the different variations of the
method
...
Quartz, SiO2, can be used to generate a
high frequency alternating current via the piezoelectric effect (see Chapter 9)
...
In this variant
of hydrothermal processing, the reactant dissolves at a higher
FIGURE 3
...
temperature, is transported up the reaction tube by convection, and crystallizes out at a
lower temperature
...
6
...
When the
autoclave is heated, the silica is dissolved in the solution and is transported along the
autoclave to the cooler part where it crystallizes out
...
In this particular case the autoclave,
which is made of steel, can act as the reaction vessel
...
Chromium Dioxide
Chromium dioxide (CrO2), which is used on audiotapes because of its magnetic
properties (see Chapter 9), contains chromium in the unusual oxidation state of +4
...
Chromium(III) oxide and chromium
trioxide (chromium(VI) oxide CrO3) are placed in an autoclave with water and heated to
623 K
...
(The pressure in the reaction vessel reaches 440 bar
...
These cavities contain exchangeable
metal cations, and can hold removable and replaceable guest molecules such as water
...
Silicon-oxygen tetrahedra are electrically neutral when connected
together in a three-dimensional network as in quartz
...
It is possible
for the tetrahedra to link by sharing two, three, or all four corners, forming a huge variety
of different structures
...
A general
method of preparing zeolites involves mixing an alkali, aluminium hydroxide and silica
sol, or an alkali, a soluble aluminate and silica sol
...
Under these conditions, zeolites instead of other aluminosilicate phases crystallize out
...
27H2O) hydrated alumina, Al2O3
...
The cooled solution is then mixed with a
solution of sodium metasilicate, Na2SiO3
...
The gel is
Solid state chemistry
164
then placed in a closed teflon bottle and heated to about 363 K over 6 hours
...
Changes in the form of the alumina, in the pH of the solution, the type of base used
(organic or inorganic) and in the proportions of alkali, aluminium compound, and silica
lead to the production of different zeolites
...
On
subsequent heating the cation is pyrolysed, but the structure retains the cavities
...
Zeolitic structures with pore sizes of 2000 to 10000 pm are known as mesoporous
solids, and can be formed by a method known as liquid crystal templating (LCT)
...
7) surrounded by a polymeric siliceous framework
...
If short-chain alkyltrimethylammonium ions, R(CH3)3N+, are used as the surfactant,
the alkyl chain length determines whether micro- or mesoporous materials are formed
...
FIGURE 3
...
Yttrium Aluminium Garnet
The preparation of yttrium aluminium garnet (Y3A15O12, YAG) illustrates a variation of
the hydrothermal method used if the starting materials have very different solubilities
from each other
...
8)
...
Preparative methods
165
3Y2O3+5A12O3=2Y3A15O12
3
...
2 HIGH PRESSURE GASES
This method is usually used to prepare metal oxides and fluorides in less stable high
oxidation states
...
Using fluorine at high pressures (>4
kbar) has also been used in the synthesis of ternary fluorides containing high oxidation
states, for example, Cs2CuF6 containing Cu(IV)
...
5
...
Applying very high pressures
tends to decrease volume and thus improve the packing efficiency; consequently,
coordination numbers tend to increase, so for instance Si can be transformed from
FIGURE 3
...
Solid state chemistry
166
FIGURE 3
...
(Courtesy of Cornell High Energy
Synchrotron Source)
...
Various designs of apparatus are available for achieving exceptionally high pressures
...
Recently, diamond anvils have been used to reach pressures of 20 GPa
...
9) but although they achieve greater pressures than
other methods, they have the disadvantage that only milligram quantities of material can
be processed, and so are more useful for investigating phase transitions than for
synthesis
...
5
...
GEC
started a research programme to mimic the geothermal conditions which produce the
natural stones
...
The molten metal acts as a catalyst, bringing down
the working temperature and pressure
...
Diamond has the highest thermal conductivity known, about five times that of copper,
hence they feel cold to the touch and are nicknamed ‘ice’
...
The isotopic enhancement takes place by producing a CVD
diamond film (see Section 3
...
This is crushed and used to
make synthetic diamond in the usual way
...
3
...
5 HIGH TEMPERATURE SUPERCONDUCTORS
High pressure increases the density of SrCuO2 by 8%, and the Cu-O coordination
changes from chains to two-dimensional CuO2 sheets
...
3
...
6 HARDER THAN DIAMOND
The search for a substance harder than diamond has recently focussed on
buckminsterfullerene, C60
...
3
...
In CVD, powders and microcrystallline compounds are prepared
from reactants in the vapour phase, and can be deposited on a substrate (such as a thin
sheet of metal or ceramic) to form single-crystal films for devices (see Section 3
...
1)
...
The whole vessel may be heated, which tends to
deposit the product all over the walls of the vessel
...
Figure 3
...
Typical starting materials are hydrides, halides, and
organometallic compounds because these compounds tend to be volatile; if an
organometallic precursor is used, the method is often referred to as MOCVD (metal
organic CVD)
...
3
...
1 PREPARATION OF SEMICONDUCTORS
The method has been widely used for preparing the III-V semiconductors and silicon, for
devices
...
10 (a) Chemical-vapour
deposition reactor; (b) cross section of
a 100 µm-thick CVD diamond film
grown by DC arc jet
...
(Courtesy of Dr
...
Mike Ashfold,
Bristol University
...
6
...
As well as being the hardest substance known, it
also has the best thermal conductivity (at room temperature), is an electrical insulator,
and has the highest transparency in the IR region of the spectrum of any known
substance
...
Early experiments managed
to deposit monocrystalline layers on to a seed diamond,
FIGURE 3
...
Li, blue; O, pale grey; C, dark
grey
...
Microcrystalline diamond layers have
also been deposited on to silicon and metal surfaces
...
3
...
3 LITHIUM NIOBATE
The sol-gel method of preparing lithium niobate used lithium and niobium alkoxides
...
One way around this problem is to use a more volatile compound of lithium
...
11)
...
Lithium niobate was deposited on the reaction
vessel which was heated to 720 K
...
Other energy sources are also used, notably electromagnetic radiation
...
3
...
Various methods have been
developed for preparing different crystalline forms such as large crystals, films, etc
...
3
...
1 EPITAXY METHODS
Vapour Phase Epitaxial (VPE) Growth
CVD methods are now used to make high purity thin films in electronics where the
deposited layers have to have the correct crystallographic orientation
...
This is an important
method for semiconductor applications where single crystals of controlled composition
are needed
...
Gallium Arsenide
In one method, arsenic(III) chloride (AsCl3, boiling temperature 376 K) is used to
transport gallium vapour to the reaction site where gallium arsenide is deposited in layers
...
One
preparation reacts trimethyl gallium (Ga(CH3)3) with the highly volatile (although toxic)
arsine (AsH3)
...
This
preparation illustrates the use of ultraviolet radiation as the energy source for
decomposition
...
As the gas passed
over the substrate, it was subjected to ultraviolet illumination and mercury telluride was
deposited
...
The use of the lower temperature enabled
later workers to build up a crystal of alternating mercury telluride and cadmium telluride
because diffusion of one layer into the other was slowed by the lower temperature
...
The production of crystals for quantum well lasers
illustrates how carefully such syntheses can be controlled
...
Very thin layers can be built up by directing a beam
FIGURE 3
...
of precursor molecules onto the substrate
...
Because of the very low pressure, the reactants need not be as volatile as in other vapour
deposition methods
...
48In0
...
47In0
...
The layers of the laser material are
depicted in Figure 3
...
Beams of aluminium, gallium, arsenic, and indium were directed onto a heated InP
crystal
...
The relative pressures of the component beams
were adjusted for each layer to give the desired compositions
...
7
...
In chemical vapour transport, a
solid or solids interact with a volatile compound and a solid product is deposited in a
different part of the apparatus
...
Magnetite
Chemical vapour transport has been used to grow magnetite crystals using the reaction of
magnetite with hydrogen chloride gas:
Fe3O4(s)+8HCl(g)=FeCl2(g)+2FeCl3(g)+4H2O(g)
Powdered magnetite is placed at one end of the reaction vessel and the tube evacuated
...
The reaction is endothermic
(
positive) and so the equilibrium moves to the right as the temperature is raised
...
At
FIGURE 3
...
13)
...
The Czochralski Process
The silicon required by the electronics industry for semiconductor devices has to have
levels of key impurities, such as phosphorus and boron, of less than 1 atom in 1010 Si
...
This is made into large single crystals by the Czochralski
process
...
14)
...
Using Temperature Gradients
This method is also used to produce large single crystals of silicon which can then be
sliced into thin wafers for the semiconductor industry
...
A moving heater
then heats the area around the seed crystal, and a molten zone is caused to traverse the
length of the rod (the float-zone process), producing a single crystal as it moves (Figure
3
...
This process also has the advantage of refining the product—so-called zonerefining—as impurities tend to stay dissolved in the melt and are thus swept before the
forming crystal to the end, where they can be cut off and rejected
...
Flame and Plasma Fusion Methods
In the Verneuil method, the powdered sample is melted in a high temperature, oxyhydrogen flame and droplets allowed to fall on to a seed crystal where they crystallize
...
Using the same method
but using a plasma torch to melt the powder, can achieve even higher temperatures
...
A power supply of up to
50 kW, 4 MHz produces radio frequency that is transferred to a coil wrapped around the
skull crucible
...
The container can be evacuated and filled with an appropriate
atmosphere
...
Solid state chemistry
174
FIGURE 3
...
(Photo courtesy of Tonie van
Ringelestijn
...
15 The float-zone method
for producing very pure crystals of
silicon
...
7
...
Various techniques can be used to induce crystallization and these include evaporating
the solvent either by heating, leaving in the atmosphere or in a desiccator, or under
reduced pressure; freezing the solvent; and addition of other components (solvent or salt)
to reduce solubility
...
The melt is then cooled slowly until the crystals form, and then the flux poured off
or dissolved away
...
3
...
Intercalation
compounds have importance as catalysts, as conducting solids and therefore electrode
materials, as a means of encapsulating molecules potentially for drug delivery systems,
and as a method of synthesizing composite solids
...
8
...
For example when potassium vapour reacts with graphite
above the melting temperature of potassium (337 K), it forms a golden compound KC8 in
which the potassium ions sit between the graphite layers, and the inter-layer spacing is
increased by 200 pm (Figure 3
...
Addition of a small amount of KO2 to the molten
potassium results in the formation of a double layer of potassium atoms between the
graphite layers and a formula close to KC4
...
Graphite electron-acceptor intercalation compounds have also
been made with NO3−, CrO3, Br2, FeCl3, and AsF5
...
FIGURE 3
...
K, blue; C, grey
...
8
...
They
can be intercalated with alkali metals (Li, Na, K) to give superconducting solids and
conducting solids that are useful for solid state battery materials
...
The solid is golden-yellow and
has a high electrical conductivity along the titanium layers
...
This compound is synthesized in the cathode
Preparative methods
177
material of the rechargeable battery described in Chapter 5, and can also be synthesized
directly by the lithiation of TiS2 with a solution of butyl lithium:
3
...
3 PILLARED CLAYS
Pillaring is a technique for building strong molecular pillars which prop the layers of a
clay sufficiently far apart to create a two-dimensional space between the layers where
molecules can interact
...
After washing with water the material is calcined,
the hydroxyls and water are lost and alumina pillars created between the silicate layers of
the clay, creating a permanently microporous substance
...
3
...
We have not, for example, covered shock or
ultrasonic methods, electrolytic methods, or the preparation of heterogeneous catalysts
...
(Indeed, several of the examples given in this chapter demonstrate that several
methods can be suitable for one substance
...
It is important that you consider the stability of compounds under the reaction
conditions and not at normal temperature and pressure
...
In what form do you want the product to be? You might choose, for example, vapour
phase epitaxy because an application requires a single crystal
...
How pure must your product be? If you require high purity, you could choose a
method that involves a volatile compound as starting material because these are generally
easier to purify than solids
...
If
you are considering a precursor method, is there a suitable precursor with the right
stoichiometry? The CVD method needs reactants of similar volatility; do your proposed
reactants meet this requirement? In microwave synthesis, does at least one of your
starting materials absorb microwaves strongly?
Solid state chemistry
178
QUESTIONS
1
...
What would be
suitable starting materials and what precaution would you have to take?
2
...
b) A single crystal
...
d) A powder of homogeneous composition
...
What are the advantages and disadvantages of using the sol-gel method to prepare
barium titanate for use in a capacitor?
4
...
2NH3 is known
...
5
...
Suggest an appropriate method
of preparation
...
In hydrothermal processes involving alumina (Al2O3), such as the synthesis of
zeolites, alkali is added to the reaction mixture
...
7
...
nH2O,
NaOH, Al2SO4, water, n-propylamine, and tetrapropylammonium bromide in an
autoclave for several days at 160°C
...
Why is tetrapropylammonium bromide used in the reaction and what is the effect of the
subsequent oxidation reaction?
8
...
Crystals of silica can be grown using the chemical vapour transport method with
hydrogen fluoride as a carrier gas
...
In the preparation of lithium niobate by CVD, argon-containing oxygen is used as
a carrier gas
...
Suggest reasons for these choices of carrier gas
...
1 INTRODUCTION
Chapter 1 introduced the physical structure of solids—how their atoms are arranged in
space
...
Some solids consist of molecules bound together by very weak forces
...
Nor
shall we be much concerned with ‘purely ionic’ solids bound by electrostatic forces
between ions as discussed in Chapter 1
...
We shall be looking at the basic bonding
theories of these solids and how the theories account for the very different electrical
conductivities of different groups of solids
...
Some of the
most important of such solids are the semiconductors
...
We shall introduce examples of some devices and explain
how the properties of semiconductors make them suitable for these applications
...
4
...
The free electron model regards a metal as a box in which electrons are free to roam,
unaffected by the atomic nuclei or by each other
...
),
Group 2 (Mg, Ca, etc
...
These metals are often referred to as simple
metals
...
If we ignore the cores then the quantum mechanical description of the outer
electrons becomes very simple
...
We start by considering an electron in a
one-dimensional solid
...
Because we are ignoring the cores, there is nothing for the electron to
Solid state chemistry
180
interact with and so it experiences zero potential within the solid
...
1)
where is Planck’s constant divided by 2π, me is the mass of the electron, V is the
electrical potential, ψ is the wave function of the electron and E is the energy of an
electron with that wave function
...
1), as follows:
If
then differentiating once gives
Differentiating twice, you should get
and multiplying this by
gives (4
...
The electron is not allowed outside the box and to ensure this we put the potential to
infinity outside the box
...
If we take the sine wave solution, then this is zero at x=0
...
Sine
functions have a value of zero at angles of nπ radians where n is an integer and so
The energy is thus quantised,
with quantum number n
...
Most solids of course are threedimensional (although we shall meet some later where conductivity is confined to one or
two dimensions) and so we need to extend the free electron theory to three dimensions
...
The
appropriate wave function is now the product of three sine or cosine functions and the
energy is given by
Bonding in solids and electronic properties
181
(4
...
However, in
three dimensions, many combinations of na, nb, and nc exist which will give the same
energy, whereas for the one-dimensional model there were only two levels of each energy
(n and −n)
...
The number of states with the same energy is known as the
degeneracy
...
If we are dealing with a crystal of say
1020 atoms it becomes difficult to work out all the combinations
...
If we substitute kx, ky, and kz for
naπ/a, nbπ/b and ncπ/c, then the energy becomes
(4
...
This gives the electron momentum as
All the combinations of quantum numbers giving rise to one particular energy
correspond to a wave vector of the same length |k|
...
The total number of wave vectors with energies up to and including that with
the given energy is given by the volume of the sphere, that is 4k3π/3 where |k| is written
as k
...
This comparison demonstrates that we have to multiply the
volume by abc/π3
...
To
find this, we define the number of states in a narrow range of k values, dk
...
Therefore, the number with values between k and
Solid state chemistry
182
k+dk is 4/3π2 V ((k+dk)3−k3), which when (k+dk)3 is expanded, gives a leading term 4/π2
V k2dk
...
In terms of the more familiar
energy, the density of states N(E)dE is given by
A plot of N(E)dE against E is given in Figure 4
...
Note that the density of states increases with increasing energy—the higher the
energy, the more states there are in the interval dE
...
For sodium, for example, each
atom contributes one 3s electron and the electrons from all the atoms in the crystal
occupy the levels in Figure 4
...
The highest occupied
level is called the Fermi level
...
Experimentally the density of states can be determined by X-ray emission spectroscopy
...
In
sodium, for example, the 2s or 2p electrons might be removed
...
Electrons from the conduction band can now jump down to the
energy level emitting X-rays as they do so
...
A scan across the emitted X-rays
will correspond to a scan across the filled levels
...
1 A density of states curve
based on the free electron model
...
Note that later in this book, energy is
plotted on the vertical axis
...
Bonding in solids and electronic properties
183
intensity of the radiation emitted will depend on the number of electrons with that
particular energy, that is the intensity depends on the density of states of the conduction
band
...
2 illustrates some X-ray emission spectra for sodium and aluminium and
you can see that the shape of these curves resembles approximately the occupied part of
Figure 4
...
If we look at the density of states found experimentally for metals with more electrons
per atom than the simple metals, however, the fit is not as good
...
1, the density reaches a maximum and
then starts to decrease with energy
...
3
...
1) (plane wave methods) can
account for the density of states in Figure 4
...
We shall however use a different model to describe these solids, one
based on the molecular orbital theory of molecules
...
We end this section by using our simple model to explain the electrical conductivity of
metals
...
2
...
For this
purpose, it is important to note that it is a vector with direction as well as
FIGURE 4
...
The
Solid state chemistry
184
slight tail at the high energy end is due
to thermal excitation of electrons close
to the Fermi level
...
3 The band structure of
nickel
...
magnitude
...
In the absence of an electric field, all directions of
the wave vector k are equally likely and so equal numbers of electrons are moving in all
directions (Figure 4
...
If we now connect our metal to the terminals of a battery producing an electric field,
then an electron travelling in the direction of the field will be accelerated and the energies
of those levels with a net momentum in this direction will be lowered
...
There will thus be more electrons moving in the direction of the field than in
other directions
...
The net velocity in an electric field is depicted in Figure 4
...
An important point to note about this explanation is it assumes that empty energy
levels are available close in energy to the Fermi level
...
The model as we have described it so far explains why metals conduct electricity but it
does not account for the finite resistance of metals
...
4 Electrons in a metal in
the absence of an electric field
...
FIGURE 4
...
4
in a constant electric field, established
by placing the rod between the
terminals of a battery
...
where R is the resistance
...
There is nothing in our theory yet that will impede the flow of electrons
...
If these were arranged
periodically on the lattice sites of a perfect crystal, and they were not able to move, then
they would not interrupt the flow of electrons
...
If the component of the electron’s
momentum in the field direction is reduced, then the current will drop
...
A set of crystal vibrations exists in
which the ionic cores vibrate together
...
An example
Solid state chemistry
186
of a crystal vibrational mode would be one in which each ionic core would be moving out
of phase with its neighbours along one axis
...
) Like vibrations in small molecules, each crystal vibration has its set of
quantised vibrational levels
...
As well as
reducing the electron flow, this mechanism increases the crystal’s vibrational energy
...
This ohmic heating effect is
put to good use in, for example, the heating elements of kettles
...
3 BONDING IN SOLIDS—MOLECULAR ORBITAL THEORY
We know that not all solids conduct electricity, and the simple free electron model
discussed previously does not explain this
...
In the molecular orbital
approach to bonding in solids, we regard solids as a very large collection of atoms
bonded together and try to solve the Schrödinger equation for a periodically repeating
system
...
However, solving such an equation for a solid is something of a tall order because
exact solutions have not yet been found for small molecules and even a small crystal
could well contain of the order of 1016 atoms
...
This linear combination of atomic orbitals (LCAO) approach can also be
applied to solids
...
For H2, we assume that the molecular orbitals are formed by
combining 1s orbitals on each of the hydrogen atoms
...
The bonding orbital is
lower in energy than the 1s and the anti-bonding orbital higher in energy
...
If the hydrogen nuclei are pulled further apart, for
example, the overlap decreases and so the decrease in energy is less
...
)
Suppose we form a chain of hydrogen atoms
...
The lowest energy orbital will be that in which all the 1s orbitals
combine in phase, and the highest energy orbital will be that in which the orbitals
combine out of phase
...
Figure 4
...
Note that as the number of atoms increases, the number of levels increases, but the
spread of energies appear to increase only slowly and is levelling off for long chains
...
A chain of hydrogen
atoms is a very simple and artificial model; as an estimate of the energy separation of the
Bonding in solids and electronic properties
187
levels, let us take a typical band in an average size metal crystal
...
FIGURE 4
...
The average separation between levels would thus be only 10–35 J
...
The separation is in fact so small
that, as in the free electron model, we can think of the set of levels as a continuous range
of energies
...
In actual calculations on crystals, it is impractical to include all 1016 atoms and so we
use the periodicity of the crystal
...
Such combinations have patterns like the sine waves
that we obtained from the particle-in-the-box calculation
...
For solids, we replace this with
where k is the wave vector, r is the position vector of a nucleus in the lattice, and ank is
the coefficient of the orbital on the nth atom for a wave vector of k
...
For most of the other atoms in the Periodic Table, it is
necessary to consider other atomic orbitals in addition to the 1s and we find that the
allowed energy levels form a series of energy bands separated by ranges of forbidden
Solid state chemistry
188
energies
...
Aluminium, for example, has the atomic configuration 1s22s22p63s23p1 and would
be expected to form a 1s band, a 2s band, a 2p band, a 3s band, and a 3p band, all
separated by band gaps
...
This arises because these orbitals are concentrated very close to
the nuclei and so there is little overlap between orbitals on neighbouring nuclei
...
Likewise for continuous solids, the greater the overlap, the greater
the spread of energies or bandwidth of the resulting band
...
Just as in small molecules, the available electrons are assigned to levels in the energy
bands starting with the lowest
...
Thus,
if N atomic orbitals were combined to make the band orbitals, then 2N electrons are
needed to fill the band
...
Because aluminium has only one 3p electron per atom, however, there would
only be N electrons in the 3p band and only N/2 levels would be occupied
...
Now let us see how
this model applies to some real solids and how we can apply the concept of energy bands
to understanding some of their properties
...
4
...
1 SIMPLE METALS
The crystal structures of the simple metals are such that the atoms have high coordination
numbers
...
This high coordination number increases the
number of ways in which the atomic orbitals can overlap
...
This can be shown
even for a small chain of lithium atoms as can be seen in Figure 4
...
For the simple metals, then, we do not have an ns band and an np band but one
continuous band instead, which we shall label ns/np
...
The simple metals have far fewer than 8N electrons available however; they have only
N, 2N, or 3N
...
Empty energy levels exist near the Fermi
level, and the metals are good electronic conductors
...
Bonding in solids and electronic properties
189
FIGURE 4
...
4
...
With these structures, the ns/np bands still overlap but the ns/np band splits
into two
...
You can think of the two bands as analogy of bonding and anti-bonding; the
tetrahedral symmetry not giving rise to any non-bonding orbitals
...
This lower band is known as the
valence band, the electrons in this band essentially bonding the atoms in the solid
together
...
The electrons in the highest occupied levels would be virtually non-bonding
...
This is
illustrated in Figure 4
...
Elements with few valence electrons will thus be expected to adopt high coordination
structures and be metallic
...
Tin (in its most stable room temperature form) and lead, although in the same group as
silicon and germanium, are metals
...
For tin, the tetrahedral structure would have two s−p bands but the band gap is almost
zero
...
8 Energy bands formed
from ns and np atomic orbitals for (a) a
body-centred cubic crystal and (b) a
crystal of diamond structure, depicting
filled levels for 4N electrons
...
The advantage of not having nonbonding levels in the
diamond structure is reduced by the small band gap
...
It is more favourable for lead to adopt a cubic close-packed
structure and, because lead has only 2N electrons to go in the p band, it is metallic
...
Another example is the formation of divalent ionic compounds
containing Pb2+ instead of tetravalent covalent compounds like those of silicon and
germanium
...
However, they belong to a class of materials known as
semiconductors
...
The conductivity of metallic conductors decreases with temperature
...
The displacement of the ionic cores from their lattice sites is thus greater and the
electrons are scattered more, reducing the net current by reducing the mobility, µ, of the
electrons
...
In these solids, conduction can only occur if electrons are
promoted to the higher s/p band, the conduction band, because only then will there be a
partially full band
...
The number of electrons able to
transport charge is given by the number promoted to the conduction band plus the
number of electrons in the valence band that have been freed to move by this promotion
...
How much this increases depends on the band gap
...
The number of electrons promoted varies with temperature in an exponential
manner so that small differences in band gap lead to large differences in the number of
electrons promoted and hence the number of current carriers
...
Germanium has an electrical resistivity of 0
...
0044 Ω m, or that of a typical insulator of around 1012
Ω m
...
Solid state chemistry
192
FIGURE 4
...
4
...
1 PHOTOCONDUCTIVITY
Forms of energy other than heat energy, for example, light, can also promote electrons
...
Promotion of electrons by light is illustrated in Figure 4
...
Semiconductors with band gap energies corresponding to photons of visible light are
photoconductors, being essentially non-conducting in the dark but conducting electricity
in the light
...
In the
xerographic process, there is a positively charged plate covered with a film of
semiconductor
...
) Light reflected from the white parts of the page to be copied hits the
semiconductor film
...
This electron then cancels the positive
charge on the film, the positive hole in the valence band being removed by an electron
from the metal backing plate entering the valence band
...
Tiny negatively charged plastic capsules of ink (toner)
are then spread on to the semiconductor film but only stick to the charged bits of the film
...
Finally, the paper is heated
to melt the plastic coating and fix the ink
...
4
...
For this reason, silicon manufactured for
transistors and other devices must be very pure
...
Such semiconductors are known as doped or extrinsic semiconductors
...
Boron has one fewer valence electron
than silicon
...
10) (i
...
, positive holes occur in the valence band and
these enable electrons near the top of the band to conduct electricity)
...
A semiconductor like this doped
with an element with fewer valence electrons than the bulk of the material is called a ptype semiconductor because its conductivity is related to the number of positive holes
(or empty electronic energy levels) produced by the impurity
...
The doping atoms form a set of
energy levels that lie in the band gap between the valence and conduction bands
...
Therefore, electrons are present close to the bottom of the conduction band and easily
promoted into the band
...
Such semiconductors are called n-type—n for negative
charge carriers or electrons
...
10 schematically depicts energy bands in intrinsic,
p-type, and n-type semiconductors
...
Solid state chemistry
194
FIGURE 4
...
4
...
3 THE p-n JUNCTION—FIELD-EFFECT TRANSISTORS
p-n junctions are prepared either by doping different regions of a single crystal with
different atoms or by depositing one type of material on top of the other using techniques
such as chemical vapour deposition
...
In the region of the crystal where n- and ptype meet, there is a discontinuity in electron concentration
...
To try and equalise the electron concentrations electrons diffuse from n- to p-type
...
The electric field thus set up encourages electrons to drift back to
the n-type
...
11
...
Applying an external electric field across such a junction disturbs the
equilibrium and the consequences of this are exploited in LEDs and transistors
...
An important feature of most transistors is a voltage
applied in the reverse direction, that is, the n-type is positive with respect to the p-type
...
We consider briefly here an important class
Bonding in solids and electronic properties
195
FIGURE 4
...
FIGURE 4
...
of transistors, the field-effect transistors (FET)
...
A simple n-channel FET consists of a block of heavily doped p-type semiconductor
with a channel of an n-type semiconductor (see Figure 4
...
Electrodes are attached to the p-type block and to the n-type channel
...
The electrode attached to the p-type
block is known as the gate electrode
...
To fulfill the transistor’s role, as amplifier or switch, a
voltage is applied to the gate electrode
...
The electrons,
therefore, fill the valence band in the p-type
...
The net result is an increased
depletion zone and because the p-type is more heavily doped, this effect is greater for the
n-type channel
...
If the voltage on the gate electrode
is reduced, then electrons flow out of the p-type, the depletion zones shrink, and the
current through the n-type channel increases
...
Transistor amplifiers consist of an electronic circuit containing a transistor and other
components such as resistors
...
The output signal is taken from the drain
...
This current produces a drain voltage that is proportional to the
incoming voltage but whose magnitude is greater by a constant factor
...
The charge on the silicon dioxide controls the size of the depletion zone
in the p-type semiconductor
...
Traditionally, transistors have been silicon based but a recent development is
field-effect transistors based on organic materials
...
5 BANDS IN COMPOUNDS—GALLIUM ARSENIDE
Gallium arsenide (GaAs) is a rival to silicon in some semiconductor applications,
including solar cells, and is used for LEDs and in a solid state laser, as discussed in
Chapter 8
...
The valence orbitals in Ga and As are the 4s and 4p and
these form two bands each containing 4N electrons as in silicon
...
Thus, GaAs can be considered as having partial ionic character because there is
a partial transfer of electrons from Ga to As
...
The band energy diagram for GaAs is illustrated in Figure 4
...
GaAs is an example of a
class of semiconductors known as III/V semiconductors in which an element with one
more valence electron than the silicon group is combined with an element with one less
valence electron
...
g
...
Moving farther along the Periodic Table, there are II/VI semiconductors such
as CdTe and ZnS
...
g
...
Bonding in solids and electronic properties
197
For the semiconducting solids, the band gap decreases down a group, for example, GaP>
GaAs>GaSb; AlAs>GaAs>InAs
...
13 Orbital energy level
diagram for gallium arsenide
...
6 BANDS IN d-BLOCK COMPOUNDS—TRANSITION METAL
MONOXIDES
Monoxides MO with structures based on sodium chloride are formed by the first row
transition elements Ti, V, Mn, Fe, Co, and Ni
...
The O 2p orbitals form a filled valence band
...
What about the 3d orbitals?
In the sodium chloride structure, the symmetry enables three of the five d orbitals on
different atoms to overlap
...
The other two d orbitals
overlap with orbitals on the adjacent oxygens
...
The
lower one, labelled t2g, can take up to 6N electrons, and the upper one, labelled eg, up to
4N electrons
...
Similarly, divalent vanadium has three d electrons and so the
lower band is half full
...
For FeO, the t2g band would be full, so it is not surprising to find that it is a
semiconductor; but MnO with only five electrons per manganese is also a semiconductor
...
It is
easier to understand these oxides using a localised d electron model
...
The 3d orbital overlap therefore decreases and the 3d band narrows
...
In a narrow band
by contrast, the electrons are more tightly bound to the nuclei
...
Consider an electron in a partly filled band moving from one nucleus to another
...
The 3d electron
moving from one nucleus to another adds an extra electron near to the second nucleus
which already has 3d electron density near it
...
For narrow bands, therefore, we have to balance gains in energy on band
formation against electron repulsion
...
The band gap between the oxygen 2p band and the metal 4s band is sufficiently wide
that the pure oxides would be considered insulators
...
The monoxides are not unique in displaying a variation of properties across the
transition series
...
Several classes of mixed oxides also exhibit a range of electronic
properties (e
...
, the perovskites LaTiO3, SrVO3, and LaNiO3 are metallic conductors;
LaRhO3 is a semiconductor; and LaMnO3 is an insulator)
...
In general, compounds with broader d bands will be metallic
...
g
...
Metallic behaviour is also more
common amongst lower oxidation state compounds and with less electronegative anions
...
In the free electron model, the electron energy is kinetic
...
The mass of an
electron is 9
...
Assume the band shown in Figure 4
...
2
...
A typical crystal has a volume of
10 m3 (corresponding to a cube of side 0
...
How many atoms would such a crystal
contain?
–12
3
...
Bonding in solids and electronic properties
199
Calculate the total number of occupied states for a sodium crystal of volume (a) 10–12 m3,
(b) 10–6 m3, and (c) 10–29 m3 (approximately atomic size)
...
A
crystal of volume 10−12 m3 contains 2
...
4
...
4 to 5
...
The band gap in selenium is 2
...
Explain why selenium is a good material to
use as a photoconductor in applications such as photocopiers
...
The band gaps of several semiconductors and insulators are given below
...
9
1
...
8
6
...
7
...
5
Defects and Non-Stoichiometry
5
...
This situation can only exist at the absolute zero of temperature, 0 K
...
These defects may be extended defects such as dislocations
...
Defects can also occur at isolated atomic positions; these are known as point
defects, and can be due to the presence of a foreign atom at a particular site or to a
vacancy where normally one would expect an atom
...
The beautiful colours of
many gemstones are due to impurity atoms in the crystal structure
...
(This is in contrast to the electronic conductivity that we
explored in the previous chapter, which depends on the movement of electrons
...
2 DEFECTS AND THEIR CONCENTRATION
Defects fall into two main categories: intrinsic defects which are integral to the crystal in
question—they do not change the overall composition and because of this are also known
as stoichiometric defects; and extrinsic defects which are created when a foreign atom
is inserted into the lattice
...
2
...
For a 1:1 solid MX, a Schottky defect consists of a pair of vacant sites, a cation
vacancy, and an anion vacancy
...
1 (a) for an alkali halide
type structure: the number of cation vacancies and anion vacancies have to be equal to
preserve electrical neutrality
...
Schottky defects are more common in 1:1 stoichiometry
and examples of crystals that contain them include rock salt (NaCl), wurtzite (ZnS), and
CsCl
...
1 Schematic illustration of
intrinsic point defects in a crystal of
composition MX: (a) Schottky pair, (b)
perfect crystal, and (c) Frenkel pair
...
This is
illustrated in Figure 5
...
This type of behaviour is seen,
for instance, in AgCl, where we observe such a cation Frenkel defect when Ag+ ions
move from their octahedral coordination sites into tetrahedral coordination and this is
illustrated in Figure 5
...
The formation of this type of defect is important in the
photographic process when they are formed in the light-sensitive AgBr used in
photographic emulsions
...
2 The tetrahedral
coordination of an interstitial Ag+ ion
in AgCl
...
This is because anions are commonly larger than the cations in the
structure and so it is more difficult for them to enter a crowded low-coordination
interstitial site
...
One reason for this is that the anions have a lower electrical charge than the
cations and so do not find it as difficult to move nearer each other
...
3
...
This of course leaves all of the larger
octahedral holes unoccupied, giving
Solid state chemistry
204
FIGURE 5
...
(a) Unit cell as a ccp
array of cations, (b) and (c) The same
structure redrawn as a simple cubic
array of anions
...
a very open structure
...
3(c),
based on a simple cubic array of F− ions
...
The two different views are
equivalent, but the cell depicted in Figure 5
...
5
...
2 THE CONCENTRATION OF DEFECTS
Energy is required to form a defect
...
It may seem surprising that defects exist in crystals at all, and yet
they do even at low temperatures, albeit in very small concentrations
...
The enthalpy of formation of the defects is thus balanced by the gain in entropy such that,
at equilibrium, the overall change in free energy of the crystal due to the defect formation
is zero according to the equation:
∆G=∆H−T∆S
The interesting point is that thermodynamically we do not expect a crystalline solid to be
perfect, contrary, perhaps to our ‘commonsense’ expectation of symmetry and order! At
any particular temperature there will be an equilibrium population of defects in the
crystal
...
1)
where ns is the number of Schottky defects per unit volume, at T K, in a crystal with N
cation and N anion sites per unit volume; ∆Hs is the enthalpy required to form one defect
...
The change in entropy will be due to the vibrations of atoms
around the defects and also to the arrangement of the defects
...
If the number of Schottky defects is ns per unit volume at T K, then there will be ns
cation vacancies and ns anion vacancies in a crystal containing N possible cation sites and
N possible anion sites per unit volume
...
2)
where W is the number of ways of distributing ns defects over N possible sites at random,
and k is the Boltzmann constant (1
...
Probability theory shows that W
is given by
(5
...
On differentiating, we obtain:
∆Hs−2kT[ln(N−ns)+1−lnns−1]=0
thus,
and of
Defects and non-stoichiometry
207
and
as N>>ns we can approximate (N−ns) by N, finally giving:
(5
...
4)
where now ∆Hs is the enthalpy required to form one mole of Schottky defects and R is
the gas constant, 8
...
The units of ∆Hs are J mol−1
...
5)
where nF is the number of Frenkel defects per unit volume, N is the number of lattice sites
and Ni the number of interstitial sites available
...
If ∆HF is the enthalpy of formation of one mole of Frenkel defects the
expression becomes:
(5
...
1 lists some enthalpy-of-formation values for Schottky and Frenkel defects in
various crystals
...
1 and Equation (5
...
Assume that ∆Hs has a middle-of-the-range value of
5×10–19 J
...
1) we find that the proportion
Solid state chemistry
208
TABLE 5
...
57
6
...
77
6
...
75
2
...
40
2
...
88
1
...
08
1
...
69
2
...
62
2
...
45
3
...
57
4
...
49
2
...
12
0
...
56
1
...
92
1
...
12
0
...
1 eV=1
...
19
of vacant sites
at 300 K is 6
...
37×10–8
...
Even when
the temperature is raised to 1000 K, we still find only of the order of one or two
vacancies per hundred million sites!
Whether Schottky or Frenkel defects are found in a crystal depends in the main on the
value of ∆H, the defect with the lower ∆H value predominating
...
We will see in a later section that in order to change the properties of crystals,
particularly their ionic conductivity, we may wish to introduce more defects into the
crystal
...
First, we have seen from the previous calculation that raising the temperature
introduces more defects
...
Second, if it were possible to decrease the enthalpy of formation of a defect, ∆Hs or ∆HF,
this would also increase the proportion of defects present
...
1), but now with a lower value for ∆Hs, for instance,
1×10–19 J allows us to see this
...
2 compares the results
...
It is difficult to see how the value of ∆H could be manipulated within a
crystal, but we do find crystals where the value of ∆H is lower than usual due to the
nature of the structure, and this can be exploited
...
Third, if we introduce impurities selectively into a
crystal, we can increase the defect population
...
2
...
For
instance, if we add CaCl2 to a NaCl crystal, each Ca2+ ion replaces two Na+ ions in order
to preserve electrical neutrality, and so one cation vacancy is created
...
An important example that you will meet later in the
chapter is that of zirconia, ZrO2
...
The charge compensation here
is achieved by the production of anion vacancies on the oxide sublattice
...
2 Values of ns/N
∆Hs=5×10−19 J
∆Hs=1×10–19 J
300
6
...
72×10–6
1000
1
...
67×10–2
T(K)
5
...
If a crystal structure were perfect, it would be
difficult to envisage how the movement of atoms, either diffusion through the lattice or
ionic conductivity (ion transport under the influence of an external electric field) could
take place
...
Two possible mechanisms for the movement of ions through a lattice are sketched in
Figure 5
...
In Figure 5
...
This is called the vacancy mechanism
...
) Figure 5
...
These simple pictures of movement in an ionic
lattice are known as the hopping model, and ignore more complicated cooperative
motions
...
7)
where n is the number of charge carriers per unit volume, Ze is their charge (expressed as
a multiple of the charge on an electron, e=1
...
Table 5
...
As we might
expect, ionic crystals, although they can conduct, are poor conductors compared with
metals
...
Equation (5
...
To understand why some ionic solids conduct better than others it is useful to look at the
definition more closely in terms of the hopping model that we have
FIGURE 5
...
TABLE 5
...
First of all, we have said that an electric current is carried in an ionic solid by the
defects
...
µ will thus refer to the mobility of these
defects in such cases
...
Take the case of NaCl, which
contains Schottky defects
...
5 will
show
...
The direct route
FIGURE 5
...
(labelled 4) is clearly going to be very unlikely because it leads directly between two Cl−
ions, which in a close-packed structure such as this, are going to be very close together
...
The
coordination of the Na+ ion will change from 6→3→4→3→6 as it jumps from one site to
the other
...
Generally, we
would expect the ion to follow the lowest energy path available
...
6
...
This means that the
Solid state chemistry
212
temperature dependence of the mobility of the ions can be expressed by an Arrhenius
equation:
(5
...
9)
where µ0 is a proportionality constant known as a pre-exponential factor
...
If the external
field is small (up to about 300 V cm−1), a temperature dependence of 1/T is introduced
into the pre-exponential factor
...
7), we arrive at an expression for the
variation of ionic conductivity with temperature that has the form:
(5
...
6 Schematic representation
of the change in energy during motion
of an ion along the lowest energy path
...
This expression accounts for the fact that ionic conductivity increases
with temperature
...
10), we obtain:
Plotting lnσT against
should produce a straight line with a slope of −Ea
...
10) is sometimes plotted empirically as
Defects and non-stoichiometry
213
because plotting either ln σT or lnσ makes little difference to the slope; both types of plot
are found in the literature
...
7
...
The other
lines on the plot are straight lines apart from the one for LiI, where we can clearly see
two lines of differing slope
...
But how about LiI? In
FIGURE 5
...
Solid state chemistry
214
FIGURE 5
...
fact, other crystals also show this kink in the plot (some experimental data is presented
for NaCl in Figure 5
...
Is it possible to explain this using the
equations that we have just set up? The answer is yes
...
At low temperatures, the
concentration of intrinsic vacancies is so small that it can be ignored because it is
dominated by the defects created by the impurity
...
µ in this extrinsic region thus
depends only on the cation mobility due to these extrinsic defects, whose temperature
dependence is given by Equation (5
...
9)
However, at the higher temperatures on the left-hand side of the graph, the concentration
of intrinsic defects has increased to such an extent that it now is similar to, or greater
Defects and non-stoichiometry
215
than, the concentration of extrinsic defects
...
1), as discussed earlier:
(5
...
11)
A plot of lnσT vs
...
12)
Similarly, for a system with Frenkel defects:
EF=Ea+½ ∆HF
(5
...
05 to
1
...
As we have seen, raising
the temperature increases the number of defects, and so increases the conductivity of a
solid
...
2 eV
...
7
...
4 SOLID ELECTROLYTES
Much of the recent research in solid state chemistry is related to the ionic conductivity
properties of solids, and new electrochemical cells and devices are being developed that
contain solid, instead of liquid, electrolytes
...
We use batteries all the
time—to start cars, in toys, watches, cardiac pacemakers, and so on
...
Once a primary battery has discharged, the
reaction cannot be reversed and it has to be thrown away, so there is also interest in solid
electrolytes in the production of secondary or storage batteries, which are reversible
because once the chemical reaction has taken place the reactant concentrations can be
Solid state chemistry
216
restored by reversing the cell reaction using an external source of electricity
...
g
...
Where possible, batteries need to
be made out of nontoxic materials
...
Chemical sensors, electrochromic devices, and fuel cells that depend on the conducting
properties of solids, are also being developed and we look at examples of all these later in
the chapter
...
4
...
One of the
earliest to be noticed, in 1913 by Tubandt and Lorenz, was a high temperature phase of
silver iodide
...
Both are based on a close-packed array of iodide ions
with half of the tetrahedral holes filled
...
If you look back to
Figure 5
...
How
can we explain this startling phenomenon?
The explanation lies in the crystal structure of α-AgI
...
9(a)
...
To see where the Ag+ ions fit into the structure,
we need to look at the bcc structure in a little more detail
...
9(b) presents the same
unit cell but with the next-nearest neighbours added in; these are the six at the bodycentres of the surrounding unit cells, and they are only 15% farther away than the eight
immediate neighbours
...
9(c))
...
9(d), which has six square faces and eight hexagonal faces corresponding to the
two sets of neighbours
...
Each vertex of the domain
lies at the centre of an interstice (like the tetrahedral and octahedral holes found in the
close-packed structures), which in this structure is a distorted tetrahedron
...
9(e)
shows two such adjacent distorted tetrahedral holes, and you can see clearly from this the
‘tetrahedral’ site lying on the face of the unit cell
...
9(e)
...
The structure
thus possesses
Defects and non-stoichiometry
217
FIGURE 5
...
(a) The body-centered cubic
array of I− ions, (b) bcc array extended
to next-nearest neighbours, (c)
Rhombic dodecahedron, (d) bcc array
with enclosed truncated octahedron;
the 24 vertices (black dots) lie at the
centres of the distorted tetrahedra
...
) (e) The positions
of two tetrahedral sites and a trigonal
site between them
...
10 sketches many of them
...
From the possible sites that we have described, 6 are distorted octahedral, 12 are
‘tetrahedral’, and 24 are trigonal—a choice of 42 possible sites—therefore, the Ag+ ions
have a huge choice of positions open to them! Structure determinations indicate that the
Solid state chemistry
218
Ag+ are statistically distributed among the twelve tetrahedral sites all of which have the
same energy
...
We can visualise the Ag+ ions moving from tetrahedral site to
tetrahedral site by jumping through the vacant trigonal site, following the paths marked
with solid lines in Figure 5
...
The paths marked with thin dotted lines in Figure
5
...
The jump that we have described only changes the
FIGURE 5
...
The thick
solid and dashed lines mark possible
diffusion paths
...
05 eV
...
The very high conductivity of α-AgI appears to arise because of a conjunction of
favourable factors, and we can list the features that have contributed to this:
• the charge on the ions is low, the mobile Ag+ ions are monovalent;
• a large number of vacant sites are available into which the cations can move;
Defects and non-stoichiometry
219
• the structure has an open framework with pathways that the ions can move through;
• the coordination around the ions is also low, so that when they jump from site to site,
the coordination changes only changes by a little, affording a route through the lattice
with a low activation energy;
• the anions are rather polarizable; this means that the electron cloud surrounding an
anion is easily distorted, making the passage of a cation past an anion rather easier
...
RbAg4I5
The special electrical properties of α-AgI inevitably led to a search for other solids
exhibiting high ionic conductivity preferably at temperatures lower than 146°C
...
This compound has an
ionic conductivity at room temperature of 25 S m−1, with an activation energy of only
0
...
The crystal structure is different from that of α-AgI, but similarly the Rb+ and I−
ions form a rigid array while the Ag+ ions are randomly distributed over a network of
tetrahedral sites through which they can move
...
This is to stop the battery short-circuiting: the electrons must only pass through the
external circuit, where they can be harnessed for work
...
Such cells operate over
a wide temperature range (−55 to +200°C), have a long shelf life, and can withstand
mechanical shock
...
4
...
The
chalcogenide structures, such as silver sulfide and selenide, tend to demonstrate
electronic conductivity as well as ionic, although this can be quite useful in an electrode
material as opposed to an electrolyte
...
4
...
3, has plenty of empty space which can
enable an F− ion to move into an interstitial site
...
Indeed, PbF2 has a low ionic conductivity at room temperature, but this
increases smoothly with temperature to a limiting value of ~500 S m−1 at 500°C
...
The cubic (fluorite) form of ZrO2 is
only formed at high temperature or when doped with another element
...
4 α-AgI-related ionic conductors
Anion structure
bcc
ccp
hcp
α-AgI
α-CuI
α-CuBr
α-Ag2Te
α-Ag2S
α-Cu2Se
α-Ag2Se
β-CuBr
other
RbAg4I5
α-Ag2HgI4
At the turn of the last century, Nernst found that mixed oxides of yttria, Y2O3, and
zirconia, ZrO2, glowed white hot if an electric current was passed, and attributed this to
the conduction of oxide ions
...
ZrO2 is found as the mineral
baddeleyite, which has a monoclinic structure
...
The cubic form
can be stabilized at room temperature by the addition of other oxides such as yttria, Y2O3
(known as yttria-stabilized zirconia, YSZ), and CaO
...
11 and shows
that at about 15 mole% CaO the new phase, known as calcia-stabilized zirconia, appears
alone and persists until about 28 mole% CaO
...
If the Ca2+ ions sit on Zr4+ sites, compensating
vacancies are created
Defects and non-stoichiometry
221
FIGURE 5
...
The
cubic calcia-stabilized zirconia phase
occupies the central band in the
diagram and is stable to about 2400°C
...
Thus, for every Ca2+ ion taken into the structure one anion vacancy
is created
...
7)
...
The best conductivity seems to be achieved when the crystal
lattice is distorted as little as possible (i
...
, when the dopant ion is similar in size to the
cation it is replacing)
...
Many other materials are also made with this type of
structure, which are based on oxides such as CeO2, ThO2, and HfO2 as well as ZrO2, and
doped with rare earth or alkaline earth oxides: these are collectively known as stabilized
zirconias and are widely used in electrochemical systems
...
Another interesting
application of stabilized zirconia is in the detection of oxygen, where it is used in both
oxygen meters and oxygen sensors, which are based on a specialized electrochemical
cell (Section 5
...
4)
...
44) has two different metal sites
which could be substituted with lower valence metal cations leading to oxygen vacancies
...
Using them in oxideion conducting devices would have the advantage of bringing down the operating
temperature
...
4
...
The
strontium-doped perovskites LaMnO3 (LSM), and LaCrO3 (LSC) have both these
properties
...
• The LAMOX family of oxide conductors, based on La2Mo2O9, has high conductivity
above 600°C, but tend to be susceptible to reduction by hydrogen
...
• The apatite structures, La10−xM6O26+y (M=Si or Ge), conduct well at very high
temperatures
...
4
...
The parent compound is sodium β-alumina, Na2O
...
(The compound was
originally thought to be a polymorph of Al2O3, and was named as such—it was only later
found to contain sodium ions! However, the original name has stuck
...
nX2O3, where n can range from 5 to 11: M is a monovalent
cation such as (alkali metal)+, Cu+, Ag+, or NH4+, and X is a trivalent cation Al3+, Ga3+, or
Defects and non-stoichiometry
223
Fe3+
...
Interest in these compounds started in 1966 when research at the Ford Motor
Company demonstrated that the Na+ ions were very mobile both at room temperature and
above
...
This can be thought of as close-packed layers of oxide ions, but in every fifth layer threequarters of the oxygens are missing (Figure 5
...
The four close-packed layers contain
the Al3+ ions in both octahedral and tetrahedral holes
...
43
...
The Na+ ions
FIGURE 5
...
(b) The ratio of atoms in each
layer of the structure
...
The overall
stoichiometry of the structure is illustrated layer by layer in Figure 5
...
The sequence
of layers is
B(ABCA) C (ACBA) B…
where the brackets enclose the four close-packed layers and the intermediate symbols
refer to the fifth oxide layer
...
13
...
Conduction in the
β-aluminas only occurs within the planes containing the oxygen vacancies; these are
known as the conduction planes
...
β-alumina is not
found in the stoichiometric form—it is usually Na2O rich, and the sodium-rich
compounds have a much higher conductivity than stoichiometric β-alumina
...
There is more than one possibility for this, but in
practice it is found that extra oxide ions provide the compensation and the overall
formula can be written as (Na2O)1+x
...
The extra sodium and oxide ions both
occupy the fifth oxide layer; the O2− ions are locked into position by an Al3+ moving out
from the spinel block, and the Na+ ions become part of the mobile pool of ions
...
β-aluminas are used as electrolytes in the manufacture of electrochemical cells
particularly for power supplies
...
13 Structure of
stoichiometric β-alumina
...
Na, purple;
Al, pink; O, red
...
43 The spinel structure,
CuAl2O4 (AB2O4)
...
FIGURE 1
...
Ca, green sphere; Ti, silver
spheres; O, red spheres
...
53 The unit cell of olivine
...
FIGURE 1
...
Key: Mg, green; Si, grey;
O, red; Na, purple
...
55 The structure of biotite
...
FIGURE 3
...
Each image is of dimension 3×2 mm
...
06 s
Solid state chemistry
228
intervals
...
(Courtesy of
Professor Ivan Parkin, University
College, London
...
13 Structure of
stoichiometric β-alumina
...
Defects and non-stoichiometry
229
FIGURE 5
...
Na, purple; Si, blue; P, brown; O, red
...
14)
...
This creates a three-dimensional system of channels through the structure
containing two types of vacant site: Type I, a single distorted octahedral site (occupied by
Na+ ions in NZP), and three larger Type II sites (vacant in NZP)
...
The balancing cations, A, are usually alkali or
alkaline earth metals, and the structural metal(s), M, is a transition metal such as Ti, Zr,
Nb, Cr, or Fe
...
The most famous member of
this family is known as NASICON (from Na SuperIonic Conductor)
...
It has the
formula Na3Zr2(PO4)(SiO4)2, and three out of the four vacant sites are occupied by Na+,
allowing a correlated motion as the ions diffuse through the channels
...
4
...
Figure 5
...
Solid state chemistry
230
FIGURE 5
...
See colour insert on previous page
...
FIGURE 5
...
The solid electrolyte, B (which is able to conduct ions but not electrons) is sandwiched
between two electrodes, A and C, which are connected by an external circuit around
which electrons can flow
...
The ions taking part in the reaction pass through an
electrolyte and are then either oxidised or reduced at an electrode
...
To be useful as a solid electrolyte in a battery, the conducting solid must have a high
ionic conductivity, but be an electronic insulator, so that it can separate the two reactants
of the device (Figure 5
...
The electrons are released at the positively
charged electrode and travel round the external circuit where they can be harnessed for
useful work
...
14)
is the standard emf of
where n is the number of electrons transferred in the reaction,
the cell (the voltage delivered under standard, zero-current conditions), and F is the
Faraday constant (96485 C mol−1 or 96485 J V−1)
...
The reason that solid state batteries are potentially useful is that they can perform over
a wide temperature range, they have a long shelf life, and it is possible to manufacture
them so that they are extremely small
...
They are used for backup power supplies and may
eventually become useful as alternative fuel sources to power cars
...
More important can be the energy density (watthours divided by battery volume in litres) or specific energy (watt-hours divided by
battery weight in kilograms)
...
Although LiI has a fairly low ionic conductivity (Figure 5
...
16)
...
LiI is the solid
electrolyte that separates the anode (lithium) from the cathode (iodine embedded in a
conducting polymer, poly-2-vinyl-pyridine), which based on Figure 5
...
Making reliable rechargeable lithium batteries has proved to be a very difficult
problem because the lithium redeposits in a finely divided state which is very reactive
and can even catch fire
...
In the 1990s, the Sony Corporation in Japan
developed rechargeable lithium-ion batteries, which now recycle reliably many times
...
17)
...
The anode is made of
lithium embedded in graphitic carbon, which also makes an intercalation compound,
typically C6Li, but one which easily releases Li+, that then travels through a conducting
polymer electrolyte (see Chapter 6) to the CoO2 cathode
...
Various cathode materials, such as CoO2,
NiO2,TiS2, and MnO2, can be used
...
16 (a) An early LiI
Greatbatch heartpacemaker battery
(1973) approximate size 5×8 cms
...
(Courtesy of Wilson Greatbatch
Technologies, Inc
...
17 Laptop computer
powered by lightweight lithium-ion
rechargeable battery
...
Sodium Batteries
Na+ conduction has been put to good use in a secondary battery that operates at high
temperatures—the sodium sulfur battery
...
From Equation (5
...
In terms of specific energy,
such a reaction can yield about 110 Wh kg−1 of material because it incorporates a highly
energetic reaction between light substances
...
The
electrolyte separates molten sodium from molten sulfur, and at the sulfur/electrolyte
interface a complex reaction forming polysulfides of sodium takes place
...
The cell reaction is given here for one such reaction (Figure 5
...
Despite the complexity of the reactions, applying a current from an external
source can reverse the electrode process
...
Currently interest has now been directed toward a similar high temperature system, the
ZEBRA Battery, which also uses β-alumina as a Na+ ion conductor
...
Contact
between the NiCl2 electrode and the solid electrolyte is poor as they are both solids, and
current flow is improved by adding a second liquid electrolyte (molten NaAlCl4) between
this electrode and the β-alumina
...
These
batteries are fully rechargeable, safe, and have been found to need no maintenance over
100000 km; they are thus considered an attractive proposition for the electric vehicles of
the future
...
18)—the difference is that
instead of the ‘fuel’ for the reaction being contained in the electrode materials as
Solid state chemistry
236
FIGURE 5
...
in a battery, it is now fed in externally to the electrodes
...
In a fuel cell, the fuels used are
usually hydrogen and oxygen (air), which react together electrochemically to produce
water, electricity, and heat
...
The electrons travel round the external circuit, and the H+ ions travel through
the electrolyte to the cathode, where they react with a supply of O2
...
The fact that hydrogen and oxygen combine at low temperatures
compared with normal combustion, means that side-reactions producing polluting NOxs
are avoided
...
This compares with 15
to 20% for internal combustion engines and 30% for diesel engines
...
Legislation in the United States
requires that a percentage of all new vehicles should emit no hydrocarbons or oxides of
nitrogen (so-called zero emission vehicles)
...
The main
contenders are electric cars which run on either batteries or fuel cells, or a combination of
the two
...
Micro-fuel cells for mobile phones and
laptops have been developed
...
The reduction of oxygen at the cathode is rather slow at low temperatures
...
If the electrolyte allows the passage of H+ ions, the cell reaction can be
written:
A
B
hydrogen electrolyte
H2(g)//Pt/C electrode//
+
C
//Pt/C electrode//O2(g)
−
Anode A: H2=2H +2e
Cathode C: ½O2+2H++2e−=H2O
The theoretical emf for this cell, calculated from the Gibbs function for the
decomposition of water, is
at 298 K, but this decreases with temperature
to about 1 V at 500 K
...
The oxygen supply comes simply from the air, but a major drawback is the supply,
transportation and storage of the hydrogen
...
Hydrogen, a gas at room
temperature, is the least dense of all the elements and has to be compressed or liquefied
in order to store it in a manageable volume
...
Liquefied
hydrogen requires cooling and must be kept very cold (boiling point is −253°C), so the
tanks must be extremely well insulated
...
Although hydrogen is probably less dangerous than a liquid hydrocarbon fuel,
public perception about its safety needs to be overcome: many people have seen old
footage of the hydrogen-filled Hindenberg airship exploding on landing
...
The alternative is to
use a reforming reaction, where hydrogen-rich sources, such as methane or methanol,
are reacted with steam to produce hydrogen and carbon dioxide
...
The reforming reaction has its own problems, in that the
catalyst is poisoned by sulfur in the fuel
...
Fuel cells have been around for quite a long time; it was in 1839 that William Grove, a
Welsh physicist, made the first working fuel cell, but not until 1959 that Tom Bacon at
Cambridge University produced a stack of 40 alkaline fuel cells that produced 5 kW of
power
...
By 1965, Pratt & Whitney had
improved (longer life) the alkaline fuel cells (AFC) for use in the Apollo missions where
they provided both power and drinking water for the astronauts
...
2004 saw the first fuel-cell powered buses in London
(Figure 5
...
FIGURE 5
...
(Courtesy of Ballard
Power Systems
...
The last four contain solid electrolytes
...
Because of the long time needed to get the cell up to its operating
temperature, it is not useful for powering vehicles, but it can be used for power
generation in buildings and industry (Figure 5
...
The cell reaction is:
A
B
C
H2(g) //electrode//
2−
solid oxide electrolyte
−
Anode A: H2+O =H2O+2e
Cathode C:½O2+2e−=O2−
//electrode// O2(g)
Defects and non-stoichiometry
239
It is vital that the solid oxide electrolyte can withstand the extreme conditions of
hydrogen at the anode at 800°C or above
...
The cathode materials used have to conduct both oxide ions and electrons
satisfactorily, but, in addition, for compatibility, they must have similar thermal
expansion coefficients as the electrolyte
...
4
...
FIGURE 5
...
(Courtesy of Siemens PG
CTET: Stationary Fuel Cells, Europe
...
Here the electrolyte is a conducting polymer membrane (see
Chapter 6), usually Nafion, which is a sulfonated fluoropolymer made by Dupont,
strengthened by Gore-Tex™
...
Output is typically 1 V at 80°C; with a current
flow of 0
...
5 V because of ohmic losses
...
To produce the correct power output, a number of cells are placed
together to form a stack
...
21), and the first hydrogen fuel-cell consumer vehicle—a Nissan 4×4
pick-up truck—went on sale in the USA in 2005
...
20)
...
Fuel cells are still used
to power the space shuttle
...
The buses run on compressed hydrogen stored in tanks in the
Solid state chemistry
240
roof with a power of 200 kW
...
FIGURE 5
...
(Courtesy
of Ballard Power Systems
...
On a smaller scale, microfuel cells might soon replace batteries in electrical equipment
such as mobile phones and palmtop computers
...
Although fuel cells offer exciting possibilities for the future, the current reality is that
the electricity produced by them is still expensive—anything up to eight times that
produced in a traditional generating plant with gas-fired turbines
...
There is no doubt, however, that they are strong contenders for the technology
of the future, offering as they do the possibility to move toward a greener ‘hydrogen
economy’, thus eliminating greenhouse gas emissions
...
Figure 5
...
Gas
pressures tend to equalize if they can and so, if p′>p″, oxygen ions, which are able to pass
through the stabilized zirconia, tend to pass through the solid from the right-hand side to
the left
...
FIGURE 5
...
Oxygen gas is reduced to O2− at the right-hand electrode (C)
...
The equation for the cell reaction is:
Anode A: 2O2−→O2(p″)+4e−
Cathode C: O2(p′)+4e−→2O2−
Overall: O2(p′)→O2(p″)
Under standard conditions, we can relate the change in Gibb’s free energy for the
preceding reaction to the standard emf of the cell:
(5
...
If the cell reaction is given by a general equation:
aA+bB+…+ne=xX+yY+…
then,
(5
...
are the activities of the reactants and products
...
The pressure of the oxygen on one side of the cell (for instance, p″) is set to
be a known reference pressure, usually either pure oxygen at 1 atm or atmospheric
oxygen pressure (~0
...
Making these two changes, we obtain:
All the quantities in this equation are now known or can be measured, affording a direct
measure of the unknown oxygen pressure p′
...
Oxygen meters find industrial uses in the detection of oxygen in waste gases from
chimneys or exhaust pipes, in investigation into the operation of furnaces, and in
measuring the oxygen content in molten metals during the production process
...
Examples include H2, F2, Cl2, CO2, SOx, and NOx
...
When an electric
current is applied to the following device (Figure 5
...
23 (a) Diagram of an
electrochromic device; (b)
electrochromic office windows
...
)
Li+ ions flow from the anode, through the colourless electrolyte to form LixWO3 at the
cathode, changing it from almost colourless to deep blue
...
Solid state chemistry
244
5
...
This is usually supported on paper or thin plastic to form
photographic film
...
They are grown very carefully in situ with as few structural defects as
possible, and they range in size from 0
...
During the photographic process,
light falling on the AgBr produces Ag atoms in some of the grains; these eventually form
the dark parts of the negative
...
It is important for the grains to be free from structural defects such
as dislocations and grain boundaries, because these interfere with the deposition of the
Ag atoms on the surface of the grains
...
AgBr and AgI both have the NaCl or rock salt crystal structure
...
For a grain to possess a latent
image, a cluster of as few as four Ag atoms forms on the surface
...
However, it is
thought to take place in several stages
...
The band gap of AgBr is 2
...
This electron eventually neutralises one of the interstitial silver ions
(Agi+):
Agi++e−=Ag
In the next stages, this Ag atom speck has to grow into a cluster of atoms on the surface
of the crystal
...
In reality, the process is even more complex than this because emulsions made from
pure AgBr are not sensitive enough, and so they also contain sensitizers, such as sulfur
or organic dyes, which absorb light of longer wavelength than AgBr and so extend the
spectral range
...
The film containing the latent image is then treated with various chemicals to produce
a lasting negative
...
The clusters of Ag
atoms act as a catalyst to this reduction process, and all the grains with a latent image are
reduced to Ag
...
The final stage in
producing a negative is to dissolve out the remaining light-sensitive AgBr
...
5
...
It was thought that the colour was
associated with a defect known then as a Farbenzentre (colour centre), now abbreviated
as F-centre
...
The colour produced by the F-centres is
always characteristic of the host crystal, so, for instance, NaCl becomes deep yellowyorange, KCl becomes violet, and KBr becomes blue-green
...
The excess
alkali metal atoms diffuse into the crystal and settle on cation sites; at the same time, an
equivalent number of anion site vacancies are created, and ionisation gives an alkali
metal cation with an electron trapped at the anion vacancy (Figure 5
...
In fact, it does
not even matter which alkali-metal is used; if NaCl is heated with potassium, the colour
of the F-centre does not change because
FIGURE 5
...
it is characteristic of the electron trapped at the anion vacancy in the host halide
...
The trapped electron provides a classic example of an ‘electron in a box’
...
There is an interesting natural example of this phenomenon: The mineral
Solid state chemistry
246
fluorite (CaF2) is found in Derbyshire, United Kingdom where it is known as ‘Blue John’,
and its beautiful blue-purple colouration is due to the presence of F-centres
...
The
H-centre is formed by heating, for instance, NaCl in Cl2 gas
...
24(b))
...
These semi-precious stones are basically crystals of silica, SiO2,
with some impurities present
...
The Al3+ substitutes for the Si4+ in the lattice, and the electrical
neutrality is maintained by H+ present in the same amount as Al3+
...
This group is the colour centre, absorbing light and producing the
smoky colour
...
On irradiation,
[FeO4]4− colour centres are produced which absorb light to give the characteristic purple
coloration
...
7 NON-STOICHIOMETRIC COMPOUNDS
5
...
1 INTRODUCTION
Previous sections of this chapter have shown that it is possible to introduce defects into a
perfect crystal by adding an impurity
...
Impurity-induced
defects are said to be extrinsic
...
Colour centres are formed if a crystal of NaCl is heated in sodium vapour; sodium is
taken into the crystal, and the formula becomes Na1+xCl
...
The solid so formed is a
non-stoichiometric compound because the ratio of the atomic components is no longer
the simple integer that we have come to expect for well-characterized compounds
...
Uranium dioxide, for instance, can
range in composition from UO1
...
25, certainly not the perfect UO2 that we might
expect! Many other examples exist, some of which we discuss in some detail
...
Breaking these
bonds usually takes quite a lot of energy, and so under normal circumstances, a particular
Defects and non-stoichiometry
247
compound does not show a wide range of composition; this is true for most molecular
organic compounds, for instance
...
We have seen,
however, that it is possible to make ionic crystals non-stoichiometric by doping them
with an impurity, as with the example of Na added to NaCl
...
Elements with a variable valency mostly occur in the transition elements,
the lanthanides and the actinides
...
They can
be made by introducing impurities into a system, but are frequently a consequence of the
ability of the metal to exhibit variable valency
...
5 lists a few non-stoichiometric
compounds together with their composition ranges
...
5 Approximate composition ranges for
some non-stoichiometric compounds
Composition rangea
Compound
TiOx
[≈TiO]
0
...
25
[≈TiO2]
1
...
000
VOx
[≈VO]
0
...
29
MnxO
[≈MnO]
0
...
000
FexO
[FeO]
0
...
957
CoxO
[≈CoO]
0
...
000
NixO
[≈NiO]
0
...
000
CeOx
[≈Ce2O3]
1
...
52
ZrOx
[≈ZrO2]
1
...
004
UOx
[≈UO2]
1
...
25
LixV2O5
0
...
33
LixWO3
0
971
92
00
03
Solid state chemistry
248
Until recently, defects both in stoichiometric and non-stoichiometric crystals were
treated entirely from the point of view that point defects are randomly distributed
...
The following sections attempt to explore the relationship between stoichiometry
and structure
...
X-ray diffraction is the usual
method for the determination of the structure of a crystal; however, this method yields an
average structure for a crystal
...
For this kind of structure determination, a technique
that is sensitive to local structure is needed, and such techniques are very scarce
...
HREM has probably done the most to clarify the understanding of defect
structures because it is capable under favourable circumstances of giving information on
an atomic scale by ‘direct lattice imaging’
...
This is widely exploited and researched by the
electronics and other industries
...
The structure of these is discussed in detail in Chapter
10
...
7
...
Accurate chemical analysis demonstrates that it is non-stoichiometric: it is always
deficient in iron
...
25) illustrates that the compositional
range of wustite increases with temperature and that stoichiometric FeO is not included in
the range of stability
...
An iron deficiency could be accommodated by a defect structure in two ways: either
iron vacancies, giving the formula Fe1−xO, or alternatively, there could be an excess of
oxygen in interstitial positions, with the formula FeO1+x
...
The easiest
method of measuring the density of a crystal is the flotation method
...
The density of that liquid
mixture must then be the same as that of the crystal, and it can be found by weighing an
accurately measured volume
...
25 Phase diagram of the
FeO system
...
The theoretical density of a crystal can be obtained from the volume of the unit cell and
the mass of the unit cell contents
...
An example of this type of calculation for FeO follows:
A particular crystal of FeO was found to have a unit cell dimension of
430
...
728 kg m−3, and an iron to oxygen ratio
of 0
...
The unit cell volume (which is a cube) is thus (430
...
956×107 (pm)3=7
...
There are four formula units of FeO in a perfect unit cell with the rock salt structure
...
85
Solid state chemistry
250
and O, 16
...
One mole of FeO weighs (55
...
00) g= 0
...
07185) kg; and four formula units weigh (4× 0
...
773×10–25 kg,
where Avogadro’s number, NA=6
...
The sample under consideration has an Fe:O ratio of 0
...
Assume, in the first
instance, that it has iron vacancies: The unit cell contents in this case will be
(4×0
...
78Fe and 4O
...
78×55
...
00)]/(NA×103) kg
...
742×103 kg m−3 for the density
...
945=1
...
The unit cell in
this case will contain 4Fe and (4×1
...
232 O
...
85)+(4
...
00)]/(NA ×103) kg, giving a density of 6
...
Comparing the two sets of calculations with the experimentally measured density of
5
...
945O
...
6
...
This is known
as Vegard’s Law
...
It is possible to determine whether the non-stoichiometry is
accommodated by vacancy or interstitial defects using density measurements
...
Now we turn our
attention to the balancing of the charges within the crystal
...
It is energetically more favourable to oxidise Fe(II)
...
In the overwhelming
majority of cases, defect creation involves changes in the cation oxidation state
...
In a later section we will look at some general cases of non-stoichiometry in simple
oxides, but before we do that we will complete the FeO story with a look at its detailed
structure
...
6 Experimental and theoretical
densities (103 kg m−3) for FeO
Theoretical density
O:Fe
ratio
Fe:O
ratio
Lattice
parameter/pm
Observed
density
Interstitial
O
Fe
vacancies
1
...
945
430
...
728
6
...
742
1
...
930
429
...
658
6
...
706
1
...
920
428
...
624
6
...
687
1
...
910
428
...
613
6
...
652
The Structure of FeO
FeO has the NaCl structure with Fe2+ ions in octahedral sites
...
If the rock salt structure were preserved, the Fe2+, Fe3+, and the
cation vacancies would be distributed over the octahedral sites in the ccp O2− array
...
Structural studies (X-ray,
neutron and magnetic) have demonstrated that some of the Fe3+ ions are in tetrahedral
sites
...
At higher values of x, the structure
contains various types of defect clusters, which are distributed throughout the crystal
...
One
possibility is known as the Koch-Cohen cluster (Figure 5
...
This has a standard NaCltype unit cell at the centre, but with four interstitial, tetrahedrally coordinated, Fe3+ ions
in the tetrahedral holes; the 13 immediately surrounding octahedral Fe2+ sites must be
vacant
...
We therefore designate them
simply as Feoct
...
26 to make the central section more visible
...
26
...
The complete cluster, allowing
for the back and front faces which are not illustrated here, contains 8 NaCl-type unit
cells, and thus 32 oxide ions
...
Taking into account the 13 octahedral vacancies,
there must be 19 Feoct ions and the 4 interstitial Fetet3+ ions making twenty-three iron
cations in all
...
It bears a
strong resemblance to the structure of Fe3O4, the next-highest oxide of iron
...
There are 32 oxide ions, so to balance them, the Fe cations overall must have 64
Solid state chemistry
252
positive charges: 12 are accounted for by the 4 Fe3+ ions in tetrahedral positions, leaving
52 to find from the remaining 19 Feoct cations
...
Suppose that xFe2+ ions and yFe3+ ions are present in octahedral sites, we
know that
x+y=19
We also know that their total charges must equal 52, so:
2x+3y=52
FIGURE 5
...
The
central section with four tetrahedrally
coordinated Fe3+ ions is picked out in
bold
...
Solving gives y=14 and x=5
...
By injecting such clusters throughout the FeO structure, the non-stoichiometric
structure is built up
...
Neutron scattering
Defects and non-stoichiometry
253
experiments indicate that as the concentration of defects increases, the clusters order into
a regular repeating pattern with its own unit cell of lower symmetry; the new structure is
referred to as a superstructure or superlattice of the parent
...
5
...
3 URANIUM DIOXIDE
Above 1127°C, a single oxygen-rich non-stoichiometric phase of UO2 is found with
formula UO2+x, ranging from UO2 to UO2
...
Unlike FeO, where a metal-deficient oxide
was achieved through cation vacancies, in this example the metal-deficiency arises from
interstitial anions
...
25 corresponds to U4O9, which is a well-characterized oxide of uranium known at
low temperature
...
The unit cell is depicted in Figure 5
...
(There are four uranium ions contained within
the cell boundaries; the eight oxide ions come from: (8×⅛)=1 at the corners;
FIGURE 5
...
Uranium positions
Solid state chemistry
254
(not shown) are in the centre of every
other cube
...
)
As more oxygen is taken into UO2, the extra oxide ions go into interstitial positions
...
This site however, is not ideal for an
extra oxide ion, as not only is it crowded, but it is also surrounded by eight ions of the
same charge
...
This is illustrated in Figure 5
...
This defect cluster can be considered as two
vacancies: one interstitial of one kind, O′, and two of another, O″, and it is called the
2:1:2 Willis cluster
...
The atomic composition of a fluorite unit cell (Figure 5
...
27(b)
...
In the oxygen-rich limit for the UO2+x nonstoichiometric structure (UO2
...
We can think of UO2+x as containing microdomains
of the U4O9 structure within that of UO2
...
5
...
4 THE TITANIUM MONOXIDE STRUCTURE
Titanium and oxygen form non-stoichiometric phases which exist over a range of
composition centered about the stoichiometric 1:1 value, from TiO0
...
25
...
00 to TiO1
...
At the stoichiometric composition of TiO1
...
Above 900°C, these
vacancies are randomly distributed, but below this temperature, they are ordered as
shown in Figure 5
...
In Figure 5
...
Every third vertical
diagonal plane has been picked out by a dashed line
...
00 structure, every other
atom along those dashed lines is missing
...
28(b)
...
This is drawn in
Figure 5
...
This is true throughout the structure
...
The new unit cell of
the superlattice is monoclinic (see Chapter 1) because the angle in the xz plane (β) is not
equal to 90°
...
As discussed in Chapter 4, unusually for a transition metal monoxide, TiC1
...
The existence of the vacant sites within the TiO
structure is thought to permit sufficient contraction of the lattice that the 3d orbitals on
titanium overlap, thus broadening the conduction band and allowing electronic
conduction
...
25, it has a different defect
structure, still based on the NaCl structure, but with all the oxygens present, and one in
every five titaniums missing (Figure 5
...
The pattern of the titanium vacancies is
shown in Figure 5
...
28 but
FIGURE 5
...
31
...
31; the
Solid state chemistry
256
line of intersection of every third
vertical diagonal plane is marked by a
dashed line, (b) The same plane in the
observed structure of TiO; every
alternate atom is removed along the
diagonal lines in (a), (c) The plane
directly beneath the layer in (b); again,
every alternate atom is removed along
the cuts made by the planes with the
intersection lines that are shown in (a)
...
with the oxygens omitted; only titaniums are marked
...
The ordering of the defects has again produced a
superlattice
...
00 and TiO1
...
00 and TiO1
...
Note that although most texts refer to the
structure as TiO1
...
8O (Ti1−xO) because this indicates that
the structure contains titanium vacancies rather than interstitial oxygens
...
29 The structure of
TiO1
...
Defects and non-stoichiometry
257
5
...
The simplest linear defect is a dislocation where there is a fault in
the arrangement of the atoms in a line through the crystal lattice
...
However,
FIGURE 5
...
25
...
8
...
The reaction of these systems to
the presence of point defects is entirely different from what has been discussed
previously
...
In these systems, a series of closely related compounds with very similar formulae and
structure exists
...
The
resulting series of oxides is known as an homologous series (like the alkanes in organic
chemistry)
...
In these compounds, we find regions of corner-linked octahedra separated from each
other by thin regions of a different structure known as the crystallographic shear (CS)
planes
...
The structure of a shear plane is quite difficult to
understand, and these structures are usually depicted by the linking of octahedra as
described in Chapter 1
...
31 (ignore the bold squares for the time being)
...
) ReO3 is made
up of [ReO6] octahedra that are linked together via their corners; each corner of an
octahedron is shared with another
...
31 (a) shows part of one layer of linked
octahedra in the structure
...
Part of the ReO3 structure is drawn in Figure 5
...
As six oxygens surround each Re, the
overall formula is ReO3
...
Look back now to the octahedra marked
in bold in Figure 5
...
The edge-sharing corresponds to shearing the structure so that
the chains of bold octahedra are displaced to the positions in Figure 5
...
This
shearing occurs at regular intervals in the structure and is interspersed with slabs of the
‘ReO3’ structure (corner linked [WO6] octahedra)
...
The direction of maximum
Defects and non-stoichiometry
259
FIGURE 5
...
density of the edge-sharing groups is called the crystallographic shear plane and is
indicated by an arrow in (b)
...
33(a)
...
33(b)); 14 of the
oxygen atoms are linked out to other octahedra (these bonds are indicated), so are each
shared by two W atoms, while the remaining 4 oxygens are only involved in the edgesharing within the group
...
Clearly, if groups of four octahedra with stoichiometry W4O11 are interspersed
throughout a perfect WO3 structure, then the amount of oxygen in the structure is reduced
and we can write the formula as WO3−x
...
If the structure sheared in such a way that the entire
structure was composed of these groups, the formula would become W4O11
...
Clearly, we can extend this process to any number of [WO6]
octahedra regularly interspersed between the groups:
W4O11+2WO3=W6O17;
w4O11+3WO3=W7O20;
W4O11+4WO3=W8O23;
w4O11+5WO3=W9O26;
W4O11+6WO3=W10O29;
W4O11+7WO3=W11O32
...
This
formula also holds for all the other formulae that are listed
...
32 (a) and (b): Part of the
ReO3 structure, showing the linking of
octahedra through the corners
...
The shear planes are found to repeat throughout a particular structure in a regular and
ordered fashion, so any particular sample of WO3−x will have a specific formula
corresponding to one of those listed previously
...
An
example of one of the structures is illustrated in Figure 5
...
A unit cell has been marked
so that the ratio of [WO6] octahedra to the groups of four is clear
...
Defects and non-stoichiometry
261
Members of the MonO3n−1 series have the same structure as their WnO3n−1 analog, even
though unreduced MoO3 does not have the ReO3 structure, but a layer structure
...
33 (a) and (b): Group of
four [WO6] octahedra sharing edges
formed by the creation of shear planes
in WnO3n−1
...
34 A member of the
WnO3n−1 homologous series with the
projection of a unit cell marked
...
The homologous series for oxygen deficient TiO2 is given by the formula TinO2n−1
...
5
...
2 PLANAR INTERGROWTHS
Many systems show examples of intergrowth where a solid contains regions of more than
one structure with clear solid-solid interfaces between the regions
...
The zeolites ZSM-5 and ZSM-11 can form
intergrowths (see Chapter 7), as can the barium ferrites (see Chapter 9)
...
The term bronze
is applied to metallic oxides that have a deep colour, metallic lustre and are either
metallic conductors or semiconductors
...
Defects and non-stoichiometry
263
We have already seen that WO3 has the rhenium oxide (ReO3) structure, with [WO6]
octahedra joined through the corners
...
31(a) and Figure 5
...
The structure contains a three-dimensional network of channels throughout the structure
and it has been found that alkali metals can be incorporated into the structure in these
channels
...
The structures are based on three main types; there are cubic phases
where the alkali metal occupies the centre of the unit cell (similar to perovskite; see
Chapters 1 and 10) and tetragonal and hexagonal phases
...
35
...
This is achieved by the change in oxidation state of some of the tungsten
atoms from VI to V (such processes are discussed in more detail in the final section
[Section 5
...
The hexagonal bronze structure illustrated is formed when potassium reacts with WO3
(K needs a bigger site) and the composition lies in the range K0
...
33WO3
...
The layers of
hexagonal structure can be either one or two tunnels wide, as depicted in Figure 5
...
Similar structures are observed for tungsten bronzes containing metals other than
potassium such as Rb, Cs, Ba, Sn, and Pb
...
37)
...
Solid state chemistry
264
FIGURE 5
...
The shaded squares represent WO6
octahedra, which are linked to form
pentagonal, square and hexagonal
tunnels
...
5
...
9
...
The
Defects and non-stoichiometry
265
intervening regions of perfect structure now change from infinite sheets to infinite
columns or blocks
...
The block size is expressed as
the number of octahedra sharing vertices
...
The block size (or sizes)
FIGURE 5
...
The tungsten
trioxide matrix is shown as shaded
squares
...
Solid state chemistry
266
determines the overall stoichiometry of the solid
...
38
...
9
...
These structures contain the basic repeating unit depicted in Figure 5
...
When these are stacked on
top of each another, a pentagonal column is formed that contains chains of alternating M
and O atoms
...
One example
is given in Figure 5
...
37 Electron micrograph of
the intergrowth tungsten bronze phase
BaxWO3, illustrating the single rows of
tunnels clearly
...
Defects and non-stoichiometry
267
FIGURE 5
...
CS planes between
the blocks have a darker contrast
...
J
...
Hutchison
...
39 (a) A pentagonal
column; (b) the structure of Mo5O14
...
This type of structure is also found in the tetragonal tungsten bronzes
...
9
...
9
...
The closely related Ta2O5−WO3 system does something even more unusual
...
The idealized structures of two of these compounds are depicted in Figure 5
...
As the composition varies, so the
wavelength of the backbone changes, giving rise to a huge number of possible ordered
structures, known as infinitely adaptive compounds
...
40 The idealized structures
of (a) Ta22W4O67 and (b) Ta30W2O81
...
The wavelength of the chains
of pentagonal columns varies with
composition in such a way that any
given anion to cation ration can be
accommodated by an ordered structure
...
10 ELECTRONIC PROPERTIES OF NON-STOICHIOMETRIC
OXIDES
Earlier, we considered the structure of non-stoichiometric FeO in some detail
...
7 Types of non-stoichiometric oxides
(MO)
Metal excess
Reduced metal M
A anion
vacancies
B interstitial
cations
MO1−x
M1+xO
TiO, VO, (ZrS)
CdO, ZnO
Metal deficiency
Oxidized metal M
C interstitial
anions
MO1+x
D cation vacancies
M1−xO
TiO, VO, MnO, FeO, CoO,
NiO
The four types are summarized in Table 5
...
41 illustrates some of the
structural possibilities for simple oxides with A, B, C, and D type non-stoichiometry,
assuming an NaCl-type structure
...
(Other
compounds falling into this category are MnO, CoO, and NiO
...
41 Structural possibilities
for binary oxides, (a) Type A oxides:
metal excess/anion vacancies, (i) This
shows the two electrons that maintain
charge neutrality, localized at the
vacancy, (ii) The electrons are
associated with the normal cations
making them into M+
...
(i)
This shows an interstitial atom,
whereas in (ii) the atom has ionized to
M2+, and the two liberated electrons
are now associated with two normal
cations, reducing them to M+
...
The charge compensation for
an interstitial anion is by way of two
M3+ ions, (d) Type D oxides: metal
deficiency/cation vacancies
...
Solid state chemistry
272
Type A oxides compensate for metal excess with anion vacancies
...
These can be trapped at a vacant anion site, as depicted in (a)(i)
...
VO1−x is an example of this type of
system
...
This is shown in (b)(i) as an interstitial atom, but it is more likely that the
situation in (b)(ii) will hold, where the interstitial atom has ionised and the two electrons
so released are now associated with two neighbouring ions, reducing them from M2+ to
M+
...
Oxygen is lost when zinc(II) oxide
is heated, forming Zn1+xO, oxide vacancies form and to compensate, Zn2+ ions migrate to
interstitial positions and are reduced to Zn+ ions or Zn atoms
...
Type C oxides compensate for the lack of metal with interstitial anions
...
Before considering the conductivity of these non-stoichiometric oxides it is probably
helpful to recap what we know about the structure and properties of the stoichiometric
binary oxides of the first-row transition elements
...
8
...
TiO and VO behave as metallic conductors and
must therefore have good overlap of the d orbitals producing a d electron band
...
Further along the series, we saw that stoichiometric MnO, FeO, CoO, and NiO are
insulators
...
(It is this
localization of the d electrons on the atoms that gives rise to the magnetic properties of
these compounds that are discussed in Chapter 9
...
Figure 5
...
Although we have described this association as
reducing neighbouring cations, this association can
be quite weak, and these electrons can be free
TABLE 5
...
00 and
TiO1
...
Cr
Mn
Fe
Does NaCl structure NaCl
structurea
not
exist
Paramagnetic
µ=5
...
Thermal energy is often sufficient to make these electrons move and so conductivity
increases with temperature
...
Chapter 4 discussed semiconductivity in terms of band theory
...
Electrons can be promoted into this conduction band by heating, leaving positive holes in
the valence band; the current is carried by both the electrons in the conduction band and
by the positive holes in the valence band
...
For instance, if a small amount of
phosphorus is incorporated into the lattice the extra electrons form impurity levels near
the empty conduction band and are easily excited into it
...
Correspondingly, doping with Ga increases the conductivity by creating
positive holes in the valence band and such semiconductors are called p-type (p for
positive)
...
Conduction in these non-stoichiometric oxides is
not easily described by band theory, for the reasons given earlier for their stoichiometric
counterparts—the interelectronic repulsions have localized the electrons on the atoms
...
Conduction then occurs by jumping or hopping from one site to another under the
influence of an electric field
...
However, when two
valence states, such as Zn2+ and Zn+, are available as in these transition metal nonstoichiometric compounds, the electron jump between them does not take much energy
...
We find that the mobility of a
charge carrier (either an electron or a positive hole), µ, is an activated process and we can
write:
(5
...
1 to 0
...
The
hopping conductivity is given by the expression
σ=neµ
(5
...
(Notice that these equations are analogous to Equation (5
...
7) in
Section 5
...
) The
density of mobile carriers, n, depends only on the composition of the crystal, and does not
Defects and non-stoichiometry
275
vary with temperature
...
16), we can see that, as for ionic conductivity,
the hopping electronic conductivity increases with temperature
...
The M3+ ions can be regarded
as M2+ ions associated with a positive hole
...
MnO, CoO, NiO, and FeO
are materials that behave in this way
...
Regarding the charge carriers as positive holes is simply a matter of convenience and the
description of a positive hole moving from Ni3+ to Ni2+ is the same as saying that an
electron moves from Ni2+ to Ni3+
...
Here we have considered some metallic examples which
can be described by band theory, such as TiO and VO, and others, such as MnO, which
are better described as hopping semiconductors
...
We also met nonstoichiometric compounds, such as calcia-stabilized zirconia and β-alumina, which are
good ionic conductors
...
It is thus difficult to make generalizations about this
complex behaviour, and each case is best treated individually
...
Much of their research is
directed at extending the composition range and thus the properties of these materials
...
Here is one example: If we add Li2O to NiO and
then heat to high temperatures in the presence of oxygen, Li+ ions become incorporated in
the lattice and the resulting black material has the formula LixNi1−xO where x lies in the
range 0 to 0
...
The equation for the reaction (using stoichiometric NiO for simplicity) is
given by:
½xLi2O+(1−x)NiO+¼xO2=LixNi1−xO
To compensate for the presence of the Li+ ions, Ni2+ ions will be oxidised to Ni3+ or the
equivalent of a high concentration of positive holes located at Ni cations
...
Indeed, at high Li concentrations, the
conductivity approaches that of a metal (although it still exhibits semiconductor
behaviour in that its conductivity increases with temperature)
...
11 CONCLUSIONS
In this chapter, we have tried to give some idea of the size and complexity of this subject
and also its fascination, without it becoming overwhelming
...
9 Defect concentration data for CsI
T/K
300
1
...
06×10−12
500
2
...
04×10–8
700
1
...
76×10–6
defects does not explain the complex structures of non-stoichiometric compounds, but
that defects cluster together and become ordered, or even eliminated, in many different
ways
...
QUESTIONS
1
...
2
...
9 gives the variation of defect concentration with temperature for CsI
...
3
...
8? How is the transition point in the graph affected by the
purity of the crystal?
4
...
What effect, if any, do you
expect small amounts of the following impurities to have on the conductivity of NaCl
crystals: (a) AgCl, (b) MgCl2, (c) NaBr, (d) Na2O?
5
...
Suggest a reason for this
...
Figure 5
...
(The anion behind this tetrahedron has been omitted for clarity
...
Describe, and sketch,
the pathway it takes in terms of the changing coordination by cations
...
Make a simple estimate of the energy of defect formation in the fluorite structure:
(a) describe the coordination by nearest neighbours and next-nearest neighbours of an
anion both for a normal lattice site and for an interstitial site at the centre of the unit cell
shown in Figure 5
...
FIGURE 5
...
(b) Use the potential energy of two ions, given by:
where Z is the charge on the other ion and r is the distance between them, to estimate the
energy of defect formation in fluorite; a=537 pm
...
The zinc blende structure of γ-AgI, a low-temperature polymorph of AgI, is
illustrated in Figure 5
...
Discuss the similarities and differences between this structure
and that of α-AgI
...
43 The zinc blende
structure of γ-AgI
...
The compounds in Table 5
...
Explain
...
Undoped β-alumina demonstrates a maximum conductivity and minimum
activation energy when the sodium excess is around 20 to 30 mole%
...
By contrast, βalumina crystals doped with Mg2+ have a much higher conductivity than do undoped
crystals
...
11 Confirm the presence of iron vacancies for a sample of wustite which has a unit
cell dimension of 428
...
910 and an experimental density of
5
...
12
...
How would you expect the formation of colour centres to affect the density of the
crystal?
14
...
44 depicts the central section of a possible defect cluster for FeO
...
15
...
28 to confirm that TiO is a one-sixth defective NaCl structure, by
counting up the atoms in the monoclinic cell
...
Figure 5
...
25 structure with both the Ti and O
sites marked
...
30 to demonstrate that the unit cell shown has the
correct stoichiometry for the crystal
...
44 A possible cluster in
Fe1−xO
...
45 A member of the
WnO3n−1 homologous series
...
How would you expect charge neutrality to be maintained in TiO1
...
Take a simple case where two metal oxide octahedra wish to eliminate oxygen by
sharing
...
Figure 5
...
To what formula
does it correspond?
20
...
What do you expect to happen to its
electronic properties if it is doped with Ga2O3 under reducing conditions?
6
Carbon-Based Electronics
6
...
The 2000 Nobel Prize for chemistry was awarded to Alan Heeger, Hideki Shirakawa, and
Alan McDiarmid for the discovery of the electrically conducting polymer, polyethyne or
poly acetylene (−CH=)n based on their work in the 1960s and 1970s
...
Polypyrroles, for
example, are commercially available and used in gas sensors
...
Crystalline organic metals are generally composed of organic molecules with
delocalised ring systems together with another organic molecule or inorganic species
...
Some of these organic
metals are even superconductors at low temperatures
...
Finally, we look at carbon itself in the form of graphite, which finds extensive use as
an electrode material, and the relatively recently discovered allotropes, the fullerenes
...
6
...
2
...
First attempts to make poly acetylene and similar solids, however, resulted in short chain
molecules or amorphous, unmeltable powders
...
Polyacetylene exists in two forms cis and trans, as depicted in Figure 6
...
Ten years after Hatano’s work, Shirakawa, and
Ikeda made films of cis-polyacetylene which could be converted into the trans form
...
To make a
Carbon-based electronics
283
large film, the catalyst solution can be spread in a thin layer over the walls of a reaction
vessel (Figure 6
...
1 cis- and transpolyacetylene
...
The polyacetylene produced in this way has a smooth shiny surface on
one side and a sponge-like structure
...
The conversion is quite rapid above 370 K
...
A way of improving the conductivity was found when Shirakawa visited McDi-armid
and Heeger in Pennsylvania later in the 1970s
...
It was a natural step to try this approach with polyacetylene
...
Solid state chemistry
284
FIGURE 6
...
The paper-thin flexible sheet of
polyacetylene is then stripped from the
walls before doping
...
Originally published in
Scientific American
...
3 Conductivities of doped
poly acetylenes: conductivities of
insulators, semiconductors and metals
are given for comparison
...
The
effect of these dopants can be to raise the conductivity from 10–3 S m−1 to as much as 105
S m−1 using only small quantities of dopant
...
For example, the polymer can be doped with alkali metals to give, for example,
[Liδ+(CH)δ−]n
...
3
...
The polymer loses its metallic
lustre and becomes brittle when exposed to air
...
Polypyrrole, polythiophene, polyaniline, polyphenylenevinylene (Figure
6
...
4 Repeating units of some
conducting polymers
...
These polymers are, however, less
sensitive to oxygen and by attaching suitable side chains can be made soluble in nonpolar
organic solvents and thereby easier to process
...
This is exploited in polypyrrole gas sensors, which
are based on the variation of conductivity of a thin polymer film when exposed to gases
such as NH3 and H2S
...
The most promising commercial applications of conjugated
polymers such as the LED described in Section 6
...
3, however, use undoped polymer
...
2
...
If we take a very long conjugated olefin,
we might expect to obtain a band of π levels, and if this band were partly occupied, we
would expect to have a one-dimensional conductor
...
Now if polyacetylene consisted of a regular evenly
spaced chain of carbon atoms, the highest occupied energy band, the π band, would be
half full and polyacetylene would be an electrical conductor
...
The crystal structure is difficult to determine accurately, but diffraction
measurements indicate that an alternation in bond lengths of about 6 pm occurs
...
Nonetheless, this does indicate that the
Solid state chemistry
286
electrons are tending to localise in double bonds instead of being equally distributed over
the whole chain
...
Just enough electrons are
available to fill the lower band
...
5, this leads to a lower energy
than the half-full single band
...
5 The band gap in
polyacetylene produced by the
alternation of long and short bonds
...
Thus although a very simple bonding picture of such solids would
suggest a half-filled band and metallic conductivity, the best that can be expected is a
semiconducting polymer
...
The
doped polyacetylene now has holes in its valence band and, like p-type semiconductors,
has a higher conductivity than the undoped material
...
6
...
3 ORGANIC LEDs
Polymer light-emitting diodes are being developed for flat panel displays in mobile
phones, laptops, and televisions
...
At the bottom is a layer of semitransparent metallic conductor, usually indium-doped tin
oxide (ITO), which acts as one electrode (Figure 6
...
On top of this is a layer of undoped
conjugated polymer such as polyphenylenevinylene and on top of that an easily ionised
metal such as Ca, Mg/Ag, or Al
...
To act as an LED,
a voltage is applied across the two electrodes such that the ITO layer is positively
charged
...
This leaves gaps in the lower energy band
...
When such an electron reaches a region of the polymer
where vacancies exist in the lower energy band, it can jump down to this band emitting
light as it does so
...
Polyphenylenevinylene LEDs emit green/yellow light,
polyphenylene-based LEDs emit blue light, and some polythiophenes emit red light
...
6 Section through a
polymer LED
...
3 MOLECULAR METALS
6
...
1 ONE-DIMENSIONAL MOLECULAR METALS
Molecular metals are molecular solids with metallic electrical conductivity
...
The first one of this class discovered was TTFTCNQ
...
These are depicted in Figure 6
...
The electrical conductivity of TTF:TCNQ is of the order of 102 S m−1 at room
temperature and increases with decreasing temperature until around 80 K when the
conductivity drops as the temperature is lowered
...
In TTFTCNQ, the columns of each type of molecule interact to form delocalised orbitals
...
The number of
electrons transferred corresponds to about 0
...
This partial
transfer only occurs with molecules such as tetrathiafulvalene whose electron donor
ability is neither too small nor too large
...
With very good electron donors such as alkali metals, one electron per TCNQ is
transferred and the acceptor band is full
...
At low temperatures, TTF-TCNQ suffers a periodic distortion and so its conductivity
drops
...
3
...
Another class
of molecular metals exists, however, which, while appearing to resemble these solids, are
less unambiguously defined as one-dimensional
...
8, forms a series of
salts with inorganic anions
...
5+)
...
Unlike TTF-TCNQ,
however, (TMTSF)2+(ClO4)− and other similar salts remain highly conducting at low
temperatures and indeed at very low temperatures become superconducting
...
As a result, the onedimensional model is not as valid as for TTF-TCNQ, and in particular, Peierls’ theorem
no longer holds
...
Other similar compounds, instead of containing chain-like stacks of organic
molecules, contain flat organic ring compounds stacked so that molecular orbitals on
different molecules overlap to form bands
...
7 Structures of (a) TTF
and TCNQ and (b) solid TTF-TCNQ,
showing alternate stacks of TTF and
TCNQ molecules
...
8 Structure of tetramethyltetraselenofulvalene (TMTSF)
...
Electrons are delocalised over the planes of organic
molecules
...
This forms molecular metals (BEDT-TTF)2X with a variety of anions including
[Cu(NCS)2]−, I3−, AuI2−, IBr2−, [Cu(N(CN)2)X]−(X=Cl or Br), [Cu(CN)3]−, GaCl4−,
SF5CH2CF2SO3−
...
Figure 6
...
Carbon-based electronics
291
FIGURE 6
...
Because of the presence of the anions, the BEDT-TTF layers are positively charged,
with a formal charge of 0
...
Thus, the highest occupied band is only
partially filled and the crystals will conduct electricity
...
Despite
the low values of the critical temperatures, the superconductivity of these materials is of
the same type as that of the high-temperature superconductors (see Chapter 10)
...
4 POLYMERS AND IONIC CONDUCTION—RECHARGEABLE
LITHIUM BATTERIES
Whittingham in the seventies developed a battery that operated at room temperature
based on the intercalation of Li in TiS2
...
The electrolyte is a lithium salt dissolved in an organic solvent
...
The setup is
illustrated in Figure 6
...
When the circuit is complete, lithium metal from the lithium electrode dissolves giving
solvated ions, and solvated ions in the solution are deposited in the titanium disulfide
...
Thus, the two electrode reactions are:
Li(s)=Li+(solv)+e−
(6
...
2)
FIGURE 6
...
FIGURE 6
...
Carbon-based electronics
293
giving an overall reaction
xLi(s)+TiS2(s)=LixTiS2(s)
(6
...
11
...
A voltage high enough to overcome the free energy of the cell
reaction will cause lithium ions to return to the solvent and lithium to be deposited on the
metal electrode, thus restoring the battery to its original condition
...
LixTiS2 is a particularly good
electrical conductor, because not only is the electronic conductivity increased by the
donation of electrons to the conduction band, but also the lithium ions themselves act as
current carriers and so the compound is both an electronic and an ionic conductor
...
Compounds other than TiS2 have proved more
useful for commercial batteries
...
Lithium polymer batteries are similar in principle to the lithium batteries described
above but the electrolyte is a polymer
...
The polymer electrolyte is a polymeralkali metal salt complex
...
Poly(propylene)oxide, poly(ethylene)succinate, poly(epichlorohydrin), and poly(ethylene
imine) have also been investigated as possible polymer bases for polymer electrolytes
...
Electrical current is carried by the ions of
the salts moving through the polymer
...
1 Conductivities of polymer-metal salt
complexes
Polymer
Molecular
mass
PEO
400
Salt
LiBF4
5×10
6
PEO
4×10
6
CH3COOLi
(O/Li=4)
PEO
4×106
CH3COOLi
PEO
LiBF4
Conductivity/Sm−1
Temperature
range/K
3
...
1×l0–5
298−450
–5
–7
10 −10
–4
298−450
–9
3
...
Some values for Li+ conductivity in various polymer-lithium salt complexes are given in Table 6
...
Conductivity of approximately 10–5 Sm−1 is suitable for
batteries
...
Compounds used as
intercalation electrodes include LiCoO2 and V6O13
...
Currently, several companies market lithium polymer batteries for use in, for example,
phones
...
5 CARBON
6
...
1 GRAPHITE
Graphite is, of course, a very familiar substance, with many uses
...
Its
absorption properties find a wide range of applications from gas masks to decolouring
food
...
Graphite is also used as a support for several industrially important
catalysts
...
12 Hexagonal structure of
graphite layers
...
Crystals of graphite are,
however, only good conductors in two dimensions, and it is the two-dimensional aspect
that we are concerned with here
...
12
...
Another form also contains
layers of interlocking hexagons but in which the layers are stacked ABCABC
...
This leaves one valence electron per carbon in a p orbital at right angles to the plane of
the layer
...
If the layer contains n carbon atoms, then n orbitals are formed, and n
electrons are available to fit in them
...
If the
orbitals were to form one band, this would explain the conductivity of graphite very
nicely because there would be a half-filled band confined to the layers
...
The delocalised orbitals in fact form two bands, one
bonding and one anti-bonding
...
) The lower
band is full and the upper band empty
...
The band structure for
graphite is illustrated in Figure 6
...
FIGURE 6
...
Because the density of states is low at the Fermi level, the conductivity is not as high as
that for a typical metal
...
6
...
2 INTERCALATION COMPOUNDS OF GRAPHITE
Because the bonding between layers in graphite is weak, it is easy to insert molecules or
ions into the spaces between layers
...
Since the 1960s, attention has been paid to intercalation
compounds as of possible importance as catalysts and as electrodes for high energydensity batteries (see previous section)
...
Amongst electron donors, the most extensively studied are the alkali metals
...
For example, potassium forms a
golden compound KC8 in which the interlayer spacing is increased by 200 pm
...
The first intercalation compound was made in 1841
...
Since then, many other electron acceptor intercalation compounds have
been made with, for example, NO3−, CrO3, Br2, FeCl3, and AsF5
...
This increases the conductivity and some of these
compounds have electrical conductivity approaching that of aluminium
...
Layered structures in which the current is carried by d electrons are common in transition
metal compounds, such as the disulfides of Ti, Zr, Hf, V, Nb, Ta, Mo, and W, and mixed
lithium metal oxides
...
It was hoped that by altering the interlayer spacing, a compound would be
found that was superconducting at higher temperatures
...
It was concluded that the
superconductivity was confined to the layers
...
As discussed in Chapter 10, however,
the crucial ingredient was a CuO layer
...
5
...
It is made by passing an electric
arc between two carbon rods in a partial atmosphere of helium
...
Curl
Jr
...
Smalley)
...
The structure is depicted in Figure 6
...
The molecule is extremely symmetrical with every carbon atom in an identical
environment; it consists of 12 pentagons of carbon atoms joined to 20 hexagons
...
Indeed, we can think of this structure as a carbon sheet with graphite-type
delocalized bonding, which bends back on itself to form a polyhedron
...
14 The structure of
buckminster fullerene, C60
...
) The molecules, commonly called buckyballs,
pack together in a cubic close-packed array in the crystals
...
The use of fullerenes has been suggested for
electronic devices and even in targeted cancer therapy
...
For instance, potassium
buckide (K3C60) has a ccp array of buckyballs, with all the octahedral holes, and
tetrahedral holes filled by potassiums: this is a metallic substance which becomes
superconducting below 18 K
...
In 1991, Sumio Iijima produced fullerene-type molecules in the form of long tubes
capped at each end
...
Nanotubes are discussed in Chapter
11
...
Which orbitals would you expect to combine to form a delocalised band in
polyphenylenevinylene?
2
...
When poly acetylene is doped with chloric (VII) acid, HClO4, part of the acid is
used to oxidise the polyacetylene and part to provide a counteranion
...
6)
...
ClO4−+8H++8e−=Cl−+4H2O
(6
...
(SN)x remains a metallic conductor down to very low temperatures
...
HMTTF-TCNQ is metallic but HMTTF-TCNQF4 is not
...
HMTTF=hexamethylenetetrathiafulvalene,
TCNQ=tetracyanoquinodimethane, TCNQF4=tetracyanotetr afluoroquinodimethane
...
Undoped polythiophene is red
...
Sketch the band structure of graphite intercalated with (a) an electron donor and (b)
an electron acceptor
...
Fullerenes consist of 12 pentagons and a number of hexagons; 20 in the case of C60
and 25 in the case of C70
...
1 INTRODUCTION
Zeolites occur naturally in large deposits, much of it in China
...
Zeolites are used as cation exchangers for water softening, and as
molecular sieves for separating molecules of different sizes and shapes (e
...
, as drying
agents)
...
Approximately 56 naturally occurring zeolites have now been
characterized, but in the quest for new catalysts, more than 150 synthetic structures have
been developed
...
About 60% of the
synthetically produced zeolites are used in detergents for softening water by ion exchange
(removing calcium ions mainly); specialized catalysts and adsorbers mainly make up the
rest of the market
...
They are a class of crystalline aluminosilicates based on rigid
anionic frameworks with well-defined pores (channels) running through them, which
intersect at cavities (cages)
...
), and can hold removable and replaceable guest molecules (water in naturally
occurring zeolites)
...
With cavity sizes falling between 200 and 2000 pm, zeolites are classified as
microporous substances
...
2 COMPOSITION AND STRUCTURE
The general formula for the composition of a zeolite is:
Mx/n[(AlO2)x(SiO2)y] mH2O
where cations M of valence n neutralize the negative charges on the aluminosilicate
framework
...
1 The zeolite building
units
...
7
...
1 FRAMEWORKS
The primary building units of zeolites are [SiO4]4− and [AlO4]5− tetrahedra (Chapter 1)
linked together by corner sharing, forming oxygen bridges (Figure 7
...
The oxygen
bridge is not usually linear—the Si/Al—O—Si/Al linkage is very flexible and the angle
can vary between 120° and 180°
...
2)
...
This is provided by exchangeable cations such as Na+, held
electrostatically within the zeolite
...
The linked tetrahedra are usually illustrated by
drawing a straight line to represent the oxygen bridge connecting two tetrahedral units
...
3(a) and Figure 7
...
3(c))
...
As we see later,
many different ring sizes are found in the various zeolite structures
...
4, and which has the shape of a truncated octahedron (Figure 7
...
Several
of the most important zeolite structures are based on the sodalite unit (Figure 7
...
The mineral sodalite is composed of these units, with each 4-ring shared directly by
two β-cages in a primitive array
...
6(a) is actually a sodalite unit (i
...
, sodalite units are
space-filling)
...
Sodalite is a highly symmetrical structure and the cavities
link together to form channels or pores, which run parallel to all three cubic crystal axes,
the entrance to these pores governed by the 4-ring window
...
2 The structure of quartz
(a) as a ball and stick representation
and (b) as linked [SiO4] tetrahedra
...
6(b)
...
A three-dimensional network of linked cavities each
with a truncated cuboctahedron shape (Figure 7
...
3 (a) 6-ring containing two
Al and four Si atoms, (b) computer
model of the 6-ring, and (c) shorthand
version of the same 6-ring
...
4 The sodalite unit
...
The computer-drawn models in Figure
7
...
The formula of zeolite A is given by:
Na12[(SiO2)12(AlO2)12]
...
In this typical example, the Si/Al ratio is unity, and we
find that in the crystal structure the Si and Al atoms strictly alternate
...
6(c)
...
The tetrahedral array encloses a large cavity (sometimes known as the
α-cage) entered through a 12-ring window
...
5 The relationship between
an octahedron, a truncated octahedron,
a cuboctahedron, and a truncated
cuboctahedron
...
6 Zeolite frameworks built
up from sodalite units: (a) sodalite
(SOD), (b) zeolite A (LTA), and (c)
faujasite (zeolite X and zeolite Y)
(FAU)
...
Zeolite X structures have a Si/Al ratio between 1 and 1
...
5 and 3
...
2
...
Some
structures were named after the parent minerals (e
...
, sodalite, faujasite), while others
were named by researchers, or after the projects which synthesized them (e
...
, ZSM
[Zeolite Socony Mobil])
...
Similarly,
ZSM-5 and its silicon-rich relation, silicalite, have the same framework and are both
designated MFI
...
g
...
FIGURE 7
...
7
...
3 Si/Al RATIOS
We saw that zeolite A has a Si/Al ratio of 1
...
5
...
2
...
5 found in mordenite, which is the most siliceous of the naturally occurring zeolite
minerals
...
The highly
siliceous zeolites are inherently hydrophobic in character, and their affinity is for
hydrocarbons
...
2
...
The presence and position of the cations in zeolites is important for several reasons
...
8 Framework and cation
sites in the Na+ form of zeolite A
(LTA)
...
(Courtesy of Dr
...
)
significantly affects the size of the molecules that can be adsorbed
...
Zeolites and related structures
309
The balancing cations in a zeolite can have more than one possible location in the
structure
...
8 depicts the available sites in the Na+ form of zeolite A
...
The presence of cations in these positions effectively reduces the size of the
rings and cages to any guest molecules that are trying to enter
...
As the divalent
cations tend to occupy the sites in the 6-rings, this opens up the 8-ring windows, thus
leaving the channels free for diffusion
...
These structures can be dehydrated by heating under vacuum, and
in these circumstances, the cations move position at the same time, frequently settling on
sites with a lower coordination number
...
7
...
5 CHANNELS AND CAVITIES
The important structural feature of zeolites, which can be exploited for various uses, is
the network of linked cavities forming a system of channels throughout the structure
...
A controlling factor in whether molecules can be adsorbed in the cavities
is the size of the window or port into the channel, thus the
Solid state chemistry
310
FIGURE 7
...
importance of the number of tetrahedra forming the window (i
...
, the ring size)
...
9 illustrates how the window sizes can vary
...
Zeolites thus have large internal surface areas and high
sorption capacities for molecules small enough to pass through the window into the
cavities
...
The zeolites fall into three main categories
...
The most symmetrical structures have cubic
symmetry
...
A typical fibrous zeolite is edingtonite (EDI), Ba[(AlO2)2(SiO2)3]
...
Lamellar zeolites
occur
frequently
in
sedimentary
rocks,
e
...
,
phillipsite
(PHI),
(K/Na)5[(SiO2)11(AlO2)5]
...
In terms of their useful
properties, zeolites are conveniently discussed by pore size
...
10 Computer model of the
zeolite A (LTA) structure, illustrating
the channels and 8-ring windows
...
6)
...
The computer model of zeolite A in Figure 7
...
Small-pore zeolites can accommodate linear chain molecules, such as straightchain
hydrocarbons and primary alcohols and amines, but not branched chain molecules
...
Values for channel and cavity sizes for various zeolites and zeotypes are listed in
Table 7
...
Medium-Pore Zeolites
In the mid-1970s, some completely novel zeolite structures were synthesized which led to
significant new developments
...
ZSM-5 is a catalyst now widely used in the industrial world
...
11 (as are the others of this group)
...
Appropriate stacking of these layers gives the
various pentasil structures
...
The pore systems in
these zeolites do not link big cavities, but they do contain intersections where larger
amounts of free space are available for molecular
TABLE 7
...
of
tetrahedra in
ring
Sodalite
SOD
4
260
600
Zeolite A
LTA
8
410
1140
Erionite-A
ERI
8
360×520
–
ZSM-5
MFI
10
510×550
540×560
–
Faujasite
FAU
12
740
1180
Mordenite
MOR
12
670×700
290×570
–
Zeolite-L
LTL
12
710
–
ALPO-5 (see Section
7
...
Figure 7
...
Figure 7
...
This
contrasts with the ZSM-11 structure which just has intersecting straight channels of
almost circular cross section (Figure 7
...
In both cases, the two-dimensional system
of pores is linked by much smaller channels
...
11 A pentasil unit together
with a slice of the structure of ZSM-5,
illustrating a linked chain of pentasil
units highlighted
...
12 (a) Computer model of
orthorhombic ZSM-5, illustrating the
straight elliptical channels along the y
direction; (b) computer model of ZSM11 showing the near-circular straight
channels which run along both the x
and y directions in the tetragonal
crystals
...
This leads to a
structure with large cavities of diameter 1180 pm entered by 12-ring windows of
diameter 740 pm, which give a three-dimensional network of channels depicted in
(Figure 7
...
The channel system for mordenite (MOR) is illustrated in Figure 7
...
Mordenite has
an orthorhombic structure and two types of channels are available, governed
Solid state chemistry
316
by 8- and 12-ring windows, respectively, all running parallel to each other and
interconnected only by smaller 5- and 6-ring systems
...
3 SYNTHESIS OF ZEOLITES
It was the pioneering work of Richard Barrer at the University of Aberdeen that led the
way in the synthesis of zeolites
...
A gel forms by a process of copolymerization of the silicate and aluminate ions
...
The product obtained is determined by the synthesis conditions:
temperature, time, pH, and mechanical movement are all possible
FIGURE 7
...
FIGURE 7
...
Solid state chemistry
318
FIGURE 7
...
variables
...
The formation of novel silicon-rich synthetic zeolites has been facilitated by the use of
templates, such as large quaternary ammonium cations instead of Na+
...
The
aluminosilicate framework condenses around this large cation, which can subsequently
be removed by chemical or thermal decomposition
...
Only a limited number of large cations can fit
into the zeolite framework, and this severely reduces the number of [AlO4] tetrahedra that
can be present, producing a silicon-rich structure
...
Several different methods are available, including extraction of the aluminium by mineral
acid, and extraction using complexing agents
...
4 STRUCTURE DETERMINATION
The structures of the zeolite frameworks have been determined by X-ray and neutron
diffraction techniques
...
Unfortunately, it is extremely difficult for diffraction techniques to determine a structure
unequivocally because Al and Si are next to each other in the Periodic Table and thus
have very similar atomic scattering factors (Chapter 2)
...
The positions of Si and Al atoms have always been assigned by applying
Loewenstein’s rule, which forbids the presence of an Al—O—Al linkage in the
structure
...
When it comes to locating the cations, other problems arise
...
Furthermore, zeolites are usually microcrystalline and for successful diffraction
studies larger single crystals are needed (although Rietveld powder techniques have been
successfully applied, especially with neutrons, see Chapter 2)
...
Five peaks can be observed for the 29Si
spectra of various zeolites, which correspond to the five possible different Si
environments
...
Si(OAl)4
2
...
Si(OAl)2(OSi)2
4
...
Si(OSi)4
Characteristic ranges of these shifts are assigned to each coordination type
...
Octahedrally coordinated [A1(H2O)6]3+ trapped as a cation in the pores with a peak at
about 0 ppm ([Al(H2O)6]3+(aq) is used as the reference)
...
Tetrahedral Al, Al(OSi)4, which gives a single resonance with characteristic Al
chemical shift values for individual zeolites in the range of 50 to 65 ppm
...
Tetrahedral [AlCl4]−, which gives a peak at about 100 ppm; such a peak can occur
when a zeolite has been treated with SiCl4 to increase the Si/Al ratio in the framework
and should disappear with washing
...
This can be extremely useful when developing new zeolites for catalysis, as much
research has concentrated on making highly siliceous varieties by replacing the Al in the
framework
...
At
high Si/Al ratios, 27Al MAS-NMR results are more sensitive and accurate and so are
preferred
...
The cation positions can give useful
information because they tend to be as close as possible to the negatively charged Al
sites
...
EXAFS has been used to
determine the local coordination geometry of the exchangeable cations and how this
changes on reaction or dehydration
...
5 USES OF ZEOLITES
7
...
1 DEHYDRATING AGENTS
Normal crystalline zeolites contain water molecules which are coordinated to the
exchangeable cations
...
In these circumstances, the cations move position, frequently settling on sites
with a much lower coordination number
...
Zeolite
A is a commonly used drying agent, and can be regenerated by heating after use
...
7
...
2 ZEOLITES AS ION EXCHANGERS
n+
The cations M in a zeolite will exchange with others in a surrounding solution
...
The water softener is reusable because it can be
regenerated by running through a very pure saline solution; this is a familiar procedure to
anyone who has used a dishwasher
...
It is possible to produce drinking water
from seawater by desalinating it through a mixture of Ag and Ba zeolites
...
Some zeolites have a strong affinity for particular cations
...
Similarly, zeolite A can be used to recover radioactive
strontium
...
7
...
3 ZEOLITES As ADSORBENTS
Because dehydrated zeolites have very open porous structures, they have large internal
surface areas and are capable of adsorbing large amounts of substances other than water
...
An individual zeolite has a highly specific sieving ability
that can be exploited for purification or separation
...
Chabazite has been used commercially to adsorb polluting SO2 emissions
from chimneys
...
Zeolites and related structures
321
The zeolites that are useful as molecular sieves do not demonstrate an appreciable
change in the basic framework structure on dehydration although the cations move to
positions of lower coordination
...
The cavities in dehydrated
zeolite A amount to about 50% of the volume
...
Table 7
...
The
zeolites are regenerated after use by heating, evacuation, or flushing with pure gases
...
As discussed earlier, one method is to change the cation
...
2 Applications of molecular sieves in
industrial adsorption processes
Fields of
application
Uses
Drying
Purification
a
Separations
Refineries and
petrochemical
industry
Paraffins, olefins,
acetylenes, reformer
gas, hydrocracking gas,
solvents
Sweetening of ‘liquid petrol gas’
and aromatics, removal of CO2
from olefincontaining gases,
purification of synthesis gas
Normal and
branched-chain
alkanes
Industrial gases
H2, N2, O2, Ar, He,
CO2, natural gas
Sweetening and CO2 removal
from natural gas, removal of
hydrocarbons from air,
preparation of protective gases
Aromatic
compounds
Industrial
furnaces
Exogas, cracking gas,
reformer gas
Removal of CO2 and NH3 from
Nitrogen and
exogas and from ammonia fission oxygen
gas
a
‘Sweetening’ is the removal of sulfur-containing compounds
...
When Na+ ions are replaced by
Ca2+ ions, the effective aperture increases
...
16)
...
This process can be useful industrially for
separating the long straight-chain hydrocarbons required as the starting materials in the
manufacture of biodegradable detergents
...
At –196°C, oxygen is freely adsorbed by Ca-zeolite A, whereas nitrogen is essentially
excluded
...
As the temperature rises, the adsorption of N2 increases to
a maximum at around –100°C
...
Over a range of 80 to 300 K, a variation of
vibrational amplitude of 10 to 20 pm could well be expected
...
This would make the window just small
enough at lower temperatures to exclude the N2 molecules
...
FIGURE 7
...
Replacement
of four sodium ions by two calcium
ions permits easy diffusion of nalkanes into the zeolite channels
...
An
increase in the proportion of Si will:
• Slightly decrease the unit cell size and thus the size of the cavities
...
• Make the zeolite more hydrophobic (literally ‘water-hating’) in character
...
Zeolites and related structures
323
7
...
4 ZEOLITES As CATALYSTS
Zeolites are very useful catalysts displaying several important properties that are not
found in traditional amorphous catalysts
...
The presence of the cavities in zeolites provides a very large
internal surface area that can accommodate as many as 100 times more molecules than
the equivalent amount of amorphous catalyst
...
Furthermore, their molecular sieve action can
be exploited to control which molecules have access to (or which molecules can depart
from) the active sites
...
The catalytic activity of decationized zeolites is attributed to the presence of acidic
sites arising from the [AlO4] tetrahedral units in the framework
...
Zeolites as normally synthesized usually have Na+ ions
balancing the framework charges, but these can be readily exchanged for protons by
direct reaction with an acid, giving surface hydroxyl groups—the Brønsted sites
...
Further heating removes water from the Brønsted site, exposing a tricoordinated
aluminum ion, which has electron-pair acceptor properties; this is identified as a Lewis
acid site
...
17
...
Brønsted sites are converted into Lewis sites as the
temperature is increased above 600°C and water is driven off
...
These ions
now place themselves so that they can best neutralize three separated negative charges on
tetrahedral Al in the framework
...
17 Scheme for the
generation of Brønsted and Lewis acid
sites in zeolites
...
This effect can be
strengthened by a reduction in the aluminium content of the zeolite so that the [AlO4]
tetrahedra are farther apart
...
It was a rare-earth substituted form of zeolite X
that became the first commercial zeolite catalyst for the cracking of petroleum in the
1960s
...
A form of zeolite Y,
that has proved more stable at high temperatures, is now used
...
The annual
catalyst usage for catalytic cracking is worth billions of £s
...
The resultant material displays the properties associated
Zeolites and related structures
325
with a supported metal catalyst and extremely high dispersions of the metal can be
achieved
...
This is
illustrated diagrammatically in Figure 7
...
• Product shape-selective catalysis: only products less than a certain dimension can
leave the active sites and diffuse out through the channels, as illustrated in Figure
7
...
A mixture of all three isomers is formed in the
cavities but only the para form is able to escape
...
18(c) for the transalkylation of dialkylbenzenes
...
If
butan-1-ol (n-butanol) and butan-2-ol (iso-butanol) are dehydrated
Solid state chemistry
326
FIGURE 7
...
either over Ca-zeolite A or over Ca-zeolite X, we see a difference in the products formed
...
Over zeolite A, however, the dehydration of
FIGURE 7
...
the straight-chain alcohol is straightforward but virtually none of the branched-chain
alcohol is converted, as it is too large to pass through the smaller windows of zeolite A
...
19
...
This is because the lattice vibrations increase with temperature, making the
pore opening slightly larger and thus beginning to admit butan-2-ol
...
Solid state chemistry
328
Product Shape-Selective Catalysis
One of the industrial processes using ZSM-5 provides us with an example of product
shape-selective catalysis: the production of 1,4-(para-)xylene
...
Xylenes are produced in the alkylation of toluene by methanol:
Zeolites and related structures
329
FIGURE 7
...
See colour insert following
page 356
...
This is confirmed by the
observation that selectivity increases with increasing temperature, indicating the
increasing importance of diffusion limitation
...
The computer models
in Figure 7
...
The xylenes isomerize within the pores,
and so para-xylene diffuses out while the ortho- and meta-isomers are trapped and have
more time to convert to the para- form before escaping
...
Using
a zeolite catalyst makes this a much greener process than using the conventional
alkylation reaction using CH3I over an AlCl3 or FeCl3 catalyst, as a pure product is
produced in good yield, and the zeolite catalyst can be regenerated
...
ZSM-5 is also the catalyst used to convert methanol into hydrocarbons—the methanol
to gasoline or MTG process
...
Subsequently, more oil was
released, prices dropped and much of the research was put into abeyance
...
New Zealand, with no oil reserves of its own, but with a supply of
natural gas (CH4) brought the first MTG plant on stream in 1986
...
This then dehydrates further to give ethene and other alkenes which react rapidly
to give a range of hydrocarbons
...
It is thought that the methanol molecules enter ZSM-5 through the more restricted zigzag
channels, react at the cavities where the pores intersect, and then the larger hydrocarbons
exit through the straight channels—a so-called molecular traffic control
...
This bimolecular reaction involves a
diphenylbenzene transition state
...
When
the catalyst used for this reaction is mordenite (Figure 7
...
(This compares with the equilibrium mixtures, in which
the symmetrically substituted isomers tend to dominate
...
It is estimated that ZSM-5 has a turnover of more
than 300 molecules per active site per minute during the cracking process, and that other
Zeolites and related structures
331
processes such as xylene isomerization are even faster, with turnovers of up to 107
molecules per active site per minute
...
6 MESOPOROUS ALUMINOSILICATE STRUCTURES
In 1992, scientists at Mobil Research and Development Corporation developed a family
of silicate and aluminosilicate materials, M41S, which had much larger pores than
conventional zeolites
...
5 to 10 nm, and
give rise to the name mesoporous solids
...
The pores are nevertheless small enough to provide shape-selective effects, and
the walls of the pores can be modified by having functional groups added
...
Applications as hosts for
nanoclusters with useful magnetic, optical and electronic properties, and the formation of
molecular wires in the channels are also being researched
...
It has a
highly ordered hexagonal array of uniformly sized mesopores, and it can have a huge
surface area of 1200 m2 per gram
...
In a solution of silicate
or silicate and aluminate anions, cationic longchain alkyl trimethylammonium
surfactants, [CH3(CH2)n(CH3)3N+]X− form rod-like micelles (Figure 7
...
These silicatecoated micelles pack together along the axes of the rods, earning the synthesis technique
the name liquid crystal templating, and under hydrothermal conditions, this mesoporous
structure precipitates out of solution
...
As
you would expect, the alkyl chain length determines the size of the pores; where n=11,
13, and 15, the pore diameters are 300, 340, and 380 nm, respectively, but when n=5,
micelles are not formed and zeolites such as ZSM-5 are formed around a single ion
template instead
...
The hexagonal arrangement of the pores in MCM-41 is found to be
very ordered, although considerable disorder occurs within the actual walls
...
The mesoporous solids have great potential for use as heterogeneous catalysts, which
have the advantage of being simpler to use than homogeneous catalysts as they can be
separated by filtration at the end of a reaction
...
The
aluminosilicate walls of mesoporous materials can be modified in various ways:
Solid state chemistry
332
FIGURE 7
...
See colour insert
following page 356
...
)
• by direct synthesis;
• by grafting on to the surface using alcohols, silanols, or organosilicon compounds;
• further modification of a functionalized surface by chemical reaction, or by heating
...
An example of a condensation reaction of an alcohol with the surface
silanol groups to modify the pore wall is shown in Figure 7
...
Zeolites and related structures
333
FIGURE 7
...
FIGURE 7
...
Transition metals and their complexes can be immobilized in the mesopores or
incorporated in the structure to make silica-supported metal catalysts
...
The grafted version makes the better catalyst for the
epoxidation of alkenes using peroxides, and has good resistance to leaching of the metal
...
Nanometre size Sn-Mo clusters have been made in this way
...
23), and
these molecular wires demonstrate significant electronic conduction, although less than
that of bulk polyaniline
...
Such materials have potential for use in information
processing as storage capacitors
...
7 OTHER FRAMEWORK STRUCTURES
Other framework structures based on zeolites have also been synthesized which contain
atoms other than aluminium and silicon, such as boron, gallium, germanium, and
phosphorus, which are tetrahedrally coordinated by oxygen
...
Pure aluminium phosphate, commonly called ALPO, and its derivatives, can
take the same structural forms as some of the zeolites such as sodalite (SOD), faujasite
(FAU), and chabazite (CHA) (e
...
, ALPO-20 is isostructural
FIGURE 7
...
with sodalite and ALPO-17 with erionite), as well as novel structures, with many new
compounds now synthesized
...
If the compound
contains silicon, or silicon and a metal, partially replacing aluminium or phosphorus, then
they become known as SAPOs
...
Consequently, there has been much
Zeolites and related structures
335
interest in recent years in these compounds as possible heterogeneous catalysts which
might be at least as good, if not better, than the zeolites
...
The aluminophosphate compounds have been formed using templates in a similar
fashion to many of the zeolites, but under more acidic conditions
...
One of
the new channel structures formed is ALPO-5, which is depicted in projection in Figure
7
...
More recently, extralarge-pore materials have been prepared
...
24(b)), which has no zeolite analogue,
and is based on β-cages separated by double four-membered rings to give 18-ring
windows and a pore diameter of between 1200 and 1300 pm
...
25), have followed
...
Other possibilities lie in
the formation of new materials
...
25 The framework of the
synthetic gallophosphate, cloverite,
represented as shaded spheres of van
der Waals radii
...
R
...
Catlow
(ed
...
Reproduced with
permission of Academic Press Ltd
...
8 NEW MATERIALS
Research in zeolites has also branched out to try to prepare new materials by
incorporating various molecules and ions in the cages of these microporous and
mesoporous structures
...
It is based on the zeolite sodalite (SOD)
structure and contains S3− ions trapped in the cages; this is the same anion found in the
mineral lapis lazuli, to which it imparts the beautiful deep blue colour
...
One area of this research has focussed on depositing semiconductor materials in
zeolite cages
...
e
...
One example of this is the narrow band gap
semiconductor CdS, which in low concentrations forms discrete cubic (CdS)4 clusters in
the sodalite cages of zeolites A, X, and Y
...
As the pore filling of the zeolite increases, the nanoparticles become
interconnected forming superclusters, and materials are produced with properties
intermediate between those of discrete particles and bulk semiconductors; the absorption
edge shifts to 420 nm, and strong emission also appears
...
Other
guests that can be incorporated into zeolite cages and into the mesoporous structures,
include the alkali metals, silver and silver salts, selenium, and various conducting
polymers
...
7
...
They are often found as components of soils and sediments, and
some large deposits, such as bentonite (consisting mainly of montmorillonite and
beidellite), are found in Cornwall, United Kingdom, and in the state of Wyoming, USA
...
26; it
consists of parallel layers of tetrahedral silicate [SiO4] sheets and octahedral aluminate
[Al(O,OH)6] sheets
...
The aluminate layers contain a plane of
octahedrally coordinated edge-linked aluminium ions, sandwiched between two inward
pointing sheets of corner-linked [SiO4] tetrahedra
...
In the smectite
clays, different structures are formed because substitution of silicon and aluminium by
metal ions can take place in both the tetrahedral and octahedral layers, the resulting
negative charge is distributed on the oxygens of the layer surface, and any charge balance
is restored by interlayer cations (usually Na+ or Ca2+)
...
The different
members of the smectite group of clays are distinguished by the type and position of the
cations in the framework
...
Molecules, such as water, and polar
organic molecules, such as glycol, can easily intercalate between the layers and cause the
clay to swell
...
Calcium montmorillonite usually has two layers of water molecules but the sodium form
can have one, two, or three water layers; this causes the interlayer spacing to increase
stepwise from about 960 pm in the dehydrated clay to 1250, 1550, and 1900 pm as each
successive layer of water forms
...
They are known as exchangeable
cations, and can be replaced easily by other cations using ion exchange methods or by
protons in the form of H3O+, to form an acidic clay
...
For many years,
modified clays were used as the catalyst for petroleum cracking to produce petrol,
although they have since been replaced by more thermally stable and selective zeolites
...
26 Idealized structure of
the layers in a smectite clay: (a)
showing only the oxygen/hydroxyl
framework; (b) also depicting
aluminium and silicon positions
...
27 Representation of the
formation of pillars in a smectite clay
where Pn+ is the pillaring cation
...
Recent research on clay catalysts has concentrated
on the introduction of metal complexes into the interlayer region to act as the catalytic
centre and on the formation of robust molecular props to hold the interlayer regions
apart—so-called pillaring
...
Much effort has
concentrated on forming temperature-stable pillars that will hold, the layers apart even at
high temperature and in the absence of a swelling solvent, to form a large interlayer
region
...
27) and the hope is that by judicious adjustment of the size and
spacings of the pillars, the pore sizes can be made bigger than those of the faujasitic
zeolites
...
Other pillars can be formed from silica, and from the
oxides of various metals, such as iron, zirconium, and tin
...
10 POSTSCRIPT
We end this chapter with a quotation from a lecture given by Professor J
...
Thomas
...
“…[Figure 7
...
Its structure was elucidated some 6 years ago
...
These two structures have
exactly the same pattern
...
’”
Solid state chemistry
340
FIGURE 7
...
In exactly
the same sequence, such 5- and 6membered rings circumscribe a central
10-membered ring in the pattern on the
left
...
Zeolite A has a single peak in the 29Si MAS NMR spectrum at 89 ppm and has a
Si/Al ratio of 1
...
2
...
It was found
that the catalytic activity also increased until the ratio was about 15:1 after which it
declined
...
Zeolite A (Ca form), when loaded with platinum, has been found to be a good
catalyst for the oxidation of hydrocarbon mixtures
...
Suggest a possible reason
...
Both ethene and propene can diffuse into the channels of a particular mordenite
catalyst used for hydrogenation
...
5
...
2%
...
When toluene is alkylated by methanol with a ZSM-5 catalyst, increase in the
crystallite size from 0
...
Suggest a possible explanation
...
The infrared stretching frequency of the hydroxyl associated with the Brønsted sites
in decationized zeolites, falls in the range 3600 to 3660 cm−1
...
What does this suggest about the
acidity of the highly siliceous zeolites?
8
Optical Properties of Solids
8
...
Of interest to the solid state chemist are two types of laser, typified by the ruby laser and
the gallium arsenide laser
...
To transmit light over long distances, the optical fibres must have
particular absorption and refraction properties, and the development of suitable
substances has become an important area of research
...
Light-emitting
diodes (LEDs) are used for displays including those on digital watches and scientific
instruments
...
Another important group of solids are the light-emitting solids
known as phosphors, which are used on television screens and fluorescent light tubes
...
These are
discussed briefly in this chapter
...
In the first, which is relevant to the ruby laser and to
phosphors for fluorescent lights, the light is emitted by an impurity ion in a host lattice
...
In the second case, which applies to LEDs and the gallium arsenide laser, the
optical properties of the delocalised electrons in the bulk solid are important
...
8
...
To a first approximation in many cases, we can think
of one electron in the atom absorbing the photon and being excited
...
In light atoms, the electron cannot change its spin and its
orbital angular momentum must change by one unit; in terms of quantum numbers ∆s=0,
Optical properties of solids
343
∆l=±1
...
Conservation of spin and angular momentum then produces these
rules
...
(There is no restriction on changes of the principal quantum number
...
Figure 8
...
The spin and orbital angular momenta are not entirely independent and coupling
between them allows forbidden transitions to occur, but the probability of an electron
absorbing a photon and being excited to a forbidden level is much smaller than the
probability of it being excited to an allowed level
...
FIGURE 8
...
An electron that has been excited to a higher energy level will sooner or later return
to the ground state
...
The electron may simply emit a photon
Solid state chemistry
344
of the correct wavelength some time after it has been excited
...
Alternatively, a second photon may come along and instead of
being absorbed may induce the electron to emit
...
The emitted photon in this
case is in phase with, and travelling in the same direction as, the photon inducing the
emission; the resulting beam of light is said to be coherent
...
These are examples of non-radiative transitions
...
Nonradiative transitions have different rules
...
Let us take as an example an ion
with one d electron outside a closed shell (Ti3+ for example)
...
In the free ion, the five 3d orbitals all have the same energy
...
This
is depicted in Figure 8
...
An electronic transition between these levels is now possible
...
In the crystal, the transition involves a change in
energy, but is still forbidden by the selection rules
...
Thus, the 3d levels may be mixed with
the 4p giving a small fraction of ‘allowedness’ to the transition
...
3 depicts an
absorption band due to a transition from t2g to eg for the ion Ti3+, which has one d
electron
...
)
We shall see now the role played by a similar forbidden transition in the operation of
the ruby laser
...
2
...
04 to 0
...
The aluminum ions, and hence the chromium ions, occupy
Optical properties of solids
345
FIGURE 8
...
FIGURE 8
...
The band is, in fact, two
overlapping bands
...
distorted octahedral sites
...
Cr3+ has three 3d electrons, and, in the ground state, these
occupy separate orbitals with parallel spins
...
This is similar to the
Solid state chemistry
346
transition discussed in the previous section, but with three electrons it is necessary to
consider changes in the electron repulsion as well as changes in orbital energies
...
Having absorbed light and undergone one of these transitions, the chromium ion could
now simply emit radiation of the same wavelength and return to the ground state
...
The chromium ion is
left in a state in which it can only return to the ground state by a transition in which an
electron changes its spin
...
The states involved are depicted schematically in Figure 8
...
The ions absorb light and go to states 3 and 4
...
Because the probability of spontaneous emission for state 2 is low,
and no convenient non-radiative route is available to the ground state, a considerable
population of state 2 can build up
...
The resulting photons will be
in phase and travelling in the same direction as the spontaneously emitted photons and
will induce further emission as they travel through the ruby
...
The reflected photons induce further emission and by this means, an appreciable beam of
coherent light is built up
...
The name laser is a reflection of this build up of intensity
...
4 The states of the Cr3+ ion
involved in the ruby laser transition
...
(Similar devices producing coherent
beams of microwave radiation are known as masers
...
5
...
The
lamp can lie alongside the crystalline rod of ruby or be wrapped around it
...
Ruby was the first material for lasers but several other crystals are now employed
...
It must also be possible to populate this level via an allowed (or at least less
forbidden) transition
...
5 Sketch of a ruby laser
...
1 Impurity ions used in lasers
Ion
Host
Wavelength emitted (nm)
3+
Fluorite (CaF2)
1046
3+
Fluorite
708
...
Some examples are given in Table 8
...
Solid state chemistry
348
8
...
2 PHOSPHORS IN FLUORESCENT LIGHTS
Phosphors are solids which absorb energy and re-emit it as light
...
However, for the
uses to which phosphors are put it is not necessary to produce intense, coherent beams of
light, and the emitting process is spontaneous instead of induced
...
In terms of tonnage produced, one of the most
important applications is the fluorescent light tube
...
The tube is coated inside with a
white powder which absorbs the ultraviolet light and emits visible radiation
...
Most phosphors for fluorescent lights
have been based on alkaline earth halophosphates such as 3Ca3(PO4)2
...
As in lasers,
the usual dopants are transition metal or lanthanide ions, but more than one impurity ion
is needed to approximate the whole visible spectrum
...
For example, in a phosphor doped with
Mn2+ and Sb3+ ions, the ultraviolet radiation from the mercury lamp is only absorbed by
the antimony (Sb3+) ions
...
Emission from this lower state produces a broad band in
the blue region of the visible spectrum
...
The excited Mn2+
ions emit yellow light and return to the ground state
...
Phosphors have been introduced which are more
efficient and give a closer approximation to daylight
...
Fluorescent lights also emit broadband radiation in the near infrared
...
In
this case, the incident light is of lower energy than the emitted light and the process is
known as upconversion
...
Obviously, a
ground state atom or ion cannot absorb a photon of one frequency radiation and then emit
a photon of higher frequency radiation from the excited state reached by the absorption
process
...
An ion absorbs a photon
of the incident radiation and goes to an excited state
...
If this second
excited state is metastable, it has time to absorb another photon before it spontaneously
Optical properties of solids
349
emits radiation and returns to a lower state
...
Emission from this higher level
produces shorter wavelength radiation than that absorbed
...
For example, low concentrations of Ho3+ in Y2O3 absorb red laser light and emit
yellow-green light
...
6
...
6)
...
In the next section, therefore, we shall consider the absorption and emission of
radiation in solids with delocalised electrons, particularly in semiconductors
...
3 ABSORPTION AND EMISSION OF RADIATION IN
SEMICONDUCTORS
Radiation falling on a semiconductor will be absorbed by electrons in delocalised bands,
particularly those near the top of the valence band, causing these electrons to be
promoted to the conduction band
...
The absorption spectrum
of GaAs, for example, is depicted in Figure 8
...
Transitions to some levels in the conduction band are more likely than transitions to
others
...
The spin selection
rule still holds; when promoted to the conduction band the electron
Solid state chemistry
350
FIGURE 8
...
does not change its spin
...
As discussed in Chapter 4, the energy levels in a
band are characterised by the wave vector, the momentum of the electron wave being
The momentum of a photon with wavelength in the infrared, visible, or
given by
ultraviolet is very small compared to that of the electron in the band and so conservation
of momentum produces the selection rule for transitions
Optical properties of solids
351
FIGURE 8
...
FIGURE 8
...
Note that in this diagram the
horizontal axis is k, not the density of
states
...
Solid state chemistry
352
between bands
...
Thus an electron in the valence band with wave vector, ki, can only undergo
allowed transitions to levels in the conduction band which also have wave vector, ki
...
Subsequently, an allowed
transition occurs at the band gap energy
...
For other semiconductors, for example silicon, the direct transition from the top of the
valence band to the bottom of the conduction band is forbidden
...
Illustrations of band structures for solids with direct and
indirect band gaps are given in Figure 8
...
Note that in these diagrams, the energy for a
band in one direction is plotted against the wave number, k
...
The simple free electron model might suggest that the lowest energy orbital in any
band is that with k=0
...
9, however, illustrates two combinations of
FIGURE 8
...
orbitals that will have k=0 for a chain because all the atomic orbitals are combined in
phase
...
If the p band lies below the s band, a transition
between these levels would be allowed and would correspond to a direct transition across
the band gap
...
One consequence of an indirect band gap is that an electron in the bottom level of the
conduction band has only a small probability of emitting a photon and returning to the
top of the valence band
...
Transitions across the band gap are also responsible for the appearance of many solids
...
Many such photons
will therefore be absorbed at or near the surface of the solid
...
Those travelling into the solid stand a
very good chance of being re-absorbed and then reemitted, again in random directions
...
If the surface is sufficiently regular, then solids which reflect visible radiation
appear shiny
...
Many metals have strong transitions between the conduction band and a higher
energy band, which lead to their characteristic metallic sheen
...
These metals appear relatively dull
...
In these elements,
the d band is full and lies some distance below the Fermi level (Figure 8
...
The
reflectivity peaks in the yellow part of the spectrum and blue and green light are less
strongly absorbed, hence the metals appear golden
...
10 Band structure of
copper
...
Insulators typically have band gaps in the ultraviolet, and unless a localised transition
occurs in the visible region of the electromagnetic spectrum, appear colourless
...
8
...
1 LIGHT-EMITTING DIODES
Light-emitting diodes (LEDs) are widely used for displays
...
Figure 8
...
The band structure depicted is for the junction in the dark and with no electric field
applied
...
e
...
Electrons will then flow from the n-type to the p-type
...
This is
more likely to happen if the transition is allowed, so that semiconductors with direct band
gaps are usually used in such devices
...
Using semiconductors of differing band gap can produce different colours
...
It should be noted that semiconductors with indirect band gaps are used for LEDs, but
in these cases, impurity levels play an important role
...
11 Energy bands near the
junction in a p-n junction
...
Silicon, however, is not suitable because a
nonradiative transition is available to electrons at the bottom of the conduction band and
these electrons donate thermal energy to the crystal lattice instead of emitting light when
they return to the valence band
...
An excess of electrons in an excited state is an
essential feature of lasers, and several semiconductor lasers are based on the p-n junction
...
8
...
2 THE GALLIUM ARSENIDE LASER
The gallium arsenide laser actually contains a layer of GaAs sandwiched between layers
of p- and n-type gallium aluminum arsenide (Ga1−xAlxAs)
...
12, the
band gap of gallium aluminum arsenide is larger than that of gallium arsenide
...
These electrons do not drift
Optical properties of solids
355
across into the gallium aluminum arsenide layer, however, because the bottom of the
conduction band in this layer is higher in energy and the electrons would thus need to
gain energy in order to move across
...
Eventually, one of these electrons drops
down into the valence band, emitting a photon as it does so
...
12 The arrangement of the
different semiconductor regions in a
GaAs laser
...
thus a coherent beam of light begins to build up
...
Eventually a beam of infrared radiation is emitted
...
e
...
It is possible to manufacture
materials with band gaps over the range of 400 to 1300 nm by carefully controlling the
ratios of the different elements
...
A compact disc consists of a plastic disc coated with a highly reflective aluminum
film and protected against mechanical damage by a layer of polymer
...
This is converted to a series
of pits in tracks on the disc spaced approximately 1
...
A laser is focused on the
disc and reflected on to a photodetector
...
The signal read by the photodetector is
read as 1 when a high intensity of light is present and as 0 when scattering reduces the
intensity
...
DVDs are similar but use a laser of shorter wavelength which can read more
closely spaced pits
...
8
...
3 QUANTUM WELLS—BLUE LASERS
Blue lasers allow higher resolution, and hence higher density of optical storage of
information, on devices such as DVDs than the infrared GaAs lasers allow
...
Lasers based on gallium nitride (GaN), first demonstrated in 1995, have
proved to have greater lifetimes
...
The active region of GaN lasers consists of of GaN containing several thin layers (30–
40 Å thick) of indium doped-GaN, InxGa1−xN
...
Electrons in this conduction band are effectively trapped
because they need to gain energy from an external source to pass into the conduction
band of the bulk GaN
...
13 illustrates schematically the bottom of the conduction
band and the top of the valence band for a series of thin layers of InxGa1−xN in GaN
...
Such boxes are quantum wells
...
The depth of the wells is controlled by the extent of
doping (i
...
, the value of x)
...
Electrons travelling from the bulk GaN enter a high level in the first well (Figure 8
...
From this level, the electron can emit a photon
Optical properties of solids
357
FIGURE 8
...
and go to a lower level or it can then tunnel through to the next well
...
More electrons
are now in the higher level than in the lowest levels, thus a population inversion exists—
the requirement for laser action
...
All these layers
are built up on a substrate, for example, sapphire
...
One use of semiconductor lasers is as the light source in fibre optics
...
4 OPTICAL FIBRES
Optical fibres are used to transmit light in the way that metal wires are used to transmit
electricity
...
The intensity, time between pulses, and the length of
a pulse can be modified to convey the contents of the call in coded form
...
Thus, much of the art of making commercial optical fibres lies in finding ways of
reducing energy loss
...
Laser beams
diverge less than conventional light beams so that using laser light helps, but even so,
some tendency exists for the beam to stray outside the fibre
...
The beam is sent
down a central core
...
This is illustrated in Figure 8
...
FIGURE 8
...
Adding selected impurities can vary the refractive index
...
14, the totally internally reflected rays travel a longer path than those that travel straight
along the core
...
One way to keep the
pulses together is to use very narrow cores so that essentially all the light travels the
straight ray path
...
The refractive index
is a measure of how fast light travels in a medium; the lower the refractive index, the
faster the speed of light
...
To see why the refractive index is altered by composition, the atomic origin of the
refractive index is considered briefly
...
Even when the radiation is not absorbed, this field has an effect
on the electrons in the solid
...
The
applied field produces a separation of the centres of positive and negative charge (i
...
, it
induces an electric dipole moment)
...
)
The oscillating field of the radiation can be considered as pulling the electrons—
alternately one way and then the other
...
This property is called the
polarisability and is higher for large ions with low charge, for example Cs+, than for
small, highly charged ions such as Al3+
...
Adjusting the refractive index by adding carefully selected
impurities is also useful in other applications
...
Lead ions, Pb2+, are highly polarisable and are used to produce glass of high
refractive index
...
The imperfections cause scattering of the light of a type known as Rayleigh
scattering
...
The amount of scattering depends on (1/λ4), where λ is the
wavelength; therefore, much less scattering occurs for longer wave-lengths
...
To reduce Rayleigh scattering, the lasers employed for optical fibre systems
usually emit infrared radiation
...
In a fibre several
kilometres long, a very small amount of impurity can give rise to substantial absorption
...
Instead of
being clear, the glass appears green
...
A
windowpane is only about half a metre across, so that you can see that in a fibre of a few
km in length, there would be considerable loss due to such absorption
...
In an optical fibre 3 km long operating at
1300 nm in the near infrared, the intensity of the Fe2+ absorption is still such that a
concentration of 2 parts in 1010 would reduce the amount of radiation by one half
...
One reason why silica has been
widely used is that high purity silicon tetrachloride, developed for the semiconductor
industry, is commercially available as a starting material
...
Using infrared radiation
means there is likely to be loss due to absorption by molecular vibrations
...
The vibrational frequencies of OH bonds are high and close to the frequencies
used for transmission
...
Even when water is excluded and no OH bonds are present,
absorption by vibrational modes cannot be neglected
...
However, the SiO absorption is very strong and the peak tails into the region of the
transmission frequency
...
Losses still occur in the fibres developed for commercial use
...
Along with
transmission of information in telephone systems and similar applications, it has been
suggested that optical devices may replace conventional electronics in more advanced
applications such as computers
...
In the last two decades, new materials have been
developed that may form the basis of integrated optical circuits
...
Solid state chemistry
360
8
...
Eli
Yablonovitch at Bell Communications Research first developed the idea of such crystals
in the 1980s
...
At each boundary between the two materials, light, or other
electromagnetic radiation, will refract and partly reflect
...
The
wavelength of the radiation, its direction of travel, the refractive index of the photonic
crystal materials, and the particular periodic arrangement determine whether two beams
will be in phase
...
The range of such forbidden wavelengths is known by
analogy with semiconductors as the photonic band gap
...
15 illustrates how a
forbidden wavelength can occur for a one-dimensional arrangement—a row of slabs of
dielectric material
...
For the right spacing of the slabs, the reflected rays from each slab are in phase with each
other but out of phase with the incident light
...
The original photonic crystal was produced by accurately drilling holes a milllimetre
in diameter in a block of material with refractive index of 3
...
This crystal had a photonic
band gap in the microwave region
...
Producing photonic crystals with band gaps at shorter
wavelengths—infrared and visible—is less straight forward
...
A GaAs laser produces radiation of wavelength 904 nm
...
45 would require a spacing of 623 nm or 0
...
Machining holes of this
size is impractical, and the production of regular periodic structures with spacings of this
order is a technical problem that needs to be overcome before integrated optical circuits
and other devices can be manufactured
...
The spheres arrange themselves into a close-packed structure
Optical properties of solids
361
FIGURE 8
...
Light travelling through can
interfere destructively with reflected
light giving rise to forbidden
wavelengths
...
In (b)
the spacing of the slabs is such that the
waves are reflected with slightly
different phases and the incident light
travels through the array
...
Solid state chemistry
362
Two-dimensional photonic materials (i
...
, materials in which light is blocked within a
plane but transmitted perpendicular to the plane) are useful as optical fibres
...
The structure is then heated and drawn until it is only a few
µm thick
...
It is also possible to replace the
central glass core by air and this enables very high power laser signals to be transmitted
along the fibre without damage to the fibre material
...
Photonic crystals have only been studied in the laboratory for two decades, but
naturally occurring examples exist, with the best known being the gemstone opal
...
These are
thought to have formed from colloidal silica solutions, and the colour depends on the size
of the spheres
...
In the oxide MnO, Mn2+ ions occupy octahedral holes in an oxide lattice
...
The five d
electrons of the Mn2+ ions occupy separate d orbitals and have parallel spins
...
2
...
16 illustrates the energy levels of Nd3+ in yttrium aluminium garnet
(Y3A15O12), which are involved in the laser action of this crystal (known as the
neodymium YAG laser)
...
3
...
This is
much more efficient at transferring energy to the impurity sites for emission than are the
phosphors based on phosphates as host
...
Suggest a reason for the
efficiency of transfer in this solid
...
Figure 8
...
Is the band gap of this solid
direct or indirect?
Optical properties of solids
363
FIGURE 8
...
FIGURE 8
...
Solid state chemistry
364
5
...
6
...
How do these
impurities increase the refractive index?
7
...
How do the
wavelengths of the photonic band gap vary with the colour?
9
Magnetic and Dielectric Properties
9
...
A
well-known example of this is ferromagnetism
...
Other cooperative magnetic effects lead to a cancelling (antiferromagnetism) or partial
cancelling (ferrimagnetism) of the magnetism of different atoms
...
Cooperative effects are not confined to magnetism; similar effects can occur for the
response of a crystal to mechanical stress and to electric fields
...
Ferroelectric materials are important in the
electronics industry as capacitors (for storing charge) and transducers (for converting, for
example, ultrasound to electrical energy)
...
For
example, quartz watches use piezoelectric quartz crystals as oscillators
...
To begin, however, we consider the weaker magnetic effects that
can be found in all types of matter
...
Following magnetic effects we look at dielectric
effects, starting with the piezoelectric effect and its applications and then considering
ferroelectric materials and in particular the oxide barium titanate (BaTiO3), which is
widely used as a capacitor
...
2 MAGNETIC SUSCEPTIBILITY
A magnetic field produces lines of force that penetrate the medium to which the field is
applied
...
The density of these lines of force is known as the
magnetic flux density
...
B=µ0H
(9
...
1 Flux density in (a) a
diamagnetic and (b) a paramagnetic
sample
...
Diamagnetic materials reduce the density of the lines of force as depicted in
Figure 9
...
Paramagnetic materials increase the flux density
...
The
magnetic flux density is now given by Equation (9
...
B=µ0(H+M)
(9
...
Diamagnetism is present in all substances but is very weak so that it is not normally
observed if other effects are present
...
Atoms or molecules with closed shells of electrons are diamagnetic
...
Simple paramagnetic
behaviour is found for substances such as liquid oxygen or transition metal complexes in
which the unpaired electrons on different centres are isolated from each other
...
The interplay of applied field and thermal randomization leads to the
temperature dependence described by the Curie law
(9
...
Different temperature dependence is observed when there
is cooperative behaviour
...
For ferromagnetism, the Curie law becomes
(9
...
For antiferromagnetism, the temperature
dependence is of the form
(9
...
These two behaviours are illustrated in Figure 9
...
FIGURE 9
...
Solid state chemistry
368
TABLE 9
...
1
Independent
Decreases
Spin and orbital
motion of
electrons on
individual
atoms
Ferromagnetism
+
Antiferromagnetism
0
...
1
Dependent
May be
dependent
Decreases
Increases
Cooperative
interaction
between
magnetic
moments of
individual
atoms
Pauli
paramagnetism
10–5
Independent
None
Spin and orbital
motion of
delocalised
electrons
+
Ferrimagnetism has a more complicated form of temperature dependence with ions on
different sites having different characteristic temperatures
...
1
...
3 PARAMAGNETISM IN METAL COMPLEXES
In solids containing metal complexes such that the unpaired electrons on the different
metal atoms are effectively isolated, the susceptibility can be discussed in terms of
magnetic moments
...
Each complex in a solid will produce its own magnetic field due to the unpaired
electrons
...
However, thermal motion causes the orientation of these
fields to be random
...
3), the temperature dependence is the
result of this thermal motion but the constant, C, gives us information on the value of the
magnetic field, known as the magnetic moment, µ, of the complex
...
The
dimensionless quantity χ in Equation (9
...
To obtain
Magnetic and dielectric properties
369
the size of the magnetic field due to an individual complex, χ is divided by the specific
gravity to give the susceptibility per unit mass of the sample and then multiplied by the
relative molecular mass to obtain the molar susceptibility χm
...
6)
(9
...
In SI units, χm is in m3 mol−1 and the magnetic
moment in joules per tesla (J T−1)
...
M
...
274×10–24 J T−1
...
The electrons possess both spin and orbital angular momentum
...
In complexes of these atoms, the magnetic moment is often close to that predicted for
spin angular momentum only (Equation (9
...
7)
where g is a constant which, for a free electron, has the value 2
...
The value of S depends on the number of unpaired electrons, and Table 9
...
Contributions from orbital angular momentum cause deviations from these values
...
For the lanthanides, the magnetic moment depends on
TABLE 9
...
73
1
3
4
5
Magnetic moment µs in Bohr
magnetons
2
...
87
2
4
...
92
Solid state chemistry
370
the total angular momentum of the electrons, J, not just or mainly on the spin angular
momentum
...
J=L+S
(9
...
9)
where
This can give rise to large magnetic moments, especially for shells that are more than half
full
...
9) of 9
...
9
...
The core electrons contribute a diamagnetic
term to the magnetic susceptibility, but the valence electrons can give rise to
paramagnetism or one of the cooperative effects we have described
...
Even in the ground state of simple molecules, such as O2, however, it can be
more favourable to have electrons in different orbitals with parallel spins than in the same
orbital with paired spins
...
In an energy band, many degenerate levels exist as well as many levels very close in
energy to the highest occupied level
...
To obtain a measurable effect, however, the number of parallel spins would
have to be comparable with the number of atoms; 103 unpaired spins would not be
noticed in a sample of 1023 atoms
...
The resulting promotion
energy would be too great to be compensated for by the loss in electron repulsion
...
When a magnetic field is applied, the electrons will acquire an extra energy term due
to interaction of their spins with the field
...
e
...
For an electron with spin antiparallel to the field, it is now worthwhile
Magnetic and dielectric properties
371
to go to a higher energy state and change spin so long as the promotion energy is not
more than the gain in magnetic energy
...
This type of paramagnetism is known as Pauli paramagnetism
...
3 (see Table 9
...
For a very few metals, however, the unpaired electrons in the conduction band can
lead to ferromagnetism
...
So, what is so special about these
elements that confers this uniqueness on them? It is not their crystal structure; they each
have different structures and the structures are similar to those of other non-ferromagnetic
metals
...
The 3d orbitals are less diffuse than the 4s and 4p (i
...
, they are concentrated nearer
the atomic nuclei)
...
Furthermore, five 3d orbitals are present, so that for a crystal of N atoms, 5N
levels must be accommodated
...
In this case, it is energetically favourable to have
substantial numbers of unpaired electrons at the cost of populating higher energy levels
...
For iron, for example, in a crystal of N atoms up to 2
...
Note the contrast with a
paramagnetic solid containing transition metal complex ions where each ion may have as
many as five unpaired electrons but, in the absence of a magnetic field, electrons on
different ions are aligned randomly
...
The 4d and 5d orbitals are more diffuse than 3d and produce wider bands so that
ferromagnetism is not observed in the second and third row transition elements
...
In titanium the valence electrons are in the 4s/4p band with low density of states and, at
the other end of the row in copper, the 3d band has dropped in energy so that the Fermi
level is in the 4s/4p band
...
Schematic band diagrams for Ti, Ni, and Cu are
given in Figure 9
...
Shading indicates the occupied levels
...
This causes a decrease in their
mobility and hence in the electrical conductivity of these elements compared to simple
metals and copper where the conduction electrons are in s/p bands
...
Some of these
Solid state chemistry
372
FIGURE 9
...
The
shading represents occupied energy
levels
...
In the lanthanide alloys, f electrons
contribute to the magnetism
...
The theoretical maximum magnetisation for
the transition metals is five electrons per atom, as only five d orbitals are present
...
In the pure lanthanide metals, the overlap of f
orbitals is so small that they can be regarded as localised
...
The interaction
between these d electrons and the localised f electrons causes alignment of the d and f
electrons to reduce electron repulsion
...
In alloys, the f electrons can align via the
transition metal d electrons, and although not all the d and f electrons are aligned, it can
be observed that high values of the magnetisation could be achieved
...
Other alloys can be made from nonmagnetic elements, such as manganese, and in these,
Magnetic and dielectric properties
373
the overlap of d orbitals is brought into the range necessary for ferromagnetism by
altering the interatomic distance from that in the element
...
The number of unpaired
electrons will determine the maximum field, but the other factors depend on the structure
of the solid and the impurities it contains, as discussed next
...
4
...
If 2
...
Within each domain, the spins are all aligned, but the
different domains are aligned randomly with respect to each other
...
4)
...
If you consider
building up a domain starting with just a few spins, initially the exchange interactions
dominate and so the spins all lie parallel
...
Eventually, the
magnetic dipole interaction overcomes the exchange interaction and the adjacent piece of
crystal has the spins aligned antiparallel to the original domain
...
FIGURE 9
...
8%
of silicon
...
Solid state chemistry
374
(From R
...
Resnick (1985)
Quantum Physics of Atoms, Molecules,
Solids, Nuclei and Particles, John
Wiley, New York
...
J
...
); (b) magnetic domain
patterns on the surface of an individual
crystal of iron
...
J
...
A
...
, New York
...
5 Movement of a domain
wall
...
The
moments twist to align with the
applied field, H, and the wall moves in
the direction of the arrow
...
The alignment can be accomplished in two ways
...
Between the two
Magnetic and dielectric properties
375
domains is an area of finite thickness known as the domain wall
...
When the
magnetic field is applied, the spins in the wall nearest the aligned domain alter their spins
to line up with the bulk of the domain
...
The net effect is to move the wall of the domain further out, as depicted in Figure 9
...
This process is reversible; the spins return to their former state after the magnetic field is
removed,
If impurities or defects are present, it becomes harder for a domain to grow; there is an
activation energy aligning the spins through the defect, and so a larger magnetic field is
required
...
In this
case the solid retains magnetisation
...
Thus, steel (which is iron with a high impurity content) remains magnetic
after the field is removed, whereas soft iron (which is much purer) retains hardly any
magnetisation
...
The two mechanisms are compared in Figure 9
...
FIGURE 9
...
The magnetic behaviour of different ferromagnetic substances is demonstrated by their
hysteresis curves
...
If we start with a nonmagnetic sample in which all the domains are randomly
aligned, then in the absence of a magnetic field, B and H are zero
...
The plot of B against H is depicted in Figure
9
...
Initially, the curve is like ‘oa’, which is not simply a straight line because the
magnetisation is increasing with the field
...
When the applied field is
reduced, the flux density does not follow the initial curve
...
A
sufficiently large field in the reverse direction to provide the activation energy for
realignment through the imperfection must be applied before the magnetisation process
can be reversed
...
The magnetisation at this point is known
Solid state chemistry
376
as the remanent magnetisation
...
9
...
2 PERMANENT MAGNETS
Substances used as permanent magnets need a large coercive force, so that they are not
easily demagnetised and preferably should also have a large remanent magnetisation
...
They are often made from
FIGURE 9
...
alloys of iron, cobalt, or nickel which form with small crystals and include non-magnetic
areas so that domain growth and shrinkage are difficult
...
The best known of these alloys is
SmCo5, which has a coercive force of 6×105 A m−1 compared to 50 A m−1 for pure iron
...
5 FERROMAGNETIC COMPOUNDS—CHROMIUM DIOXIDE
Chromium dioxide (CrO2) crystallises with a rutile structure and is ferromagnetic with a
Curie temperature of 392 K
...
In chromium dioxide, however, this band is very narrow and so, similar to Fe, Co,
and Ni, chromium dioxide displays ferromagnetism
...
g
...
TiO2 has no 3d
electrons and is an insulator
...
It does, however, undergo a phase transition to a metal at 340 K, when it
becomes Pauli paramagnetic
...
Because the
metal atoms are farther apart in the dioxides than in the elemental metals, the narrow
bands that give rise to ferromagnetism occur earlier in the row than for the metallic
elements
...
5
...
Recording tape usually consists of a polyester tape impregnated with needle-like crystals
of a magnetic material such as chromium dioxide or γ -Fe2O3
...
Sound
waves from the voice or music to be recorded hit a diaphragm in the microphone
...
This causes a fluctuating electric current in the coil; the current depends on the
frequency of the motion of the coil and hence on the frequency of the sound waves
...
This in turn magnetises the particles on the tape and the
strength and direction of this magnetisation is a record of the original sound
...
Materials for recording tape therefore need to retain their magnetisation so that the
recording is not accidentally erased
...
Chromium dioxide fulfills these requirements and has a high magnetisation giving a large
range of response and thus a high quality of reproduction
...
9
...
In this section
we shall see that their magnetic properties are equally varied
...
These oxides were metallic conductors
...
MnO, FeO, CoO, and
NiO have localised 3d electrons and are paramagnetic at high temperatures
...
The Néel temperatures for this transition
are 122 K, 198 K, 293 K, and 523 K, respectively
...
Antiferromagnetic materials, therefore,
show a drop in magnetic susceptibility at the onset of cooperative behaviour
...
2(c))
...
So how do we reconcile these two sets of properties?
The magnetic interaction in these compounds is thought to arise indirectly through the
oxide ions, a mechanism known as superexchange
...
The
orbital on the nickel can overlap with the
2pz on oxygen, leading to partial covalency
...
The oxide ion has a closed shell and so there is another
2pz electron, which must have opposite spin
...
As
next nickel and so the
shown in Figure 9
...
The alternating spin magnetic moments in antiferromagnets such as NiO can be
observed experimentally using neutron diffraction
...
X-rays on the other hand
FIGURE 9
...
Magnetic and dielectric properties
379
FIGURE 9
...
have no magnetic moment and respond to electron density and hence to atomic positions
...
When the
structure is determined by neutron diffraction, however, extra peaks appear which can be
interpreted as giving a magnetic unit cell twice the length of the X-ray determined unit
cell
...
9
...
The magnetic unit cell is
bounded by identical atoms with identical spin alignment
...
The spins of all nickel ions in a
given layer are aligned parallel but antiparallel to the next layer (see Section 2
...
1)
...
7 FERRIMAGNETISM—FERRITES
The name ferrite was originally given to a class of mixed oxides having an inverse spinel
structure and the formula AFe2O4 where A is a divalent metal ion
...
The spinel structure is a common mixed oxide structure, typified by spinel itself
MgAl2O4, in which the oxide ions are in a face-centred cubic close packed array (see
Section 1
...
3 and Figure 1
...
For an array of N oxide ions, there are N octahedral holes,
and the trivalent ions (Al3+) occupy half of the octahedral sites (Figure 9
...
In addition, there are 2N tetrahedral sites, and the divalent ions (Mg2+) occupy oneeighth of these
...
Ions on octahedral sites interact directly with each other and their spins align parallel
...
Solid state chemistry
380
FIGURE 9
...
In ferrites, AFe2O4, the Fe3+ ions on tetrahedral sites are aligned antiparallel to those on
octahedral sites, so that there is no net magnetisation from these ions
...
This
produces a net ferromagnetic interaction for ferrites in which A2+ has unpaired electrons
...
11
...
One way of looking at the electronic
structure of this oxide is to consider it as an array of O2− ions and Fe3+ ions,
FIGURE 9
...
Magnetic and dielectric properties
381
with the electrons that would have made half the Fe ions divalent delocalised over all the
ions on octahedral sites
...
Since
there can only be five 3d electrons of one spin on any atom, the delocalised spin must
have the opposite spin
...
Hence, the two ions must have their spins aligned, and these
spins must be aligned with those of all other Fe ions on octahedral sites
...
Magnetite is the ancient lodestone used as an early compass
...
9
...
8
...
In 1988, it was found that for certain
metallic multilayer materials, the application of a magnetic field of strength of 1 to 3 mT
caused the resistivity to drop to half or less of its zero field value
...
Within a decade, commercial devices, such as
computer hard disk read heads, based on GMR were available
...
e
...
g
...
Within a single ferromagnetic layer, all the
spins are aligned, but the coupling between adjacent ferromagnetic layers depends on the
thickness of the intervening nonmagnetic layer
...
When a magnetic field is applied, this aligns the layers in a ferromagnetic manner and
causes a significant drop in electrical resistance
...
In ferromagnetic materials, there is a much higher
density of electrons of one spin state and these electrons will carry most of the current
...
(This model can also account for the value 2
...
M
...
) For one spin species (e
...
, spin up), the 3d bands will be full
...
Because the spin up 3d band
is full, the spin up current carriers occupy a higher energy s/p band, whereas the spin
down current carriers are in the 3d band
...
Now, suppose one ferromagnetic layer has a majority of spin up electrons
...
12(a)), then current can flow
readily from one ferromagnetic layer to the next
...
12(b)), then the current from the
Solid state chemistry
382
FIGURE 9
...
first layer has to be carried by the minority spin electrons in their 3d band, and thus the
conductivity is reduced
...
9
...
2 HARD DISK READ HEADS
In hard disk read heads, one ferromagnetic layer has its spin orientation fixed by coupling
to an antiferromagnetic layer (Figure 9
...
A second ferromagnetic layer separated from
the first by a nonmagnetic metal, is free to change its spin orientation when a field is
applied
...
13 Two ferromagnetic
layers, as in a magnetic hard disk read
head, illustrating pinning by an
antiferromagnetic layer
...
The
information on the hard disk is coded as a series of 0s and 1s corresponding to the
different orientations of the magnetic field on the disk, and these give rise to a high or
low current in the read head
...
Their development has
led to the high capacity hard disks found in current (2005) laptop computers
...
9
...
3 TUNNELLING AND COLOSSAL MAGNETORESISTANCE
A related phenomenon, tunnelling magnetoresistance (TMR), has aroused interest as
the basis for magnetic sensor and storage devices
...
Electrons flow from one ferromagnetic layer to the next by
quantum mechanical tunnelling
...
g
...
In these compounds, a
change in electrical resistance of orders of magnitude is observed, but large magnetic
fields of the order of several tenths of a Tesla (that is a hundred times stronger than those
that produce giant magnetoresistance) or larger are needed
...
The trivalent RE ions and divalent M ions occupy the A sites in the
perovskite structure (Figure 9
...
The Mn ions
occupy the octahedral B sites
...
14 Perovskite structure
...
The environment of the Mn3+(d4) ions is distorted due to the
Jahn-Teller effect and for small values of x, a cooperative distortion occurs
...
The Mn4+ ions couple antiferromagnetically with each
other via superexchange as in NiO
...
Mn3+ ions couple to Mn4+ ions in a process known as double
exchange
...
Mn↑↓O↑Mn→Mn↑O↓↑Mn
This produces ferromagnetic coupling
...
These phases can be described in terms of
band theory
...
Unusually there is a
large band gap between the two so that at low temperatures, one band is empty and one
partly full
...
) The ferromagnetism disappears at the Curie temperature
...
As the
ferromagnetic phase approaches the Curie point, the electrical resistance rises as thermal
energy starts to overcome the double exchange
...
A strong magnetic field applied to the manganite realigns the spins
restoring the half metallic state and thus decreasing the resistivity
...
9 ELECTRICAL POLARISATION
Although solids consist of charged particles (nuclei and electrons) a solid has no overall
charge
...
Even if a solid is composed of molecules with
permanent dipole moments (e
...
, ice), the molecules are generally arranged in such a way
that the unit cell of the crystal has no net dipole moment and so the solid has none
...
This field arises from two sources, a distortion of the electron cloud of
the atoms or molecules and slight movements of the atoms themselves
...
P=ε0χeE
(9
...
85×10–12 F m−1) and χe is the
(dimensionless) dielectric susceptibility
...
The susceptibility is often determined experimentally by determining
the capacitance of an electric circuit with and without the solid present
...
(9
...
The dielectric constant εr is related to the susceptibility by
εr=l+χe
(9
...
Electromagnetic radiation in the visible and ultraviolet regions
provides such a field and the refractive index of a material is a measure of the electron
contribution to the dielectric constant
...
Although most solids do not have a dipole moment in the absence of an electric field,
the classes of solids that do are commercially important, and so form the subject matter of
the rest of this chapter
...
10 PIEZOELECTRIC CRYSTALS—α-QUARTZ
A piezoelectric crystal is one that develops an electrical voltage when subject to
mechanical stress for example if pressure is applied to it, and conversely develops strain
when an electric field is applied across it
...
For it
to be piezoelectric, a crystal must be made up from units that are non-centrosymmetric
(i
...
, they do not possess a centre of symmetry)
...
α-quartz is based on SiO4 tetrahedra
...
However, these tetrahedra are arranged in such a way (Figure 9
...
External stress changes the Si—O—Si bond angles between tetrahedra so that the
dipole moments no longer cancel and the crystal has a net electrical polarisation
...
01 of the input
FIGURE 9
...
Note that the oxygens around
each silicon are arranged in a distorted
tetrahedron and that the silicons
themselves project a distorted
hexagon
...
81
...
An electric
field causes distortion of quartz, and if an alternating electric field is applied, the crystal
vibrates
...
The importance of α-quartz in devices such
as watches is due to the fact that for some crystallographic cuts, a natural frequency of
the crystal is independent of temperature and so the crystal will oscillate at the same
frequency, and the watch will keep time, no matter how hot or cold the day is
...
Some piezoelectric crystals are electrically polarised in the absence of mechanical
stress; one example is gem-quality tourmaline crystals
...
Although there should
be a surface charge, this is rapidly neutralised by charged particles from the environment
and from the crystal itself
...
If tourmaline is
heated its polarisation decreases and it loses some of its surface charges
...
Such crystals are known as pyroelectric, and ferroelectric crystals are a special subclass
of pyroelectric crystals
...
11 THE FERROELECTRIC EFFECT
Ferroelectric crystals possess domains of different orientation of electrical polarisation
that can be reorientated and brought into alignment by an electric field
...
This substance has a very large dielectric constant (around
1000) and is widely used in capacitors
...
44 (see Chapter 1) with Ba2+ ions in the centre, Ti4+ ions at the cube corners and
an octahedron of O2− ions around each titanium ion
...
At 393 K, the structure changes to a
tetragonal one in which the Ti atom moves off-centre along a Ti-O bond
...
The three distortions are given in Figure 9
...
This figure magnifies the
effect: the Ti atom is moved about 15 pm off-centre
...
To illustrate how
ferroelectricity arises, we use the tetragonal structure as an example
...
Similar to ferromagnetics, however, ferroelectrics have domains within
which there is a net polarisation but different domains have their polarisation in different
directions thus giving a net zero polarisation
...
Neighbouring
domains, as a result, have polarisations that are either at 90° or at 180° to each other (e
...
,
Figure 9
...
Solid state chemistry
388
A domain can be of the order of 10–5 m or even more
...
Figure 9
...
Note the sharpness of the domain boundaries
...
As with ferromagnetics, the response to the field exhibits
FIGURE 9
...
FIGURE 9
...
Magnetic and dielectric properties
389
hysteresis; the polarisation grows until the whole crystal has its dipoles aligned, this
polarisation remains while the field is reduced to zero and only declines as a field of
opposite polarity is applied
...
19 is a hysteresis curve for barium titanate
...
18 A photograph of a thin
slice of barium titanate taken under the
polarizing microscope, picturing
domains of different polarisation
...
Guinier and R
...
9, p
...
Reproduced by permission of
Oxford University Press
...
19 A plot of polarization
vs
...
The electric susceptibility and dielectric constant of ferroelectric substances obey a Curie
law dependence on temperature (Equation (9
...
13)
where ε∞ is the permittivity at optical frequencies and Tc is the Curie temperature
...
Above the Curie temperature, the structure has a centre of
symmetry and no net dipole moment
...
In PbZrO3, which also has a perovskite structure, the offset atoms are arranged
alternately in opposite directions
...
PbZrO3 with
some zirconium replaced by titanium gives the widely used ferroelectric materials, PZT
(PbZr1−xTixO3)
...
Polyvinylene fluoride,
as a thin film (approximately 25 µm thick) is used in Shockwave experiments to measure
stress
...
In the β-phase of polyvinylene fluoride (PVDF), the CF2 groups in a polymer chain are
all pointing in the same direction (Figure 9
...
20 Alignment of −CF2
groups in β-polyvinylene fluoride
...
Within a domain, the CF2 groups on different chains are aligned
...
9
...
1 MULTILAYER CERAMIC CAPACITORS
Capacitors are used to store charge
...
The capacitor then remains charged until a current is required
...
In order to retain a high capacitance (i
...
, to store
a large amount of electrical energy while remaining small), a material needs a high
permittivity
...
Pure barium titanate has a high permittivity (about 7000) close to the
Curie temperature, but this rapidly drops with temperature to the room temperature value
of 1 to 2000
...
It is also necessary for
some applications, for the permittivity to be constant with temperature over a range of
180 K, from 218 K to 398 K
...
temperature curve
...
Materials made in this way consist of several phases mixed
together each with a different Curie temperature, and it is this that gives rise to the flatter
permittivity versus temperature curve
...
On the surface of the tetragonal crystals, the structure
is cubic, so that for small particles with a large surface to volume ratio there is a high
proportion of cubic material
...
For very small particles, no ferroelectric effect
exists
...
To manufacture multilayer capacitors, barium titanate of suitable grain size and
appropriately doped is interleaved with conducting plates (Figure 9
...
This enables one
device to be used in place of several single disc capacitors in parallel
...
21 A section through a
multilayer capacitor
...
Other oxides with the
perovskite structure are also ferroelectric (e
...
, lead titanate and lithium niobate)
...
These, like barium titanate, have small ions in O6 cages
which are easily displaced
...
4H2O), salts with anions which possess
dipole moments, such as NaNO2, and copolymers of poly vinylidene fluoride
...
Chapter 10 covers the exciting field of superconductors, including high-temperature
superconductors, many of which have structures related to the perovskite structure
...
Although manganese is not ferromagnetic, certain alloys such as Cu2MnAl are
ferromagnetic
...
What effect would this have on the 3d band of manganese? Why would this cause the
alloy to be ferromagnetic?
2
...
Its neutron diffraction patterns at high and low
temperatures are identical
...
ZnFe2O4 has the inverse spinel structure at low temperatures
...
In transition metal pyrite disulfides, MS2, the M2+ ions occupy octahedral sites
...
Consider the information on
some sulfides given next, and decide whether the 3d electrons are localised or
Magnetic and dielectric properties
393
delocalised, which band the electrons are in if delocalised, and, in the case of
semiconductors, between which two bands the band gap of interest lies
...
FeS2 diamagnetic, semiconductor
...
5
...
What does this suggest about the origin of
the ferroelectric transition in these compounds?
6
...
Replacing some K ions by Li does, however, produce a ferroelectric material
...
10
Superconductivity
10
...
Their findings were thought to be so important that it was
only a year later that they were awarded the Nobel Prize in Physics by the Royal Swedish
Academy of Sciences
...
First, they have zero electrical resistance and, therefore, carry current with no
energy loss: this could revolutionize power transmission in cities, for instance, and is
already exploited in the windings of superconducting magnets used in NMR
spectrometers
...
The superconductors can float or ‘levitate’ above a magnetic
field: the Japanese have an experimental frictionless train that floats above magnetic rails
and has achieved speeds of over 500 km h−1 (300 m
...
h
...
t
...
This, of course, made any use of
superconductors extremely expensive
...
Over 50
high temperature superconductors, almost all containing copper oxide layers, are now
known
...
Low temperature superconductivity has been observed in organic
polymers, and in doped C60
...
Although this temperature is not
high enough for liquid nitrogen cooling, it is technologically important as mains-operated
cryocoolers are now available that can reduce temperatures to 30 K so that devices made
from this material would not require liquid helium cooling
...
All these exciting developments are discussed, but we begin by looking at the
properties of the low temperature superconductors that were discovered nearly a century
ago
...
2 CONVENTIONAL SUPERCONDUCTORS
10
...
1 THE DISCOVERY OF SUPERCONDUCTORS
In 1908, Kamerlingh Onnes succeeded in liquefying helium, and this paved the way for
many new experiments to be performed on the behaviour of materials at low
temperatures
...
In 1911, Onnes was
measuring the variation of the electrical resistance of mercury with temperature when he
was amazed to find that at 4
...
He called this
effect superconductivity and the temperature at which it occurs is known as the
(superconducting) critical temperature, Tc
...
1
...
Once an electrical current is established, it demonstrates no
discernible decay for as long as experimenters have been able to watch!
For more than 20 years, little progress was made in the understanding of
superconductors and only more substances exhibiting the effect were found
...
2), as can thousands of alloys
...
10
...
2 THE MAGNETIC PROPERTIES OF SUPERCONDUCTORS
Meissner and Ochsenfeld found that when a superconducting material is cooled below its
critical temperature, Tc, it expels all magnetic flux from within its interior (Figure
10
...
Because B=µ0H(1+χ),
when B=0, χ must equal −1 (i
...
, superconductors are perfect diamagnets)
...
3(b)) and
the superconductor repels a magnet
...
4,
where a magnet is seen floating in mid-air above a superconductor
...
A typical plot of Tc against increasing magnetic field is depicted in Figure 10
...
It follows that a superconducting material can be made non-superconducting by the
application of a large enough magnetic field
...
Type I
Solid state chemistry
396
FIGURE 10
...
temperature, T, illustrating the drop
to zero at the critical temperature, Tc,
for a superconductor, and the finite
resistance of a normal metal at
absolute zero
...
2 The superconducting
elements
...
3 (a) (i) Superconductor
with no magnetic field
...
When the temperature drops below the
critical temperature (ii), the magnetic
flux is expelled from the interior
...
superconductors, which includes most of the pure metal superconductors, have a single
critical field
...
Type II superconductors tend to have higher critical temperatures than
type I superconductors
...
This is known as the Silsbee effect
...
Solid state chemistry
398
FIGURE 10
...
(Courtesy of Darren Peets,
UBC Superconductivity Group
...
5 The variation of the
critical field strength, Hc, for lead
...
10
...
3 JOSEPHSON EFFECTS
In 1962, Josephson predicted that if two superconducting metals were placed next to each
other separated only by a thin insulating layer (such as their surface oxide coating) then a
current would flow in the absence of any applied voltage
...
This is known as the d
...
Josephson
effect
...
c
...
c
...
These two
properties are of great interest to the electronics and computing industries where they can
be exploited for fastswitching purposes
...
2
...
Physicists worked for many years to find a theory that explained superconductivity
...
However, in
1950, an isotope effect was first observed: for a particular metal, the critical temperature
was found to depend on the isotopic mass, M, such that
(10
...
2)
where µ is the reduced mass of the molecule, and k the force constant of the bond
...
The vibrational modes of a lattice are quantised, as are
the modes of an isolated molecule: the quanta of the lattice vibrations being called
phonons
...
Very simply, the mechanism
works like this: as a conduction electron passes through the lattice, it can disturb some of
the positively charged ions from their equilibrium positions, pushing them together and
giving a region of increased positive charge density
...
The net effect is that the two electrons have interacted with one another,
using the lattice vibration as an intermediary
...
It is the scattering of conduction electrons by the lattice vibrations, phonons, which
produces electrical resistance at room temperature
...
) Contrary
to what we might have expected intuitively, a superconductor will have high resistance at
room temperature, because it has strong electron/phonon interactions
...
Superconductors do not have low electrical resistance above the superconducting critical
temperature, Tc
...
It predicts that under certain conditions, the attraction
between two conduction electrons due to a succession of phonon interactions can slightly
exceed the repulsion that they exert directly on one another due to the Coulomb
interaction of their like charges
...
It is these Cooper pairs that are responsible for
superconductivity
...
They are described by a wave function,
known as an order parameter
...
BCS theory demonstrates that several conditions have to be met for a sufficient
number of Cooper pairs to be formed and superconductivity to be achieved
...
The relatively high
critical temperature of MgB2 is thought to be due to the high vibrational frequencies
associated with the light B atoms and the strong interaction between the electrons and
lattice vibrations
...
Cooper pairs are weakly bound, with typical separations of 106 pm for the two
electrons
...
Thus, enormous overlap occurs between different pairs, and the pairing is a
complicated dynamic process
...
When
an external electrical field is applied, the Cooper pairs move through the lattice under its
influence
...
Because the pairs cannot be scattered by the lattice
the resistance is zero and the system is a superconductor
...
3 HIGH TEMPERATURE SUPERCONDUCTORS
By 1973, the highest temperature found for the onset of superconductivity was 23
...
Their Nobel Prize
citation states, “Last year, 1986, Bednorz and Müller reported finding superconductivity
in an oxide material at a temperature 12°C higher than previously known
...
2, with a structure based on that of K2NiF4, a perovskite-related layer compound:
Superconductivity
401
they observed the onset of superconductivity at 35 K
...
The idea was soon born that it might be possible to raise the temperature even further
by substitution with different metals
...
The onset of
superconductivity for 1–2–3 occurs at 93 K
...
FIGURE 10
...
10
...
1 The Crystal Structures of High Temperature Superconductors
All the high Tc superconductors discovered so far, with one exception, contain weakly
coupled copper oxide, CuO2, planes
...
The structures of all the cuprate superconductors are based on, or related to, the
perovskite structure
...
The structure of NaxWO3 is also based on the
perovskite structure
...
6
...
4): many oxides of general formula ABO3 adopt this structure (also fluorides, ABF3
and sulfides, ABS3)
...
6
...
The perovskite structure can be equally well represented by moving the origin of the unit
cell to the body-centre: this has the effect of putting Ca (A) atoms at each corner, Ti (B)
atoms at the body centre, and an O atom in the centre of each face (Figure 10
...
Solid state chemistry
402
FIGURE 10
...
The crystal structure of the 1–2–3 superconductor, YBa2Cu3O7−x is depicted in Figure
10
...
Figure 10
...
If we discuss it in
terms of the perovskite structure ABO3, where B=Cu, the central section is now an Atype perovskite unit cell and above and below it are also A-type perovskite unit cells with
their bottom and top layers missing
...
The atom at the body-centre of
the cell (i
...
, in the centre of the middle section) is yttrium
...
8(b)):
this would give an overall formula of YBa2Cu3O9
...
The unit cell, in fact, contains only approximately seven oxygen atoms
(YBa2Cu3O7−x): when x=0, the oxygen atoms on the vertical edges of the central cube are
not there and two are also missing from both the top and bottom faces (Figure 10
...
A
unit cell containing seven oxygen atoms has an average copper oxidation state of 2
...
In the 1–2–3 structure (when x=0), the yttrium atom is coordinated by 8 oxygens and
the barium atoms by 10 oxygens
...
8(d))
...
These copper/oxygen nets
seem to be a common feature of all the new high temperature superconductors
...
5 (x=0
...
The oxygen is not lost at random but goes from specific
sites, gradually changing the square-planar coordination of the Cu along the c direction
into the twofold linear coordination characteristic of Cu+ and the arrangement of the
copper and oxygen atoms in the base of the pyramids is not affected
...
It is not until the oxygen content is
increased to YBa2Cu3O6
...
It is thought that this compound contains copper in
all three oxidation states: I, II, and III
...
Clearly, the oxidation state of the coppers in the structure
(and thus their bonding connections and bond lengths) is extremely important in
determining both, whether superconductivity occurs at all, and the temperature below
which it occurs (Tc)
...
8 The structure of 1–2–3:
(a) the metal positions; (b) an idealized
unit cell of the hypothetical
Superconductivity
405
YBa2Cu3O9, based on three perovskite
A-type unit cells; (c) idealized
structure of YBa2Cu3O7−x; and (d) the
extended structure of YBa2Cu3O7,
depicting copper-oxygen planes, with
the copper-oxygen diamonds in
between
...
) Key: Cu, blue; Ba, green;
Y, aqua; O, red
...
The structures of these solids fall into one of three
classes, 1201 based on HgBa2CuO4, 1212 based on HgBa2CaCu2O6, and 1223 based on
HgBa2Ca2Cu3O8
...
In 1993, however, it was found that annealing these compounds in
oxygen resulted in oxygen atoms being inserted into the (½, ½, 0) position in the Hg layer
and HgBa2CuO4+δ was superconducting
...
By replacing some of the Hg atoms by
metal atoms in higher oxidation states, compounds with extra oxygen in the Hg layer
were formed which were more stable at normal pressures
...
8Tl0
...
33
...
9
...
Ba occupies sites close to the
apices of these pyramids and the Ca positions are just above or below the bases
...
In the centre of the cell is the Hg layer
...
In 1–2–3, La2−xBaxCuO4 and the mercury cuprates, the average oxidation state of the
Cu is greater than 2 and as a result positive holes are formed in the valence bands
...
In 1–2–3 and the mercury cuprates, adding oxygen forms positive
holes, but other methods are available
...
9 Structure of
HgBa2Ca2Cu3O8, depicting copper
oxygen diamonds between the Ca
layers and the copper oxygen layers
forming the bases of the pyramids
...
In the
superconductor
Hg0
...
2Ba2Ca2Cu3O8+0
...
(See colour insert
following page 356
...
superconductivity is induced by the insertion of fluorine and in the collapsed
oxycarbonates, such as TlBa2Sr2Cu2(CO3)O7, superconductivity can be produced by
shearing so that a shift appears along one plane every n octahedra (where n is typically 3
to 5), which leaves the CuO2 layers unchanged and mixes the TlO and CO layers
...
Until 1988, all the high temperature superconductors that had been found were p-type,
and it was assumed by many that this would be a feature of high temperature
superconductors
...
17 (samarium, europium, or praeseodymium can
Superconductivity
407
also be substituted for the neodymium)
...
The superconductivity occurs at Tc≤25 K for
these compounds
...
The
superconductivity takes place in these planes and the other elements present and the
spacings between the planes changes the superconducting transition temperature—
exactly how is not yet understood
10
...
2 THEORY OF HIGH Tc SUPERCONDUCTORS
The consensus is that, in common with the conventional superconductors, high
temperature superconductors contain Cooper pairs (see Section 10
...
4)
...
The Cooper pairs in conventional superconductors couple to
give a total angular momentum of zero and are described by an order parameter of swave symmetry
...
The pairing state in BCS theory does not need to be caused by electronphonon interaction, and it is thought that pairing in the d state is due to antiferromagnetic
spin fluctuations, or electron-magnon coupling
...
This could be achieved if the pairs
had angular momentum (i
...
, if they were described by p- or d-waves)
...
As in BCS theory for
conventional superconductors, the coupling is a collective property and the pairing is a
dynamic process
...
Experiment suggests that the quasi-two-dimensional organic superconducting polymers
(see Chapter 6) are also d-wave superconductors
...
Collaborators at Berkeley
and Tokyo led by J
...
Séamus Davis and Shin-ichi Uchida used STM to measure
differential tunnelling conductance on a specimen of bismuth strontium calcium copper
oxide with zinc atoms replacing a small number of copper atoms
...
This should be zero within a defined energy above
the highest occupied levels known as the superconducting symmetry gap
...
The Zn atoms broke the superconducting pairs at their positions so that a conductance
peak appeared at the positions of the Zn atoms
...
Solid state chemistry
408
10
...
It was therefore with surprise that solids were recently discovered that are
both ferromagnetic and superconducting
...
This has a crystal structure almost
identical to La2CuO4, the parent compound of the high Tc superconductor 1–2–3
...
5 K, superconducting
...
The Ru is in the centre of an octahedron
of oxygen, and so the d bands are split into t2g and eg
...
It is the electrons close to the highest occupied levels of this band that are
responsible for the superconductivity
...
The wave function of the Cooper pair must be antisymmetric with respect to
exchange of electrons
...
For a triplet pair, both electrons have
the same spin and so the order parameter must be odd
...
10
...
Strong magnets are used to remove impurities from food and raw materials
...
The latest NMR spectrometers employ superconducting magnets to provide
large magnetic fields, so improving sensitivity
...
Conventional electromagnets (made by passing an electric current through insulated
copper wire wound around an iron core) can produce fields of about two tesla
...
Such superconducting magnets are both
lighter and more powerful (~10 tesla) than their conventional counterparts, consume very
little power, and produce little heat—but they have to be cooled to 4 K to become
superconducting
...
These consist of a loop of superconductive wire with either one built-in
Josephson junction (RF SQUID) or two (DC SQUID)
...
SQUIDs are being used in medical research
to detect small changes in magnetic field in the brain
...
Physicists use SQUIDs for research
into fundamental particles, and it is thought that there may be military applications in
detecting the change in the earth’s magnetic field caused by submarines
...
A change to
high temperature superconductors in the devices could make them cheaper and more
flexible to operate
...
The first maglev trains used conventional electromagnets which produce an
attractive force between the guideway and the train
...
Germany is the only Western country that had
solid plans for a maglev railway recently
...
This has now been shelved, but Transrapid is working on
exporting its system
...
The trains reach a speed of 430 kph (270 mph)
...
In this project,
superconductors on the train are repelled by magnetic fields produced by coils of wire on
the track, lifting the train 4 to 6 inches above the guideway
...
Use of the new high temperature superconductors should reduce the refrigeration costs
of the project
...
Using high temperature superconductors would reduce costs in some applications
...
Progress has been made on
overcoming these problems
...
These have been processed into long wires by packing a powdered
precursor into a silver tube, heating to form the superconductor and drawing the silver
tubes to form a wire
...
Wires that can carry 100 A per strand at 77 K are
available in lengths of 100 m
...
In 1997, a high Tc superconducting magnet was installed
in the beamline of a carbon-dating van der Graaf accelerator at the Institute for
Geological and Nuclear Sciences in Wellington, New Zealand
...
4 tesla
superconducting magnet close to the 23
...
Solid state chemistry
410
The absence of electrical resistance could be extremely useful in the distribution of
electricity throughout the country, as the copper and aluminum wires now used lose 5 to
8% of the power due to the resistance of these elements
...
Although superconductors carry direct current (dc) with
no loss of power and without generating heat, a small loss of power occurs when they
carry alternating current (ac) due to the production of radio waves
...
The National Grid is unlikely to be
replaced by superconducting cables in the near future but such cables are capable of
providing a solution to the problem of providing extra power to cities
...
Many conduits running power into large cities and towns are
full and to provide extra power would mean buying up land and digging new conduits
...
In May 2001, 150 000 residents of Copenhagen received electricity
through a 30 m high temperature superconductor cable
...
The total mass of this high temperature cable was 70
times less than the copper it replaced
...
S
...
Applications are expected to increase in the future
...
QUESTIONS
1
...
Unfortunately, the night is dark and moonless, and the field is known to contain
deep potholes
...
2
...
4
...
Repeat this procedure for the
perovskite B-type unit cell
...
Complete the following table, summarising types of superconductivity
...
Calculate the average oxidation state of Cu in the mercury cuprate
Hg0
...
2Ba2Ca2Cu3O8
...
Assume T1 is present as Tl3+ and Hg as Hg2+
...
1 INTRODUCTION
We felt that we could not leave this book without a brief look at the latest ‘hot’ topic
...
In a now famous lecture given in 1959 entitled ‘There’s
Plenty of Room at the Bottom’, Nobel Prize-winning physicist Richard Feynman said,
“The principles of physics, as far as I can see, do not speak against the possibility of
manoeuvring things atom by atom,” and that is the nub of what scientists are now trying
to do
...
Already the dream is beginning to be realized,
and some, but by no means all, of this science falls into the remit of solid state chemistry
...
A hydrogen atom is
about 0
...
Therefore, what is
different about nanoscience and nanotechnology from what chemists have always done?
Current research has two crucial strands
...
Chemists have roles here in synthesizing these particles, investigating their
properties, and developing new uses for them; it covers such topics as nanotubes,
coatings, new alloys, composites, particles for sunscreens, catalysts, colloids, and
quantum dots, to name but a few
...
Some techniques and processing, such as
photolithography for the printing of silicon chips, are so-called top-down processes
because they are carving out or etching nanometre size structures; these are clearly based
in technology, although the processes are often chemical
...
Nanoparticles are usually considered to have at least one dimension less than 100 nm,
although this is not a rigid definition and dimensions of several hundred nanometres can
fall into this research
...
A
10 nm diameter nanoparticle has about 15% of the atoms on the surface; by comparison,
this drops to <1% for a bulk solid
...
Nanoscience
413
Unfortunately because ‘nano’ has become somewhat of a buzzword and is currently
attracting a lot of research funding, the term is being used loosely to cover a huge range
of topics and techniques to do with anything that is fairly small, and it can be difficult to
separate what is important
...
Nanotechnology is the production and application of structures,
devices, and systems for controlling shape and size at nanometre scale
...
We will not discuss this type of work here, but in the following
sections will concentrate only on areas that relate in some way to solid-state chemistry
...
To try and bring some order to the discussion,
we have grouped the examples into one-dimensional (1-D), two-dimensional (2-D), and
three-dimensional (3-D) systems
...
11
...
For instance, small particles may melt at much lower temperatures than the bulk and are
often much harder: 6 nm copper grains are five times as hard as bulk copper
...
2
...
This
can lead to unusual crystal structures such as thin films of bcc copper, compared with the
normal bulk structure which is ccp
...
Under high pressures (2
GPa), these transform to the six-coordinate NaCl (rock salt) structure
...
It is thought that this
may be a resistance to the exposure of high-index crystal planes
Solid state chemistry
414
FIGURE 7
...
(Courtesy of Dr
...
)
FIGURE 7
...
FIGURE 7
...
Solid state chemistry
416
FIGURE 10
...
Key: Cu, blue; Ba, green; Y,
aqua; O, red
...
9 Structure of
HgBa2Ca2Cu3O8, depicting copper
oxygen diamonds between the Ca
layers and the copper oxygen layers
forming the bases of the pyramids
...
In the
Solid state chemistry
418
superconductor
Hg0
...
2Ba2Ca2Cu3O8+0
...
Key: Cu, grey;
Ca, red; Ba, blue; Hg/Tl, green; O,
aqua
...
2 The band gap of a
semiconductor depends on its size
...
7 The colour of the
fluorescence from a nano-sized particle
depends on its dimensions
...
Varying the conditions of deposition of the film in CVD can alter the morphology of
the nanocrystals formed; Figure 11
...
1(b) show nanosized diamond
crystals in diamond films grown with 111 (octahedral) and 100 (cubic) faces
...
Many nanomaterials can be made in different forms
...
MoS2 can be made as nanotubes, ‘onions’ (multi-walled
fullerene-type structures), and thin films
...
However, the synthetic techniques used are so particular to each system that they make a
subject in their own right and we will not attempt to cover them here
...
2
...
For crystals of, for instance, micrometre
dimensions, the number of energy levels is so large and the gap between them
FIGURE 11
...
2% PH3, showing
(100) square facets and (b) a diamond
film grown at lower substrate
temperature—now the crystals are
predominantly (111) triangular
facetted
...
P
...
May
and Professor M
...
R
...
)
so small that we could treat them as essentially infinite solids with continuous bands of
allowed energy
...
The result is that in
nanoparticles, we can still distinguish bands of energy, but the gaps between the bands
may differ from those found in larger crystals and, within the bands, the energy levels do
Nanoscience
421
not quite form a continuum so that we can observe effects due to the quantised nature of
levels within bands
...
2, for nano-sized crystals of
semiconductor (quantum dots)
...
2(a)
...
The orbital density of states
diagrams illustrate that, in general, a lower density of states exists at the top and bottom
of the band and a higher density of states exists in the middle (indicated by shading)
...
If electrons are promoted from the valence
band to the empty conduction band by supplying sufficient energy for them to jump the
band gap (with heat or light, for instance), then the solid conducts
...
The orbitals are removed from each of the band edges (cf
...
6) until, at a point when the crystal is very small—a ‘dot’—the bands
are no longer a continuum of orbitals, but individual quantised orbital energy levels
(Figure 11
...
At the same
FIGURE 11
...
See
colour insert following page 356
...
As the size of the
crystal continues to shrink, so does the number of orbital energy levels decrease and the
Solid state chemistry
422
band gap increases
...
The band gap in CdSe crystals, for example, is approximately 1
...
5 nm, but approximately 3 eV for crystals of diameter 1
...
Quantum dots are nanometre scale in three dimensions, but structures that are only
nanometre scale in two dimensions (quantum wires) or one dimension (quantum wells or
films) also display interesting properties
...
Schematic, theoretical density of states
diagrams for bulk material, quantum wells, quantum wires, and quantum dots are
pictured in Figure 11
...
Figure 11
...
The density of states for carbon nanotubes is predicted to show sharp peaks
(known as van Hove singularities) corresponding to specific energy levels
...
In Figure 11
...
We associate this band gap with semiconductors
...
Electrical conductance in solids (other than ionic conductors) depends on the
availability of delocalised orbitals close enough together in energy to form bands
...
3 Theoretical density of
states diagrams for (a) bulk material,
Nanoscience
423
(b) quantum well, (c) quantum wire,
and (d) quantum dot
...
4 The density of states
for a semiconducting nanotube
...
Under
certain conditions, electrical conductance through a nanostructure is quantised and
increases in a stepwise fashion with increasing voltage
...
5)
...
The
conductance thus drops until the voltage is increased to a value V such that the energy,
e×V, is sufficient to raise the energy of the electrons in the adjacent solid so that they can
reach the next energy level, when the current increases again
...
6, for example,
depicts the increase of conductance with gate voltage along a quantum wire connecting
two GaAs/AlGaAs interfaces in a transistor
...
2
...
Solid state chemistry
424
The last section revealed that semiconductor band gaps for nanostructures vary with
the size of the structure
...
Thus, different
colour fluorescence emission can be obtained from different-sized particles of the same
substance (e
...
, different sized quantum dots of CdSe irradiated with UV emit different
colours of light)
...
An electron is excited to a
FIGURE 11
...
Nanoscience
425
FIGURE 11
...
level in the conduction band, from where it reaches the lowest energy level in the
conduction band through a series of steps by losing energy as heat
...
7)
...
7(a)
depicts the irradiation of a large quantum dot (smaller band gap)
...
If the
smaller quantum dot (larger band gap) (Figure 11
...
From the Einstein equation E=hv, the higher energy photon will have the higher
frequency and thus be closer to the blue end of the spectrum, accounting for the
difference in colour
...
Thus, 5
...
3 nm diameter particles emit turquoise light
...
7 The colour of the
fluorescence from a nano-sized particle
depends on its dimensions
...
...
For example, 11
...
2 nm show features resembling molecular absorption
bands shifted about 200 nm to shorter wavelengths, as depicted in Figure 11
...
The colours produced by nanoparticles of gold (colloidal gold) have been used since
Roman times where we find them in the glass of the famous Lycurgus cup (British
Museum) which appears green in reflected light and red in transmission
...
In metals, light interacts with surface electrons and is
then reflected
...
8 The absorption
spectrum of 11
...
2 nm
show features resembling molecular
absorption bands shifted about 200 nm
to shorter wavelengths
...
The oscillation frequency, and hence the colour,
depends on the size of the particle
...
Oscillation frequencies in the visible region are only observed for Ag, Au, Cu, and their
alloys, as well as the Group 1 metals
...
The even smaller nano-sized particles, however, are
transparent because the scattering efficiency is reduced
...
These will still absorb ultraviolet light but will
scatter less visible light
...
2
...
Domains typically have
dimensions of approximately 10 to 1000 nm
...
Such single
domain crystals have all the electron spins in the crystal aligned
...
3
...
If the crystal size is reduced, as the single domain region is
approached, it becomes harder to demagnetise the crystal by applying a magnetic field
...
If the particle size is decreased still further, however, the number of
spins decreases and the force aligning them becomes weaker
...
The crystal is then no longer ferromagnetic but
superparamagnetic
...
9 is a plot of the magnetic field needed to demagnetise
ferromagnetic particles
FIGURE 11
...
The
particle becomes single domain at
radius Dc
...
The radius DC is that at which the
particle becomes single domain
...
1
...
Below the blocking temperature, there is insufficient kinetic energy to overcome the
energy barrier to reorientation of the spins
...
In the superparamagnetic state, the particles, like
paramagnetic solids, do not show hysteresis
...
When nanosized
grains are in close contact, the magnetic effects can differ
...
Chapter 9 revealed that thin layers of magnetic
material could have the spin state pinned by an adjacent antiferromagnetic
TABLE 11
...
Exchange coupling between grains of hard and soft magnetic materials can produce
nanocomposites with high remanence and high coercivity, that is they remain strongly
magnetic when the applied magnetic field is reduced to zero and need a large magnetic
field to de-magnetise them
...
2
...
For example, down to µm-size grains, the resistance to plastic deformation
increases with decreasing grain size
...
The effect has been attributed to a different
mechanism for plastic deformation in nano-sized grains
...
Such movements are
inhibited by grain boundaries
...
Eventually, as the grain size
reaches 5 to 30 nm, movement of dislocations becomes negligible, but deformation
through atoms sliding along grain boundaries becomes favourable
...
11
...
6 MELTING
Nanocrystals show a melting temperature depression with decreasing size
...
The surface energy becomes an increasing
factor as the size of a crystal becomes smaller; thermodynamics predicts a lowering of the
melting temperature if the surface energy of the solid is higher than that of the liquid
...
3 EXAMPLES
To bring some semblance of order to such a huge and diverse area, we have grouped our
examples under 1-D, 2-D, and 3-D headings, where 1-D refers to materials with one
dimension in the nanometre range and are extended in two dimensions; 2-D is confined to
nanometres in two dimensions but extended in one dimension; and 3-D is confined to
nanometre dimensions in all three directions
...
3
...
For example, nanoscale coatings to
protect and enhance modern plastic spectacle lenses have been developed, including selfassembling top coatings for nonreflective lenses to protect the antireflective
FIGURE 11
...
layer from dirt, dust, and skin oils as well as super-hard coatings of carbides to protect
from scratching
...
10)
...
)
The development of electronics using organic compounds (see Chapter 6) has led to
nanofilm electronic devices
...
Two types of displays are used: thin-film transistor liquid-crystal display (TTFLCD) and organic light-emitting diodes (OLEDs)
...
By
making the bank of transistors a film of organic material 20 nm thick instead of a 2 mm
thick layer of silicon, thinner, lighter, more flexible screens can be produced
...
The flexibility of thin film organic electronic devices means that they can be printed
onto paper and material
...
The incorporation of electronics into cloth has inspired
some interesting proposals for their use
...
Another suggestion is for LEDs to be printed onto
curtains to provide light when the curtains are closed
...
The electronic and magnetic properties of nanolayers are important in devices formed
from electronic materials that are more conventional
...
Quantum well lasers may be an important
component of light-based computers
...
2)
...
3
...
Similar in structure to buckyballs, they
consist of sheets of graphite which roll up to form cylinders
...
Single-walled
nanotubes, SWNTs (Figure 11
...
The tubes are capped at each end by half of a fullerene-type structure
...
They can adsorb 100 times their volume of hydrogen and, therefore, could be developed
as a safe storage medium for hydrogen for fuel cells (see Chapter 5)
...
They can also be made as conductors and semiconductors, and one use has
been found in car bumpers, where they not only provide strength, but also prevent the
buildup of static electricity
...
Graphite itself is a 2-D metal, exhibiting metallic conductivity within the
Solid state chemistry
432
layers
...
12, notice that the line joining rows of
hexagons in the vertical direction is a simple zigzag, but that at right angles to this, socalled ‘armchair lines’ join the rows
...
If graphite
sheets roll up along the zigzag lines, with the armchairs along the axis of the tube (zigzag
nanotubes) or if the sheets roll up along any other
FIGURE 11
...
FIGURE 11
...
direction except the zigzag or the armchair lines, forming helical nanotubes, a band gap is
introduced, and the tubes can be semiconducting
...
At the time of writing, no preparative method is available for making
the type of nanotube needed consistently, they have to be selected by hand from mixtures,
but it is hoped that advances will eventually allow the miniaturization of circuitry well
beyond that of the silicon chip and ultimately to a molecular computer
...
Safety Concerns
Early experiments involving the exposure of mice to nanotubes show that they develop
an immune response to them, causing the nanotubes to clump together when inhaled
causing lung tissue damage
...
Nanowires
Nanowires with lengths of several micrometres and diameters of <20 nm have been made
from various semiconducting materials, for example, silicon, indium phosphide, and
gallium nitride
...
Nanowires can also be deposited from a flowing liquid causing them to lie in the same
direction and forming arrays
...
The thrust of this type of research is aimed at miniaturization, and
ultimately with producing a molecular computer
...
3
...
In catalysis, this is exploited to improve the rate
of production in commercial processes, and in the structure of electrodes to improve the
performance of batteries and fuel cells (see Chapter 5, Section 5
...
4 and Chapter 7,
Section 7
...
6)
...
Because the dimensions of nanoparticles are less than the wave-length of visible light
(400–700 nm), visible light is no longer scattered by them, rendering them transparent;
this is a useful property for the manufacture of cosmetics and coatings
...
Within the modern era,
since the turn of the 20th century, carbon black has been produced for use in printing inks
and from the 1940s fumed silica (small particles of silica) has been added to solids and
liquids to improve the flow properties
...
5)
...
Indeed, 50 nm nanoparticles of
cobalt tungsten carbide are found to be much harder than the bulk material
...
Carbon Black
Carbon black is made by the vapour-phase incomplete pyrolysis of hydrocarbons to
produce a fluffy fine powder
...
It is
used as a reinforcing agent in rubber products such as tyres (20–300 nm), as a black
pigment (<20 nm) in printing inks, paints, and plastics, in photocopier toner, and in
electrodes for batteries and brushes in motors
...
The
resulting SiO2 particles with dimensions 7 to 50 nm, have an amorphous structure
...
When added to liquids this
3-D network traps the liquid and increases the viscosity, but when the thickened liquid is
subsequently brushed out or sprayed, the liquid and any trapped air is released
...
This property is known as thixotropy,
and is very useful in paints for preventing the settling of pigments, and for improving the
flow properties of paints, coatings, and resins
...
Quantum Dots
A quantum dot or nanocrystal is defined as a crystal of a semiconductor which is a few
nanometres in diameter typically containing only 102 to 104 atoms
...
2, quantum dots exhibit quantum-size effects in their physical properties,
having interesting electronic, magnetic, and optical properties which are a consequence
of their size rather than their chemical composition
...
3 nm gives out turquoise fluorescent light when irradiated with
UV light, but a dot of dimension 5
...
7)
...
Considerable practical difficulties arise in making quantum dots of a regular size and
shape, and in preventing the dots, once made, from coalescing into a larger crystal
...
The size of the dots is controlled by the time they remain in the
hot liquid
...
Now we must ask how the unusual properties of quantum
dots are being exploited
...
As
we have seen, quantum dots of different sizes emit light of different wavelengths, and if
made reliably to a particular size, can be used to make LEDs, but of a very pure colour
...
The purity of the colour produced by quantum dots is also leading to research into
their use in special dyes and polymers which could be used, for instance, to combat
counterfeiting, as they will be extremely difficult to reproduce
...
They have been used both in vivo and
in vitro; if they can be attached to a biological molecule of interest, such as an antibody
or a protein, they can be used to follow the reactions of that molecule
...
In an area of interest which has already been discussed (Chapter 7, Section 7
...
This gives the prospect of forming new semiconducting materials useful for data storage
...
Research is also looking at the possibility of a quantum dot laser, which would allow
rapid light pulses from a minute source to further increase the speed of circuitry and
communications
...
Explosives
Aluminium particles are made with diameters in the range of 20 to 200 nm, with a
protective shell of aluminium oxide about 4 nm thick and, mixed with a suitable
oxidising agent, are used for rocket propulsion fuels
...
This is the reaction
traditionally used to weld rail tracks together in situ: 2Al(s)+Fe2O3(s)=2Fe(l) + Al2O3(s),
which produces so much heat that molten iron is produced, but it can also be used to
produce other less easily reduced metals, such as Mo, from their oxides
...
Solid state chemistry
436
Magnetic Nanoparticles
Nanoparticles of iron oxides (γ-Fe2O3 or Fe3O4) are superparamagnetic, having zero
remanence, that is, a magnetic field induces magnetism which disappears when the field
is removed
...
The particles are coated with a functional group that will
attach to the required component in the solution
...
Iron oxide nanoparticles, acting as contrast agents, are used to enhance magnetic
resonance imaging (MRI) scans
...
There are other promising medical uses for these magnetic nanoparticles
...
If a drug molecule could be attached
to the surface of a magnetic nanoparticle, then a magnetic field could be used to draw the
drug toward the site of the infection, thus targetting the drug more efficiently
...
These were invented by NASA as a way to control
liquid rocket fuels in space, because the flow can be controlled by magnetic fields
...
A magnetic fluid containing nanoparticles
of iron nitride (Fe3N) in kerosene has been produced by reacting iron carbonyl (Fe(CO)5)
and ammonia
...
Cobalt clusters embedded in silver display giantmagnetoresistance (GMR), with an
increase in resistance of up to 20%, and are used for magnetic recording and data storage
...
Silver nanoparticles have been found to have very good antibacterial action, and are being used to impregnate bandages; they are also used to
impregnate socks and added to underarm deodorants because the antibacterial action kills
the bacteria responsible for the unpleasant smells
...
TiO2 (and ZnO) has been used in sunscreens for many years because of its
ability to absorb the ultraviolet (UV) radiation which is harmful to the skin
...
Its use in the sunscreens and
sunblocks with the highest factor numbers has, for many years, made them appear white
on the skin and not very attractive
...
Larger nanoparticles of
TiO2 are being used to impregnate fabrics to make clothing with a built-in sun protection
...
Many people still feel that there may be safety issues to consider in the
use of nanoparticles in sunscreens and cosmetics, as little is known about their
metabolism and absorption through the skin
...
Possible methods of preventing free-radical production
include coating or doping the particles
...
Nanoparticles of zirconium oxide (ZrO2) are being used in the new UVcured dental fillings
...
Rare-earth oxides can also be used
...
4 MANIPULATING ATOMS AND MOLECULES
Perhaps one of the most awesome achievements of recent technological advances has
been the development of techniques that can deal with single atoms or molecules
...
One of the drivers for this research has
been the production of ever yet smaller electronic circuits
...
Currently, the patterns are
produced using photolithography, but the spacing of components using this technique is
limited by diffraction effects to about 100 nm
...
It is possible to use variations
on the existing approach by, for example, using UV radiation, X-rays, or electron beams
in place of visible light
...
For example, if a current is passed
through the probe tip raising its temperature, it can soften a thermoplastic polymer in the
immediate vicinity of the tip producing a small indentation
...
Because we want to concentrate on chemistry at the single-molecule level, we
have chosen to look at methods of producing integrated circuits only when they involve
this latter approach
...
4
...
As explained in Chapter 2, in STM experiments, a sharp metallic tip formed by
etching a wire to a very fine point (as small as 20 nm in diameter) is brought close to a
conducting or semiconducting surface
...
Electrons from the surface travel to the tip through quantum
mechanical tunnelling, producing a current measured in nanoamperes
...
A picture of the surface can be built up by keeping the current constant and
Solid state chemistry
438
recording the changes in distance needed
...
As well as presenting a picture of the surface and any molecules on it, STM can also
be used to move atoms and molecules across a surface and to make molecules react
...
If this force is attractive, moving the tip across
the surface pulls the molecule along after it
...
Figure 11
...
FIGURE 11
...
(Reprinted with
permission from the Annual Review of
Physical Chemistry, vol
...
annualreview
...
Hla and Karl H
...
)
Repulsive forces between the tip and surface (produced by reversing the sign of the
voltage) can push molecules away from the tip across the surface
...
The famous
picture of xenon atoms forming IBM on a nickel surface was produced by increasing the
voltage so that the Xe became attached to the tip, sliding the atom across the surface, and
then decreasing the voltage again at the position required
...
The energy
can both dissociate bonds and provide the activation energy for bond formation
...
4
...
The most broadly
applicable is atomic force microscopy (AFM)
...
The standard method
does not yield any information as to the composition of surface species, but by attaching
a particular molecule to the tip, the AFM can be made responsive to certain molecules or
groups of molecules and not others
...
AFM is often used to study
biological molecules and some groups have used modified tips to extract particular
molecules, for example proteins from cell membranes
...
One example is the application of a voltage to an AFM tip to oxidise strips of silicon
with nanometre dimensions
...
Dip-pen Lithography
In dip-pen lithography, molecules (such as thiols) are placed on the AFM tip and
delivered to a substrate surface (such as gold) via a water meniscus
...
In damp air, a water meniscus
Solid state chemistry
440
naturally forms between the tip and the sample so that when the tip is close to the
substrate the molecules are delivered to the surface via the meniscus, and form a selfassembled monolayer
...
The size of the deposit is dependent on the tip radius of curvature, the
relative humidity (which controls the size of the water droplet) and any diffusion of the
molecules across the surface
...
The technique has the advantage that the same instrument can be used to both build the
nanostructure and image it
...
One tip is slightly (0
...
The other tips all lay
down identical structures
...
4
...
11
...
4 OPTICAL TWEEZERS
The interaction between the electric dipole of light and the polarisability of molecules or
dielectric particles produces a force of the order of piconewtons
...
Presently, building up a
structure in this way is too slow to be technologically useful
...
4
...
By modifying the DNA so that a compound only attaches
to some sequences in a DNA strand, we can ensure that a following reaction takes place
only where that compound is, or only where it is absent
...
A protein
was then polymerised on a probe DNA molecule
...
Thus, specific lengths of DNA were
covered by the protein and others left bare
...
Where aldehyde groups were free (i
...
, not covered by the filament), the silver nitrate was
reduced to silver
...
This produced a gold wire that was a few
micrometres long and 50 to 100 nm in width
...
4
...
A
method has been put forward that involves a large array of AFM tips and a polymercoated storage disk
...
The polymer in the immediate vicinity of the tip is softened
Nanoscience
441
producing a small indentation
...
This system is expected to
increase storage capacity by a factor of more than 20, which is sufficient, for instance, to
turn a mobile phone into both a computer and music player
...
org/)
...
R
...
Cox, P
...
(1987) The Electronic Structure and Chemistry of Solids, Oxford University Press,
Oxford
...
K
...
(eds
...
Bruce, D
...
(eds
...
,
Chichester
...
and Dwight, K
...
, New York
...
T
...
West, A
...
(1995) Basic Solid State Chemistry, 2nd edn, John Wiley and Sons Ltd
...
Rao, C
...
R
...
(1997) New Directions in Solid State Chemistry, 2nd edn,
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E
...
CHAPTER 1 CRYSTALLOGRAPHY AND SYMMETRY
Wells, A
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Hyde, B
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and Andersson, S
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Hahn, T
...
) (1987) International Tables for Crystallography, Vol
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Cotton, F
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(1971) Chemical Applications of Group Theory, 2nd edn, John Wiley, New York
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A
...
F
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(1996) The United Kingdom Chemical Database
Service, J
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Inf
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Sci
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LATTICE ENERGIES AND BORN-HABER CYCLES
Johnson, D
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(1982) Some Thermodynamic Aspects of Inorganic Chemistry, 2nd edn, Cambridge
University Press, Cambridge
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K
...
(1987) Solid State Chemistry: Techniques, Oxford University Press,
Oxford
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A
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, Rankin, D
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H
...
(1991) Structural Methods in Inorganic
Chemistry, 2nd edn, Blackwell Scientific Publications, Oxford
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F
...
and Palmer, R
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(1993) Structure Determination by X-ray Crystallography, 3rd edn,
Plenum, New York
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L
...
E
...
) (1989) Modern Powder Diffraction: Reviews in Mineralogy, Vol
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C
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W
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Catlow, C
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A
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N
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Young, R
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(1993) The Rietveld Method, International Union of Crystallography, Oxford
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(1998) Crystal Structure Determination, Oxford University Press, Oxford
...
W
...
(2001) True Optical Microscopy, Mater
...
CHAPTER 3 SYNTHESIS
Rao, C
...
R
...
Mater
...
, 9, 1–14
...
(ed
...
Rao, C
...
R
...
(eds
...
Opinion Solid
State Mater
...
Rao, C
...
R
...
(eds
...
Opinion Solid
State Mater
...
Segal, D
...
(1994) Chemical Synthesis of Advanced Ceramic Materials, Cambridge Univer-sity
Press, Cambridge
...
M
...
Society Rev
...
Patil, K
...
, Aruna, S
...
, and Mimani, T
...
Opinion
Solid State Mater
...
CHAPTER 4
Moore, W
...
(1967) Seven Solid States, Chapters II and III, W
...
Benjamin Inc
...
McWeeny, R
...
Cox, P
...
(1987) Electronic Structure and Chemistry of Solids, Chapters 1, 4, and 7, Oxford
University Press, Oxford
...
R
...
Duffy, J
...
(1990) Bonding, Energy Levels and Bands in Inorganic Solids, Chapters 4 and 7,
Longman, London
...
M
...
Kittel, C
...
Further reading
444
CHAPTER 5 NON-STOICHIOMETRY
Tilley, R
...
D
...
Greenwood, N
...
(1968) Ionic Crystals, Lattice Defects and Non-stoichiometry, Butterworths
...
M
...
A
...
, (2001) Understanding Batteries, The Royal Society of Chemistry,
Cambridge
...
fuelcells
...
CHAPTER 6 REVIEWS
Higgins, S
...
, Eccleston, W
...
, and Raja, M
...
Clery, D
...
CHAPTER 7
Breck, D
...
(1974) Zeolite Molecular Sieves, John Wiley, New York
...
M
...
Dyer, A
...
Catlow, C
...
A
...
) (1992) Modelling of Structure and Reactivity in Zeolites, Academic Press,
London
...
S
...
C
...
Opinion Solid State Mater
...
Maschmeyer, T
...
Opinion Solid State Mater
...
CHAPTER 8
Duffy, J
...
(1990) Bonding, Energy Levels and Bands in Inorganic Solids, Longman, London
...
M
...
V
...
P
...
Today (October
2000), 31–6
...
Photonic crystals, Sci
...
(December 2001), 47–55
...
Goodman, C
...
R
...
Further reading
445
CHAPTER 9
Awschalom, D
...
E
...
Spintronics, Sci
...
, (June 2002) 68–73
...
and Julien, R
...
Newnham, R
...
, Trolier-Mckinstry, S
...
R
...
CHAPTER 10 BOOKS
Buchel, W
...
Waldram, J
...
(1996) Superconductivity of Metals and Cuprates, IOP, London
...
et al
...
Vanderah, T
...
) (1999) Chemistry of Superconductor Materials, Noyes Publications, Park Ridge,
NJ
...
Industry warms to superconductors, Phys
...
http://physicsweb
...
(1996) Recent developments in the crystal chemistry of high Tc superconductors, Curr
...
Sci
...
Gross Levi, B
...
Today
(March 2000), 17–8
...
, Rice T
...
, and Sigrist M
...
Today ( 2001 January),, 42–7
...
and Buzdin, A
...
Ferromagnetic Superconductors, Phys
...
http://physicsweb
...
Gough C
...
World ( April 2001),
http://physicsweb
...
CHAPTER 11
Nalwa, H
...
(ed
...
Timp, G
...
) (1998) Nanotechnology, AIP Press, College Park, MD
...
Materials Chem
...
[The whole issue is devoted to new developments in
nanomaterials
...
N
...
and Cheetham, A
...
(2001) Science and technology of nanomaterials: current status
and future prospects, J
...
Chem
...
Cox, J
...
Britain, 21–5
...
(a) NF3
...
62(a) shows the threefold (C3) axis and three planes of symmetry
...
Figure 1
...
(c) ClF3
...
62(c) shows the twofold (C2) axis and two planes of symmetry
...
There are four
...
5
...
)
(By choosing a different line, you
and
These are equally
7
...
63 shows the three planes: (a) 100 (b) 110 (c) 111
...
The 110 plane contributes an
area
and contains (2×½+4×¼)=2 atoms
...
414:2
...
atoms
...
9
...
There are (6×½)=3 sulfurs at the centres of the faces and
at the
corners
...
*Answers to even-numbered questions are found in the Solutions Manual
...
62 (a) threefold (C3) axis
in NF3, and three planes of symmetry
in NF3, (b) twofold axis (C2) in SF4,
Answers to Odd-numbered questions*
448
and two planes of symmetry in SF4, (c)
twofold axis (C2) in ClF3, and two
planes of symmetry in ClF3
...
63 The diagrams show
different planes in the face-centred unit
Answers to Odd-numbered questions*
450
cell of the ccp structure: (a) 100, (b),
110, and (c) 111
...
The relative molecular mass of NaCl is (22
...
453)=58
...
Four
molecules are in the unit cell, so the relative mass of the unit cell in kg is:
The volume of the unit cell is:
(564×10–12 m)3=1
...
Assuming that anion-anion contact occurs as in Figure 1
...
15
...
63
...
64) which now has two additional atoms
...
83:2
...
e
...
Remember
that the radius of a tetrahedral hole is
Answers to Odd-numbered questions*
451
FIGURE 1
...
only 0
...
Therefore, although we
can think in terms of the carbon atoms occupying tetrahedral holes in a close-packed
structure, they are actually too big to do so, and so this description this is only useful in
terms of the relative geometry, in the same way as we discussed for the fluorite
structure
...
The Madelung constant, A=−3
...
There are seven ions in the structure in Figure
1
...
First, calculate the contribution to the potential
energy of interactions of the six cations with the central anion
...
Each cation also interacts with a diametrically opposite cation (distance 2r0)
...
99
FIGURE 1
...
19
...
65
...
We wish to calculate [E(S)+E(S−)], which we can do if L(FeS,s) can be calculated
...
If the lattice energy relationship of
equation 1
...
From the cycle in Figure 1
...
9–200=−377
...
21
...
15 to calculate a value for the lattice energy: For NH4Cl,
v=2, Z+=1, Z−=1, r+=151 pm, r−=167 pm, giving L= −679 kJ mol−1
...
58:
The addition of a proton to the ammonia molecule is an exothermic process
...
The spacings for these planes are d100=a,
reflections occur in the order 100, 110, and 111
...
If the 100 and 110 reflections are absent then the crystal is likely to be face-centred
cubic
...
The sin2θ values do not have the ratio 1:2:3:4:5:6:8……, or 1:2:3:4:5:6:7:8……
...
If it is face-centred then the common
factor A will be 0
...
0560= 0
...
Dividing the sin2θ values by the common
factor gives the h2+k2 +l2 values and these are listed in Table 2
...
h k l only takes values where h k l are either all even or all odd, so
the data fits a face-centred cubic structure
...
If the mass of the unit cell contents is M and the unit cell volume is V then the
density, ρ is given by
but
V=(563
...
6 Powder diffraction data for NaCl
θhkl
sin2θ
h2+k2+l2
Hkl
13°41′
0
...
0746
4
200
22°44′
0
...
2052
11
311
28°14′
0
...
2984
16
400
36°32′
0
...
3731
20
420
42°0′
0
...
5036
27
511, 333
50°36′
0
...
6529
35
531
55°2′
0
...
7462
40
620
The mass of one mole of
NaCl=(22
...
45)×10–3 kg
dividing by the Avogadro constant we get that the mass of one formula unit of
and if there are Z formula units in one unit cell, then the mass of the unit cell contents is
So
Answers to Odd-numbered questions*
455
and rearranging gives
Z=3
...
Z=4
11
...
7), we know that
A cubic-close
packed structure has a face-centred unit cell
...
Thus,
and
and
In a close-packed structure where the atoms are considered to be in contact, the radius
of an atom, r, is ¼ of the length of the body-diagonal
...
732×363
...
4 pm
13
...
The 001 is not observed for F, but would be present in a P unit cell
...
Answers to Odd-numbered questions*
456
15
...
If you mark these values on the chart in Figure 2
...
17
...
After treatment with SiCl4, (b) the amount of Al in
the framework has been reduced considerably, but a very strong peak exists due to
[A1C14]− (at 100 ppm) and a peak due to octahedral aluminium at 0 ppm
...
19
...
The second exotherm at 90°C does not coincide
with any weight loss and must therefore be due to a phase change (this is the
melting temperature)
...
ANSWERS TO CHAPTER 3
1
...
The reactants would have to be very well mixed and the reaction
vessel would have to be closed to prevent loss of the volatile sulfur (see SmS
preparation)
...
Advantages—more homogeneous product with a smaller range of grain sizes; thin
layers can be formed for microcapacitors
...
5
...
A method that
employs temperatures of this order and can produce compounds in unusual
oxidation states is hydrothermal synthesis
...
The tetrapropylammonium ion acts as a template and directs the formation of the
network of channels around the propyl ligands
...
9
...
Thus, the crystals grow at the hotter end of the tube
...
For the Fermi level in sodium, E=4
...
11×10–31 kg
...
5×10–19=½×9
...
9×105 m s−1
3
...
11×10–31×4
...
055×10–34)3
=2
...
135×1022
(c) 0
...
As you can see, the agreement between the number of filled levels
predicted by this very simple theory and the number needed to accommodate the
available electrons is very good
...
5
...
Carborundum like silicon and germanium has 4N valence electrons for a crystal of
N atoms
...
ANSWERS TO CHAPTER 5
1
...
10 Schottky defect concentration in
MX compound at various temperatures
Temperature °C
Temperature K
ns/N
ns/mol−1
27
300
3
...
33×106
227
500
3
...
15×1013
427
700
3
...
08×1016
627
900
1
...
45×1017
3
...
It does, however, increase the value of σ (and thus of Inσ) in the extrinsic
region
...
46)
...
5
...
This means
that the coulombic interactions will be stronger and thus the energy of defect
formation will be higher (see Table 5
...
7
...
3(c) is surrounded by six
anions at distance and by four cations at a distance of 0
...
The interstitial site
at the body-centre of the unit cell in Figure 5
...
43a and by six cations at a distance of
For the normal anion site:
r=0
...
5 ×537×10–12 m
and Z=−1, for interaction with the six anions
...
302×10–19 J) (6
...
84×10–18 J
For the interstitial site:
=−(4
...
395)
=−2
...
32×10–18 J)−(−2
...
2×10–19 J
The experimental value for fluorite is given in Table 5
...
49×10–19 J
...
I−, S2−, Se2−, and Te2− are all polarizable anions
...
Unit cell volume is (428
...
8513×10–29 m3
...
86×0
...
00)]/(NA×103) kg,
giving a density of 5
...
85)+(4×16
...
910)]/(NA×103) kg
giving a density of 6
...
13
...
We would expect,
therefore, that the density would be lower than that of the colourless crystal
...
Titanium vacancies: There are 8 at the corners (8×⅛)=1, and (2× ½)=1 on cell
faces
...
Cell faces, (8×½)=4 on the top and bottom
...
The titanium
stoichiometry of the unit cell is obviously representative of the whole structure: of the 12
sites, 10 are occupied, and 2 are vacant
...
Oxygen vacancies: cell faces, (4×½)=2
...
Cell edges, (8×¼)=2
...
17
...
For every absent Ti2+ ion
there must be two Ti3+ present or one Ti4+
...
Figure 5
...
Within the boundary,
one group of four edge-sharing octahedra and four [WO6] octahedra are present
...
ANSWERS TO CHAPTER 6
1
...
It is likely
that this is also delocalised over the conjugated double bond and hence to the
benzene ring of the next unit
...
3
...
5)
5
...
The conducting properties of solids like TTF-TCNQ
arise from partial transfer of electrons from one type of molecule to the other
...
Answers to Odd-numbered questions*
460
FIGURE 6
...
Therefore, HMTTF-TCNQF4 has no partially full bands and hence is not a metallic
conductor
...
Figure 6
...
ANSWERS TO CHAPTER 7
1
...
26 shows that the most likely Si environment for zeolite A is
Si(OAl)3(OSi)
...
It was
spectroscopic work on this structure (and on zeolite ZK-4) that eventually
confirmed the Si(OAl)4 structure of zeolite A with strict alternation of Si and Al
and led to the extended ranges shown in the chart
...
This system demonstrates reactant shape-selective catalysis
...
5
...
The straight-chain n-hexane can pass
through the windows and undergo reaction but the branched-chain 3-methylpentane
is excluded
...
7
...
This indicates a
decrease in the covalent bond strength making ionization of H+ easier (i
...
, an
increase in acid strength)
...
In Mn2+, an electron can only go from one 3d level to another if it changes its spin
...
3
...
When
the phosphor is illuminated, electrons are promoted to the conduction band
...
5
...
In photo-voltaic cells, electrons are
promoted from the valence band to the conduction band and are then used to do
electrical work
...
In LEDs, the return of the
electrons to the valence band by emitting light is important
...
Promotion to the conduction band in the solar cell will also be of
low probability, but no competing non-radiative route is available
...
The photonic band gap wavelength increases as the size of the spheres increase, so
that it will be larger for the longer wavelength orange-red colours
...
Because the Mn atoms are further apart, the overlap of the 3d orbitals will be less
...
With a narrower
band, there is a larger interelectronic repulsion, and a state with a number of
unpaired spins comparable to the number of atoms becomes favourable
...
3
...
The net moment of the
Fe3+ ions is zero
...
5
...
Answers to Odd-numbered questions*
462
ANSWERS TO CHAPTER 10
1
...
Because of the ordered
collective motion, scattering from defects—tripping over potholes—cannot take
place! The analogy breaks down in that it allows for overlap only between adjacent
pairs rather than over large numbers; in addition, the loss of superconductivity
leads to the scattering of individual electrons, not of individual Cooper pairs
...
Material
Order Parameter Symmetry of
Spin State
Metals and Alloys
s-wave
singlet
Superconducting Cup rates
d-wave
singlet
Ferromagnetic Superconductors
p-wave
triplet
Index
1–2–3 superconductor, YBa2Cu3O7−x, 346
3Ca3(PO4)2
...
c
...
6H20, 60
CuFe2O4, 126
cubic close-packing, ccp, 3, 31
cubic structure, 8
Curie law, 314
Curie temperature, 315
cyclic hydrocarbons, 274
Czochralski process, 148
D
d
...
Josephson effect, 343
DIAMOND, 104
DNA, 376
DSC, 114
DTA, 113
DVD, 305
467
Index
d-wave order parameter, 350
DaimlerChrysler, 206
Daresbury, UK, 104
data reduction, 95
de Broglie relationship, 97
Debye-Scherrer method, 82
defect cluster, 217
degeneracy, 157
degree of covalency, 50
density of a crystal, ρ, 87, 214
density of states, 116, 158, 358
depletion regions, 169
desalination, 274
destructive interference, 85, 93
dextrorotatory, 51
diamagnetism, 314, 340
diamond, 29, 36, 39, 51, 57, 80
diamond films, 144, 357
dielectric heating, 135
dielectric susceptibility, 332
differential scanning calorimetry, DSC, 114
differential thermal analysis, DTA, 113
diffraction grating, 79
diffractometer, 82, 95
diffusion, 183
dihexyl ether, 288
dimerization of oleic acid, 288
diopside, 59
dioptase, 60
dipole-dipole interaction, 29, 53, 112
dip-pen lithography, 375
direct band gap, 301
direct methods, 96
dislocation, 175, 222
domain, 189, 321, 363
doped or extrinsic semiconductors, 168
doped poly acetylene, 245, 247
doping, 182
double electron affinity, 69
double exchange, 330
double shear, 228
drying agents, 273
E
EDAX, 102
eg, 172, 295
ESR, 211
EXAFS, 104
EXPO 67, 256
edingtonite, 266
effective ionic radii, 46
468
Index
469
effective nuclear charge, 46
Einstein, Albert, 355
Einstein equation, E=hv, 362
electric dipole, 53
electrical conductivity, 319
electrical polarisation, 331
electrical resistance, 161
electrochemical cell, 198
electrochromic devices, 209
electrode, 198
electrode material, 192
electrolyte, 198
electron affinity, E, 63, 69
electron density distribution, 94
electron density map, 46
electron (particle) in a box, 155, 212, 305
electron spin resonance, ESR, 211
electronic charge, 64
electronic conduction, 220
electronic watches, 323
electrophotography, 167
electrostatic attraction, 29
emerald, 60
emf, 198
enantiomorph, 18, 51
endothermic process, 178
energy band, 163
energy density, 199
energy dispersive analysis of X-rays, EDAX, 102
Engelhardt, G
...
, 112
enstatite, 59
enthalpy change, 62, 70
enthalpy of formation, 181
entropy, 178
epitaxy, 146, 227
ethanoic acid, 290
ethene, 290
ethyl acetate, 290
EuO, 338
exchange coupling, 365
exchangeable cations, 264, 273, 288
extended covalent arrays, 50
extended defects, 222
extended X-ray absorption fine structure, EXAFS, 104
extended-calculation values, 67
extrinsic defects, 175, 186, 212
extrinsic region, 187
F
Fcalc or Fc, 96
FAU, 285
Index
FETs, 170, 367
F-centre, 211
face-centred unit cell, 21
Faraday, Michael, 362
fast-ion conductors, 189
faujasite, FAU, 262, 285
Fe(MgFe)O4, 41
Fe(ZnFe)O4, 41
Fe2O3, 136
Fe3O4, 41, 136, 147, 214, 217, 327
FeTiO3, 44
FeO, 214, 233, 325
FeS2, 338
feldspars, 60
Fermi level, 158, 163, 318
ferrimagnetism, 100, 315, 327
ferrites, MFe2O4, 131, 326
ferroelectric, 130, 334
ferrofluids, 371
ferromagnetism, 100, 315
ferromagnetic domains, 363
ferromagnetic superconductors, 351
Feynman, Richard, 355
fibrous zeolite, 266
field-effect transistors, FETs, 170, 367
fine structure, 107
fission, 97
flame fusion, 148
float-zone process, 150
flotation method, 214
fluorescence, 360
fluorescent light tubes, 298
fluorite structure, 35, 177, 193, 212, 218
flux, 150
Fobs, Fo, 96
forbidden transitions, 294
form factor, 93
formula unit, 30, 32
Fourier series, 94
Fourier transform, 94
fractional coordinates, 27, 94
freeze-drying, 130
Frenkel defects, 175
Frohlich, 344
fuel cells, 202
fullerenes, 257
fumed silica, 369
G
GMR, 328, 372
GaAs, 146, 171, 299, 304
470
Index
GaP, 171, 303
GaSb, 171
gallium arsenide, GaAs, 146, 171, 299, 304
gallium arsenide laser, 304
gallophosphate, 286
garnets, 59
gas constant, 180
gas sensors, 246
gasoline, 278
gaussian, 91
Ge, 51, 165, 173
gel, 131
geodesic dome, 256
germanium, 51, 165, 173
giant magnetoresistance, GMR, 328, 372
giant molecule, 51
Gibbs free energy, 180, 198, 201
glide plane, 17
glycol, 288
gold, 302
Goldschmidt, 46
grain boundary, 175, 222, 365
grains, 210
granite, 62
graphite, 51, 253
graphite intercalation compound, 151
Greatbatch, Wilson, 199
Grenoble, 98
Grubb, Willard, 204
Grove, William, 204
H
hcp, 3
H-centre, 212
HMTTF-TCNQ, 257
HMTTF-TCNQF4, 257
HREM, 102, 214
H2O, 57
Hagman, and Kierkegaard, 197
half metals, 331
hard disk read-heads, 329
helical nanotubes, 367
helices, 51
hemimorphite, 59
Hermann-Mauguin notation, 10
Hess’s Law, 62
hexagonal close-packing, hcp, 3
hexene, 288
HfO2, 194
Hg0
...
2Ba2Ca2Cu3O8+0
...
11A12O3, 195
Na2S2O3, 211
NaCl, 30, 36, 46, 62, 65, 68, 80, 93, 175, 184, 211
NaCl (rocksalt) structure, 325, 338, 356
NaNO2, 338
Nafion, 206
nanocomposites, 369
nanocrystal, 370
nanoparticles, 369
nanoscience, 355–6
nanostencils, 375
nanotechnology, 356
nanotubes, 204, 257, 359, 367
nanowires, 368
Nb3Ge, 345
Nb3Sn, 352
NbO, 173
NbTi, 352
Nd2−x ThxCuO4−y, 350
Nd2CuO4, 350
Nd2Fe14B, 319
Nd2−xCexCuO4−y, 350
near-field scanning optical microscopy, NSOM, 101
Néel temperature, 315, 325
Nernst equation, 193, 208
neutron diffraction, 97, 214, 272, 325, 338
neutron scattering factors, 98
NiAs, 33
NiO, 136, 233, 325
nickel arsenide structure, 33
Niedrach, Leonard, 204
Nobel prize, 77, 79, 169, 243, 256, 339, 355, 373
non-radiative transitions, 295
non-stoichiometric compound, 212
non-stoichiometric oxides, 234
nuclear charge, 47
nuclear reactor, 97
O
OLED, 366
O2PtF6, 72
OF2, 12
Oak Ridge, 98
476
Index
477
oblique unit cell, 16
Ochsenfeld, and Meissner, 340
octahedra, 34, 39, 41
octahedral holes, 3, 31, 34, 36, 39, 41–42, 44–45, 58, 177, 257
octane-number, 276
octant, 36, 178
olivine, 58, 59
one-dimensional lattice, 15
one-dimensional solid, 155
opals, 310
optical fibres, 133, 306
optical tweezers, 375
order parameter, 345
organic light-emitting diodes, OLED, 366
orthosilicates, 58
orthosilicic acid, 58
ortho-xylene, 280
oxygen meter, 194, 207
oxygen sensor, 194, 207
P
PEO, 252
PEM, 206
PZT, 336, 338
p-n junction, 169, 304
p-type semiconductor, 168, 237
p-type superconductors, 349
p-wave order parameter, 350
packing efficiency, 3, 8
packing of spheres, 1
paramagnetism, 314
para-xylene, 280
Patterson method, 96
Pauli paramagnetism, 319, 325
Pauling, 46, 67
Pb3O4, 136
PbF2, 177
PbO2, 136
PbZrO3, 336
Peierl’s theorem, 246, 248
pentagonal column structures, 229
pentasil, 267
permanent magnets, 323
permeability of free space, µ0, 313
permittivity of a vacuum, 64
perovskite, 40, 42, 172, 329, 334, 346
petrol, 278
petroleum cracking, 288
phase, 92
phase diagram, 214
phase problem, 95
Index
phillipsite, 266
phonons, 161, 344
phosphors, 298
phosphorus, 51
photocatalyst, 366
photoconductors, 167
photodetector, 93
photographic emulsion, 210
photographic process, 176
photonic band gap, 309
photonic crystals, 308
piezoelectric effect, 138, 332
pigment, 286
pillared clays, 152, 288
piston and cylinder apparatus, 142
planar defects, 222
plane of symmetry, 10
plasma fusion, 150
plastic deformation, 365
point defects, 175, 210
point symmetry, 10
polar molecule, 54
polarizability, 48, 68, 191, 307
polarization correction, p, 95
poly(epichlorohydrin), 252
poly(ethylene imine), 252
poly(ethylene)oxide, PEO, 252
poly(ethylene)succinate, 252
poly(propylene)oxide, 252
polyacetylene, 243
polyaniline, 245, 285
polyester fibres, 280
polymer LED, 247
polymorph, 33, 57
polyphenylvinylene, 245
polythiophene, 245
polyvinylidene fluoride, 336, 338
pore-openings, 276
pores, 259, 260, 265
port, 265
potassium buckide, 257
powder diffraction pattern, 81
Pratt, and Whitney, 204
Prewitt, and Shannon, 46
precursor method, 130
primary battery, 188
primitive cubic structure, 6
primitive unit cell, 16
product-selective catalysis, 278
proton affinity, 69
proton exchange membrane fuel cells, PEM, 206
pyroelectric, 333
478
Index
pyrophyllite, 288
pyroxenes, 59
Q
quantum dot, 287, 358, 370
quantum mechanical tunnelling, 305, 329
quantum size effects, 287, 370
quantum wells, 305, 359
quantum wires, 359
quantum-cascade lasers, 147
α-quartz, 332
quartz, 51, 138, 140, 260
quartz watches, 333
R
R factor, 96
radial distribution function, 108
radiationless transition, 296
radius ratio, r+/r−, 47, 49
Rayleigh scattering, 307
RbAg4I5, 192
RbCl, 67
reactant-selective catalysis, 278
rechargeable battery, 152
reflection, 8, 80
reforming reaction, 204
refractive index, 307
remanent magnetisation, 323
ReO3, 41, 223
residual index, R, 96
resonance scattering, 98
Rh2O3, 41
rhenium trioxide structure, 40
rhombic dodecahedron, 189
Rietveld analysis, 90, 100, 272
Rochelle salt, 333
rock salt structure, 30, 45, 175
rocket propulsion fuel, 371
Rohrer, and Binnig, 373
Röntgen, 77
rotational axes, 8
rotational symmetry, 8
Royal Institution, 362
rubidium chloride, 67
ruby laser, 296
Rutherford laboratory, 98
rutile structure, 37
S
SAPO, 285
SEM, 101
479
Index
480
S3−, 286
SOD, 285
SOFC, 205
SQUID, 352
SSI, 197
STEM, 103
STM, 114, 373
SWNT, 367
(SN)x, 248
samarium sulfide, 128
Sc2Si2O7, 59
scanning electron microscopy, SEM, 102
scanning microdensitometer, 93
scanning transmission electron microscopy, STEM, 103
scanning tunnelling microscopy, STM, 114, 373
scattering factor, 93, 107
Schoenflies notation, 10
Schottky defects, 175
Schrödinger equation, 156
scintillation counter, 93
screening of nuclear charge, 47
screw axis, 17
second ionization energy, 71
secondary batteries, 189
selection rules, 293, 299
selenium, 51, 167
self-propagating high-temperature synthesis, 136
semiconductor, 166, 287
sensitizers, 211
Shannon, and Prewitt, 46
shape-selective catalysis, 276, 278
Si, 173
Si(OH)4, 57
SiC, 51, 173
SiO2, 39, 51, 57, 61, 126, 138
silica, SiO2, 39, 51, 57, 61, 126, 138
silicalite, 263, 268
silicates, 30, 55
silicon, 51, 57, 165, 173
silicon carbide, 51, 173
Silsbee effect, 343
silver sulfide, 192
simultaneous equation, 218
single crystal X-ray diffraction, 91
single-walled nanotube, SWNT, 367
site symmetry, 14
skull melting, 150
SmCo5, 319, 323
smectite clay, 288
smoky quartz, 212
SnCl2, 136
SnO, 136
Index
481
sodalite, 260, 286
sodalite, SOD, 285
sodium chloride, see NaCl
sodium sulfur battery, 201
sodium thiosulfate, 211
sodium zirconium phosphate, 197
sodium β-alumina, 195
sol-gel method, 131
solid electrolytes, 188
solid oxide fuel cells, SOFC, 194, 205
solid-state batteries, 198
solid-state ionic devices, SSIs, 197
space groups, 20
space-symmetry, 10
spallation source, 98
specific energy, 199
spin exchange coupling, 364
spinel, 41, 195
spin-spin coupling, 363
spontaneous emission, 294, 296
spray-drying, 130
Sr2RuO4, 351
SrCl2, 67
SrCuO2F2+δ, 349
SrF2, 177
SrHfO3, 43
SrSnO3, 43
SrTiO3, 43
SrVO3, 172
SrZrO3, 43
stabilized zirconia, 193
stack, 206
stained glass, 369
standard enthalpy of formation, 62
statistical mechanics, 178
Steno, 15
stimulated emission, 294
Stirling’s approximation, 179
Stockbarger method, 148
stoichiometric defects, 175
storage batteries, 188
straight chain alkanes, 274
strontium chloride, 67
structure factor, Fhkl, 94
sunscreens, 363, 372
superconductivity, 248, 257
superconducting magnets, 352
superconducting quantum interference devices, SQUIDs, 352
superconducting critical temperature, Tc, 340
superexchange, 325
superlattice, 218, 220
superparamagnetism, 363
Index
482
superstructure, 218
surfactant, 140
symmetry, 9
symmetry element, 10
symmetry operation, 10
synchrotron radiation, 104
synthesis wave, 136
synthetic diamond, 142
systematic absence, 84, 87
T
t2g, 172, 295
TDS, 118
TEM, 101
TGA, 114
TMR, 330
TMTSF, 248
TPD, 118
TPO, 118
TPR, 117
TPS, 118
TTF-LCD, 366
TTF-TCNQ, 248
talc, 60
television, 298
tellurium, 51
temperature gradient, 139
temperature programmed desorption, TPD, 118
temperature programmed oxidation and sulfidation, TPO and TPS, 118
temperature programmed reduction, TPR, 117
template, 140, 272, 283, 286
terephthalic acid, 280
tetragonal, 39
tetrahedral, 257
tetrahedral hole, 4, 34–6, 41, 58, 177, 185
tetra-n-propyl ammonium ion, 286
thermal analysis, 113
thermal desorption spectroscopy, TDS, 118
thermal motion, 96
thermite reaction, 371
thermochemical cycle, 70
thermochemical radii, 69
thermogravimetric analysis, TGA, 114
thin-film transistor liquid-crystal display, TTF-LCD, 366
thixotropy, 369
ThO2, 177, 194
Thomas, 290
thortveitite, 59
Ti2N, 39
Ti2O3, 41
TiO, 172, 220, 234
Index
TiO1
Title: SOLID state
Description: Easy understanding and applied solid state book written by Smart and Moore
Description: Easy understanding and applied solid state book written by Smart and Moore