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Title: Atomic bonding and crystal structure
Description: These notes contain whole chapter of Atomic bonding and crystal structure
Description: These notes contain whole chapter of Atomic bonding and crystal structure
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Atomic Bonding
and
Crystal Structure
Metallic Bond
F
F
ก
F
Electron
ก
F
ก
F
Electron Charge Cloud
F F
F
Fก
F
F
F
กก Fก
ก
ก
ก
F ก ก
ก
ก
F
F
F F
F
ก F Interatomic Distance
F
ก F
a0 = 2 R
ก
Bonding Energy = E0 - Emin
F Bonding Energy
F
Crystal Structure
Principle Metallic Crystal Structures
Body Centered Cubic
Face Centered Cubic
Hexagonal Closed Pack
BCC
FCC
HCP
Body Centered Cubic
a 2 + a 2 = 2a 2
= 2a
a
a
( 2a ) + a
2
2
= 2a 2 + a 2
= 3a
a
2a
Atomic Packing Factor (APF)
APF = total sphere volume
total unit cell volume
=
Vatom
4 3 1 4 3
= (1) πR + (8) πR
8 3
3
= 8
...
32 R 3
a=
3a = 4 R
3
Vatom 8
...
68
3
Vunit 12
...
35092 nm
...
Face Centered Cubic
Vatom
1 4 3
1 4 3
= (6 ) πR + (8) πR
8 3
2 3
16 3
= πR
4
3
a=
R
Vunit = a
3
a3 =
2a = 4 R
Vatom
APF =
Vunit
3
R3
2
64 3
=
R
2 2
=
16 3
πR
= 3 3
= 0
...
2
...
ก
F
F F
F
Fก 1
ก
F F F กF 1
F
x, y
x,y,z
Cubic
F
z
Atomic Position in Cubic Unit Cell
Direction in Cubic Unit Cell
F
F
F
[ xyz ]
F F comma
ʽ F Square Bracket
Direction in Cubic Unit Cell
ก
ก Destination
F
ก
Origin
2
...
F F
Square Bracket
xyz
F comma
4
...
Direction in Cubic Unit Cell
Direction in Cubic Unit Cell
Example
( 1 ,1, 1 ) − (0,0,0) = [ 1 − 0,1 − 0, 1 − 0]
2
2
2
2
= [ 1 ,1, 1 ]
2
2
= 2 × [ 1 ,1, 1 ]
2
2
= [121]
Direction in Cubic Unit Cell
Example
(− 2 ,1, 1 ) − (0,0,0) = [− 2 ,1, 1 ]
3
3
3
3
= 3 × [− 2 ,1, 1 ]
3
3
= [ 2 31]
Direction in Cubic Unit Cell
Exercises
Draw the following direction vectors in cubic
unit cells
a)[100]and [110]
b)[112]
c)[ 1 10]
d )[ 3 2 1 ]
[???]
[???]
Crystallographic Plane in Cubic Unit Cells
Crystallographic Plane in Cubic Unit Cells
ก
1
...
ก
3
...
ก
ก xyz
F
F
F
F
F
F
5
...
361 nm
...
361
2
2
2
(2) 2 + (2) 2 + (0) 2
= 0
...
Family of Direction and Plane
Some planes and directions are “Crystallographic equivalent”
Directions
[100], [010], [001], [100], [010], [001]
< 100 >
Planes
(100), (010), (001)
{100}
Comparison of FCC and HCP
Volume and Planar Density Calculations
Volume Density
mass / unit cell
ρv =
volume / unit cell
= g / cm3
Volume and Planar Density Calculations
Cu has FCC crystal structure and an atomic radius of 0
...
Calculate a
theoretical density of copper in g/cm3
...
54 g/mol
2a = 4 R
4 R (4)(0
...
361 nm
2
2
m
ρv =
v
(4 atom)(63
...
22 ×10 − 22 g
6
...
361×10 m) = 4
...
70 ×10
− 23
3
cm
− 29
m
3
3
− 22
m 4
...
98 3
− 23
3
v 4
...
of center of atom
ρp =
selected area
= atoms / mm 2
Volume and Planar Density Calculations
Calculate the planar atomic density on the (110) plane of α iron in
atoms/mm2
...
287 nm
...
2
2
nm 2
2 (0
...
2 × 10
mm 2
( )
Crystal Structure Analysis
Off-Phase
In-Phase
nλ = MP + PN
nλ = 2d hkl sin θ
λ = 2d hkl sin θ
X-Ray
Diffractometer
Example
A sample of BCC iron was placed in an x-ray diffractrometer using incoming
x-rays with a wavelength 0
...
Diffraction from the {110} planes was
obtained at 2θ = 44
...
Calculate a value for the lattice constant a of BCC
iron
...
704o
θ = 22
...
1541 nm
=
= 0
...
3803)
a = d hkl h 2 + k 2 + l 2
= 0
...
2026 nm)(1
...
287 nm
Title: Atomic bonding and crystal structure
Description: These notes contain whole chapter of Atomic bonding and crystal structure
Description: These notes contain whole chapter of Atomic bonding and crystal structure