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Title: Lab report for Alloys experiment
Description: 2nd year lab report with introduction, theory, experimental procedure, results, discussion and references.
Description: 2nd year lab report with introduction, theory, experimental procedure, results, discussion and references.
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Establishing the Lead-Tin Phase
Diagram using Cooling Curves
Sagarika Jain
9587184
School of Physics and Astronomy
The University of Manchester
Second year laboratory report
March 2016
This experiment was performed in collaboration with James Fotheringham
...
Using these cooling curves, a phase diagram was
plotted to find the eutectic concentration and temperature of the mixture
...
74 ±4
...
26 ±4
...
The phenomenon of supercooling was also observed
in the experiment and has been shown by a temperature drop on the cooling curve
...
Introduction
The alloys of tin and lead are widely used as electrical solders [1]
...
In this experiment,
the cooling curves of tin-lead alloys are used to determine the eutectic concentration of the mixture,
which is the concentration at which the mixture acts as a pure substance and solidifies at a single
temperature
...
Eutectic compositions contribute towards a lot of
commercial alloys
...
Casting alloys are also based upon eutectic compositions for minimization of input or alloy
segregation [1]
...
This happens when a
substance is cooled to a temperature less than its freezing point without it turning into a solid
...
A
...
’ [2]
...
When this reduction decreases the melting point to
below the actual temperature at that point, supercooling occurs [1]
...
2
...
The relationship is given by the equation,
𝐹 = 𝐶 − 𝑃 + 2,
[3]
(1)
where F is the number of degrees of freedom, C is the number of components in the system and P
is the number of phases [3] [4]
...
This reduces the Phase rule to
𝐹 = 𝐶 − 𝑃 + 1
...
[3]
2
(3)
This equilibrium will be represented by an open area on the phase diagram with the two variables
being temperature and concentration
...
[3]
(4)
This equilibrium will be represented by a line defining the liquidus state
...
[3]
Lastly, for 3-phase equilibrium,
𝐹 = 2 − 3 + 1 = 0
...
The 3-phase equilibrium, thus,
occurs at a particular concentration and temperature
...
This point is known as the eutectic point [3]
...
The liquidus lines represent the temperature at
which solidification starts and the solidus line represents the temperature at which solidification is
complete [5]
...
Experimental approach
The apparatus consisted of a furnace in which varying quantities of lead and tin, measured in a
beam balance, were melted to form alloys
...
A pinch of charcoal dust was added to the mixture to avoid
oxidation of the components of the mixture
...
time chart
recorder that gave the cooling curves
...
Lead melted at 327
...
The chart recorder was calibrated
by plotting the cooling curve of 25 g of pure lead
...
The difference between the initial
and final temperatures divided by the time lapsed then gave the calibration i
...
the value of
temperature that each division on the chart corresponded to
...
12 ±
5
...
The experiment was commenced by obtaining cooling curves of 25g lead and 5g tin and then
increasing the amount of tin by 5g each time till a ratio of 1:1 was obtained
...
The measurements for
the temperature at which the mixture first started solidifying, P, were noted from each cooling
curve
...
concentration graph was plotted to find out the
eutectic concentration
...
Results
The cooling curves for the tin-lead alloys were plotted at 10 different concentrations (as mentioned
in section 3)
...
P
Q
Figure 2: Cooling curve of an alloy obtained from the chart recorder with 62
...
5% Tin
...
Y-axis: temperature, x-axis: time
...
It was observed that lead did not
start freezing at its normal freezing point (327℃)
...
38 ± 5
...
The slope of the graph
then became less steep since the rate of cooling slowed down
...
3 ± 5
...
Below this temperature, the
solid mixture further cooled down with time
...
The P temperature was noted from all the graphs at the different concentrations
...
On the x-axis, there was pure tin at one end and
pure lead at the other
...
Pb = 0
Pb = 100
Figure 3: Temperature vs
...
The eutectic concentration and temperature are marked by the blue lines
...
The
straight line equations for the two lines were equated, with the y-value being the eutectic
temperature (183℃)
...
This was found to be at 33
...
26% tin
...
The values of m and c and the errors on them were found using the
linearfit function of MATLAB
...
The error on concentration was thus calculated to
be ±4
...
74 ±4
...
26 ±4
...
At the eutectic concentration, the cooling curve of the alloy looked like that of a pure substance
...
5% lead and 62
...
The mixture solidified at one temperature (Q) and there was no
defined value of P
...
5% tin and 32
...
This mixture acts closely like a
eutectic mixture and it can be seen that there is no defined value for P and the mixture solidifies at
Q, the eutectic temperature (where the graph goes horizontal)
...
A dip in the temperature can be seen
in Figure 5 before the substance freezes completely
...
6
Supercooling
Fugure 5: Cooling curve of 25g of tin
...
This is due to supercooling
...
Discussion
The melting points of tin and lead from literature are 232℃ and 327 ℃ [7] and the values measured
from the cooling curves were 327
...
In the cooling curve (Figure 2), at temperature P, the lead starts solidifying but the tin
remains molten
...
At Q, the curve becomes horizontal and the mixture solidifies as a whole
...
The values of eutectic
concentration and temperature from literature are 61
...
The eutectic
concentration lies within one standard deviation of the measured value showing that the
experimental value is quite accurate
...
This could have
been minimized by using a more precise chart recorder in which one division corresponded to a
lesser value of temperature and running the recorder at low chart speeds
...
6
...
The freezing point where the entire mixture
solidifies remains same for varying concentrations and is also the eutectic temperature, 183℃
...
At the eutectic point, 33
...
References
[1] Campbell, FC, Elements of Metallurgy and Engineering Alloys, ASM International , 1st
Edition, 2008
...
[3] Ashraf, AM, A Laboratory Manual of Metals and Alloys, I
...
International Publishing
House Pvt
...
, 2009
...
[5]
co
...
html> Metal Basics, Martin Tarr,
Date accessed (09/03/2016)
[6]
nist
...
html>Phase
Diagrams
and
Computational Thermodynamics, National Institute of Standards and Technology, Date
accessed (09/03/2016)
[7] Duncan, A, The Technique of Leaded Glass, Dover Publications, Inc, 1st Edition, 1975
[8] Tan, AC, Tin and Solder Plating in the Semiconductor Industry, Chapman & Hall, 1st
Edition, 1993
Title: Lab report for Alloys experiment
Description: 2nd year lab report with introduction, theory, experimental procedure, results, discussion and references.
Description: 2nd year lab report with introduction, theory, experimental procedure, results, discussion and references.