Purpose
1.
To investigate the
heterogeneous equilibrium between solid and liquid phases of a two-component
system.
2.
To construct the phase diagram
by measuring the cooling curves.
3.
To determine the eutectic
temperature and composition of the mixture.
Principles
Solid-liquid
phase diagrams are of great value in the technical study of alloys, ceramics
and in the recovery of a salt by crystallization from a mixture of salts. The
binary solid-liquid phase diagram in Figure 1 shows the stability of different
phases as a function of temperature at a given pressure. This example shows a
case where the two substances are miscible in the liquid state and insoluble in
the solid state. In this diagram we are plotting temperature versus the mole
fraction of substance B. At the left, the curve intersects at the melting point
of pure A or pure B. This is a phenomenon of freezing point depression. The
minimum in the freezing-point curve is called the eutectic, and a horizontal
line has been draw along the eutectic temperature.
Figure
1.
To
construct a phase diagram for a binary mixture, phase transition temperature
data for mixtures of different compositions of the two components must be
collected. This can be achieved by recording cooling curves for the different
mixtures as shown in Figure 1. Samples containing known amounts of both components
are places in containers and heated until completely melting. Then allow it to
cool slowly and measure the temperature at regular time intervals. Cooling
curve 1 in figure 1 is for pure A. The sample cools at an approximately
constant rate. Once the temperature is reached melting point of A, a “halt” is
observed in the cooling curve. The temperature of the substance remains
constant until all of the sample freezes. Then the temperature drops rapidly
again. The same thing happens at the composition of a eutectic (curve 3) and
pure B (cooling curve 5). Cooling curve 2 is for a mixture with composition
between pure A and the eutectic. On this cooling curve we have a changing point
where solid A is crystallizing out. Because the heat evolved by solidification
partly offsets the heat lost by radiation and conduction to the cold
surroundings, a slow rate of cooling is observed. The melt becomes richer in
component B as component A is separating out, and the freezing point of the
melting decreases along the curve. When we rich point “b” the liquid has
reached the eutectic composition and a “halt” is observed in the cooling curve
(line b-c). At this temperature, both pure A and pure B will crystallize together.
Since three phases are in equilibrium at constant pressure, the number of
degrees of freedom falls to f’ = C- Φ+1 = 2-3+1 = 0. If we
continue to remove heat from the mixture the system will remain at eutectic
temperature until all of the remaining liquid has solidified. Cooling curve 3
is for a mixture with composition between the eutectic and cooling curve 4 is
for a mixture with composition between the eutectic and pure B. For each
mixture studied, the cooling curve is examined to determine the temperatures at
which changes in slope or plateau occur. A phase diagram is prepared by plotting
the points of the corresponding breaks and halts in the cooling curves and
connecting these points by smooth curves.
Chemicals
1.
Tin (metal basis, A.R.)
2.
Bismuth (metal basis, A.R.)
Apparatus
1.
Electronic furnace
2.
Thermocouple
3.
Crucibles
4.
Ebulliometer (use to adjust the
thermocouple)
5.
Barometer
6.
Computer and data receiver
7.
Hardened test tube
Procedure
Preparation of Samples
1.
Prepare 0%、30%、57%、80%、100%(Bi w/w) Bi-Sn
alloy 50g with an analytical balance to nearest 0.0001g.
2.
Add some rosin in the test tube
to prevent the sample been oxidized at high temperature.
Drawing Cooling Curves
1.
Set up the apparatus as Figure 2.
2.
Turn the heater on and adjust
he voltage until all solids melt. Transfer the crucible out from a hotter furnace
to a steel rank to cool down and start recording the temperature.
3.
Repeat these steps for
different samples.
Experimental Record
Sample
|
d.d. H2O
|
Tin
|
Bismuth
|
Melting Point (Literature) (/℃)
|
100
|
232
|
271
|
Experimental (/℃)
|
99.58
|
224.44
|
247.65
|
Table
1.
Cooling Curve of Samples：
Sample Bi/Sn x 100%(w/w)
|
Bi
0%(w/w)
|
Bi
29.97%(w/w)
|
Bi
56.96%(w/w)
|
Bi
80.00% (w/w)
|
Bi
99.99% (w/w)
|
T1
(℃)
|
224.44
|
173.01
|
131.06
|
193.47
|
265.05
|
T2
(℃)
|
-
|
125.86
|
-
|
125.67
|
-
|
Table
1. Raw Data
Analysis
Draw a calibration
curve for the thermocouple set:
Calibration curve
|
y = -3.01901 +
1.03902*x
|
Sample Bi/Sn x 100%(w/w)
|
Bi
0%(w/w)
|
Bi
29.97%(w/w)
|
Bi
56.96%(w/w)
|
Bi
80.00% (w/w)
|
Bi
99.99% (w/w)
|
T1
(℃)
|
230.18
|
176.74
|
130.14
|
198.00
|
254.29
|
T2
(℃)
|
-
|
127.75
|
-
|
127.55
|
-
|
Table
2. Calibration data
Complete the phase diagram with other
known data[1]：
Add some colors and sign：
Finally, analysis the phase diagram
with Gibbs' phase rule: F = C - P + n
here n=1 because it is at a
constant pressure. Then we can get the degrees of freedom of each phase.
Item
|
Phase (P)
|
Degrees of Freedom
|
α
|
1
|
1
|
β
|
1
|
1
|
α+β
|
1
|
2
|
α+L
|
2
|
1
|
β+L
|
2
|
1
|
Liquid phase
|
1
|
2
|
Melting Curve
|
2
|
1
|
Minimum Melting Eutectic Point
|
3
|
0
|
References
[1] 虞覺奇, 易文質. 二元合金狀態圖集. 上海: 上海科學技術出版社,
1995: 250-251
[2] 傅献彩, 沈文霞, 姚天扬. 物理化学, 上册欧4 版. 北京:高等教育出版社, 1990:144.
[3] 清华大学化学系物理化学实验编写组. 物理化学实验. 北京：清华大学出版社, 1991.
[4]
Robert C. Wcast Handbook of Chemistry and Physics. Physics. 58th ed.
Ohio: CRC Press, 1977.
[5] 朱文涛. 物理化学. 北京：清华大学出版社，1995.
[6] http://www.materials.ucsb.edu/~matclass/101/pdffiles/Lecture_13.pdf
