Solid-Liquid Phase Diagram - Physical Chemistry - Lu Le Laboratory

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