Physical Chemistry Third Edition

6.6 Phase Diagrams of Nonideal Mixtures 287

7798 C

9618 C

10838 C

7798 C

700

900

1100

600

tC

/^8 C

Time

0.00 0.20 0.40

Mole fractions of copper

0.60 0.80 1.00

Figure 6.19 Cooling Curves for the Silver–Copper System.From R. E. Dickerson,

Molecular Thermodynamics, W. A. Benjamin, Inc., New York, 1969, p. 371.

Solid–liquid phase diagrams like that of Figure 6.18 can be constructed by analyzing

experiments in which a mixture of known composition is heated above its melting point

and then allowed to cool slowly. Figure 6.19 showscooling curvesrepresenting the

temperature of mixtures of silver and copper as a function of time for various mole

fractions of copper. The cooling curves for the pure substances (mole fraction 0.00

and 1.00) exhibit horizontal line segments representing freezing of the substance. The

temperature of the pure substance cannot drop below its freezing temperature until all

of the liquid has frozen. The cooling curve for copper mole fraction equal to 0.80 drops

smoothly until a copper-rich solid solution begins to freeze out at about 950◦C. At this

point the slope of the curve changes but the cooling curve does not become horizontal.

The principal reason for this is that the composition of the liquid changes as the solid

solutionβis removed since the solid solution is richer in copper than the liquid solution.

The slope of the curve is less steep than that of the first portion because the enthalpy

change of freezing is being evolved. When the eutectic temperature is reached at 779◦C,

a second solid solution, mostly silver and saturated in copper, begins to freeze out. With

three phases present the temperature must remain constant. A horizontal portion of the

cooling curve results, called theeutectic halt. Only when the system is entirely frozen

can the temperature drop further. The phase diagram is constructed by plotting the

points at which the slope of the cooling curve changes.

Phase diagrams can also be constructed from data obtained by the technique of

differential scanning calorimetry(abbreviatedDSC). In this technique a sample of the

material to be studied is placed in a small pan with a cover, usually made of aluminum,

since aluminum has a rather large thermal conductivity. The sample can be as small as

10 mg, which makes the method quite versatile. An identical pan is usually left empty,

but could contain a blank substance. Each of the pans is fitted with a temperature-

measuring device and an electrical heater. Both of the pans are gradually heated and

the amount of electrical energy added to each pan is monitored.

The additional electrical energy required to maintain the sample pan at the same

temperature as the blank pan is determined as the temperature is increased. The heat