Page 127 - Instant notes

Phase diagrams of mixtures 113

At state point d, the boundary with the solid A and solid B region is reached. Here the
remaining liquid solidifies to form solid A and solid B before passing into the two-phase
solid region on further cooling and on to state point e.
The same procedure can be used at high x A to show that the region bordered by the
freezing point curve and the horizontal line at the temperature T eu must consist of the
two-phase region where solid A and liquid are in equilibrium. This means that cooling
past the freezing point will produce an increasing amount of solid A and a liquid richer in
B until, at T eu, solid A and solid B are formed.

Cooling curves

The easiest way experimentally to study the cooling of mixtures is by producing a
cooling curve. From the example above (Fig. 2a), the cooling curve is produced by
removing energy from the system at a composition x A1, cooling the liquid from its state
point a at a constant rate, whilst monitoring the change in temperature, T, of the system
with time, t (Fig. 2b).
Initially, simple cooling of the liquid occurs and the temperature decreases linearly
with time. At the temperature T b corresponding to state point b, solid B will start to form.
The formation of intermolecular bonds in solid B is exothermic and will give out heat,
slowing the cooling rate of the system and leading to a break in gradient of the curve, or a
break point. As the system is cooled further through state point c, solid B continues to be
produced and the cooling continues to be slowed but at the point d and the temperature
T eu, the boundary with the two-phase solid A and solid B region, the first solid A starts to
form. This means that there are three phases at equilibrium, and from the phase rule,
F′=3−P=0; as a consequence, the temperature cannot vary without first changing the
number of phases present, and so the temperature decrease stops. This is called a halt
point. During this time, energy is still being removed from the system and the liquid is
being steadily converted to solid A and solid B at a constant rate, but the heat removed
from the system is exactly balanced by the heat given out by the solidification process.
The halt point lasts until all the liquid has been converted to the solids A and B, which
means that the length of the halt point is proportional to the amount of liquid that
remained when the system reached the solid A and solid B boundary, given by the Lever
rule. Then, as the number of phases, P, is reduced to 2 again, and as no more energy can
be evolved by the solidification process, the cooling of the system is resumed.
In contrast, cooling a liquid system at the eutectic composition, x eu, produces a very
different cooling curve (Fig. 2c). On cooling the liquid from state point h, the system
does not enter either two-phase region where solid and liquid are present, and therefore it
is the only composition on the diagram to not show a break point. At state point i, the first
solid A and solid B are formed, and three phases (solid A, solid B and liquid) are present.
This again results in a halt point, but this is the longest possible halt point, as all the
liquid must be converted to solid A and solid B before cooling can recommence.
Thus phase diagrams can be used to predict cooling curves at any composition. In fact,
the reverse is also true, and experimental cooling curves, measured across the
composition range, are the usual method by which experimental phase diagrams are