Solid solutions should be distinguished from composites,which are mate-
rials formed from two or more solid components that never actually dissolve.
Recall that a solution is a mixture that has a consistent composition through-
out the system. For example, salt water has a consistent composition at a
macroscopic level, even though it is composed of H 2 O and NaCl. However,
plywood does not, since it is easy to see that it is composed of layers of differ-
ent material. Composites are not true solid solutions.
For solid/solid solutions, the interesting phase change occurs between pos-
sible different solid phases and between solid and liquid phases. In fact, there
is a similarity between liquid-gas phase changes and solid-liquid phase changes,
which is that the compositions of the phases in a system at equilibrium are not
necessarily the same. For solid/solid solutions, the composition of a liquid
phase in equilibrium with a solution is a point that must be considered.
The following example shows that the Gibbs phase rule holds for solid so-
lutions as well.
Example 7.12
For a temperature-composition phase diagram of a two-component solid so-
lution, how many degrees of freedom are necessary to describe the system in
the following cases?
a.The system is completely solid.
b.There is an equilibrium between solid and liquid phases.
In each case, suggest what variables the degrees of freedom might be.Solution
a.Using the Gibbs phase rule, for a one-phase solid solution we would have
FCP 2 2 1 2
F 3
The degrees of freedom might be pressure, temperature, and mole fraction of
one component. (The other mole fraction is determined by subtraction.)
b.For the case of a solid in equilibrium with a liquid phase, we have
FCP 2 2 2 2
F 2
In this case, we might specify temperature and mole fraction of one compo-
nent. Since we know that there are two phases in equilibrium, the pressure is
dictated by the phase diagram and the equilibrium line between solid and
liquid phases at a particular composition and temperature.An understanding of temperature-composition phase diagrams for solid-
liquid phase changes (the most common type) of solid solutions includes an
issue brought up in the last section. When a liquid solution reaches a temper-
ature at which solidification occurs, usually a pure phasesolidifies from the so-
lution. In doing so, the remaining liquid becomes more concentrated in the
othercomponent. This sounds like fractional distillation, and suggests that a
phase diagram like Figure 7.10 or 7.11 might be applicable to solid-liquid
phase changes, also. However, it is a little more complicated than that.
First of all, it should be understood that the addition of any solute lowers
the freezing point of any solvent—a topic considered in more detail later. For
7.7 Solid/Solid Solutions 189