Conditions for De-Mixing of Solutions

Abstract

The expression for Gibbs’ free energy per gram-atom for the ideal solution:

$$ G = \bar{G}_{A}^{0}{X_{A}} + \bar{G}_{B}^{0}{X_{B}} + RT\left( {{X_{A}}\log {X_{A}} + + {X_{B}}\log {X_{B}}} \right) = {G_{0}} + \Delta {G_{m}}, $$

where:

$$ \mathop G\nolimits_0 = \mathop {\bar G}\nolimits_A^0 \mathop X\nolimits_A + \mathop {\bar G}\nolimits_B^0 \mathop X\nolimits_B , $$

shows that at constant pressure and composition the solid solution will always be more stable than any other combination such as, for example, the mixture of the pure constituents by mechanical means. In fact, the curve ΔG _m of excess free energy of mixture takes the form shown in Figure 6 whatever the temperature, always concave upwards. This is because the entropy of mixing is always positive, whence the second term of the preceeding expression is always negative. Thus there is no possibility of de-mixing whatever the temperature:

$$ \Delta {G_{m}} = RT\left[ {{X_{A}}\log {X_{A}} + {X_{B}}\log {X_{B}}} \right] \leqslant 0. $$