Introduction

We consider the following subjects in this chapter: random solid solutions of binary systems; derivation of the free energy composition relation for such solutions and the free energy of mixtures of solid solutions. This knowledge is then used to determine the equilibrium distribution of phases in a binary system at a given temperature. We then investigate the graphical significance of the partial molar free energy; non-random solutions; and various models for describing the energies and entropies of these solid solutions. Models that evaluate the excess free energy due to difference in atom or ion radius or a difference in bond length between components, the strain free energy, is then investigated. Factors other than atomic size that affect the enthalpy and entropy of solid solutions are briefly considered. Finally, the activity and activity coefficient of solutions are defined and some behavior of these parameters is described.

1. Random Solutions in Binary Systems

1.1. Free energy of a random binary solution

The free energy of a solution is given by

We assume that the enthalpy of the random solution, and its first and second derivatives with respect to composition are finite and continuous functions of composition. These assumptions are in agreement with experimental measurements of the composition dependence of the enthalpy of solutions and with first principle calculations.

In addition to the entropy contributions that exist in the pure components there will be a positional contribution to the entropy of a random binary solution. The latter contribution stems from the fact that...