Sublattice solution phases

In the substitutional solutions discussed in Section 20.4 all lattice sites were equivalent and a solution was formed from a pure substance by substituting new kinds of atoms for the initial one. However, relatively few crystalline phases belong to this class. The great majority have different kinds of lattice sites and can be described by using two or more sublattices. Examples of such phases will be discussed in this chapter. It will be demonstrated that a great variety of such phases can be modelled in a very direct way using an approach often called the compound energy model or formalism. It is a crude model in the sense that it assumes random mixing within each sublattice. The expression for the entropy of such phases is simple and was presented in Section 19.8, ‘Restricted random mixtures’, but the excess Gibbs energy can easily become very complicated. However, it should be realized that actual calculations of equilibria, and even of whole phase diagrams, can now be carried out with sophisticated computer programs which only require that the expression for the molar Gibbs energy of each phase is defined.

Section 19.8 gave the expression for the entropy assuming random mixing of all the components present in each sublattice. The result was expressed in terms of the site fraction variable, yi, and in Section 19.10 it was then applied to interstitial solutions, which are a special case of solution phases with sublattices.