A common formalism for excess energy expressions is the Redlich-Kister-Muggianu relation, which for a binary system can be written as

Gex = X, XjX Lk, ij(X, — Xj)k [11]

k

where L is the coefficient of the expansion in k, which can also have a temperature dependence typically of the form a + bT. Thus, a regular solu­tion is defined as k equals zero leaving a single energetic term. This approach is related to the Bragg-Williams description, with random mixing of constituents yet with enthalpic energetic terms such that

Gex = XaXbEbw [12]

Here, XAXB represents a random mixture of A and B components and is thus the probability that A-B is a nearest-neighbor pair, and EBW is the Bragg — Williams model energetic parameter.

In a relevant example, Kaye eta/.16 have generated a solution model for the five-metal white phase noted above and more extensively discussed in Chapter 2.20, Fission Product Chemistry in Oxide Fuels. A binary constituent of the model is the fcc-structure Pd-Rh system, which at elevated temperatures forms a single solid solution across the entire compositional range. The phase diagram of Figure 2 also shows a low — temperature miscibility gap, that is, two coexisting identically structured phases rich in either end member. The excess Gibbs free energy expression for

the fcc phase was determined from an optimization using tabulated thermochemical information together with the phase equilibria and yielded

Gex = XPdXRh [21247 + 2199XRh

-(2.74 — 0.56XRh)T] [13]