A cell theory for solid solutions: Application to hard sphere mixtures

We consider the application of the cell theory to the properties of solid solutions. In contrast with previous implementations of the cell theory for mixtures we include all types of cell partition function which arise from different nearest neighbor compositions and arrangements of the nearest neighbors, a feature which is necessary for a realistic treatment of substitutionally disordered solid solutions with components of different molecular sizes. An efficient algorithm for the simultaneous calculation of all contributing cell partition functions is presented. The theory is applied to the properties of binary hard sphere mixtures forming substitutionally disordered solid solutions. Solid–fluid equilibria are determined by using the cell theory for the solid phase together with an accurate fluid phase equation of state. Good agreement with Monte Carlo simulations is obtained.