Vacancy thermodynamics for intermediate phases using the compound energy formalism

The compound energy formalism is widely used for thermodynamic descriptions of intermediate phases containing vacancies. For a two-sublattice model, represented by (A,B,Va)0.5:(A,B,Va)0.5(A,B,Va)0.5:(A,B,Va)0.5, it is physically necessary to take the reference state Gibbs energy of the pure vacancy end member, GVa:Vao, as zero, irrespective of temperature, pressure, or the chemical composition and structure of the actual intermediate phase containing the vacancies. This assumption leads to more than one possible solution for the calculated value of the equilibrium vacancy concentration. The assumption can be avoided if the compound end members are regarded as cluster solution members and an ideal dilute solution reference state is used for the vacancy clusters. In this case, GVa:Vao does depend on the host as well as on temperature and pressure. An analysis of the thermodynamic properties of the B2 phase in the Al–Ni system is used as a demonstration of this alternative view.