Thermodynamic modelling of vacancies as a constituent

The role of vacancies in thermodynamic models based on the compound energy formalism, CEF, is studied by application to a binary phase with two sublattices where the two components occupy one sublattice each. Vacancies were introduced in CEF by considering them as a chemical component. It is argued that this is not correct and their content is rather an internal variable. The variation in constitution is illustrated with a square-shaped diagram with corners representing the end-members. On two sides, the model degenerates to substitutional models of vacancies in either component. They meet in a corner representing only vacancies. For consistency, it may seem that all three models should represent the same physical state in that corner which is not true. The conflict was resolved by studying the molar Gibbs energy expressions of the models. The problem with multiple solutions is analyzed in terms of a critical state where the first, second and third derivative of the molar Gibbs energy vanish.