A quasicrystalline model of a binary liquid in which two sublattices containing randomly distributed vacancies is developedvia statistical thermodynamics. The relative partial molar quantities are obtained. The constraints imposed upon the adjustable model parameters to ensure that the Schottky constant increases with increasing temperature but never exceeds unity are developed, as well as the constraints entering upon application to a AC system forming a congruently melting, narrow homogeneity-range compound AC (s). The model is an extension of an earlier version for liquids and of analogous models for narrow homogeneity-range compounds, AC (s), in that the excess Gibbs energies of vacancy creation are cubic functions of the atomic fraction. The model is also an alternative to associated solution models which would assume a single equiatomic associated species. The model is then applied to systems of varying polarity but all forming a narrow homogeneityrange crystalline compound whose stoichiometric composition is 50 at. pct. Quantitatively good fits are obtained for the Hg-Te, Cd-Te, Zn-Te, and Pb-Te systems and, for the first three systems, are comparable to fits obtained with the associated solution model using the same experimental data. Quantitatively good fits are also obtained for the less polar In-Sb and Ga-Sb systems, and these are comparable to those obtained by us with a Margules-type model in which the enthalpy of mixing for the liquid is a quartic function of atom fraction and a quadratic function of temperature. Finally, the predictions for the enthalpy of mixing at temperatures above the present range of experimental data are given and discussed for the various systems and models. It appears the model given here is appropriate for the type of systems tested.