A density-functional theory of nonuniform fluid mixtures—based on a generalization of the one-component weighted-density approximation—is both presented and applied to freezing transitions in binary mixtures of hard spheres. A necessary step in this application is the specification of the crystal structure of the solid phase. Several different structures have been considered, namely, a disordered-fcc structure, three common ordered structures—the CsCl, NaCl, and zinc-blende structures—and a ‘‘sublattice-melt’’ structure (modeling fast-ion conductors). In the case of the disordered-fcc structure, results are reported for the temperature-concentration phase diagram and for freezing parameters, including the coexisting fluid and solid packing fractions, the latent heat of transition, and the Lindemann ratios. Especially interesting is the dependence of these results on the hard-sphere diameter ratio α. In particular, as a function of α the phase diagram is predicted to evolve from a spindle type in the range 1>α>0.94, to an azeotropic type in the range 0.94>α>0.87, and finally to a eutectic type for α<0.87. In comparison with available simulation data, the predictions of the theory are in excellent agreement when normalized to account for small discrepancies in the one-component case, yet in qualitative disagreement with the predictions of earlier density-functional theories, based on different approximations.

Also investigated are the relative stabilities, as a function of α, of the different crystal structures in coexistence with a fluid of equal concentrations of smaller and larger spheres. In particular, in the range 1>α>0.76 the most stable structure is predicted to be disordered fcc. For α<0.76 the two components are found to be completely immiscible in the disordered-fcc solid and the most stable structure is then predicted to be a pure fcc solid composed entirely of larger spheres. The ordered CsCl and NaCl structures are predicted to be metastable (relative to the stable structures) in the ranges 0.86>α>0.63 and 0.63>α>0.05, respectively, the sublattice-melt structure metastable (relative to NaCl) in the range 0.60>α>0.15, and the zinc-blende structure always mechanically unstable. These results for the relative stabilities are again in considerable disagreement with predictions of earlier theories.

• Received 13 August 1990

DOI:https://doi.org/10.1103/PhysRevA.42.7312