Weighted-density-functional theory of nonuniform fluid mixtures: Application to freezing of binary hard-sphere mixtures

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Abstract
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