Density-Functional Theory of Freezing of Hard-Sphere Mixtures into Substitutional Solid Solutions

Abstract

The density-functional theory of freezing is extended to investigate the crystallization of binary hard-sphere mixtures. As the ratio of diameters $\alpha =\frac{{\alpha }_1}{{\alpha }_2}$ is lowered, the fluid-solid phase diagram for disordered alloys evolves from a spindle shape ($1>\mathrm{}\alpha >0.94\mathrm{}$) into an azeotropic diagram ($0.94>\mathrm{}\alpha >0.92\mathrm{}$) and finally into a eutectic diagram ($0.92>\mathrm{}\alpha >0.85\mathrm{}$). Below $\alpha =0.85\mathrm{}$, nearly complete immiscibility is predicted, in agreement with the empirical Hume-Rothery rule for metallic alloys.