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

The density-functional theory of freezing is extended to investigate the crystallization of binary hard-sphere mixtures. As the ratio of diameters α=α₁α₂ is lowered, the fluid-solid phase diagram for disordered alloys evolves from a spindle shape (1>α>0.94) into an azeotropic diagram (0.94>α>0.92) and finally into a eutectic diagram (0.92>α>0.85). Below α=0.85, nearly complete immiscibility is predicted, in agreement with the empirical Hume-Rothery rule for metallic alloys.