Computer simulation of solid-liquid coexistence in binary hard sphere mixtures

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Abstract
We present the results of a computer simulation study of the solid-liquid coexistence of a binary hard sphere mixture for diameter ratios in the range 0·85 ⩽ ğa ⩽ 1>·00. For the solid phase we only consider substitutionally disordered FCC and HCP crystals. For 0·9425 < α < 1·00 we find a solid-liquid coexistence curve of the ‘spindle’ type. For α = 0·9425 this becomes an azeotropic and for α = 0·875 a eutectic diagram. We compare these results with the predictions of the density functional theory of Barrat, Baus and Hansen. We observe that the density functional theory accurately predicts the point where the spindle diagram transforms into an azeotrope. However, the density functional theory differs from the simulation results on a number of counts. The greatest differences between computer simulations and theory are that the changeover from an azeotropic to a eutectic diagram is found to occur at α = 0·875, rather than at the predicted value of α = 0·92, that the density difference between the solid and the liquid at liquid-solid coexistence is found to have a minimum as a function of the mole fraction of the large spheres, while density functional theory predicts a maximum, and finally that the solubility of large spheres in a solid mixture of small spheres is much larger than predicted.