Crystal-melt interfacial free energy of binary hard spheres from capillary fluctuations

Using molecular-dynamics simulation coupled with an analysis of equilibrium capillary fluctuations in interfacial position, we compute the magnitude and anisotropy of the interfacial free energy gamma for a binary hard-sphere system with a diameter ratio alpha=0.9. This system, in which the fluid mixture coexists with a randomly substituted face-centered-cubic solid solution, is a useful reference model for alloys. Our results show that gamma increases with increasing mole fraction of the smaller sized particle when temperature is held constant. However, after rescaling the results to fixed pressure and varying temperature, we find that gamma decreases with increased alloying by the smaller particle (corresponding to lower temperatures). Thus, gamma is seen to decrease with increasing concentration of the lower melting point solute, consistent with earlier simulations on Ni/Cu and Lennard-Jones mixtures. The anisotropy in gamma is such that the inequality gamma(100)>gamma(110)>gamma(111) holds for all concentrations studied. Using the classification scheme of Haxhimali , [Nat. Mater. 5, 660 (2006)] we find that the anisotropy in gamma is consistent with a predicted < 100 > primary dendrite growth direction.