Calculation of the crystal-melt interfacial free energy for the binary hard-sphere system with the diameter ratio of 0.9 at the azeotrope

Using the analysis of equilibrium cappillary fluctuations in molecular dynamics simulations,we compute the magnitude and anisotropy of the interfacial free energy $\gamma$ of the crystal-melt interface for the binary hard-sphere system with $\alpha = 0.9$ at the azeotrope. We found $\gamma_{100} = 0.62(2)$, $\gamma_{110} = 0.60(2)$, and $\gamma_{111} = 0.58(2)$. We compare our results with the values of the interfacial free energy of the same system but at points other than azeotrope, as well as with the interfacial free energy of a single hard sphere system. Our results show the relation $\gamma_{100} > \gamma_{110} > \gamma_{111}$ being consistent with the simulation results for various metals, Lennard-Jones (LJ) system, and single hard-sphere system.