The kinetic coefficient of hard-sphere crystal-melt interfaces from molecular-dynamics simulations

The kinetic coefficient for a crystal melt interface, $\mu$, is the ratio of the interface growth velocity to the undercooling $(T_M - T)$, where $T_M$ is the melting point. In this work we determine the kinetic coeffiecient for the hard-sphere system by analyzing capillary fluctuations in interface position using molecular dynamics (MD) simulation [Hoyt \emph{et al}, Mat. Sci. Eng. $\bf R~41$, 121-163 (2003)]. We report the kinetic coefficient for the three interfaces: (100), (110), and (111). Our results for $\mu_{100}, \mu_{110}$, and $\mu_{111}$ are 1.15(4) $(k_B/(m T_M))^{1/2}$, 0.85(6) $(k_B/(m T_M))^{1/2}$, and 0.57(8) $(k_B/(m T_M))^{1/2}$, respectively, which gives the relation $\mu_{100} > \mu_{110} > \mu_{111}$. This ordering is consistent with the recent results of MD simulations for a variety of metals. The anisotropy ratios $\mu_{100}/\mu_{110}$, and $\mu_{100}/\mu_{111}$ are 1.35(11), and 2.0(3), respectively. We compare our results to those of classical density functional theory (DFT) of [Mikheev and Chernov, J. Cryst. Growth $\bf 112$, 591-596 (1991)].