Direct Calculation of the Hard-Sphere Crystal<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>/</mml:mi></mml:math>Melt Interfacial Free Energy

Abstract

We present a direct calculation by molecular-dynamics computer simulation of the crystal/melt interfacial free energy $\ensuremath{\gamma}$ for a system of hard spheres of diameter $\ensuremath{\sigma}$. The calculation is performed by thermodynamic integration along a reversible path defined by cleaving, using specially constructed movable hard-sphere walls, separate bulk crystal, and fluid systems, which are then merged to form an interface. We find the interfacial free energy to be slightly anisotropic with $\ensuremath{\gamma}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0.62\ifmmode\pm\else\textpm\fi{}0.01$, $0.64\ifmmode\pm\else\textpm\fi{}0.01$, and $0.58\ifmmode\pm\else\textpm\fi{}{0.01k}_{B}T/{\ensuremath{\sigma}}^{2}$ for the (100), (110), and (111) fcc crystal/fluid interfaces, respectively. These values are consistent with earlier density functional calculations and recent experiments.