Kinetic Coefficient for Hard-Sphere Crystal Growth from the Melt

Using molecular-dynamics simulation, we determine the magnitude and anisotropy of the kinetic coefficient (μ) for the crystal growth from the melt for the hard-sphere system through an analysis of equilibrium capillary fluctuations in interfacial height. We find μ₁₀₀=1.44(7), μ₁₁₀=1.10(5), and μ₁₁₁=0.64(3) in units of √k_B/(mT_m), where k_B is Boltzmann’s constant, m is the particle mass, and T_m is the melting temperature. These values are shown to be consistent, with some exceptions, with those obtained in recent simulation results a variety of fcc metals, when expressed in hard-sphere units. This suggests that the kinetic coefficient for fcc metals can be roughly estimated from C√R/(MT_m), where R is the gas constant, M is the molar mass, and C is a constant that varies with interfacial orientation.