Thermodynamics and kinetics of the crystal-melt interface for single and binary hard-sphere system: A simulation study

The crystal-melt interfacial free energy, gamma, is the reversible work per unit area needed to create an interface between a crystal and its melt. The kinetic coefficient, mu, of crystal-melt interface is the ratio of the interface growth velocity to the undercooling (TM - T), where TM is the melting point. These two thermodynamic and kinetic parameters are very important in crystal growth. In this work we determine gamma and mu for the single and binary hard-sphere systems by analyzing capillary fluctuations in interface position using molecular dynamics (MD) simulation [Hoyt et al, Mat. Sci. Eng. R 41, 121-163 (2003)]. Our results of mu for the single hard-sphere system for the three orientations (100), (110), and (111) are in agreement with other simulation and experimental results for metals. The results we obtained give the relation mu100 > mu110 > mu111, which is also consistent with the ordering of experiments and simulations for metals, but is different from the ordering predicted by the density functional theory (DFT) for the hard-sphere system in which the orientation (110) is the lowest. Our results of gamma for the single hard-sphere is also consistent with the previous simulation results for the hard-sphere system, performed by two methods, cleaving method and fluctuation method. It also gives the relation gamma100 > gamma 110 > gamma111, which is also in agreement with the literature. Our simulation result for the binary hard-sphere system also gives the relation gamma 100 > gamma110 > gamma111. The interfacial free energy for the binary hard-sphere system is slightly higher than that for the single hard-sphere system, but after scaling its pressure to the pressure of the single hard-sphere system to keep the pressures the same, it becomes slightly smaller, which is in consistent with the gamma of the Cu-Ni alloy being slightly smaller than that of Ni. Our calculation for the mu of the binary hard-sphere system also gives the relation mu100 > mu 110 > mu111, and its values are smaller than that of the single hard-sphere system.