Determination of the crystal-melt interface kinetic coefficient from molecular dynamics simulations

The generation and dissipation of latent heat at the moving solid-liquid boundary during non-equilibrium molecular dynamics (MD) simulations of crystallization can lead to significant underestimations of the interface mobility. In this work we examine the heat flow problem in detail for an embedded atom description of pure Ni and offer strategies to obtain an accurate value of the kinetic coefficient, mu. For free-solidification simulations in which the entire system is thermostated using a Nose-Hoover or velocity rescaling algorithm a non-uniform temperature profile is observed and a peak in the temperature is found at the interface position. It is shown that if the actual interface temperature, rather than the thermostat set point temperature, is used to compute the kinetic coefficient then mu is approximately a factor of 2 larger than previous estimates. In addition, we introduce a layered thermostat method in which several sub-regions, aligned normal to the crystallization direction, are indepently thermostated to a desired undercooling. We show that as the number of thermostats increases (i.e., as the width of each independently thermostated layer decreases) the kinetic coefficient converges to a value consistent with that obtained using a single thermostat and the calculated interface temperature. Also, the kinetic coefficient was determined from an analysis of the equilibrium fluctuations of the solid-liquid interface position. We demonstrate that the kinetic coefficient obtained from the relaxation times of the fluctuation spectrum is equivalent to the two values obtained from free-solidification simulations provided a simple correction is made for the contribution of heat flow controlled interface motion. Finally, a one-dimensional phase field model that captures the effect of thermostats has been developed. The mesoscale model reproduces qualitatively the results from MD simulations and thus allows for an a priori estimate of the accuracy of a kinetic coefficient determination for any given classical MD system. The model also elucidates that the magnitude of the temperature gradients obtained in simulations with a single thermostat depends on the length of the simulation system normal to the interface; the need for the corrections discussed in this paper can thus be gauged from a study of the dependence of the calculated kinetic coefficient on system size.