Kinetics of solid–liquid interface motion in molecular dynamics and phase-field models: crystallization of chromium and silicon

Abstract

The results of molecular dynamics (MD) simulations of the crystallization process in one-component materials and solid solution alloys reveal a complex temperature dependence of the velocity of the crystal–liquid interface featuring an increase up to a maximum at 10–30% undercooling below the equilibrium melting temperature followed by a gradual decrease of the velocity at deeper levels of undercooling. At the qualitative level, such non-monotonous behaviour of the crystallization front velocity is consistent with the diffusion-controlled crystallization process described by the Wilson–Frenkel model, where the almost linear increase of the interface velocity in the vicinity of melting temperature is defined by the growth of the thermodynamic driving force for the phase transformation, while the decrease in atomic mobility with further increase of the undercooling drives the velocity through the maximum and into a gradual decrease at lower temperatures. At the quantitative level, however, the diffusional model fails to describe the results of MD simulations in the whole range of temperatures with a single set of parameters for some of the model materials. The limited ability of the existing theoretical models to adequately describe the MD results is illustrated in the present work for two materials, chromium and silicon. It is also demonstrated that the MD results can be well described by the solution following from the hodograph equation, previously found from the kinetic phase-field model (kinetic PFM) in the sharp interface limit. The ability of the hodograph equation to describe the predictions of MD simulation in the whole range of temperatures is related to the introduction of slow (phase field) and fast (gradient flow) variables into the original kinetic PFM from which the hodograph equation is obtained. The slow phase-field variable is responsible for the description of data at small undercoolings and the fast gradient flow variable accounts for local non-equilibrium effects at high undercoolings. The introduction of these two types of variables makes the solution of the hodograph equation sufficiently flexible for a reliable description of all nonlinearities of the kinetic curves predicted in MD simulations of Cr and Si. This article is part of the theme issue ‘Transport phenomena in complex systems (part 1)’.

Two-temperature molecular dynamics simulations of crystal growth in a tungsten supercooled melt

“…Between 0.6T m and T m , we observe a good fit of the simulation data with equation ( 8), however, the equation predicts a much faster decrease of the crystallization front speed at low temperatures. A similar discrepancy is reported in [47], where the authors compared the Wilson-Frenkel equation, based on the phenomenological transition state theory, with results from MD simulations of the crystallization process in Cr melt. We can also notice an unphysically large value of Q h , exceeding the enthalpy of melting, both in the current study and in [47], suggesting that a simplified theory is not adequate for the description of crystallization process in a wide temperature range.…”

“…A similar discrepancy is reported in [47], where the authors compared the Wilson-Frenkel equation, based on the phenomenological transition state theory, with results from MD simulations of the crystallization process in Cr melt. We can also notice an unphysically large value of Q h , exceeding the enthalpy of melting, both in the current study and in [47], suggesting that a simplified theory is not adequate for the description of crystallization process in a wide temperature range. The LCI mobility plays not only an important role in the determination of solidification rates but also growth morphology and it is generally characterized by the kinetic coefficient µ = dvLCI d(Tm−T) | T=Tm .…”

“…In figure 4(b), we also show an attempt to fit the speed of the crystallization front by a simple analytical model of the Wilson-Frenkel type for a diffusion-limited crystal growth [46,47]:…”

Transport phenomena in complex systems (part 1)

“…This theory is compared with molecular-dynamics simulations on nickel crystal growth. The next paper by Karim et al [21] demonstrates that the molecular dynamics results can be well described by the solution following from the hodograph equation, previously found from the phase-field model in the sharp interface limit. The ability of the hodograph equation to describe the molecular dynamics simulation in the whole range of temperatures is related to the introduction of slow and fast variables into the original kinetic phase-field model from which the hodograph equation is obtained.…”