Computing the crystal growth rate by the interface pinning method

Abstract

An essential parameter for crystal growth is the kinetic coefficient given by the proportionality between supercooling and average growth velocity. Here, we show that this coefficient can be computed in a single equilibrium simulation using the interface pinning method where two-phase configurations are stabilized by adding a spring-like bias field coupling to an order-parameter that discriminates between the two phases. Crystal growth is a Smoluchowski process and the crystal growth rate can, therefore, be computed from the terminal exponential relaxation of the order parameter. The approach is investigated in detail for the Lennard-Jones model. We find that the kinetic coefficient scales as the inverse square-root of temperature along the high temperature part of the melting line. The practical usability of the method is demonstrated by computing the kinetic coefficient of the elements Na and Si from first principles. A generalized version of the method may be used for computing the rates of crystal nucleation or other rare events. C 2015 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution 3.0 Unported License. [http://dx

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“…The theory presented above predicts the thermodynamics of freezing and melting from a single coexistence state point. The theory also enables one to calculate the deviations from the invariance of several quantities along the melting line predicted by the hard-sphere melting picture 22 16 30 31 32 . The theory is analytic for LJ type systems, that is, systems involving a pair potential that is a difference of two inverse power laws, but the framework developed applies to any system with hidden scale invariance, including molecular systems.…”

“…The below study shows how the thermodynamics of freezing and melting for a large class of systems may be predicted to a good approximation from computer simulations carried out at a single coexistence state point. In particular, the theory developed quantifies the deviations from the above mentioned hard-sphere predicted melting-line invariants 16 22 30 31 32 . The theory is validated by computer simulations of the standard 12-6 LJ system.…”

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