Computing the crystal growth rate by the interface pinning method

TL;DR

This paper introduces an equilibrium simulation method, called interface pinning, to compute crystal growth rates and kinetic coefficients efficiently, demonstrated on Lennard-Jones and elemental models, offering an alternative to rare event sampling techniques.

Contribution

The paper presents a novel equilibrium simulation approach to determine crystal growth rates, applicable to various materials, and compares it with existing rare event sampling methods.

Findings

Kinetic coefficient scales as inverse square-root of temperature.

Method successfully applied to Lennard-Jones model and elements Na, Mg, Al, Si.

Provides a practical and efficient way to compute growth rates from equilibrium simulations.

Abstract

An essential parameter for crystal growth is the kinetic coefficient given by the proportionality between super-cooling 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 an 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, Mg, Al and Si from first principles. It is briefly discussed how a generalized version of the method is an alternative to forward flux sampling methods for computing rates along trajectories of rare events.