Numerical Study of Crystal Size Distribution in Polynuclear Growth

TL;DR

This study numerically investigates how crystal size distribution in polynuclear growth depends on growth and diffusion parameters, revealing linear relationships and conditions for monodisperse crystal formation.

Contribution

It introduces a coupled map lattice model to analyze crystal size distribution and explains the linear dependence of distribution width on growth parameters.

Findings

Width of size distribution depends linearly on c/D at small values.

Monodisperse crystals form on specific lattice types under certain conditions.

Theoretical evaluation of the slope in the linear dependence.

Abstract

The crystal size distribution in polynuclear growth is numerically studied using a coupled map lattice model. The width of the size distribution depends on c/D, where c is the growth rate at interface sites and $D$ is the diffusion constant. When c/D is sufficiently small, the width W increases linearly with c/D and saturates at large c/D. Monodisperse square and cubic crystals are obtained respectively on square and cubic lattices when c/D is sufficiently small for a small kinetic parameter b. The linear dependence of W on c/D in a parameter range of small c/D is explained by the eigenfunction for the first eigenvalue in a two-dimensional model and a mean-field model. For the mean-field model, the slope of the linear dependence is evaluated theoretically.