Numerical Study of Crystal Size Distribution in Polynuclear Growth

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 li...

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Published in:arXiv.org 2015-05
Main Authors: Sakaguchi, Hidetsugu, Ohishi, Takuma
Format: Article
Language:English
Subjects:
Crystal growth
Crystal lattices
Crystals
Dependence
Diffusion rate
Eigenvalues
Eigenvectors
Lattices (mathematics)
Mathematical models
Parameters
Size distribution
Two dimensional models
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description 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.
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subjects Crystal growth
Crystal lattices
Crystals
Dependence
Diffusion rate
Eigenvalues
Eigenvectors
Lattices (mathematics)
Mathematical models
Parameters
Size distribution
Two dimensional models
title Numerical Study of Crystal Size Distribution in Polynuclear Growth
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