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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Bibliographic Details
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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Summary: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.
ISSN:2331-8422
DOI:10.48550/arxiv.1505.00309