Model for faceting in a kinetically controlled crystal growth

A. A. Golovin*, S. H. Davis, A. A. Nepomnyashchy

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

59 Scopus citations


A two-dimensional anisotropic nonlinear evolution equation is derived to model the formation of facets and corners in the course of kinetically controlled crystal growth. The equation is solved numerically in particular cases corresponding to the faceting of [001], [111], and [110] growing crystal surfaces, and the formation of hill-and-valley structures in the form of square, triangular, and rhombic pyramids; grooves are observed as well. The pyramidal slopes far from the vertices are found analytically, and in particular cases exact solutions of the equation are found. The pyramidal structures coarsen in time, and the rate of coarsening is studied.

Original languageEnglish (US)
Pages (from-to)803-825
Number of pages23
JournalPhysical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
Issue number1
StatePublished - 1999
Externally publishedYes

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Condensed Matter Physics


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