open access

https://doi.org/10.14943/84035

https://hdl.handle.net/2115/69694

A microscopic time scale approximation to the behavior of the local slope on the faceted surface under a nonuniformity in supersaturation

英語

maximal stable region

2007-11-28

Department of Mathematics, Hokkaido University

Hokkaido University Preprint Series in Mathematics

885

1-29

The morphological stability of a growing faceted crystal is discussed. It has been explained hat the interplay between nonuniformity in supersaturation on a growing facet and nisotropy of surface kinetics derived from the lateral motion of steps leads to a faceted nstability. Qualitatively speaking, as long as the nonuniformity in supersaturation on the acet is not too large, it can be compensated by a variation of step density along the facet nd the faceted crystal can grow in a stable manner. The problem can be modeled as a amilton-Jacobi equation for height of the crystal surface. The notion of a maximal stable egion of a growing facet is introduced for microscopic time scale approximation of the riginal Hamilton-Jacobi equation. It is shown that the maximal stable region keeps its hape, determined by profile of the surface supersaturation, with constant growth rate by tudying large time behavior of solution of macroscopic time scale approximation. As a esult, a quantitative criterion for the facet stability is given.

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