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A microscopic time scale approximation to the behavior of the local slope on the faceted surface under a nonuniformity in supersaturation
| Title: | A microscopic time scale approximation to the behavior of the local slope on the faceted surface under a nonuniformity in supersaturation |
| Authors: | Yokoyama, Etsuro Browse this author | | Giga, Yoshikazu Browse this author | | Rybka, Piotr Browse this author |
| Keywords: | facet instability | | Hamilton-Jacobi equation | | viscosity solution | | macroscopic ime scale approximation | | maximal stable region |
| Issue Date: | 28-Nov-2007 |
| Publisher: | Department of Mathematics, Hokkaido University |
| Journal Title: | Hokkaido University Preprint Series in Mathematics |
| Volume: | 885 |
| Start Page: | 1 |
| End Page: | 29 |
| Abstract: | 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. |
| Type: | bulletin (article) |
| URI: | http://hdl.handle.net/2115/69694 |
| Appears in Collections: | 理学院・理学研究院 (Graduate School of Science / Faculty of Science) > Hokkaido University Preprint Series in Mathematics
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Submitter: 数学紀要登録作業用
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