2024-03-28T21:26:22Zhttps://eprints.lib.hokudai.ac.jp/dspace-oai/requestoai:eprints.lib.hokudai.ac.jp:2115/696942022-11-17T02:08:08Zhdl_2115_45007hdl_2115_116A microscopic time scale approximation to the behavior of the local slope on the faceted surface under a nonuniformity in supersaturationYokoyama, EtsuroGiga, YoshikazuRybka, Piotropen accessfacet instabilityHamilton-Jacobi equationviscosity solutionmacroscopic ime scale approximationmaximal stable region410The 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.Department of Mathematics, Hokkaido University2007-11-28engdepartmental bulletin paperVoRhttps://doi.org/10.14943/84035http://hdl.handle.net/2115/6969410.14943/84035Hokkaido University Preprint Series in Mathematics885129https://eprints.lib.hokudai.ac.jp/dspace/bitstream/2115/69694/1/pre885.pdfapplication/pdf509.81 KB2007-11-28