Open AccessThe asymptotic analysis of interfacial stability with surface tension anisotropy for directional solidification of alloys
Author(s) -
Zhijun Wang,
Jincheng Wang,
Yang Gencang
Publication year - 2008
Publication title -
wuli xuebao
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.199
H-Index - 47
ISSN - 1000-3290
DOI - 10.7498/aps.57.1246
Subject(s) - surface tension , anisotropy , supercooling , directional solidification , materials science , instability , dispersion (optics) , zero (linguistics) , dispersion relation , surface (topology) , condensed matter physics , asymptotic analysis , mechanics , thermodynamics , physics , mathematical analysis , optics , mathematics , microstructure , composite material , geometry , linguistics , philosophy
An asymptotic analysis of interfacial stability with the surface tension anisotropy is derived for directional solidification of alloys. The zero and first order solution for multi-scale and the zero order solution for single-scale are obtained. The dispersion relation adapted to all wave-length is presented by combining the short and the long wave-length solutions. It was concluded that the zero order asymptotic solution is equivalent to constitutional undercooling theory and the first order solution is consistent with M-S theory. The instability zone of control parameter enlarges with the surface tension anisotropy,especially for the high temperature gradient and high pulling velocitycases.