Spinodal decomposition without diffuse interface theory-I. Theory

R. W. Hopper, D. R. Uhlmann

Research output: Contribution to journalArticle

14 Scopus citations

Abstract

It has been shown that when higher derivative tenns of the diffuse interface expansion are included in the theory of spinodal decomposition, exceptional results are obtained. Within a mean field pair interaction (MFPI) interpretation, the coefficients of terms ▽2nc in the extended diffuse interface expansion eventually become infinite in magnitude. These anomalies are discussed and circumvented in a new analysis of spinodal decomposition. Within the MFPI interpretation a Fourier analysis of the composition is made at an earlier stage in the analysis. The result is a diffusion equation which can be related to the usual diffusion equation of spinodal decomposition. In the early stages, the only change encountered is that the factor κβ2 in the amplification factor is replaced by a function K(β). When κ is defined, K(β) approaches κβ2 in the limit of small β. When, because of long-range intermolecular potentials, the standard definition of κ does not converge, K(β) remains well defined but no longer increases as β2 in the small β limit. This can result in amplification factors which are qualitatively different from those predicted by the standard theory.

Original languageEnglish (US)
Pages (from-to)35-42
Number of pages8
JournalActa Metallurgica
Volume21
Issue number1
DOIs
StatePublished - Jan 1973
Externally publishedYes

ASJC Scopus subject areas

  • Engineering(all)

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