Stochastic modeling of nucleation and growth in a thin layer between two interfaces

Takashi Tagami, Shunichiro Tanaka

Research output: Contribution to journalArticle

18 Citations (Scopus)

Abstract

A stochastic modeling method is presented for the analysis of nucleation and growth in a thin layer between two interfaces. In this layer, nucleation occurs randomly and growth stops at the interfaces after instantaneous growth. This halting of the growth causes non-random impingement because phantom crystallites in the Kolmogorov-Johnson-Mehl-Avrami (KJMA) model shrink to an effective size. This stochastic model successfully deals with effective size using a factor γ which accounts for the overlap between a phantom crystallite and a crystallite. This leads to a phenomenological equation for non-random impingement: dX(t)/dVex = [1 - X(t)]i, where X(t) is the transformed fraction and Vex is the KJMA extended volume fraction. It is shown that the exponent is clearly expressed as i = 2 - γ. An analytical solution of the transformed fraction agrees very well with the numerical simulations.

Original languageEnglish
Pages (from-to)3341-3347
Number of pages7
JournalActa Materialia
Volume45
Issue number8
DOIs
Publication statusPublished - 1997 Jan 1
Externally publishedYes

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Ceramics and Composites
  • Polymers and Plastics
  • Metals and Alloys

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