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Excursions in Programming: Phase Changes in Materials: Spinodal Decomposition in Binary Mixtures

Richard J. Gaylord
Organization: University of Illinois at Urbana-Champaign
Department: Department of Material Science and Engineering
Kazume Nishidate
Organization: Iwate University
Department: Department of Electrical and Electronic Engineering
Journal / Anthology

Mathematica in Education and Research
Year: 1996
Volume: 5
Issue: 4
Page range: 22-26

Binary alloy systems undergo non-equilibrium phase separation in which domains of two stable phases grow from a thermodynamically unstable homogeneous phase as a result of quenching below a critical temperature.

Traditionally, phase ordering phenomena has been theoretically modeled by numerically solving nonlinear partial differential equations (viz the Ginzburg-Landau and Cahn-Hilliard equations), which amounts to space-time discretizing a continuum model. An alternative approach is to use a space-time discrete lattice from the start. This type of model is referred to as a cell dynamic scheme or CDS (coupled maps and cellular automata are examples of CDS's).


We will present two programs for the deterministic CDS model of the evolution of the order parameter field for phase ordering phenomenon: one program in which the order parameter is conserved and one program in which the order parameter is not conserved.

*Engineering > Materials and Metallurgical Engineering
*Mathematics > Discrete Mathematics > Cellular Automata
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