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Excursions in Programming: Phase Changes in Materials: Spinodal Decomposition in Binary Mixtures
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| Organization: | University of Illinois at Urbana-Champaign |
| Department: | Department of Material Science and Engineering |
| Organization: | Iwate University |
| Department: | Department of Electrical and Electronic Engineering |
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| Mathematica in Education and Research |
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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).
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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.
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| PhaseChange54.nb (558.2 KB) - Mathematica Notebook |
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