96-199 Giambattista Giacomin and Joel L. Lebowitz

Exact Macroscopic Description of Phase Segregation in Model Alloys with Long Range Interactions (26K, AmsTeX) May 15, 96

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Abstract. We derive an exact nonlinear non-local macroscopic equation for the time evolution of the conserved order parameter $\rho({\text{\bf r}}, t)$ of a microscopic model binary alloy undergoing phase segregation: a $d$--dimensional lattice gas evolving via Kawasaki exchange dynamics, satisfying detailed balance for a Hamiltonian with a long range pair potential $\gamma^d J(\gamma \vert x \vert)$. The macroscopic evolution is on the spatial scale $\gamma^{-1}$ and time scale $\gamma^{-2}$, in the limit $\gamma \to 0$. The domain coarsening, described by interface motion, is similar to that obtained from the Cahn-Hilliard equation. \hfill\break \phantom{a}\hfill\break \phantom{a}\hfill\break Pacs numbers: 05.20.-y, 02.30Jr, 02.50Cw, 64.75+g, 64.70.Kb

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