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Monte-Carlo simulation of the Cahn-Hillard model of spinodal decomposition

โœ Scribed by A. Milchev; D.W. Heermann; K. Binder


Publisher
Elsevier Science
Year
1988
Weight
754 KB
Volume
36
Category
Article
ISSN
0001-6160

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โœฆ Synopsis


A lattice version of the nonlinear Cahn-Hilliard equation describing spinodal decomposition of binary alloys is studied via Monte-Carlo simulation, considering a two-dimensional system at critical concentration. The linearization approximation is found to be rather inaccurate even if the final temperature of the quench is very low and thermal fluctuations are unimportant. The structure function is found to exhibit anisotropy consistent with the chosen square lattice geometry. The relation of this study to Ising model simulations and experimental work is briefly discussed. Resum&Une version d'une grille de 1'Bquation non-1inCaire "Cahn-Hilliard" est CtudiCe avec Monte Carlo simulation dans le but d'tcrire sur la d&composition spinodale et en considkrant un systeme d deux dimensions $ concentration critique. I1 se trouve que l'approximation de lintarisation est tris inexacte m&me lorsque la temptrature finale de "l'experiment d'effrayment" est t&s basse et des fluctuations thermiques pour cela ont peu d'importance. La function de la structure montre de l'anisotropie selon la gOomCtrie choisie des grilles carries. La relation de cette recherche avec des simulations avec le modtle Ising et des travaux experimentals est courtement discutke. Zusammenfassung-Eine Gitterversion der nichtlinearen Cahn-Hilliard Gleichung zur Beschreibung der spinodalen Entmischung binHrer Legierungen wird mittels Monte-Carlo Simulation studiert, wobei ein zweidimensionales System bei der kritischen Konzentration betrachtet wird. Die Linearisierungs-Niiherung stellt sich selbst dann als ziemlich ungenau heraus, wenn der Endzustand des "Abschreck-Experiments" bei einer sehr tiefen Temperatur liegt und thermische Fluktuationen daher unwichtig sind. Die Strukturfunktion zeigt Anisotropie entsprechend der gewlhlten Quadratgitter-Geometrie. Der Zusammenhang dieser Untersuchung mit Simulationen am Ising-Model1 und experimentellen Arbeiten wird kurz diskutiert.


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