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Modeling of structure formation in casting of alloys involves several length scales, ranging from the atomic level to macroscopic scale. Intermediate length scales are used to define the microstructure of the growing phases and the grain structure. This article discusses the principles and applications of phase field method and cellular automaton method for modeling the direct evolution of structure at the intermediate length scales, where transport phenomena govern the spatial and temporal evolution of the structure that involves nucleation and growth.

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Ch.-A. Gandin, I. Steinbach, Direct Modeling of Structure Formation, Casting, Vol 15, ASM Handbook, Edited By Srinath Viswanathan, Diran Apelian, Raymond J. Donahue, Babu DasGupta, Michael Gywn, John L. Jorstad, Raymond W. Monroe, Mahi Sahoo, Thomas E. Prucha, Daniel Twarog, ASM International, 2008, p 435–444,

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