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Direct modeling of structure formation
Modeling of structure formation in casting of alloys involves several length scales, ranging from the atomic level (10-10– 10-9 m) to the casting dimensions, i.e. the macroscopic scale, (10-2–1 m). Intermediate length scales are used to define the microstructure of the growing phases (i.e., 10-7–10-4 m, e.g., dendritic or eutectic patterns) and the grain structure (i.e., 10-4–10-2 m, e.g., equiaxed and columnar grains). This article concentrates on these intermediate length scales, where transport phenomena govern the spatial and temporal evolution of the structure. To calculate this evolution, conservation equations are written for each individual phase (liquid or solid), with the most challenging aspect being the treatment of the interfaces between phases and the nonequilibrium condition of the liquid metal during the solidification state.