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EVOLUTION FOR BINARY ALLOY SOLIDIFICATION

The thermally controlled solidification of a binary alloy, nucleated at isolated sites, is described by the evolution of a probability distribution function, whose variables include grain size and distance to nearest neighbor, together with descriptors of shape, orientation, and such material properties as orientation of nonisotropic elastic modulus and coefficient of thermal expansion. The relevant Liouville equation is described and coupled with global equations for energy and solute transport. Applications are discussed for problems concerning nucleation and impingement and the consequences for final size and size distribution. The goal of this analysis is to characterize the grain structure of the solidified casting and to enable the description of its probable response to thermal treatment, machining, and the imposition of mechanical insults.