Abstract
This chapter discusses the fundamentals of phase field theory. This theory provides an alternative method for solving dynamical problems involving crystallization from a melt. The sharp solid liquid interface of the classical model is replaced by a diffuse interface by introducing an auxiliary variable ( , the phase field, that indicates the phase. The phase field model can be derived on the basis of an entropy functional. It is possible to formulate thermodynamically consistent phase field models for solidification from the melt, for pure materials, and for alloys, including hydrodynamics. The complexity of these models, however, increases drastically with the complexity of the system being modeled. Using these models for computations is certainly possible, especially for pure materials, and has led to a number of interesting results.
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