ABSTRACT
This chapter shows how to use the grand potential ensemble to reformulate the multi-order-parameter phase field model of solidification of Ofori-Opoku et al. into an easy-to-use multi-order parameter theory for multi-component solidification. It discusses some general ideas about the interpretation of operating phase field model in the limit of a sharp interface model, and deals with non-equilibrium solidification theory. The interpretation of the phase filed is not practically important in the sharp interface limit of solidification, but is important when connecting phase field models arising from microscopic theories. Phase field models have been applied to a wide range of phenomena ranging from single-crystal solidification, directional and polycrystalline solidification, grain growth, elasticity and precipitation. Quantitative calculations with phase field models requires detailed asymptotic boundary layer analysis, which prescribes how to match their behaviour with appropriate sharp interface models in the limit when a suitable scale separation exists between the length of diffusion of impurities.
