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Abstract

This lecture reviews the phase-field method that is generally applicable to homogeneous and heterogeneous systems at the mesoscopic scale. Reviewed first are general aspects about first- and second-order phase transitions that need to be considered to understand the theoretical background of a phase field. The mesoscopic model equations are defined by a coarse-graining procedure from a microscopic model in the continuum limit on the atomic scale. Special emphasis is given to the question of how to separate the interface and bulk contributions to the generalized thermodynamic functional, which forms the basis of all phase-field models. Numerical aspects of the discretization are discussed at the lower scale of applicability. Several examples are highlighted regarding coupled non-equilibrium transformations.