The phase-field method has emerged as a method of choice for the description of microstructure evolution and phase transitions in metallic materials. Following a general thermodynamic extremal principle a set of evolution equations for the structural variables of the system, the so called phase-fields, are derived. The paper reviews shortly the historical and theoretical background of the multi-phase-field method that is an extension of the classical phase-field method to multi-phase multi-component materials. Examples are given from solidification, solid state transformations and grain growth.
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