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Phase-field models in materials science; a tutorial review
The phase-field method is reviewed against its historical and theoretical background. Starting from Van der Vaals considerations on the structure of interfaces in materials the concept of the phase-field method is developed along the historical lines. Basic relations are summarized in a comprehensive way. The multi-phase-field method for transformations in multi-grain multi-phase structures in multicomponent materials is outlined with extension to elastic interactions and fluid flow. Examples are collected demonstrating the applicability of the method in different fields of materials science.