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A phase field concept for multiphase systems
The phase field theory describing the evolution of a dual phase boundary is extended to multiphase problems: Each phase is identified with an individual phase field and the transformation between all pairs of phases is treated with its own characteristics. The governing differential equations for the evolution of the multiphase system are derived by minimizing the free energy functional. This free energy functional is expanded in a series over the pair energies between the different phases, where the local fluctuations of one phase are treated with respect to its counter-phase. The proposed generalized multiphase concept reproduces the dual phase system as a limiting case. The relevance of the model for metallic systems is discussed with respect to eutectic and peritectic solidification and grain growth.