A PHASE FIELD CONCEPT FOR MULTIPHASE SYSTEMS

The phase field theory describing the evolution of a dual phase bounda ry is extended to multiphase problems: Each phase is identified with a n individual phase field and the transformation between all pairs of p hases is treated with its own characteristics. The governing different ial equations for the evolution of the multiphase system are derived b y minimizing the free energy functional. This free energy functional i s expanded in a series over the pair energies between the different ph ases, where the local fluctuations of one phase are treated with respe ct to its counter-phase. The proposed generalized multiphase concept r eproduces the dual phase system as a limiting case. The relevance of t he model for metallic systems is discussed with respect to eutectic an d peritectic solidification and grain growth.