Multi-phase equilibrium of crystalline solids

A continuum model of crystalline solid equilibrium is presented in which th e underlying periodic lattice structure is taken explicitly into account. T his model also allows for both point and line defects in the bulk of the la ttice and at interfaces, and the kinematics of such defects is discussed in some detail. A Gibbsian variational argument is used to derive the necessa ry bulk and interfacial conditions for multi-phase equilibrium (crystal-cry stal and crystal-melt) where the allowed lattice variations involve the cre ation and transport of defects in the bulk and at the phase interface. An i nterfacial energy, assumed to depend on the interfacial dislocation density and the orientation of the interface with respect to the lattices of both phases, is also included in the analysis. Previous equilibrium results base d on nonlinear elastic models for incoherent and coherent interfaces are re covered as special cases for when the lattice distortion is constrained to coincide with the macroscopic deformation gradient, thereby excluding bulk dislocations. The formulation is purely spatial and needs no recourse to a fixed reference configuration or an elastic-plastic decomposition of the st rain. Such a decomposition can be introduced, however, through an increment al elastic deformation superposed onto an already dislocated state, but lea ds to additional equilibrium conditions. The presentation emphasizes the ro le of configurational forces as they provide a natural framework for the de scription and interpretation of singularities and phase transitions. (C) 20 00 Elsevier Science Ltd. All rights reserved.