Strain Controlled Morphologies in the Two-Phase State

Abstract

Phase transformation in solids usually involve crystal lattice rearrangement with the islands of the new phase inside the parent phase matrix. Crystal lattice mismatch produced by phase transformation is accomodated by elastic displacements generating the elastic strain field within the body. The elastic energy contained in the strain field may contribute considerably to the thermodynamics of the phase transformation, but the main effect of the elastic strain is far beyond the trivial renormalization of elastic energy. Unlike the “chemical” free energy depending only on the volume of phases, the elastic energy also depends on the morphology, shape, dispersion and mutual location of inclusions. In such a case the morphology of the alloy becomes an internal thermodynamic parameter that can be found from the free energy minimization. This, in fact, means that the conventional thermodynamics of phase transformations based on the free energy additivity should be questioned and validity of certain classical results has to be reexamined. To make more clear how far we can go in revising the theory of phase transformation when elastic energy is involved, it is noteworthy to look at the other cases when the bulk free energy proves to be dependent on morphology. The other cases where this situation takes place are ferromagnets and ferroelectrics whose magnetostatic and electrostatic energy also depend on shape, size and mutual location of domains. This dependence manifests itself, for example, in appearance of the so-called demagnetization factor, and it affects the ground state of ferromagnets.KeywordsElastic EnergyHabit PlaneCrystal Lattice ParameterMagnetostatic EnergyInvariant Plane StrainThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.