Non-local elasticity of polydomain phases

Abstract

In solid state phase transformations a single crystal or a grain of a polycrystal are often transformed into a regular system of structural domains which are differently oriented variants of the transformed phase. These domains appear as a result of the reduction in crystal symmetry caused by the transformation and are related to each other in a twin-like fashion. An assembly of plane-parallel twins forms a polysynthetic twin or polytwin.[1] Polytwins, in turn, may be parts of more complex hierarchical structures. Polysandwich structures of this kind are characteristic of many types of structural phase transli~rmations in solids, martensitic, ferroelastic, ordering and decomposition.[2] These polydomain structures arise in both first and second order phase transformations. If the polydomain region is embedded in an matrix, interactions between domains mediated by the matrix lead to the formation of an equilibrium polydomain structure corresponding to a minimum of the tree energy. Therefi~l'e, these domains have been termed elastic domains. If the characteristic length of the domain structure is small in comparison to the characteristic size of the solid, this homoor heterophase polydomain structure can be treated as a special type of polydomain phase with domain structure parameters as additional internal thermodynamical variables. These variables control the properties of the polydomain phase as well as the thermodynamics and kinetics of phase transformations to a considerable extent.