Thermodynamics of polydomain heterostructures. I. Effect of macrostresses

The thermodynamic principles of the formation of a new class of materials, polydomain heterostructures, are formulated. The polydomain heterostructures can be formed as a result of phase transformations in constrained layers, composed of epitaxial couples or multilayers. Due to the elastic interaction between the layers of a heterostructure, these layers transform into sets of periodically alternating lamellae, or elastic domains. A polydomain layer can consist of either differently oriented domains of the same phase (twins) or domains of different phases. The goal of this article is to determine the parameters of the polydomain heterostructures and the conditions for their formation, i.e., their dependence on the characteristics of phase transformations, lattice misfits, and the film thickness, as well as external fields. Heterostructures containing ferroelectric and superconductor oxide layers will be considered as examples. In part I the necessary conditions for the formation of polydomain heterostructures have been established on the basis of the analysis of thermodynamic effects of internal and external macrostresses on phase transformations. The thermodynamic criteria are formulated in terms of a few energy parameters: the misfit energies of the phases that form the heterostructure and the energies of interaction between domains. Together with the free energies of the unconstrained phases, these parameters give a quantitative thermodynamic description of polydomain heterostructures provided that the interface effects are negligible. It is shown that polytwin structures are always more stable than single domain structures and therefore, their formation is always possible at some external stresses and temperatures. The stability of heterophase polydomain structures depends on the parameter of incompatibility between the domains, i.e., the ratio of the energy of direct interactions between the domains through their interface to the energy of indirect interaction between domains through the elastic surrounding matrix. If the interdomain interfaces are mobile, their movement may result in superelastic deformation and essential softening of the effective elastic modulus.