Thermodynamics of polydomain heterostructures. III. Domain stability map

A map showing regions of stability of possible domain structures and relative fractions of domains in a polytwin structure is developed for epitaxial heterostructures with active layers which undergo a cubic–tetragonal or a tetragonal–orthorhombic transformation. This map, which is also applicable to epitaxial film–substrate systems, shows the dependence of the polytwin structure on misfit strain, lattice parameters of the product phase, and mechanical stress. A uniaxial stress field applied during cooling down from the growth temperature strongly affects the domain structure selection and perfect single-domain structures may be obtained with such fields. For polytwin layers with thicknesses close to the critical thickness for domain formation, microstresses must be taken into consideration and the domain stability map is modified accordingly. Misfit dislocation generation at the deposition temperature is taken into account through a temperature dependent effective substrate lattice parameter. As examples, ${\mathrm{PbTiO}}_3\text{(001)}$ films grown on MgO(001) and ${\mathrm{SrTiO}}_3\text{(001)}$ substrates are analyzed. Theoretical predictions are in good agreement with experimental results from the literature. The maps for epitaxial ${\mathrm{BaTiO}}_3\text{(001)}$ films grown on various substrates are also included. Experimental observations for ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{\text{7−x}}$ films strongly support the ideas developed in this paper.