Engineering of elastic domain structures in a constrained layer Original Research Article

The theoretical analysis and phase-field modeling of elastic domain structures in constrained layers depending on their misfit and thickness are presented. Domain diagrams that demonstrate how different domain structures can be obtained by manipulating parameters of constraints are constructed for a model system with cubic–tetragonal transformation. It is shown that depending on the misfit, three-domain stress-free structures (hierarchical and cellular) and two-domain uniaxially stressed structures are the equilibrium states for relatively thick films. When the film thickness decreases, the area of a three-domain hierarchical structure shrinks and disappears followed by the disappearing cellular domain structures. In thin films, two-domain structures with asymmetric architectures are stable at negative symmetric misfit (in-plane contraction), while two-domain structures with symmetric domain architectures are stable at positive symmetric misfit (in-plane expansion). The results of the phase-field modeling are discussed in connection with the experimental data available for film/substrate ferroelectric heterostructures.