Fig. 1
From: Demonstration of ultra-high recyclable energy densities in domain-engineered ferroelectric films
Energy storage in ferroelectrics and optimal design of their domain structures. a A normal ferroelectric P – E loop, b a slim ferroelectric P – E loop, and c P – E loops (partially shown) for a single-domain and an engineered polydomain ferroelectric film. The green-shaded areas represent the recyclable energy densities, while the shaded areas within the loops are the energy losses of one charge–discharge cycle. d Free energies \(\left( {\tilde F} \right)\) vs. misfit strain ε M for a film with a single-domain rhombohedral phase (R I, \({\tilde F_{{R_{\rm{I}}}}}\)or R II, \({\tilde F_{{R_{{\rm{II}}}}}}\)), a single-domain tetragonal phase (T, \({\tilde F_T}\)), T/R heterophase polydomains \(\left( {{{\tilde F}_{{\rm{hp}}}}} \right),\) and rhombohedral polytwins (R I/R II, \({\tilde F_{{\rm{tw}}}}\)). Stable regions of the polydomain structures are determined by the common tangent method applied to the free energy curves of single-domain films. ε T and ε tw are the spontaneous strains of the T and R II domains with respect to the R I domain. Schematics of the polydomain structures are shown in e for a T/R heterophase polydomain, and f for hierarchical rhombohedral polytwins formed in a (001)-oriented epitaxial ferroelectric film with a bulk rhombohedral phase
