Ferroelastic twin domain patterns and polar domain walls of BiVO₄ thin films via phase-field simulations

Polar domain walls in centrosymmetric ferroelastics (e.g., BiVO₄ films) give rise to inhomogeneity and offer promises for solar energy conversion applications via expediting charge-carrier separation. However, the origin of polar domain walls and the relationship between them and spontaneous strain from structural phase transition remain elusive at the mesoscale in BiVO₄ films. Here, from the perspective of phenomenological thermodynamics, the relationship between four variants of monoclinic (M) phase and the corresponding lattice parameters during the tetragonal-monoclinic (T-M) phase transition is revealed. Using phase-field simulations, it suggests that the formation of four variants of ferroelastic twin domains arises from spontaneous strain from T-M phase transition. Moreover, it is demonstrated that (i) polar domain walls in BiVO₄ films originate from the flexoelectric effect induced by strain gradient across the domain walls during phase transition process; (ii) shear strain gradient dominates the contribution to the polarization vectors at the domain walls; (iii) 180° head-to-head or tail-to-tail in-plane polarization configurations emerge at the adjacent domain walls. The stability of several types of ferroelastic domain walls is also analyzed from the point of view of total free energy. These results not only provide a fundamental understanding of the origin of polar domain walls and the formation mechanisms of ferroelastic twin patterns, but also stimulate potential applications of polar domain walls of non-polar BiVO₄ films in energy conversion.