Predicting Complex Grain Boundary Structures in Oxide Ferroelectrics via Machine-Learning Accelerated Grand Canonical Monte Carlo

Grain boundaries of oxide perovskites exhibit diverse structural and electronic phenomena, including complex local stoichiometry, band structure modification, and nanoscale ferroelectricity. While ab initio Grand Canonical Monte Carlo (ai-GCMC) has been applied to predict grain boundary (GB) structures in binary oxides with density functional theory (DFT) accuracy, its computational cost severely limits exploration of the vast configurational and compositional space of oxide perovskite GBs. To overcome this limitation, we extend the ai-GCMC theory to Σ5(310)[001] SrTiO₃ grain boundaries using a universal machine-learning interatomic potential (uMLIP), which enables efficient sampling of the phase space. The resulting chemical potential phase diagram reveals four stable grain boundary phases: large Sr kite, small Sr kite, Sr-deficient, and Ti-rich structures. Extending GCMC simulations to Σ5(210)[001] and Σ17(410)[001] grain boundaries further demonstrates that the misorientation angle of the grain boundary affects the balance between the small and large kite structures and Ti accommodation in them. Using Σ5(310)[001] SrTiO₃ grain boundaries as examples, our DFT calculations show that grain boundaries can host either positive or negative interfacial charges, with compensating electrons or holes localized on adjacent grains. These local charge distributions delicately depend on the composition and structure of four stabilized phases, modulating the spontaneous flexoelectric polarizations. Finally, we demonstrate the generality of our method by applying it to HfO₂, revealing how the intriguing grain boundary structures of HfO₂ at different misorientation angles favor the polar orthorhombic or non-polar tetragonal phase. Our study establishes the applicability of the GCMC utilizing uMLIP to predict the structural and compositional properties of grain boundaries in oxide ferroelectrics, opening new pathways for designing and rationalizing grain boundary properties.