The structure of grain boundaries in strontium titanate: Theory, simulation, and electron microscopy

We review a combination of theoretical and experimental techniques that have been applied to the study of grain boundaries in SrTiO₃, with particular attention to σ3 and ( 100 )-oriented grain boundaries. Electron microscopy, which includes high-resolution transmission and high-angle annular dark-field methods, is discussed, with successful applications to mapping atomic columns and testing theoretical models. Then, we compare and contrast different techniques of electron holography that may be used to map electrostatic potentials. Problems with the current methods of interpretation in holography and impedance spectroscopy are highlighted in an attempt to reconcile their respective estimates of electrostatic potentials at grain boundaries. Then, standard theoretical tools for the atomistic simulation of boundary structures are critically reviewed, which include classical potentials and density functional theory. A promising genetic algorithm for discovering low-energy grain boundary structures is described and tested. Finally, the synergy of experiment, theory, and simulation that is required to understand boundaries is demonstrated, and we identify major challenges to understanding multicomponent systems.