Bayesian Statistical Model for Imaging of Single La Vacancies in LaMnO 3

Abstract

We report an approach for three-dimensional imaging of single vacancies using high precision quantitative high-angle annular dark-field Z-contrast scanning transmission electron microscopy (STEM). Vacancies are identified by both the reduction in scattered intensity created by the missing atom and the distortion of the surrounding atom positions. Vacancy positions are determined laterally to a unique lattice site in the image and in depth to within one of two lattice sites by dynamical diffraction effects. 35 single La vacancies are identified in images of a LaMnO3 thin film sample. The vacancies are randomly distributed in depth and correspond to a La vacancy concentration of 0.79%, which is consistent with the level of control of cation stoichiometry within our synthesis process (~1%) and with the equilibrium concentration of La vacancies under the film growth conditions. This work demonstrates an approach to characterizing low concentrations of vacancies with high spatial resolution.