Reliability of atom column positions in a ternary system determined by quantitative high-resolution transmission electron microscopy

Employing an iterative structure refinement procedure, we hare determined the atomistic structure of the Sigma 3 (111) grain boundary in strontium titanate (SrTiO3) from high-resolution transmission electron microscopy (HRTEM) images. This grain boundary serves as a model system to study the effect of column occupancies on the reliability of the column positions. In this paper we introduce a method to derive confidence regions for the positions of individual atom columns at crystal defects. Based on a statistical approach we first determine the reliabilities of different types of atom columns in regions of unfaulted crystal. Next rye extrapolate these reliabilities to obtain the reliabilities of individual atom columns at the grain boundary. The method accounts correctly for random errors and promises to be generally applicable provided that repetitive units of unfaulted crystal structure are contained in the HRTEM image, Under the conditions of the present study, the reliability of a column position correlates with the projected electrostatic potential of the column. Accordingly the reliabilities of the column positions at the boundary vary with the column type: 0.008 nm for Sr-O columns, 0.014 nm for Ti columns, and 0.018 nm for O-O columns.