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 determi ned the atomistic structure of the Sigma 3 (111) grain boundary in str ontium titanate (SrTiO3) from high-resolution transmission electron mi croscopy (HRTEM) images. This grain boundary serves as a model system to study the effect of column occupancies on the reliability of the co lumn positions. In this paper we introduce a method to derive confiden ce regions for the positions of individual atom columns at crystal def ects. Based on a statistical approach we first determine the reliabili ties of different types of atom columns in regions of unfaulted crysta l. Next rye extrapolate these reliabilities to obtain the reliabilitie s of individual atom columns at the grain boundary. The method account s correctly for random errors and promises to be generally applicable provided that repetitive units of unfaulted crystal structure are cont ained in the HRTEM image, Under the conditions of the present study, t he reliability of a column position correlates with the projected elec trostatic potential of the column. Accordingly the reliabilities of th e 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 colum ns.