Atomic-precision determination of the reconstruction of a 90∘90∘ tilt boundary in YBa2Cu3O7-δYBa2Cu3O7-δ by aberration corrected HRTEM

Aberration corrected high-resolution transmission electron microscopy is used to determine the reconstruction of atomic bonds of a 90∘90∘ [1 0 0] grain boundary in YBa2Cu3O7-δYBa2Cu3O7-δ. A precise measurement of atom positions within the grain boundary and the assessment of the oxygen stoichiometry require at the same time a high control of residual lens aberrations of the electron microscope and a good signal-to-noise ratio. This goal is achieved by the combination of spherical-aberration correction in the microscope with the numerical exit-plane wave function reconstruction from focal series. Atomic column positions for individual cations and anions are determined by the regression analysis of peak maxima in the phase image of the retrieved exit-plane wave function. The measurement accuracy is quantitatively assessed, including the statistical error related to residual noise. Changes in bondlengths between copper atoms and the apical oxygen are measured, indicating the distortion of the square pyramidal oxygen coordination of plane copper sites and the square coordination of chain copper sites in the grain boundary.