Analysis of Grain-Boundary Structures by Quantitative Hrtem

Abstract

HRTEM (high-resolution transmission electron microscopy) constitutes a powerful technique to investigate the atomistic structure of grain boundaries. However, interpreting HRTEM images of grain boundaries in terms of “projected structure” may lead to errors: Near a boundary, the contrast patterns of atom columns may differ from the corresponding patterns in regions of unfaulted crystal. Even worse, dynamic diffraction and lens aberrations may displace the contrast patterns against the actual (projected) positions of the columns. Nevertheless, it is possible to interpret such images safely by comparing them with simulated images of structure models. This method becomes powerful if one compares experimental and simulated images not merely by visual inspection but quantitatively, by means of digital image processing.For a given HRTEM image of a grain boundary we iterate such quantitative image comparisons to perform an automatic structure refinement, which determines the structure that yields the best-matching simulated image to the experimental image (Fig. 1). While we can refine the positions of atom columns to any numerical precision, the coordinates only have a limited reliability. This arises because it is impossible to simulate HRTEM images perfectly – even if one knew the structure of the specimen. To quantify error limits for the column coordinates we explore how the simulated image of the refined structure changes with small displacements of the columns. It turns out that our method delivers the coordinates of atom columns with a precision in the order of 0.01 nm. The method also accounts for the damage that electron beam irradiation introduces in the specimen. By means of “beam damaging experiments” we estimate the maximum duration of irradiation to be allowed before damaging interferes with determining the structure at a given precision.