Auto-Correlation Analysis of High-Resolution Electron Micrographs of Near-Amorphous Thin Films

Abstract

Many electron micrographs of thin films of amorphous materials give the impression that small ordered regions are present (Fig. 1). However, for cases where little order exists it is difficult to decide whether small regular patches are indictions of ordering or just chance occurances. In order to quantitatively characterize the degree of local ordering of nearamorphous materials from information contained in this kind of micrographs, we have developed a new method in which 2-D auto-correlation functions are obtained from small image regions and then rotated relative to each other so that similar features coincide. By summing up of these auto-correlation functions, sane statistical information of the local orderig for the whole image is obtained.Under certain limiting conditions, the intensity distribution of electron micrographs may be related directly to the projection of the charge or potential distribution of a thin film [1]. Then the 2-D auto-correlation function is equivalent to a 2-D form of Patterson Function (PF), well known in X-ray crystallography in that it represents a map of inter-atomic vectors [2]. Fran different area of the image, PFs may be similar but have mutual rotations so that when they are added together, the orientation information is lost; only the Radial Distribution Function (RDF) is obtained (fig. 4). It is therefore necessary to do sane kind of alignment before the summation.