Quantitative comparison of convergent-beam electron diffraction (CBED) patterns

Abstract

The development of large-dynamic-range, solid-state-array detectors, such as position sensors and charge-coupled devices (CCDs), has made possible the direct recording of CBED patterns in digital form with high precision. This, in turn, makes feasible the quantitative comparison of experimental CBED patterns with those from computer simulations. Such quantitative comparison provides a means for confirming the model structure of the local sample area from which the CBED pattern is obtained. This may prove to be useful in solving the structure of radiation-sensitive materials such as some catalysts of industrial interest. The method of using relative entropy in doing such quantitative comparison is presented, and is compared with the more conventional method of using the correlation coefficient (or standard covariance). The major difference between the two methods is found to be that, while both can be used as measures of the similarity between two patterns, relative entropy is much more sensitive to the dissimilarity of two look-alike patterns. It is therefore sensible to use relative entropy as a measure of dissimilarity between experimental and simulated CBED patterns. And, since relative entropy obeys the x 2- distribution , we have an absolute criterion in model to judge whether such dissimilarity is caused by the shot noise which is always present in an experimental CBED pattern, or caused by the parameter errors in the model from which the simulated CBED is calculated.