Different types of HOLZ-line interactions and their use in structure factor determination

Abstract

Characteristic splitting configurations occur at the intersection of mirror-related deficit HOLZ lines in the CBED central disc from a centro-symmetric crystal. In this paper essentially two types of splitting are found for special combinations of specimen thickness, structure factors and accelerating voltage in the three-beam approximation, referred to as the horizontal and vertical splitting, respectively. From the magnitude of these splittings, structure factors can be determined, and this has previously been discussed extensively for the horizontal splitting. For vertical splittings this paper discusses two methods for structure factor determination. The first method, based on a direct angle measurement in the CBED pattern, yields a value with a relative error equal to the relative error in specimen thickness and an accuracy up to 5% for higher-order structure factors. The second method is based on a least-squares refinement of both the structure factor and specimen thickness and consists of fitting a measured intensity profile in the central CBED disc to the calculated profile. This method does not suffer from an uncertainty in specimen thickness, but is more sensitive to random noise and the influence of spurious reflections which makes it more applicable (better than 5%) to lower-order structure factors. Energy filtering did not significantly improve the accuracy of this method.