On the analysis of electron diffraction patterns from twist grain boundaries

In a recent paper an electron diffraction technique was developed to study the structure of high angle 〈001〉 twist boundaries. Extra reflections (0-reflections) were observed which were attributed to diffraction from a periodic displacement field in the boundaries. In order to demonstrate that these reflections were not produced by double diffraction by the two crystals adjoining the boundary, a limited analysis of the double diffraction possibilities was performed. In order to put this technique on a firmer footing a more general analysis is developed in the present work which considers the contribution by double diffraction of all possible combinations of crystal reflections to the experimentally observed 0-reflections. It is shown that for all twist boundaries it is geometrically possible for double diffraction to contribute to the 0-reflections, under the assumption of an Ewald sphere of infinite radius. It is then demonstrated that when the curvature of the Ewald sphere is taken into account, the possibility of double diffraction can be discounted. Additional experimental work is cited to confirm this conclusion.