Formation of double-diffracted higher-order Laue zone lines

Abstract

In crystals with a glide plane perpendicular to the incident beam, higher-order Laue zone (HOLZ) lines formed by double diffraction (DD)Mayappear as fine bright lines in the forbidden zero-order Laue zone discs of a convergent-beam electron diffraction pattern. In this paper the formation of DD HOLZ lines has been studied systematically. A pseudo-kinematical analysis has been carried out, enabling the positions and directions of DD HOLZ lines to be predicted. Simulations based on this analysis agree well with experimental results. Using the pseudo-kinematical formulation it can be demonstrated that extinction exists between overlapping conjugately paired DD HOLZ reflections as a result of opposite signs of the combined structure factors and approximately equal contributions of excitation error terms for the two reflections. In the dynamical analysis, a method to display branches of the dispersion surface has been devised and extensively used to investigate the calculated results of the Bloch wave dynamical theory related to DD HOLZ lines. The principal areas on the dispersion surface which contribute to the DD HOLZ line intensity have been located. The apparent extinction line between two conjugately paired DD HOLZ lines is due to incomplete destructive interference between two waves with equal amplitudes, opposite initial phases and slightly different eigenvalues (wave-vectors); this results in an approximate cancellation. By contrast, the GjØnnes-Moodie dynamical extinction condition corresponds to a situation where the degeneracy of eigenvalues occurs, resulting in completely destructive interference between waves and leading to exact cancellation.