Computer Simulation of Dislocation Images in Quartz

Abstract

Transmission electron microscopy (TEM) has become one of the most important tools in the characterization of crystal defects. TEM yields images of individual dislocations, making it invaluable in the determination of slip systems. These images are a result of a diffraction process and as such must be interpreted with considerable care. Since the introduction of the two-beam dynamical theory of electron diffraction for imperfect crystals by Howie and Whelan (1961) many calculations of the contrast produced by various crystal defects have been made and they showed good agreement with experiments. From this theory many general rules for the contrast of various defects have been formed. The invisibility criteria for dislocations in an isotropic crystal (g · b = 0 and g · b × u = 0) can be derived directly from the equations of the dynamical theory. In general, however, such rules cannot be established for more complicated situations. It has been shown, for example (Head et al., 1967; Head, 1967; Humble, 1968), that the above invisibility criteria are not valid for anisotropic crystals. In such cases numerical solutions of the Howie-Whelan equations may be necessary to interpret the contrast arising from the dislocations. Since most rock-forming minerals have compositions, structures, and properties more complicated than the materials (primarily metals) for which many of these general rules have been developed, it is important that theoretical calculations be made before attempting to apply any of them.