Black-white contrast on transmission electron microscope images of small dislocation loops in elastically anisotropic crystals

Abstract

The black-white contrast of small dislocation loops in elastically anisotropic crystals is calculated using the first-order perturbation solution for the dynamical two-beam diffraction condition. It is shown that under realistic conditions the contrast is given essentially by the projection of the displacement field of the dislocation loop onto the image plane. From the Fourier representation [gtilde](k) of the Green's function of the displacement field of point forces the projected displacement field of the loop is obtained by two-dimensional inversion of the Fourier transformation. The final result is applicable for arbitrary directions of the incident electron beam and implies as the critical step the determination of the six roots of the denominator of [gtilde](k) in the image plane. Examples referring to crystals of cubic symmetry demonstrate that the orientation and shape of the black-white contrast figure becomes more and more insensitive to the actual directions of the loop normal n and the loop Burgers vector b as the elastic anisotropy increases.