Electron microscope images of dislocations meeting a free surface

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Abstract
Expressions for the derivatives of the displacements caused by an arbitrary dislocation meeting the free surface of an elastically isotropic solid at an arbitrary angle have been derived. They have been incorporated into computer programs which use a dynamical theory of electron diffraction, incorporating a column approximation, to calculate the images of dislocations in specimens with two free surfaces. Two-beam images, and weak-beam images calculated on a systematic four-beam approximation, have been computed. These are compared with images computed on the more usual basis-assuming the dislocation to be contained in an infinite elastic medium. For two-beam images the differences are generally small, but there are three cases, one for a screw dislocation and two for edge dislocations, where the differences are probably large enough to be observed experimentally. No major differences have been found for weak-beam images.