Identification of grain boundary dislocations

Abstract

An examination is made of the method for identifying grain boundary dislocations (GBDs) by applying g · b rules to images taken under conditions where one crystal is oriented for good two-beam diffraction and the other is not diffracting any beam strongly. It is suggested that the use of g · b rules is unreliable and that there is a need for image computation. However, these diffraction conditions are unsuitable for this purpose since they involve many-beam diffraction in the ‘non-diffracting’ crystal for which no simple approximation was found which would make routine image computation practical. A method of identifying GBDs is proposed using images taken when both crystals are simultaneously in good two-beam diffracting conditions. It is shown that, in general, it should be possible to approximate these conditions by a simple two-beam theory of diffraction in each crystal which may therefore be used to obtain theoretical micrographs of GBDs for image matching. The expression for the displacement field of a dislocation lying in a plane welded boundary between two elastically anisotropic half-spaces is given and the way in which this is used in integrating the Howie–Whelan equations to produce theoretical images of GBDs is described. The conditions which need to be satisfied to provide a reliable identification of GBDs are discussed.