Elastic scattering of partially coherent beams of fast electrons by a crystal with a defect

Scattering of a quasi-monochromatic electron beam by a crystal with a defect is described with the use of the mutual coherency function and the formalism of quasi-Bloch waves. An expression correlating the mutual intensity on the exit and entrance surfaces of the crystal in terms of the scattering matrix has been found. The matrix elements are determined by a system of integro-differential equations, which have been obtained without using the column approximation. It has been shown that calculations of the matrix elements can be significantly simplified when the approximation of the small-angle scattering of quasi-Bloch waves by the defect displacement field is satisfied. Such an approximation can be applied in many cases, e.g. to a crystal with a dislocation. The mutual intensity on the crystal entrance surface has been found for the general case of defocused illumination. As an example of applying the new approach, expressions for the intensity in convergent-beam electron diffraction (CBED) and large-angle CBED (LACBED) patterns have been obtained. The LACBED patterns of a crystal with a dislocation have been simulated. It has been shown that the developed approach allows a more exact simulation of the LACBED than do the conventional approaches using the column approximation and the approximation of independent plane waves filling the illumination cone.