Simulations of electron elastic diffuse scattering patterns from individual nanometre-sized dislocation loops. I. Kinematical methodology

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A new experimental technique has recently been developed for characterizing small dislocation loops in the electron microscope by collecting elastic diffuse scattering patterns in the vicinity of Bragg reflections. In this paper we develop the theory and computational approaches for simulating such patterns. We apply the anisotropic elastic theory of displacement fields of planar dislocation loops of arbitrary shape to compute the distortion diffuse scattering amplitudes. To do this we extend methods based on kinematical scattering theory, previously used to simulate X-ray and neutron diffuse scattering patterns. We demonstrate significant differences in the diffuse scattering patterns for the electron scattering case that arise from the small width of the incident electron beam, and under weak-beam conditions. We show that the method may be used to distinguish between individual, very small, vacancy or interstitial loops. We also show that elastic anisotropy may have an influence on elastic diffuse scattering patterns from loops, to an extent that varies with the magnitude of the deviation parameter.