Simulations of weak-beam diffraction contrast images of dislocation loops by the many-beam Howie–Basinski equations

Abstract

A computer program has been developed to solve numerically the Howie–Basinski equations of electron diffraction theory, which avoid the so-called column approximation. In this paper we describe the basis of the numerical approach, and apply it to simulate images of small loops in copper under a variety of weak-beam imaging conditions. Simulations were carried out for faulted Frank loops of size 2–10 nm with systematic variations in imaging parameters (the loop orientation, the diffraction vector, the deviation parameter, the loop depth, the foil thickness and beam convergence). Comparisons are made with experiments in ion-irradiated copper. The simulated images were found to be in good qualitative agreement with experimental TEM micrographs. We are able to reach conclusions on the likely visibility of very small clusters, and we discuss the implications of the simulations for experimental measurements of loop number densities and sizes.

Acknowledgements

We are grateful to Professors P.B. Hirsch, D.J.H. Cockayne, C.B. Carter and R. Schäublin for stimulating discussions. Zhongfu Zhou is grateful to the EURATOM/UKAEA Fusion Association for the provision of a studentship. He also wishes to thank St Hugh's College, Oxford, for the award of a Wei Lun Scholarship. Work at UKAEA was funded by the UK Engineering and Physical Sciences Research Council (EPSRC), by the EXTREMAT integrated project and by EURATOM.