Formal conditions for unambiguous residual strain determination by CBED

Abstract

The method of residual strain determination using convergent beam electron diffraction (CBED) is attractive because of its good spatial resolution. However, attempts to obtain all six independent strain components from a CBED pattern lead to ambiguous results. This paper contains analysis of the ambiguities based on the complete algorithm for matching experimental and strain-dependent simulated CBED patterns. The strain parameters which are not determinable by the CBED method are identified by examination of the most common goodness-of-fit functions. The indeterminable parameters are confirmed to be the ‘13’ and ‘23’ components and a combination of the diagonal components of the tensor given in the Cartesian systems having the ‘3’ axis parallel to the beam direction. The ambiguity can be eliminated based on multiple diffraction patterns. It is shown that two different patterns may be insufficient to get a unique strain tensor. The ambiguity can be removed only if certain characteristics of the two patterns are different, or if more than two patterns are used.

Acknowledgements

The work was performed in the framework of a project supported by the European Community under a Marie Curie Intra-European Fellowship (proposal no. 007762). The author would like to thank Dr E. Bouzy (Université de Metz) for the pattern shown in figure 1.

Notes

Email: [email protected]

This choice is based on the assumption that the areas of polygons are less sensitive to errors caused by dynamic effects at the intersections of HOLZ lines. That argument is questionable because both the distances and the areas are based on line locations, and the triangle areas are directly related to the distances (via Heron's formula).

Except some special cases in which the rank can be lower, e.g. when the orientations differ by a rotation about the microscope axis.