Lattice refinement strategies

Abstract

This article quantitatively reconciles crystallographic and mechanics approaches to lattice refinement as part of X-ray diffraction procedures. The equivalence between the refinement based on unit-cell parameters to that based on a lattice deformation tensor is established from a fixed reference configuration. Justification for the small strain assumption, commonly employed in X-ray diffraction based stress analysis, is also derived. It is shown that relations based on infinitesimal strains are correct to within an error of quadratic order in strain. This error may be important to consider for high-precision or high-strain experiments. It is hoped that these results are of use for facilitating communication and collaboration between crystallography and experimental mechanics communities, for studies where X-ray diffraction data are the fundamental measurement.