Edmiston John K, Bernier Joel V, Barton Nathan R, Johnson George C
University of California, Berkeley, California, USA.
Acta Crystallogr A. 2012 Mar;68(Pt 2):181-7. doi: 10.1107/S010876731105598X. Epub 2012 Jan 27.
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.
本文作为X射线衍射程序的一部分，定量地协调了晶格细化的晶体学方法和力学方法。从固定参考构型出发，建立了基于晶胞参数的细化与基于晶格变形张量的细化之间的等价关系。还推导了X射线衍射基应力分析中常用的小应变假设的合理性。结果表明，基于无限小应变的关系在应变的二次方误差范围内是正确的。对于高精度或高应变实验，考虑这个误差可能很重要。希望这些结果有助于晶体学和实验力学领域之间的交流与合作，适用于以X射线衍射数据为基本测量手段的研究。
