In situ synchrotron X-ray and neutron diffraction experiments provide a powerful approach to measure lattice strains in bulk polycrystalline materials. They are being increasingly used for quantitative characterization of microscale deformation within and between grains and phases. Here we use a self-consistent micromechanics model to obtain a general analytic solution of the grain-level lattice strains and diffraction elastic constants for a broad class of elastically isotropic polycrystals with cubic crystal symmetry. This analytic solution reveals a direct linear relationship between the reciprocal of the elastic diffraction constant and the orientation index parameter along the direction of any diffraction vector, including tensile loading and transverse directions. The straightforward numerical implementation of this solution provides diffraction elastic constants for 26 representative cubic polycrystals. Analytic solutions of this kind can serve to benchmark in situ diffraction measurements of lattice strains and also facilitate high-throughput studies of microscale stresses and diffraction elastic constants in polycrystalline materials.

原位同步加速器X射线和中子衍射实验提供了一种强大的方法来测量块状多晶材料中的晶格应变。它们正越来越多地用于晶粒和相内和相之间的微观形变的定量表征。在这里，我们使用一个自洽的微力学模型来获得具有立方晶体对称性的一类广泛的各向同性多晶的晶粒级晶格应变和衍射弹性常数的一般解析解。该解析解揭示了弹性衍射常数的倒数与取向指数参数之间沿任何衍射矢量方向（包括拉伸载荷和横向）的直接线性关系。该解决方案的直接数值实现提供了26个代表性立方多晶的衍射弹性常数。此类分析解决方案可以用作基准晶格应变的原位衍射测量，也有助于对多晶材料中的微观应力和衍射弹性常数进行高通量研究。