Broadening and displacement of x-ray powder diffraction lines under nonhydrostatic stress: Cubic, hexagonal, and tetragonal materials

Abstract

Non-hydrostatic stress is an unavoidable feature of high-pressure x-ray diffraction experiments and can significantly influence diffraction peak positions and shapes. In this work, we implement a generalized framework for predicting diffraction line displacement and broadening arising from uniaxial stress in polycrystalline materials, extending previous elastic-theory treatments beyond cubic systems to include hexagonal and tetragonal crystal symmetries. We implement this approach in a software package, which combines elastic theory with variable angle-dispersive diffraction geometries to calculate orientation-dependent lattice strains and corresponding diffraction profiles. Simulations reproduce established results for face-centered cubic Au and demonstrate how stress-induced broadening and asymmetry emerge in cubic and lower-symmetry systems such as hexagonal ϵ-Fe and tetragonal β-Sn. We also show that the peak splitting in trigonal wüstite (FeO) above 40 GPa, first observed more than 40 years ago, arises from stress-induced broadening. These results illustrate how non-hydrostatic stress can produce diffraction features that may complicate data interpretation and provide a practical route for assessing such effects in high-pressure x-ray diffraction experiments.