Reflection splitting-induced microstrain broadening

Abstract

Crystal structure determination on the basis of powder diffraction data frequently involves the question how the given diffraction data with some appreciably hkl-dependent line broadening should be interpreted. In many cases, such line broadening may either: (i) reasonably well be reconciled with a certain high-symmetry structure model or (ii) with a variant of the former with lower symmetry crystal family, which frequently will give a somewhat better fit in Rietveld refinement. In this work, it is shown mathematically that symmetry reduction induced reflection spitting masked by other line broadening contributions, thus leading to some reflection splitting-induced line broadening, shows a similar hkl dependence as typically adopted for anisotropic microstrain broadening with respect to the high-symmetry structure. This implies that Rietveld refinement on the basis of the low-symmetry model (including typically isotropic line broadening) and on the basis of the high-symmetry model with anisotropic microstrain broadening can both lead to similar qualities of the fit. Hence, the refinement results for both possibilities should be carefully considered in combination with possibly available additional information (e.g. results of first-principles calculations) to arrive at adequate conclusions concerning the true symmetry of the material under investigation.