The bootstrap method as a test for non-centrosymmetricity – Application to tazheranite (Zr,Ca,Ti)O2

Abstract

Abstract The bootstrap statistical method is applied to the analysis of single-crystal X-ray diffraction data of tazheranite [(Zr,Ca,Ti)O2; cubic, a = 5.117 Å], in order to establish the significance of statistical estimators of noncentrosymmetricity. The lack of the inversion centre is successfully proved showing that the average structure of tazheranite has space group F[unk]3m, due to a different repartition of oxygen vacancies between two sites of the fluorite-type structure. Instead, classical estimators of the intensity distribution and of the refinements were not able to discriminate between Fm[unk]m and F[unk]3m space groups.