Revealing phase boundaries by weighted parametric structural refinement

Parametric Rietveld refinement from powder diffraction data has been utilized in a variety of situations to understand structural phase transitions of materials in situ. However, when analysing data from lower-resolution two-dimensional detectors or from samples with overlapping Bragg peaks, such transitions become difficult to observe. In this study, a weighted parametric method is demonstrated whereby the scale factor is restrained via an inverse tan function, making the phase boundary composition a refinable parameter. This is demonstrated using compositionally graded samples within the lead-free piezoelectric (BiFeO₃)_x(Bi_0.5K_0.5TiO₃)_y(Bi_0.5Na_0.5TiO₃)_1–x–y and (Bi_0.5Na_0.5TiO₃)_x(BaTiO₃)_1–x systems. This has proven to be an effective method for diffraction experiments with relatively low resolution, weak peak splitting or compositionally complex multiphase samples.