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.