Fitting Full X-Ray Diffraction Patterns for Quantitative Analysis: A Method for Readily Quantifying Crystalline and Disordered Phases

Fitting of full X-ray diffraction patterns is an effective method for quantifying abundances during X-ray diffraction (XRD) analyses. The method is based on the principal that the observed diffraction pattern is the sum of the individual phases that compose the sample. By adding an internal standard (usually corundum) to both the observed patterns and to those for individual pure phases (standards), all patterns can all be normalized to an equivalent intensity based on the internal standard intensity. Using least-squares refinement, the individual phase proportions are varied until an optimal match is reached. As the fitting of full patterns uses the entire pattern, including background, disordered and amorphous phases are explicitly considered as individual phases, with their individual intensity profiles or “amorphous humps” included in the refinement. The method can be applied not only to samples that contain well-ordered materials, but it is particularly well suited for samples containing amorphous and/or disordered materials. In cases with extremely disordered materials where no crystal structure is available for Rietveld refinement or there is no unique intensity area that can be measured for a traditional RIR analysis, full-pattern fitting may be the best or only way to readily obtain quantitative results. This approach is also applicable in cases where there are several coexisting highly disordered phases. As all phases are considered as discrete individual components, abundances are not constrained to sum to 100%.