2.6 Data Analysis
Rietveld refinement is popular because it provides a means to measure pattern intensity and to calculate the best-fit set of patterns based upon modified crystal structure models. The method works by generating a theoretical pattern based on structural models for each of the phases and then compares this calculated pattern to the observed one. Differences between the two can be reduced by altering some of the model parameters. The refinement procedure involves minimizing the sum of the weighted, squared differences between the observed and calculated peak intensities point-by-point over the entire diffraction pattern [19]. The full-pattern approach provides a more precise intensity measurement over that of individual peaks, but each crystalline component must be identified and included in the analysis to ensure proper calculation of the scale (intensity) factors and phase fractions. This approach has been standardized, as described in ASTM C1365 [5, 19].