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Modern practice fits the whole pattern simultaneously — peak positions, intensities, widths, and background — against a structural model, a procedure called Rietveld refinement. Software packages such as GSAS-II implement this as a nonlinear least-squares problem that minimizes the weighted residual between an observed and a calculated pattern across every measured point [ 6 ] . Refinement quality is reported as a weighted profile R-factor, $R_{wp} = \sqrt{\frac{\sum_i w_i \left(y_i^{\mathrm{obs}} - y_i^{\mathrm{calc}}\right)^2}{\sum_i w_i \left(y_i^{\mathrm{obs}}\right)^2}}$. alongside a goodness-of-fit statistic that compares $R_{wp}$ to the value expected from counting statistics alone. A low $R_{wp}$ is necessary but not sufficient evidence of a correct structure: a wrong space group with enough adjustable…

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