Figure 3 shows a composite plot of the raw data, the calculated peak locations for each phase (tic marks at base of plot), the calculated pattern (green trace), and difference plot. Graphical comparison of the observed versus the calculated pattern, the difference plots, the normalized error distribution and normal probability plots (Figure 4) are perhaps the best means by which to judge the quality of the fit. For the normal probability plot of the residuals, a linear plot with a zero intercept and unit slope indicates that the error is normally distributed. Numerical assessment of the fit is made using the chi-squared value, with lower values reflecting an improvement in the fit. The refinement was stopped when the fit could not be significantly improved.
Figure 3. Refined data for sample 1a showing raw,
best-fit, and difference curves. The tic marks show peak positions for
(bottom up) alite, belite (
and 
forms), ferrite, cubic and orthorhombic aluminates, and periclase.
Figure 4. The quality of the fit is reflected through the normalized error distribution. Deviations reflect mis-matches between measured and fit data. A straight normal probability plot of the errors indicates their distribution is well approximated by a Gaussian.