Figure 5 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, residual plots, the normalized error distribution and normal probability plots of the residuals (Figure 6) are perhaps the best means by which to judge the quality of the fit. For the normal probability plot of the normalized residuals, a linear plot with a zero intercept and unit slope indicates that the error is standard normally distributed. Numerical assessment of the fit is made using a chi-squared value, with lower values reflecting an improved fit. The refinement was stopped when the fit could not be significantly improved.
Figure 6: Refined data for sample 1a showing raw, best-
fit, and difference curves. The tic marks show peak positions for (bottom up) a
lite, belite ( β and 
forms), ferrite, cubic and orthorhombic aluminates, and periclase.