Simultaneous refinement of X-ray diffraction patterns of multiple phases allows quantitative analysis using the following relationship, whose variables (aside from Z) are all refined in the fitting process:
Wp = (Sp (ZMV)p ) / (Σ[S (ZMV)])
where
| Wp | = the mass fraction of phase p, | |
| S | = the Rietveld scale factor, | |
| Z | = the number of formula units per unit cell, | |
| M | = the mass of the formula unit, and | |
| V | = the unit cell volume. |
Initial estimates of the phase fractions were used to estimate the linear absorption coefficient of the mixture. A second quantitative estimate using a Brindley absorption correction, based upon a mean particle size of 2 µ m, established the final analyses.