International
Tables for Crystallography Volume H Powder diffraction Edited by C. J. Gilmore, J. A. Kaduk and H. Schenk © International Union of Crystallography 2018 
International Tables for Crystallography (2018). Vol. H, ch. 3.9, pp. 354355
Section 3.9.5.2. Demonstration of the Zevin approach^{a}CSIRO Mineral Resources, Private Bag 10, Clayton South 3169, Victoria, Australia,^{b}TU Bergakademie Freiberg, Institut für Mineralogie, Brennhausgasse 14, Freiberg, D09596, Germany, and ^{c}Bruker AXS GmbH, Oestliche Rheinbrückenstr. 49, 76187 Karlsruhe, Germany 
The sample 1 suite from the IUCr CPD round robin on QPA again provides an ideal platform for demonstrating the applicability of this method due to the wide variation of concentration of the constituent phases. A measure of intensity was derived using an hkl_phase (see Section 3.9.6) in which the peak positions were constrained to the space group and unitcell parameters but the individual peak intensities were refined to empirical values using a pure subsample of each of the three phases. For the analysis of the samples, the relative peak intensities were fixed and an overall scale factor S for each phase in each sample (eight samples, three replicates, three phases), multiplied by the mass absorption coefficient calculated from the XRFdetermined composition, was used as the measure of intensity. These values then formed the intensity matrix I in equations (3.9.37) and (3.9.38) while all values in the vector L were assumed to be 1.0 (i.e. all samples were assumed to be fully crystalline). Microsoft Excel provides a useful platform for these calculations since it contains all of the matrixmanipulation functions required by equation (3.9.38). The determined values for C for the three phases are given in Table 3.9.3. The values in the C/C_{corundum} column should be compared with the values derived in Section 3.9.4.3 above.

Application of these C values to the analysis of all samples via equation (3.9.34) yields the results given in Fig. 3.9.9. The results, displayed as bias from the known values, show that at all concentration ranges the analyses are within about ±1% of the weighed values. The important point to note here is that there has been no prior calibration conducted to obtain this result; the system is selfcalibrating and has only relied on having a wide range of concentrations of the three phases in the sample suite. The only prior knowledge used in the analysis is (i) a measure of peak intensity embodied in the empirical phase scale factor and (ii) an estimate of for each sample calculated from the elemental composition.