International
Tables for
Crystallography
Volume H
Powder diffraction
Edited by C. J. Gilmore, J. A. Kaduk and H. Schenk

International Tables for Crystallography (2018). Vol. H, ch. 3.9, pp. 354-355

Section 3.9.5.2. Demonstration of the Zevin approach

I. C. Madsen,a* N. V. Y. Scarlett,a R. Kleebergb and K. Knorrc

aCSIRO Mineral Resources, Private Bag 10, Clayton South 3169, Victoria, Australia,bTU Bergakademie Freiberg, Institut für Mineralogie, Brennhausgasse 14, Freiberg, D-09596, Germany, and cBruker AXS GmbH, Oestliche Rheinbrückenstr. 49, 76187 Karlsruhe, Germany
Correspondence e-mail:  ian.madsen@csiro.au

3.9.5.2. Demonstration of the Zevin approach

| top | pdf |

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[link]) in which the peak positions were constrained to the space group and unit-cell parameters but the individual peak intensities were refined to empirical values using a pure sub-sample 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 XRF-determined composition, was used as the measure of intensity. These [S\mu_m^*] values then formed the intensity matrix I in equations (3.9.37)[link] and (3.9.38)[link] 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 matrix-manipulation functions required by equation (3.9.38)[link]. The determined values for C for the three phases are given in Table 3.9.3[link]. The values in the C/Ccorundum column should be compared with the values derived in Section 3.9.4.3[link] above.

Table 3.9.3| top | pdf |
Phase calibration constants for corundum, fluorite and zincite determined using the Zevin (Zevin & Kimmel, 1995[link]) and Knudsen (Knudsen, 1981[link]) method

The RIR values were derived earlier in this chapter.

PhaseCC/CcorundumRIR
Corundum 240.91 1.0 1.0
Fluorite 874.27 3.629 3.617
Zincite 1190.81 4.943 4.856

Application of these C values to the analysis of all samples via equation (3.9.34)[link] yields the results given in Fig. 3.9.9[link]. 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 self-calibrating 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 [\mu_m^*] for each sample calculated from the elemental composition.

[Figure 3.9.9]

Figure 3.9.9 | top | pdf |

Plot of the bias (known − determined) in the analysed phase abundances using the Zevin & Kimmel (1995[link]) approach for corundum (black diamonds), fluorite (open triangles) and zincite (crosses). The 72 determinations derive from three replicates of eight mixtures containing three phases each.








































to end of page
to top of page