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

International Tables for Crystallography (2018). Vol. H, ch. 3.10, p. 377

Section 3.10.4. Powder-diffraction data analysis

L. León-Reina,a A. Cuesta,b M. García-Maté,c,d G. Álvarez-Pinazo,c,d I. Santacruz,c O. Vallcorba,b A. G. De la Torrec and M. A. G. Arandab,c*

aServicios Centrales de Apoyo a la Investigación, Universidad de Málaga, 29071 Málaga, Spain,bALBA Synchrotron, Carrer de la Llum 2–26, Cerdanyola, 08290 Barcelona, Spain,cDepartamento de Química Inorgánica, Cristalografía y Mineralogía, Universidad de Málaga, 29071 Málaga, Spain, and dX-Ray Data Services S.L., Edificio de institutos universitarios, c/ Severo Ochoa 4, Parque tecnológico de Andalucía, 29590 Málaga, Spain
Correspondence e-mail:

3.10.4. Powder-diffraction data analysis

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All powder patterns were analysed by the Rietveld method using the GSAS software package (Larson & Von Dreele, 2000[link]) with the pseudo-Voigt peak-shape function (Thompson et al., 1987[link]) for RQPA. The refined overall parameters were phase scale factors, background coefficients (linear interpolation function), unit-cell parameters, zero-shift error, peak-shape parameters and preferred-orientation coefficient, when needed. The March–Dollase preferred-orientation adjustment algorithm was employed (Dollase, 1986[link]). The modelling direction must be given as input for the calculations. In this case, the directions for the different phases were taken from previous studies. Alternatively, this direction can be extracted from the pattern from an analysis of the differences between observed and calculated intensities for non-overlapped diffraction peaks. The crystal structures used are reported in Table 3.10.1[link].

In order to provide a single numerical assessment of the performance of each analysis, a statistic based on the KLD distance was used (Kullback, 1968[link]). This approach was previously used to evaluate the accuracy of RQPA applied to standard mixtures (Madsen et al., 2001[link]; Scarlett et al., 2002[link]; León-Reina et al., 2009[link]). Both phase-related KLD distances and absolute values of the Kullback–Leibler distance (AKLD) were calculated. Accurate analyses are mirrored by low values of AKLD.

The overall amorphous content was determined from the internal standard methodology approach (De la Torre et al., 2001[link]; Aranda et al., 2012[link]) with quartz as an internal standard [using isotropic atomic displacement parameters (ADPs) of 0.045 and 0.0087 Å2 for Si and O, respectively]. If the original sample contains an amorphous phase, the amount of standard will be overestimated in RQPA. From the (slight) overestimation of the standard, the amorphous content of the investigated sample can be derived (De la Torre et al., 2001[link]). The important role of the values of the ADPs in the results of RQPA mainly in amorphous content determinations using the internal-standard method has been discussed previously (Madsen et al., 2011[link]).


Aranda, M. A. G., De la Torre, Á. G. & León-Reina, L. (2012). Rietveld quantitative phase analysis of OPC clinkers, cements and hydration products. Rev. Mineral. Geochem. 74, 169–209.Google Scholar
De La Torre, A. G., Bruque, S. & Aranda, M. A. G. (2001). Rietveld quantitative amorphous content analysis. J. Appl. Cryst. 34, 196–202.Google Scholar
Dollase, W. A. (1986). Correction of intensities for preferred orientation in powder diffractometry: application of the March model. J. Appl. Cryst. 19, 267–272.Google Scholar
Kullback, S. (1968). Information Theory and Statistics, pp. 1–11. New York: Dover.Google Scholar
Larson, A. C. & Von Dreele, R. B. (2000). General Structure Analysis System (GSAS). Los Alamos National Laboratory Report LAUR 86-748.Google Scholar
León-Reina, L., De la Torre, A. G., Porras-Vázquez, J. M., Cruz, M., Ordonez, L. M., Alcobé, X., Gispert-Guirado, F., Larrañaga-Varga, A., Paul, M., Fuellmann, T., Schmidt, R. & Aranda, M. A. G. (2009). Round robin on Rietveld quantitative phase analysis of Portland cements. J. Appl. Cryst. 42, 906–916.Google Scholar
Madsen, I. C., Scarlett, N. V. Y., Cranswick, L. M. D. & Lwin, T. (2001). Outcomes of the International Union of Crystallography Commission on Powder Diffraction Round Robin on Quantitative Phase Analysis: samples 1a to 1h. J. Appl. Cryst. 34, 409–426.Google Scholar
Madsen, I. C., Scarlett, N. V. Y. & Kern, A. (2011). Description and survey of methodologies for the determination of amorphous content via X-ray powder diffraction. Z. Kristallogr. 226, 944–955.Google Scholar
Scarlett, N. V. Y., Madsen, I. C., Cranswick, L. M. D., Lwin, T., Groleau, E., Stephenson, G., Aylmore, M. & Agron-Olshina, N. (2002). Outcomes of the International Union of Crystallography Commission on Powder Diffraction Round Robin on Quantitative Phase Analysis: samples 2, 3, 4, synthetic bauxite, natural granodiorite and pharmaceuticals. J. Appl. Cryst. 35, 383–400.Google Scholar
Thompson, P., Cox, D. E. & Hastings, J. B. (1987). Rietveld refinement of Debye–Scherrer synchrotron X-ray data from Al2O3. J. Appl. Cryst. 20, 79–83.Google Scholar

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