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. 344-373
https://doi.org/10.1107/97809553602060000954

Chapter 3.9. Quantitative phase analysis

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

References

Ahtee, M., Nurmela, M., Suortti, P. & Järvinen, M. (1989). Correction for preferred orientation in Rietveld refinement. J. Appl. Cryst. 22, 261–268.Google Scholar
Alexander, L. E. & Klug, H. P. (1948). Basic aspects of X-ray absorption in quantitative diffraction analysis of powder mixtures. Anal. Chem. 20, 886–889.Google Scholar
Ballirano, P. & Caminiti, R. (2001). Rietveld refinements on laboratory energy dispersive X-ray diffraction (EDXD) data. J. Appl. Cryst. 34, 757–762.Google Scholar
Barnes, P., Colston, S., Craster, B., Hall, C., Jupe, A., Jacques, S., Cockcroft, J., Morgan, S., Johnson, M., O'Connor, D. & Bellotto, M. (2000). Time- and space-resolved dynamic studies on ceramic and cementitious materials. J. Synchrotron Rad. 7, 167–177.Google Scholar
Batchelder, M. & Cressey, G. (1998). Rapid, accurate phase quantification of clay-bearing samples using a position-sensitive X-ray detector. Clays Clay Miner. 46, 183–194.Google Scholar
Bergmann, J., Friedel, P. & Kleeberg, R. (1998). Bgmn – a new fundamental parameters based Rietveld program for laboratory X-ray sources; its use in quantitative analysis and structure investigations. IUCr Commission on Powder Diffraction Newsletter, 20, 5–8.Google Scholar
Bergmann, J. & Kleeberg, R. (1998). Rietveld analysis of disordered layer silicates. Mater. Sci. Forum, 278–281, 300–305.Google Scholar
Bergmann, J., Kleeberg, R., Haase, A. & Breidenstein, B. (2000). Advanced fundamental parameters model for improved profile analysis. Mater. Sci. Forum, 347–349, 303–308.Google Scholar
Bette, S., Dinnebier, R. E. & Freyer, D. (2015). Structure solution and refinement of stacking-faulted NiCl(OH). J. Appl. Cryst. 48, 1706–1718.Google Scholar
Bish, D. L. & Howard, S. A. (1988). Quantitative phase analysis using the Rietveld method. J. Appl. Cryst. 21, 86–91.Google Scholar
Bish, D. L. & Post, J. E. (1993). Quantitative mineralogical analysis using the Rietveld full-pattern fitting method. Am. Mineral. 78, 932–940.Google Scholar
Bogue, R. H. (1929). Calculation of the compounds in Portland cement. Ind. Eng. Chem. Anal. Ed. 1, 192–197.Google Scholar
Bordas, J., Glazer, A. M., Howard, C. J. & Bourdillon, A. J. (1977). Energy-dispersive diffraction from polycrystalline materials using synchrotron radiation. Philos. Mag. 35, 311–323.Google Scholar
Brindley, G. W. (1945). The effect of grain or particle size on X-ray reflections from mixed powders and alloys, considered in relation to the quantitative determination of crystalline substances by X-ray methods. London Edinb. Dubl. Philos. Mag. J. Sci. 36, 347–369.Google Scholar
Brindley, G. W. (1980). Crystal structures of clay minerals and their X-ray identification. Mineralogical Society Monograph No. 5, edited by G. W. Brindley & G. Brown, pp. 125–195. London: Mineralogical Society.Google Scholar
Bruker AXS (2013). Topas v5: General profile and structure analysis software for powder diffraction data. Version 5. https://www.bruker.com/topas.Google Scholar
Buhrke, V. E., Jenkins, R. & Smith, D. K. (1998). A Practical Guide for the Preparation of Specimens for X-Ray Fluorescence and X-ray Diffraction Analysis. New York: Wiley-VCH.Google Scholar
Buras, B., Gerward, L., Glazer, A. M., Hidaka, M. & Staun Olsen, J. (1979). Quantitative structural studies by means of the energy-dispersive method with X-rays from a storage ring. J. Appl. Cryst. 12, 531–536.Google Scholar
Casas-Cabanas, M., Rodríguez-Carvajal, J. & Palacín, M. R. (2006). FAULTS, a new program for refinement of powder diffraction patterns from layered structures. Z. Kristallogr. Suppl. 23, 243–248.Google Scholar
Cernik, R. J., Hansson, C. C. T., Martin, C. M., Preuss, M., Attallah, M., Korsunsky, A. M., Belnoue, J. P., Jun, T. S., Barnes, P., Jacques, S., Sochi, T. & Lazzari, O. (2011). A synchrotron tomographic energy-dispersive diffraction imaging study of the aerospace alloy Ti 6246. J. Appl. Cryst. 44, 150–157.Google Scholar
Cheary, R. W. & Coelho, A. (1992). A fundamental parameters approach to X-ray line-profile fitting. J. Appl. Cryst. 25, 109–121.Google Scholar
Cheary, R. W., Coelho, A. A. & Cline, J. P. (2004). Fundamental parameters line profile fitting in laboratory diffractometers. J. Res. Natl Inst. Stand. Technol. 109, 1–25.Google Scholar
Chipera, S. J. & Bish, D. L. (2002). FULLPAT: a full-pattern quantitative analysis program for X-ray powder diffraction using measured and calculated patterns. J. Appl. Cryst. 35, 744–749.Google Scholar
Chipera, S. J. & Bish, D. L. (2013). Fitting full X-ray diffraction patterns for quantitative analysis: a method for readily quantifying crystalline and disordered phases. Adv. Mater. Phys. Chem. 3, 47–53.Google Scholar
Chung, F. H. (1974a). Quantitative interpretation of X-ray diffraction patterns of mixtures. I. Matrix-flushing method for quantitative multicomponent analysis. J. Appl. Cryst. 7, 519–525.Google Scholar
Chung, F. H. (1974b). Quantitative interpretation of X-ray diffraction patterns of mixtures. II. Adiabatic principle of X-ray diffraction analysis of mixtures. J. Appl. Cryst. 7, 526–531.Google Scholar
Chung, F. H. & Smith, D. K. (2000). Industrial Applications of X-ray Diffraction, edited by F. H. Chung & D. K. Smith, ch. 1, pp. 3–10, and ch. 2, pp. 13–32. New York: Marcel Dekker.Google Scholar
Cline, J. P., Von Dreele, R. B., Winburn, R., Stephens, P. W. & Filliben, J. J. (2011). Addressing the amorphous content issue in quantitative phase analysis: the certification of NIST standard reference material 676a. Acta Cryst. A67, 357–367.Google Scholar
Coelho, A. A., Evans, J. S. O. & Lewis, J. W. (2016). Averaging the intensity of many-layered structures for accurate stacking-fault analysis using Rietveld refinement. J. Appl. Cryst. 49, 1740–1749.Google Scholar
Coelho, A. A., Chater, P. A. and Kern, A. (2015). Fast synthesis and refinement of the atomic pair distribution function. J. Appl. Cryst. 48, 869–875Google Scholar
Cowley, J. M. (1976). Diffraction by crystals with planar faults. I. General theory. Acta Cryst. A32, 83–87.Google Scholar
Cressey, G. & Schofield, P. F. (1996). Rapid whole-pattern profile-stripping method for the quantification of multiphase samples. Powder Diffr. 11, 35–39.Google Scholar
De La Torre, A. G., Ángeles, G., Bruque, S., Campo, J. & Aranda, M. A. G. (2002). The superstructure of C3S from synchrotron and neutron powder diffraction and its role in quantitative phase analyses. Cem. Concr. Res. 32, 1347–1356.Google Scholar
De la Torre, A. G. & Aranda, M. A. G. (2003). Accuracy in Rietveld quantitative phase analysis of Portland cements. J. Appl. Cryst. 36, 1169–1176.Google Scholar
Debye, P. & Scherrer, P. (1916). Interferenzen an regellos orientierten Teilchen im Röntgenlicht Phys. Z. 17, 277–283.Google Scholar
Debye, P. & Scherrer, P. (1917). X-ray interference produced by irregularly oriented particles: Constitution of graphite and amorphous C. Phys. Z. 18, 291–301.Google Scholar
Dohrmann, R., Rüping, K. B., Kleber, M., Ufer, K. & Jahn, R. (2009). Variation of preferred orientation in oriented clay mounts as a result of sample preparation and composition. Clays Clay Miner. 57, 686–694.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
Drits, V. A. & Tchoubar, C. (1990). X-ray diffraction by disordered lamellar structures: Theory and application to microdivided silicates and carbons. Heidelberg: Springer Verlag.Google Scholar
Eberl, D. D. (2003). User's guide to rockjock - a program for determining quantitative mineralogy from powder x-ray diffraction data. U.S. Geological Survey Open-File Report 2003-78. http://pubs.er.usgs.gov/publication/ofr200378.Google Scholar
Egami, T. & Billinge, S. J. L. (2003). Underneath the Bragg Peaks: Structural Analysis of Complex Materials. Oxford: Elsevier.Google Scholar
Ehrenberg, H., Senyshyn, A., Hinterstein, M. & Fuess, H. (2013). Modern Diffraction Methods, edited by E. J. Mittemeijer & U. Welzel, pp. 491–517. Weinheim: Wiley-VCH Verlag GMBH & Co.Google Scholar
Elton, N. J. & Salt, P. D. (1996). Particle statistics in quantitative X-ray diffractometry. Powder Diffr. 11, 218–229.Google Scholar
Fawcett, T. G., Kabekkodu, S. N., Blanton, J. R. & Blanton, T. N. (2017). Chemical analysis by diffraction: the Powder Diffraction File. Powder Diffr. 32, 63–71.Google Scholar
Fawcett, T. G., Needham, F., Faber, J. & Crowder, C. E. (2010). International Centre for Diffraction Data round robin on quantitative Rietveld phase analysis of pharmaceuticals. Powder Diffr. 25, 60–67.Google Scholar
Frost, D. J. & Fei, Y. (1999). Static compression of the hydrous magnesium silicate phase d to 30 GPa at room temperature. Phys. Chem. Miner. 26, 415–418.Google Scholar
Glazer, A. M., Hidaka, M. & Bordas, J. (1978). Energy-dispersive powder profile refinement using synchrotron radiation. J. Appl. Cryst. 11, 165–172.Google Scholar
Gualtieri, A. F. (2000). Accuracy of XRPD QPA using the combined Rietveld–RIR method. J. Appl. Cryst. 33, 267–278.Google Scholar
Gualtieri, A. F., Viani, A., Banchio, G. & Artioli, G. (2001). Quantitative phase analysis of natural raw materials containing montmorillonite. Mater. Sci. Forum, 378–381, 702–709.Google Scholar
Hall, C., Barnes, P., Cockcroft, J. K., Colston, S. L., Häusermann, D., Jacques, S. D. M., Jupe, A. C. & Kunz, M. (1998). Synchrotron energy-dispersive X-ray diffraction tomography. Nucl. Instrum. Methods Phys. Res. B, 140, 253–257.Google Scholar
Hall, C., Colston, S. L., Jupe, A. C., Jacques, S. D. M., Livingston, R., Ramadan, A. O. A., Amde, A. W. & Barnes, P. (2000). Non-destructive tomographic energy-dispersive diffraction imaging of the interior of bulk concrete. Cem. Concr. Res. 30, 491–495.Google Scholar
Hendricks, S. & Teller, E. (1942). X-ray interference in partially ordered layer lattices. J. Chem. Phys. 10, 147–167.Google Scholar
Hill, R. J. (1983). Calculated X-ray powder diffraction data for phases encountered in lead/acid battery plates. J. Power Sources, 9, 55–71.Google Scholar
Hill, R. J. (1991). Expanded use of the Rietveld method in studies of phase abundance in multiphase mixtures. Powder Diffr. 6, 74–77.Google Scholar
Hill, R. J. (1992). The background in X-ray powder diffractograms: a case study of Rietveld analysis of minor phases using Ni-filtered and graphite-monochromated radiation. Powder Diffr. 7, 63–70.Google Scholar
Hill, R. J. & Howard, C. J. (1987). Quantitative phase analysis from neutron powder diffraction data using the Rietveld method. J. Appl. Cryst. 20, 467–474.Google Scholar
Hill, R. J., Howard, C. J. & Reichert, B. E. (1991). Quantitative phase abundance in Mg-PSZ by Rietveld analysis of neutron and X-ray diffraction data. Mater. Sci. Forum, 34–36, 159–163.Google Scholar
Hill, R. J. & Madsen, I. C. (2002). Structure Determination from Powder Diffraction Data, edited by W. David, K. Shankland, L. McCusker & C. Baerlocher, ch. 6, pp. 98–116. Oxford University Press.Google Scholar
Hubbard, C. R., Evans, E. H. & Smith, D. K. (1976). The reference intensity ratio, I/Ic, for computer simulated powder patterns. J. Appl. Cryst. 9, 169–174.Google Scholar
Hubbard, C. R. & Snyder, R. L. (1988). RIR – measurement and use in quantitative XRD. Powder Diffr. 3, 74–77.Google Scholar
Hull, A. W. (1917). A new method of X-ray crystal analysis. Phys. Rev. 10, 661–696.Google Scholar
Hull, A. W. (1919). A new method of chemical analysis. J. Am. Chem. Soc. 41, 1168–1175.Google Scholar
ICDD (2015). The Powder Diffraction File, database of the International Centre for Diffraction Data, release PDF4+, 2015. ICDD, 12 Campus Boulevard, Newton Square, Pennsylvania 19073–3273, USA.Google Scholar
Kaduk, J. A. (2000). In Industrial Applications of X-ray Diffraction, edited by F. H. Chung & D. K. Smith, pp. 207–253. New York: Marcel Dekker.Google Scholar
Kleeberg, R. (2005). Results of the second Reynolds Cup contest in quantitative mineral analysis. IUCr Commission on Powder Diffraction Newsletter, 30, 22–26.Google Scholar
Klug, H. P. & Alexander, L. E. (1974). X-ray Diffraction Procedures: For Polycrystalline and Amorphous Materials. New York: Wiley.Google Scholar
Knorr, K. & Bornefeld, M. (2013). Proceedings of Process Mineralogy '12, 7–9 November 2012. Cape Town, South Africa, pp. 651–652. http://www.proceedings.com/16755.html.Google Scholar
Knudsen, T. (1981). Quantitative X-ray diffraction analysis with qualitative control of calibration samples. X-ray Spectrom. 10, 54–56.Google Scholar
Langford, J. I. (2004). In Diffraction Analysis of the Microstructure of Materials, edited by E. J. Mittemeijer & P. Scardi, pp. 3–11. Berlin: Springer-Verlag.Google Scholar
Larson, A. C. & Von Dreele, R. B. (2004). General Structure Analysis System (GSAS). Report LAUR 86-748, Los Alamos National Laboratory, New Mexico, USA.Google Scholar
Le Bail, A., Duroy, H. & Fourquet, J. L. (1988). Ab-initio structure determination of LiSbWO6 by X-ray powder diffraction. Mater. Res. Bull. 23, 447–452.Google Scholar
Le Bail, A. & Jouanneaux, A. (1997). A qualitative account for anisotropic broadening in whole-powder-diffraction-pattern fitting by second-rank tensors. J. Appl. Cryst. 30, 265–271.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
Leoni, M., Gualtieri, A. F. & Roveri, N. (2004). Simultaneous refinement of structure and microstructure of layered materials. J. Appl. Cryst. 37, 166–173.Google Scholar
Lippmann, F. (1970). Functions describing preferred orientation in flat aggregates of flake-like clay minerals and in other axially symmetric fabrics. Contr. Miner. Petrol. 25, 77–94.Google Scholar
McCarty, D. K. (2002). Quantitative mineral analysis of clay-bearing mixtures: The `Reynolds Cup' contest. IUCr Commission on Powder Diffraction Newsletter, 27 12–16.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
Madsen, I. C., Scarlett, N. V. Y., Riley, D. P. & Raven, M. D. (2013). Modern Powder Diffraction, edited by E. J. Mittemeijer & U. Welzel, pp. 283–320. Weinheim: Wiley-VCH.Google Scholar
Madsen, I. C., Scarlett, N. V. Y. & Whittington, B. I. (2005). Pressure acid leaching of nickel laterite ores: an in situ diffraction study of the mechanism and rate of reaction. J. Appl. Cryst. 38, 927–933.Google Scholar
Michalski, E. (1988). The diffraction of X-rays by close-packed polytypic crystals containing single stacking faults. I. General theory. Acta Cryst. A44, 640–649.Google Scholar
Michalski, E., Kaczmarek, S. M. & Demianiuk, M. (1988). The diffraction of X-rays by close-packed polytypic crystals containing single stacking faults. II. Theory for hexagonal and rhombohedral structures. Acta Cryst. A44, 650–657.Google Scholar
Morris, R. E., Harrison, W. T. A., Nicol, J. M., Wilkinson, A. P. & Cheetham, A. K. (1992). Determination of complex structures by combined neutron and synchrotron X-ray powder diffraction. Nature, 359, 519–522.Google Scholar
Murray, J., Kirwan, L., Loan, M. & Hodnett, B. K. (2009). In-situ synchrotron diffraction study of the hydrothermal transformation of goethite to hematite in sodium aluminate solutions. Hydrometallurgy, 95, 239–246.Google Scholar
Navias, L. (1925). Quantitative determination of the development of mullite in fired clays by an X-ray method. J. Am. Ceram. Soc. 8, 296–302.Google Scholar
Norby, P., Cahill, C., Koleda, C. & Parise, J. B. (1998). A reaction cell for in situ studies of hydrothermal titration. J. Appl. Cryst. 31, 481–483.Google Scholar
O'Connor, B. H. & Raven, M. D. (1988). Application of the Rietveld refinement procedure in assaying powdered mixtures. Powder Diffr. 3, 2–6.Google Scholar
Omotoso, O., McCarty, D. K., Hillier, S. & Kleeberg, R. (2006). Some successful approaches to quantitative mineral analysis as revealed by the 3rd Reynolds Cup contest. Clays Clay Miner. 54, 748–760.Google Scholar
Ottner, F., Gier, S., Kuderna, M. & Schwaighofer, B. (2000). Results of an inter-laboratory comparison of methods for quantitative clay analysis. Appl. Clay Sci. 17, 223–243.Google Scholar
Parrish, W. (1965). Editor. X-ray Analysis Papers, 2nd ed. Eindhoven: Centrex Publishing Company.Google Scholar
Pawley, G. S. (1980). EDINP, the Edinburgh powder profile refinement program. J. Appl. Cryst. 13, 630–633.Google Scholar
Pawley, G. S. (1981). Unit-cell refinement from powder diffraction scans. J. Appl. Cryst. 14, 357–361.Google Scholar
Peplinski, B., Kleeberg, R., Bergmann, J. & Wenzel, J. (2004). Quantitative phase analysis using the Rietveld method – estimates of possible problems based on two interlaboratory comparisons. Mater. Sci. Forum, 443-444, 45–50.Google Scholar
Popa, N. C. (1998). The (hkl) dependence of diffraction-line broadening caused by strain and size for all Laue groups in Rietveld refinement. J. Appl. Cryst. 31, 176–180.Google Scholar
Raven, M. D. & Self, P. G. (2017). Outcomes of 12 years of the Reynolds Cup quantitative mineral analysis round robin. Clays Clay Miner. 65, 122–134.Google Scholar
Reynolds, R. C. (1985). Newmod, a computer program for the calculation of one-dimensional diffraction patterns of mixed-layered clays. Hanover, USA.Google Scholar
Reynolds, R. (1989). Quantitative mineral analysis of clays. In CMS Workshop Lectures 1, edited by D. R. Pevear & F. A. Mumpton, pp. 4–37. Boulder: The Clay Minerals Society.Google Scholar
Reynolds, R. C. (1994). Wildfire, a computer program for the calculation of threee-dimensional powder X-ray diffraction patterns for mica polytypes and their disordered variations. Hanover, USA.Google Scholar
Reynolds, R. C. & Hower, J. (1970). The nature of interlayering in mixed-layer illite-montmorillonites. Clays Clay Miner. 18, 25–36.Google Scholar
Rietveld, H. M. (1969). A profile refinement method for nuclear and magnetic structures. J. Appl. Cryst. 2, 65–71.Google Scholar
Rowles, M. R., Styles, M. J., Madsen, I. C., Scarlett, N. V. Y., McGregor, K., Riley, D. P., Snook, G. A., Urban, A. J., Connolley, T. & Reinhard, C. (2012). Quantification of passivation layer growth in inert anodes for molten salt electrochemistry by in situ energy-dispersive diffraction. J. Appl. Cryst. 45, 28–37.Google Scholar
Scarlett, N. V. Y. & Madsen, I. C. (2006). Quantification of phases with partial or no known crystal structures. Powder Diffr. 21, 278–284.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
Scarlett, N. V. Y., Madsen, I. C., Evans, J. S. O., Coelho, A. A., McGregor, K., Rowles, M., Lanyon, M. R. & Urban, A. J. (2009). Energy-dispersive diffraction studies of inert anodes. J. Appl. Cryst. 42, 502–512.Google Scholar
Scarlett, N. V. Y., Madsen, I. C., Pownceby, M. I. & Christensen, A. N. (2004). In situ X-ray diffraction analysis of iron ore sinter phases. J. Appl. Cryst. 37, 362–368.Google Scholar
Scarlett, N. V. Y., Madsen, I. C. & Whittington, B. I. (2008). Time-resolved diffraction studies into the pressure acid leaching of nickel laterite ores: a comparison of laboratory and synchrotron X-ray experiments. J. Appl. Cryst. 41, 572–583.Google Scholar
Scarlett, N. V. Y., Pownceby, M. I., Madsen, I. C. & Christensen, A. N. (2004). Reaction sequences in the formation of silico-ferrites of calcium and aluminum in iron ore sinter. Metall. Mater. Trans. B, 35, 929–936.Google Scholar
Schmitt, B., Brönnimann, C., Eikenberry, E. F., Gozzo, F., Hörmann, C., Horisberger, R. & Patterson, B. (2003). Mythen detector system. Nucl. Instrum. Methods Phys. Res. A, 501, 267–272.Google Scholar
Smith, D. K. (1992). Particle statistics and whole pattern methods in quantitative x-ray powder diffraction analysis. Adv. X-ray Anal. 35, 1–15.Google Scholar
Smith, D. K., Johnson, G. G., Scheible, A., Wims, A. M., Johnson, J. L. & Ullmann, G. (1987). Quantitative X-ray powder diffraction method using the full diffraction pattern. Powder Diffr. 2, 73–77.Google Scholar
Snyder, R. L. & Bish, D. L. (1989). In Modern Powder Diffraction, edited by D. L. Bish & J. E. Post, pp. 101–142. Washington DC: Mineralogical Society of America.Google Scholar
Stephens, P. W. (1999). Phenomenological model of anisotropic peak broadening in powder diffraction. J. Appl. Cryst. 32, 281–289.Google Scholar
Stinton, G. W. & Evans, J. S. O. (2007). Parametric Rietveld refinement. J. Appl. Cryst. 40, 87–95.Google Scholar
Stutzman, P. E. & Leigh, S. (2000). Proceedings of the Twenty-Second International Conference on Cement Microscopy, 11–13 September 2000, Quebec City, Canada. https://cemmicro.org/publications/.Google Scholar
Styles, M. J., Rowles, M. R., Madsen, I. C., McGregor, K., Urban, A. J., Snook, G. A., Scarlett, N. V. Y. & Riley, D. P. (2012). A furnace and environmental cell for the in situ investigation of molten salt electrolysis using high-energy X-ray diffraction. J. Synchrotron Rad. 19, 39–47.Google Scholar
Taylor, J. C. (1991). Computer programs for standardless quantitative analysis of minerals using the full powder diffraction profile. Powder Diffr. 6, 2–9.Google Scholar
Taylor, J. C. & Rui, Z. (1992). Simultaneous use of observed and calculated standard profiles in quantitative XRD analysis of minerals by the multiphase Rietveld method: the determination of pseudorutile in mineral sands products. Powder Diffr. 7, 152–161.Google Scholar
Taylor, R. M. & Norrish, K. (1966). The measurement of orientation distribution and its application to quantitative X-ray diffraction analysis. Clay Miner. 6, 127–142.Google Scholar
Toraya (2016a). A new method for quantitative phase analysis using X-ray powder diffraction: direct derivation of weight fractions from observed integrated intensities and chemical compositions of individual phases. J. Appl. Cryst. 49, 1508–1516Google Scholar
Toraya (2016b). A new method for quantitative phase analysis using X-ray powder diffraction: direct derivation of weight fractions from observed integrated intensities and chemical compositions of individual phases. Corrigendum. J. Appl. Cryst. 50, 665.Google Scholar
Toraya, H. & Tsusaka, S. (1995). Quantitative phase analysis using the whole-powder-pattern decomposition method. I. Solution from knowledge of chemical compositions. J. Appl. Cryst. 28, 392–399.Google Scholar
Treacy, M. M. J., Newsam, J. M. & Deem, M. W. (1991). A general recursion method for calculating diffracted intensities from crystals containing planar faults. Proc. R. Soc. London Ser. A, 433, 499–520.Google Scholar
Ufer, K., Kleeberg, R., Bergmann, J., Curtius, H. & Dohrmann, R. (2008). Refining real structure parameters of disordered layer structures within the Rietveld method. Z. Kristallogr. Suppl. 27, 151–158.Google Scholar
Ufer, K., Kleeberg, R., Bergmann, J. & Dohrmann, R. (2012). Rietveld refinement of disordered illite-smectite mixed-layer structures by a recursive algorithm. II: powder-pattern refinement and quantitative phase analysis. Clays Clay Miner. 60, 535–552.Google Scholar
Ufer, K., Roth, G., Kleeberg, R., Stanjek, H. & Dohrmann, R. (2004). Description of x-ray powder pattern of turbostratically disordered layer structures with a Rietveld compatible approach. Z. Kristallogr. 219, 519–527.Google Scholar
Ufer, K., Stanjek, H., Roth, G., Dohrmann, R., Kleeberg, R. & Kaufhold, S. (2008). Quantitative phase analysis of bentonites by the Rietveld method. Clays Clay Miner. 56, 272–282.Google Scholar
Wang, X., Li, J., Hart, R. D., van Riessen, A. & McDonald, R. (2011). Quantitative X-ray diffraction phase analysis of poorly ordered nontronite clay in nickel laterites. J. Appl. Cryst. 44, 902–910.Google Scholar
Warren, B. E. (1941). X-ray diffraction in random layer lattices. Phys. Rev. 59, 693–698.Google Scholar
Webster, N. A. S., Madsen, I. C., Loan, M. J., Knott, R. B., Naim, F., Wallwork, K. S. & Kimpton, J. A. (2010). An investigation of goethite-seeded Al(OH)3 precipitation using in situ X-ray diffraction and Rietveld-based quantitative phase analysis. J. Appl. Cryst. 43, 466–472.Google Scholar
Webster, N. A. S., Pownceby, M. I. & Madsen, I. C. (2013). In situ X-ray diffraction investigation of the formation mechanisms of silico-ferrite of calcium and aluminium-I-type (SFCA-I-type) complex calcium ferrites. ISIJ Int. 53, 1334–1340.Google Scholar
Westphal, T., Füllmann, T. & Pöllmann, H. (2009). Rietveld quantification of amorphous portions with an internal standard – mathematical consequences of the experimental approach. Powder Diffr. 24, 239–243.Google Scholar
Williams, R. P., Hart, R. D. & van Riessen, A. (2011). Quantification of the extent of reaction of metakaolin-based geopolymers using X-ray diffraction, scanning electron microscopy, and energy-dispersive spectroscopy. J. Am. Ceram. Soc. 94, 2663–2670.Google Scholar
Yuan, H. & Bish, D. (2010). NEWMOD+, a new version of the NEWMOD program for interpreting X-ray powder diffraction patterns from interstratified clay minerals. Clays Clay Miner. 58, 318–326.Google Scholar
Zevin, L. & Viaene, W. (1990). Impact of clay particle orientation on quantitative clay diffractometry. Clay Miner. 25, 401–418.Google Scholar
Zevin, L. S. & Kimmel, G. (1995). Quantitative X-ray Diffractometry. Springer-Verlag New York, Inc.Google Scholar
Zhao, Y., Von Dreele, R. B., Shankland, T. J., Weidner, D. J., Zhang, J., Wang, Y. & Gasparik, T. (1997). Thermoelastic equation of state of jadeite NaAlSi2O6: an energy-dispersive Rietveld refinement study of low symmetry and multiple phases diffraction. Geophys. Res. Lett. 24, 5–8.Google Scholar