Skip to main content
SpringerLink
Log in

Automated Fitting of X-Ray Powder Diffraction Patterns from Interstratified Phyllosilicates

  • Published:
Clays and Clay Minerals

Abstract

NEWMOD®, developed by R.C. Reynolds, Jr., has been an important tool for evaluating quantitatively X-ray diffraction (XRD) patterns from interstratified clay minerals for more than 20 years. However, a significant drawback to the NEWMOD® approach is that analyses are done by forward simulation, making results sensitive to user input and starting-model assumptions. In the present study, a reverse-fitting procedure was implemented in a new program, FITMOD, which automatically minimizes the differences between experimental and simulated XRD patterns. The differences are minimized by varying model parameters (such as Reichweite, crystal-size distribution, cation content, type of disorder, etc.) using the downhill simplex method. The downhill simplex method is a non-linear optimization technique for determining minima of functions. This method does not require calculation of the derivatives of the functions being minimized, an important consideration with many of the parameters in NEWMOD- type simulations. Instead, the downhill simplex method calculates pseudo-derivatives by evaluating sufficient points to define a derivative for each independent variable. The performance of FITMOD was evaluated by fitting a series of synthetic XRD patterns generated by NEWMOD+, yielding agreement factors, Rwp, of <0.3%. As long as the correct interstratified system was specified (e.g. illite-smectite), excellent fits were obtained irrespective of the starting parameters for the simulations. FITMOD was also tested using experimental XRD patterns, which gave very good fits, in agreement with previously published results. The optimization routine yields good fits for both synthetic and experimental XRD profiles in a reasonable time, with the possibility of varying all important structural parameters. FITMOD automatically provides optimum fits to experimental XRD data without operator bias, and fitting efficiency and accuracy were, therefore, significantly improved.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Bergmann, J., Kleeberg, R., and Taut, T. (1994) A new structure refinement and quantitative phase analysis method based on predetermined true peak profiles. Zeitschrift für Kristallographie, Supplement issue No. 8, European Crystallogrpahy Meeting 15, Abstracts volume, p. 580.

    Google Scholar 

  • Berkgaut, V., Singer, A., and Stahr, K. (1994) Palagonite reconsidered — paracrystalline illite-smectites from regoliths on basic pyroclastics. Clays and Clay Minerals, 42, 582–592.

    Google Scholar 

  • Bethke, C.M. and Reynolds, R.C. (1986) Recursive method for determining frequency factors in interstratified clay diffraction calculations. Clay and Clay Minerals, 34, 224–226.

    Google Scholar 

  • Bish, D.L. (1989) Evaluation of past and future alterations in tuff at Yucca Mountain, Nevada, based on the clay mineralogy of drill cores USW G-1, G-2, and G-3. Los Alamos National Laboratory Report. LA-10667-MS, 19–22.

    Google Scholar 

  • Bish, D.L. and Aronson, J.L. (1993) Paleogeothermal and paleohydrologic conditions in silicic tuff from Yucca Mountain, Nevada. Clays and Clay Minerals, 41, 148–161.

    Google Scholar 

  • Casas-Cabanas, M., Palacin, M.R. and Rodriguez-Carvajal, J. (2005) Microstructural analysis of nickel hydroxide: Anisotropic size versus stacking faults. Powder Diffraction, 20, 334–344.

    Google Scholar 

  • Cases, J.M., Berend, I., Besson, G., Francois, M., Uriot, J.P., Thomas, F., and Poirier, J.E. (1992) Mechanism of adsorption and desorption of water-vapor by homoionic montmorillonite.1. The sodium-exchanged form. Langmuir, 8, 2730–2739.

    Google Scholar 

  • Coelho, A.A. (2003) TOPAS. User Manual. Version 3.1. Bruker AXS GmbH, Karlsruhe, Germany.

    Google Scholar 

  • Cuadros, J. and Dudek, T. (2006) FTIR investigation of the evolution of the octahedral sheet of kaolinite-smectite with progressive kaolinization. Clays and Clay Minerals, 54, 1–11.

    Google Scholar 

  • David, W.I.F. (2004) Powder diffraction: Least-squares and beyond. Journal of Research of the National Institute of Standards and Technology, 109, 107–123.

    Google Scholar 

  • de la Fuente, S., Cuadros, J., and Linares, J. (2002) Early stages of volcanic tuff alteration in hydrothermal experiments: Formation of mixed-layer illite-smectite. Clays and Clay Minerals, 50, 578–590.

    Google Scholar 

  • Drits, V.A. and Sakharov, B.A. (1976) X-ray Analysis of Mixed-layer Clay Minerals. Nauka, Moscow, 256 pp. (in Russian).

    Google Scholar 

  • Drits, V.A. and Tchoubar, C. (1990) X-ray Diffraction by Disordered Lamellar Structures. Springer Verlag, Berlin, Heidelberg, 371 pp.

    Google Scholar 

  • Drits, V.A., Sakharov, B.A., Lindgreen, H. and Salyn, A. (1997a) Sequential structure transformation of illite-smectite-vermiculite during diagenesis of Upper Jurassic shales from the North Sea and Denmark. Clay Minerals, 32, 351–371.

    Google Scholar 

  • Drits, V., Srodon, J. and Eberl, D.D. (1997b) XRD measurement of mean crystalline thickness of illite and illite/smectite: Reappraisal of the Kubler index and the Scherrer equation. Clays and Clay Minerals, 45, 461–475.

    Google Scholar 

  • Drits, V.A., Sakharov, B.A., Dainyak, L.G., Salyn, A.L., and Lindgreen, H. (2002) Structural and chemical heterogeneity of illite-smectites from Upper Jurassic mudstones of East Greenland related to volcanic and weathered parent rocks. American Mineralogist, 87, 1590–1606.

    Google Scholar 

  • Drits, V.A., Sakharov, B.A., Salyn, A.L., and Lindgreen, H. (2005) Determination of the content and distribution of xed ammonium in illite-smectite using a modied X-ray diffraction technique: Application to oil source rocks of western Greenland. American Mineralogist, 90, 71–84.

    Google Scholar 

  • Dudek, T., Cuadros, J., and Fiore, S. (2006) Interstratified kaolinite-smectite: Nature of the layers and mechanism of smectite kaolinization. American Mineralogist, 91, 159–170.

    Google Scholar 

  • Eberl, D.D., Nuesch, R., Sucha, V., and Tsipursky, S. (1998) Measurement of fundamental illite particle thicknesses by X-ray diffraction using PVP-10 intercalation. Clays and Clay Minerals, 46, 89–97.

    Google Scholar 

  • Ferrage, E., Lanson, B., Sakharov, B.A., and Drits, V.A. (2005a) Investigation of smectite hydration properties by modeling experimental X-ray diffraction patterns: Part I. Montmorillonite hydration properties. American Mineralogist, 90, 1358–1374.

    Google Scholar 

  • Ferrage, E., Lanson, B., Malikova, N., Plancon, A., Sakharov, B.A. and Drits, V.A. (2005b) New insights on the distribution of interlayer water in bi-hydrated smectite from X-ray diffraction profile modeling of 00l reflections. Chemistry of Materials, 17, 3499–3512.

    Google Scholar 

  • Gruner, J.W. (1934) The structure of vermiculites and their collapse by dehydration. American Mineralogist, 19, 557–575.

    Google Scholar 

  • Gualtieri, A.F., Ferrari, S., Leoni, M., Grathoff, G., Hugo, R., Shatnawi, M., Paglia, G., and Billinge, S. (2008) Structural characterization of the clay mineral illite-1M. Journal of Applied Crystallography, 41, 402–415.

    Google Scholar 

  • Guinier, A. (1964) Theorie et technique de la radiocristallographie. Pp. 490–636 in: Diffraction par les Reseaux Cristallins Imparfaits. Dunod, Paris.

    Google Scholar 

  • Hendricks, S.B. and Teller, E. (1942) X-ray interference in partially ordered layer lattices. Journal of Chemical Physics, 10, 147–167.

    Google Scholar 

  • Hillier, S. and Velde, B. (1992) Chlorite interstratified with a 7-A mineral — An example from offshore Norway and possible implications for the interpretation of the composition of diagenetic chlorites. Clay Minerals, 27, 475–486.

    Google Scholar 

  • Howard, S.A. and Preston, K.D. (1989) Profile fitting of powder diffraction patterns. Pp. 217–275 in: Modern Powder Diffraction (D.L. Bish and J.E. Post, editors). Reviews in Mineralogy, 20, Mineralogical Society of America, Washington, D.C.

    Google Scholar 

  • Howard, S.A. and Snyder, R.L. (1983) An evaluation of some profile models and the optimization procedures used in profile fitting. Advances in X-ray Analysis, 26, 73–81.

    Google Scholar 

  • Jaboyedoff, M. and Cosca, M.A. (1999) Dating incipient metamorphism using Ar40/Ar39 geochronology and XRD modeling: a case study from the Swiss Alps. Contributions to Mineralogy and Petrology, 135, 93–113.

    Google Scholar 

  • Jaboyedoff, M. and Thelin, P. (1996) New data on low-grade metamorphism in the Brianconnais domain of the Prealps, Western Switzerland. European Journal of Mineralogy, 8, 577–592.

    Google Scholar 

  • Koyama, K. and Takeuchi, Y. (1977) Clinoptilolite — distribution of potassium atoms and its role in thermal stability. Zeitschrift fur Kristallographie, 145, 216–239.

    Google Scholar 

  • Leoni, M., Gualtieri, A.F., and Roveri, N. (2004) Simultaneous refinement of structure and microstructure of layered materials. Journal of Applied Crystallography, 37, 166–173.

    Google Scholar 

  • MacEwan, D.M.D. (1958) Fourier transform methods for studying X-ray scattering from lamellar systems. II. The calculation of X-ray diffraction effects from various type of interstratification. Kolloidzeitschrift, 156, 61–67.

    Google Scholar 

  • MacEwan, D.M.C., Ruiz-Amil, A. and Brown, G. (1961) Interstratified clay minerals. Pp. 393 in: The X-ray Identification and Crystal Structures of Clay Minerals (G.W. Brindley and G. Brown, editors). The Mineralogical Society, London.

    Google Scholar 

  • Marquardt, D.W. (1963) An algorithm for least-squares estimation of nonlinear parameters. Journal of the Society for Industrial and Applied Mathematics, 11, 431–441.

    Google Scholar 

  • Mering, J. (1949) X-ray diffraction in disordered layer structures. Acta Crystallographica, 2, 371–377.

    Google Scholar 

  • Moore, D.M. and Reynolds, R.C., Jr. (1997) X-ray Diffraction and the Identification and Analysis of Clay Minerals. Oxford University Press, New York, 369 pp.

    Google Scholar 

  • Nelder, J.A. and Mead, R. (1965) A simplex method for function minimization. Computer Journal, 7, 308–313.

    Google Scholar 

  • Pevear, D.R. and Schuette, J.F. (1993) Inverting the NEWMOD X-ray diffraction forward model for clay minerals using genetic algorithms. Pp. 20–41 in: Computer Applications to X-ray Powder Diffraction Analysis of Clay Minerals (R.C. Reynolds Jr. and J.R. Walker, editors). CMS Workshop Lectures, Vol. 5, The Clay Minerals Society, Boulder, Colorado, USA.

    Google Scholar 

  • Plancon, A. (1981) Diffraction by layer structures containing different kinds of layers and stacking-faults. Journal of Applied Crystallography, 14, 300–304.

    Google Scholar 

  • Plancon, A. (2002) New modeling of X-ray diffraction by disordered lamellar structures, such as phyllosilicates. American Mineralogist, 87, 1672–1677.

    Google Scholar 

  • Press, W.H., Teukolsky, S.A., Vetterling, W.T. and Flannery, B.P. (1992) Numerical recipes in C: The Art of Scientific Computing, 2nd edition. Cambridge University Press, Cambridge, UK.

    Google Scholar 

  • Proffen, T. and Neder, R.B. (1997) DISCUS: A program for diffuse scattering and defect-structure simulation. Journal ofApplied Crystallography, 30, 171–175.

    Google Scholar 

  • Renac, C. and Meunier, A. (1995) Reconstruction of palaeothermal conditions in a passive margin using illitesmectite mixed-layer series (Ba1 Scientific Deep Drill-Hole, Ardeche, France). Clay Minerals, 30, 107–118.

    Google Scholar 

  • Reynolds, R.C. (1967) Interstratified clay systems: Calculation of the total one-dimensional diffraction function. American Mineralogist, 52, 661–672.

    Google Scholar 

  • Reynolds, R.C. (1980) Interstratified clay minerals: Pp. 249–303 in: Crystal Structures of Clay Minerals and their X-ray Identification (G.W. Brindley and G. Brown, editors). Mineralogical Society, London.

    Google Scholar 

  • Reynolds, R.C., Jr. (1985) NEWMOD, a Computer Program for the Calculation of Basal X-Ray Diffraction Intensities of Mixed-Layered Clays. R.C. Reynolds, Hanover, New Hampshire, 03755, USA.

    Google Scholar 

  • Reynolds, R.C., Jr. (1989) Diffraction by small and disordered crystals. Pp. 143–182 in: Modern Powder Diffraction (D.L. Bish and J.E. Post, editors). Reviews in Mineralogy, 20, Mineralogical Society of America, Washington, D.C.

    Google Scholar 

  • Schreyer, W., Medenbach, O., Abraham, K., Gebert, W., and Muller, W.F. (1982) Kulkeite, a new metamorphic phyllosilicate mineral — ordered 1–1 chlorite talc mixed-layer. Contributions to Mineralogy and Petrology, 80, 103–109.

    Google Scholar 

  • Shannon, R.D. (1976) Revised effective ionic-radii and systematic studies of interatomic distances in halides and chalcogenides. Acta Crystallographica Section A, 32, 751–767.

    Google Scholar 

  • Simoncic, P. and Armbruster, T. (2004) Peculiarity and defect structure of the natural and synthetic zeolite mordenite: a single-crystal X-ray study. American Mineralogist, 89, 421–431.

    Google Scholar 

  • Srodon, J., Elsass, F., McHardy, W.J., and Morgan, D.J. (1992) Chemistry of illite-smectite inferred from TEM measurements of fundamental particles. Clay Minerals, 27, 137–158.

    Google Scholar 

  • Srodon, J., Eberl, D.D., and Drits, V.A. (2000) Evolution of fundamental-particle size during illitization of smectite and implications for reaction mechanism. Clays and Clay Minerals, 48, 446–458.

    Google Scholar 

  • Toby, B.H. (2006) R factors in Rietveld analysis: How good is good enough? Powder Diffraction, 21, 67–70.

    Google Scholar 

  • Treacy, M.M.J., Newsam, J.M., and Deem, M.W. (1991) A general recursion method for calculating diffracted intensities from crystals containing planar faults. Proceedings of the Royal Society of London, A: Mathematical and Physical Sciences, 433, 499–520.

    Google Scholar 

  • Ufer, K., Kleeberg, R., Bergmann, J., Curtius, H., and Dohrmann, R. (2008) Refining real structure parameters of disordered layer structures within the Rietveld method. Zeitschrift fur Kristallographie, 151–158.

    Google Scholar 

  • Walker, J.R. (1993) An introduction to computer modeling of X-ray diffraction patterns of clay minerals: A guided tour of NEWMOD. Pp. 1–18 in: Computer Applications to X-ray Powder Diffraction Analysis of Clay Minerals (R.C. Reynolds Jr. and J.R. Walker, editors). CMS Workshop Lectures series, vol. 5, The Clay Minerals Society, Boulder, Colorado, USA.

    Google Scholar 

  • Wilson, P.N., Parry, W.T. and Nash, W.P. (1992) Characterization of hydrothermal tobelitic veins from black shale, Oquirrh Mountains, Utah. Clays and Clay Minerals, 40, 405–420.

    Google Scholar 

  • Yuan, H.J. and Bish, D.L. (2010) NEWMOD+, a new version of the NEWMOD program for interpreting X-ray powder diffraction patterns from interstratified clay minerals. Clays and Clay Minerals, 58, 318–326.

    Google Scholar 

  • Young, R.A. (1993) Introduction to the Rietveld method. Pp. 1–38 in: The Rietveld Method (R.A. Young, editor). International Union of Crystallography, Oxford University Press. Oxford, UK.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Geological Sciences, Indiana University, Bloomington, IN, 47405, USA

    Hongji Yuan & David L. Bish

Authors
  1. Hongji Yuan
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. David L. Bish
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Hongji Yuan.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Yuan, H., Bish, D.L. Automated Fitting of X-Ray Powder Diffraction Patterns from Interstratified Phyllosilicates. Clays Clay Miner. 58, 727–742 (2010). https://doi.org/10.1346/CCMN.2010.0580601

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1346/CCMN.2010.0580601

Key Words

Search

Navigation