Hostname: page-component-848d4c4894-nr4z6 Total loading time: 0 Render date: 2024-05-22T05:04:42.350Z Has data issue: false hasContentIssue false
  • English
  • Français

Improved Matrix Methodology for Calculating Diffraction Intensity Profiles from Interstratified Phyllosilicates

Published online by Cambridge University Press:  01 January 2024

Hongji Yuan  and
David L. Bish Open the ORCID record for David L. Bish [Opens in a new window]
Hongji Yuan*
Affiliation:
Department of Earth & Atmospheric Sciences, Indiana University, Bloomington, IN 47405, USA
David L. Bish
Affiliation:
Department of Earth & Atmospheric Sciences, Indiana University, Bloomington, IN 47405, USA
*
*E-mail address of corresponding author: hongjiyuan@gmail.com
Get access Rights & Permissions [Opens in a new window]

Abstract

Diffraction effects from interstratified phyllosilicates have been studied extensively, and several computer programs such as NEWMOD© are available to facilitate interpretation of X-ray diffraction (XRD) profiles. However, accurate quantification of samples containing multiple interstratified phyllosilicate minerals is difficult due to the generally subjective nature of interpretations. More recent automated fitting interpretations require extensive computational effort, involving numerous calculations of profiles with different fitting-parameter values. Computational cost in time per calculation is the key factor influencing the overall efficiency of automated profile fitting. In general, the matrix methodology developed by Kakinoki and Komura is more efficient than the NEWMOD© architecture. A new matrix methodology was developed that reduces the number of matrix operations such as multiplication and addition, and these modifications improve calculation efficiency by up to a factor of three, with even greater improvement for small crystallite sizes (< 20 layers). A new computer program, ClayStrat, based on the modified matrix methodology, was developed to calculate one-dimensional XRD profiles from interstratified phyllosilicates along the Z direction.

Keywords

ClayStratInterstratificationMatrix MethodologyNEWMOD
Type
Article
Information
Clays and Clay Minerals , Volume 67 , Issue 5 , October 2019 , pp. 399 - 409
Copyright
Copyright © Clay Minerals Society 2020

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Aplin, A. C., Matenaar, I. F., McCarty, D. K., & van der Pluijm, B. A. (2006). Influence of mechanical compaction and clay mineral diagenesis on the microfabric and pore-scale properties of deep-water Gulf of Mexico mudstones. Clays and Clay Minerals, 54, 500–514.CrossRefGoogle Scholar
Bethke, C. M., & Reynolds, R. C. Jr. (1986). Recursive method for determining frequency factors in interstratified clay diffraction calculations. Clays and Clay Minerals, 34, 224–226.CrossRefGoogle Scholar
Bish, D. L., & Von Dreele, R. B. (1989). Rietveld refinement of nonhydrogen atomic positions in kaolinite. Clays and Clay Minerals, 37, 289–296.CrossRefGoogle Scholar
Cromer, D. T., & Waber, J. T. (1965). Scattering factors computed from relativistic Dirac-Slater wave functions. Acta Crystallographica, 18, 104–109.CrossRefGoogle Scholar
Drits, V. A., Sakharov, B. A., Lindgreen, H., & Salyn, A. (1997). Sequential structure transformation of illite-smectite-vermiculite during diagenesis of Upper Jurassic shales from the North Sea and Denmark. Clay Minerals, 32, 351–371.CrossRefGoogle Scholar
Drits, V.A., & Sakharov, B.A. (1976). X-ray analysis of mixed-layer clay minerals. Nauka, Moscow, 256 pp. (in Russian).Google Scholar
Drits, V. A., & Tchoubar, C. (1990). X-ray diffraction by disordered lamellar structures (p. 371). Berlin: Springer-Verlag.CrossRefGoogle Scholar
Gruner, J. W. (1934). The structure of vermiculites and their collapse by dehydration. American Mineralogist, 19, 557–575.Google Scholar
Hendricks, S. B., & Teller, E. (1942). X-ray interference in partially ordered layer lattices. Journal of Chemical Physics, 10, 147–167.CrossRefGoogle Scholar
International Tables for X-ray Crystallography. (1974). Volume IV. Birmingham, UK: Kynoch Press.Google Scholar
Jaboyedoff, M., Bussy, F., Kubler, B., & Thelin, P. (2001). Illite “crystallinity” revisited. Clays and Clay Minerals, 49, 156–167.CrossRefGoogle Scholar
Kakinoki, J., & Komura, Y. (1952). Intensity of X-ray diffraction by one-dimensionally disordered crystals. I: General derivation in the case of the “Reichweite” S=0 and 1. Journal of Physical Society of Japan, 7, 30–35.CrossRefGoogle Scholar
Kakinoki, J., & Komura, Y. (1965). Diffraction by a one-dimensionally disordered crystal. I. The intensity equation. Acta Crystallographica, 19, 137–147.CrossRefGoogle Scholar
Leoni, M., Gualtieri, A. F., & Roveri, N. (2004). Simultaneous refinement of structure and microstructure of layered materials. Journal of Applied Crystallography, 37, 166–173.CrossRefGoogle 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
Méring, J. (1949). X-ray diffraction in disordered layer structures. Acta Crystallography, 2, 371–377.CrossRefGoogle Scholar
Plançon, A. (1981). Diffraction by layer structures containing different kinds of layers and stacking-faults. Journal of Applied Crystallography, 14, 300–304.CrossRefGoogle Scholar
Plançon, A., & Tchoubar, C. (1976). Stacking-faults in partially disordered kaolinites. 2. Stacking models dealing with rotational faults. Journal of Applied Crystallography, 9, 279–285.CrossRefGoogle Scholar
Plançon, A., & Tchoubar, C. (1977). Determination of structural defects in phyllosilicates by X-ray powder diffraction. 1. Principle of calculation of diffraction phenomenon. Clays and Clay Minerals, 25, 430–435.CrossRefGoogle Scholar
Reynolds, R. C. Jr. (1967). Interstratified clay systems – calculation of total one-dimensional diffraction function. American Mineralogist, 52, 661–672.Google Scholar
Reynolds, R. C. Jr. (1989). Diffraction by small and disordered crystals. In Bish, D. L. & Post, J. E. (Eds.), Modern powder diffraction (pp. 145–181). Washington, D.C: Reviews in Mineralogy, 20, Mineralogical Society of America.CrossRefGoogle Scholar
Reynolds, R.C. Jr. (1985). NEWMOD, a computer program for the calculation of basal x-ray diffraction intensities of mixed-layered clays. Software manual, Hanover, NH, 03755, 22 pp.Google Scholar
Reynolds, R. C. Jr. (1993). Three-dimensional X-ray powder diffraction from disordered illite: simulation and interpretation of the diffraction patterns. In Reynolds, R. C. Jr. & Walker, J. R. (Eds.), Computer applications to X-ray powder diffraction analysis of clay minerals (pp. 43–78). Boulder, CO.: The Clay Minerals Society.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. Proceedingsof the Royal Society of London Series A–Mathematical Physical and Engineering Sciences, 433, 499–520.Google Scholar
Wright, A. C. (1973). A compact representation for atomic scattering factors. Clays and Clay Minerals, 21, 489–490.CrossRefGoogle Scholar
Yuan, H. J., & Bish, D. L. (2010a). 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.CrossRefGoogle Scholar
Yuan, H. J., & Bish, D. L. (2010b). Automated fitting of X-ray powder diffraction patterns from interstratified phyllosilicates. Clays and Clay Minerals, 58, 727–742.CrossRefGoogle Scholar
Yuan, H. J., Bish, Y., Bish, D. L. (2011). Quantitative analysis of multiplecomponent phyllosilicate systems using full X-ray powder diffraction profiles. In 48th Annual Meeting of the Clay Minerals Society. Stateline, Nevada, USA, abstract, p. 104.Google Scholar