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AUTOMATED FULL-PATTERN SUMMATION OF X-RAY POWDER DIFFRACTION DATA FOR HIGH-THROUGHPUT QUANTIFICATION OF CLAY-BEARING MIXTURES

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Clays and Clay Minerals

Abstract

X-ray powder diffraction (XRPD) is found consistently to be the most accurate analytical technique for quantitative analysis of clay-bearing mixtures based on results from round-robin competitions such as the Reynolds Cup (RC). A range of computationally intensive approaches can be used to quantify phase concentrations from XRPD data, of which the ‘full-pattern summation of prior measured standards’ (FPS) has proven accurate and parsimonious. Despite its proven utility, the approach often requires time-consuming selection of appropriate pure reference patterns to use for a given sample. As such, applying FPS to large and mineralogically diverse datasets is challenging. In the present work, the accuracy of an automated FPS algorithm implemented within the powdR package for the R Language and Environment for Statistical Computing was tested on a set of 27 samples from nine RC contests. The samples represent challenging and diverse clay-bearing mixtures with known concentrations, with the added advantage of allowing the accuracy of the algorithm to be compared with results submitted to previous contests. When supplied with a library of 201 reference patterns representing a comprehensive range of phases that may be encountered in natural clay-bearing mixtures, the algorithm selected appropriate phases and achieved a mean absolute bias of 0.57% for non-clay minerals (n = 275), 2.37% for clay minerals (n = 120), and 4.43% for amorphous phases (n = 14). This accuracy would be sufficient for top-3 placings in all nine RC contests held to date (RC1 = 2nd, RC2 = 2nd, RC3 = 1st; RC4 = 2nd; RC5 = 1st; RC6 = 3rd; RC7 = 3rd; RC8 = 1st; RC9 = 2nd). The comparatively low values of absolute bias in combination with the competitive placings in all RC contests tested is particularly promising for the future of automated quantitative phase analyses by XRPD.

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References

  • 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. CPD Newsletter, 20.

  • Bish, D. & Post, J. (editors) (1989). Modern Powder Diffraction. Reviews in Mineralogy, 20 Mineralogical Society of America, Chantilly, Virginia, USA.

  • Butler, B. & Hillier, S. (2020). powdR: Full Pattern Summation of X-Ray Powder Diffraction Data. R package version 1.2.3. URL: https://CRAN.R-project.org/package=powdR

  • Butler, B. M. & Hillier, S. (2021). powdR: An R package for quantitative mineralogy using full pattern summation of X-ray powder diffraction data. Computers and Geosciences, 107, 104662.

  • Brent, R. P. (1971). An algorithm with guaranteed convergence for finding a zero of a function. The Computer Journal, 14, 422–425.

    Article  Google Scholar 

  • Broyden, C. G. (1970). The convergence of a class of double-rank minimization algorithms 1. General considerations. IMA Journal of Applied Mathematics, 6, 76–90.

    Article  Google Scholar 

  • Butler, B. M., O’Rourke, S. M., & Hillier, S. (2018). Using rule-based regression models to predict and interpret soil properties from X-ray powder diffraction data. Geoderma, 329, 43–53.

  • Butler, B. M., Sila, A. M., Shepherd, K. D., Nyambura, M., Gilmore, C. J., Kourkoumelis, N., & Hillier, S. (2019). Pre-treatment of soil X-ray powder diffraction data for cluster analysis. Geoderma, 337, 413–424.

  • Butler, B. M., Palarea-Albaladejo, J., Shepherd, K. D., Nyambura, K. M., Towett, E. K., Sila, A. M., & Hillier, S. (2020). Mineral–nutrient relationships in African soils assessed using cluster analysis of X-ray powder diffraction patterns and compositional methods. Geoderma, 375, 114474.

  • Casetou-Gustafson, S., Hillier, S., Akselsson, C., Simonsson, M., Stendahl, J., & Olsson, B. A. (2018). Comparison of measured (XRPD) and modeled (A2M) soil mineralogies: A study of some Swedish forest soils in the context of weathering rate predictions. Geoderma, 310, 77–88.

    Article  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. Journal of Applied Crystallography, 35, 744–749.

    Article  Google Scholar 

  • Clark, G. L., & Reynolds, D. H. (1936). Quantitative analysis of mine dusts: an X-ray diffraction method. Industrial & Engineering Chemistry Analytical Edition, 8, 36–40.

    Article  Google Scholar 

  • Costanzo, P. A., & Guggenheim, S. (2001). Baseline studies of the Clay Minerals Society Source Clays: preface. Clays and Clay Minerals, 49, 371–371.

  • Doebelin, N., & Kleeberg, R. (2015). Profex: a graphical user interface for the Rietveld refinement program BGMN. Journal of Applied Crystallography, 48, 1573–1580.

    Article  Google Scholar 

  • Eberl, D. D. (2003). User’s guide to ROCKJOCK – A program for determining quantitative mineralogy from powder X-ray diffraction data. Technical report, USGS, Boulder, Colorado, USA.

  • Fletcher, R. (1970). A new approach to variable metric algorithms. The Computer Journal, 13, 317–322.

    Article  Google Scholar 

  • Gates-Rector, S., & Blanton, T. (2019). The Powder Diffraction File: a quality materials characterization database. Powder Diffraction, 34, 352–360.

    Article  Google Scholar 

  • Goldfarb, D. (1970). A family of variable-metric methods derived by variational means. Mathematics of Computation, 24, 23–26.

    Article  Google Scholar 

  • Hillier, S. (1999). Use of an air brush to spray dry samples for X-ray powder diffraction. Clay Minerals, 34, 127–135.

    Article  Google Scholar 

  • Hillier, S. (2000). Accurate quantitative analysis of clay and other minerals in sandstones by XRD: comparison of a Rietveld and a reference intensity ratio (RIR) method and the importance of sample preparation. Clay Minerals, 35, 291–302.

    Article  Google Scholar 

  • Hillier, S. (2003). Quantitative Analysis of Clay and other Minerals in Sandstones by X-Ray Powder Diffraction (XRPD). Clay Mineral Cements in Sandstones, 34, 213–251.

    Google Scholar 

  • Hillier, S. (2015). X-ray powder diffraction full-pattern summation methods for quantitative analysis of clay bearing samples. In Euroclay 2015 Programme and Abstracts, page 174.

  • Hillier, S. (2018). Quantitative analysis of clay minerals and poorly ordered phases by prior determined X-ray diffraction full pattern fitting: procedures and prospects. In 9th Mid-European Clay Conference Book, page 6.

  • ICDD (2016). PDF-4+ 2016 (Database). International Center for Diffraction Data, Newtown Square, PA, USA.

  • Kleeberg, R., Monecke, T., & Hillier, S. (2008). Preferred orientation of mineral grains in sample mounts for quantitative XRD measurements: How random are powder samples? Clays and Clay Minerals, 56, 404–415.

    Article  Google Scholar 

  • Lawson, C. L. & Hanson, R. J. (1995). Solving least squares problems, volume 15. Siam.

  • Microsoft & Weston, S. (2017). foreach: Provides Foreach Looping Construct for R. R package version 1.4.4. URL: https://CRAN.R-project.org/package=foreach

  • Microsoft & Weston, S. (2018). doParallel: Foreach Parallel Adaptor for the ‘parallel’ Package. R package version 1.0.14. https://CRAN.R-project.org/package=doParallel

  • Mullen, K. M. & van Stokkum, I. H. M. (2012). nnls: The Lawson-Hanson algorithm for non-negative least squares (NNLS). R package version 1.4. https://CRAN.R-project.org/package=nnls

  • Navias, L. (1925). Quantitative determination of the development of mullite in fired clays by an X-ray method. Journal of the American Ceramic Society, 8, 296–302.

    Article  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 and Clay Minerals, 54, 748–760.

    Article  Google Scholar 

  • R Core Team. (2020). R: A Language and Environment for Statistical Computing. Vienna, Austria: R Foundation for Statistical Computing.

    Google Scholar 

  • Raven, M. D., & Self, P. G. (2017). Outcomes of 12 years of the Reynolds Cup quantitative minerals analysis round robin. Clays and Clay Minerals, 65, 122.

    Article  Google Scholar 

  • Rietveld, H. M. (1969). A profile refinement method for nuclear and magnetic structures. Journal of Applied Crystallography, 2, 65–71.

    Article  Google Scholar 

  • Shanno, D. F. (1970). Conditioning of quasi-newton methods for function minimization. Mathematics of Computation, 24, 647–656.

    Article  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 Diffraction, 2, 73–77.

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Vogt, C., Lauterjung, J., & Fischer, R. X. (2002). Investigation of the clay fraction (<2 μm) of The Clay Minerals Society reference clays. Clays and Clay Minerals, 50, 388–400.

    Article  Google Scholar 

  • Woodruff, L. G., Cannon, W. F., Eberl, D. D., Smith, D. B., Kilburn, J. E., Horton, J. D., Garrett, R. G., & Klassen, R. A. (2009). Continental-scale patterns in soil geochemistry and mineralogy: results from two transects across the United States and Canada. Applied Geochemistry, 24, 1369–1381.

    Article  Google Scholar 

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ACKNOWLEDGMENTS

This work was supported by a Macaulay Development Trust Fellowship, United Kingdom, Grant No. MDT-50. The support of the Scottish Government’s Rural and Environment Science and Analytical Services Division (RESAS) is also gratefully acknowledged. The authors thank the three anonymous reviewers and the Editorial Board for their useful comments which helped to improve this paper.

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Funding sources are as stated in the Acknowledgments.

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Correspondence to Benjamin M. Butler.

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(Received 17 June 2020; revised 30 October 2020; AE: Peter Ryan)

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M. Butler, B., Hillier, S. AUTOMATED FULL-PATTERN SUMMATION OF X-RAY POWDER DIFFRACTION DATA FOR HIGH-THROUGHPUT QUANTIFICATION OF CLAY-BEARING MIXTURES. Clays Clay Miner. 69, 38–51 (2021). https://doi.org/10.1007/s42860-020-00105-6

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