Hostname: page-component-848d4c4894-4hhp2 Total loading time: 0 Render date: 2024-06-01T21:22:41.842Z Has data issue: false hasContentIssue false

Automated Full-Pattern Summation of X-Ray Powder Diffraction Data for High-Throughput Quantification of Clay-Bearing Mixtures

Published online by Cambridge University Press:  01 January 2024

Benjamin M. Butler*
Affiliation:
The James Hutton Institute, Craigiebuckler, Aberdeen AB15 8QH, UK
Stephen Hillier
Affiliation:
The James Hutton Institute, Craigiebuckler, Aberdeen AB15 8QH, UK Department of Soil and Environment, Swedish University of Agricultural Sciences (SLU), SE-75007, Uppsala, Sweden
*
*E-mail address of corresponding author: Benjamin.Butler@huton.ac.uk

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.

Type
Article
Copyright
Copyright © The Clay Minerals Society 2021

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

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.Google Scholar
Bish, D. & Post, J. (Editors) (1989). Modern Powder Diffraction. Reviews in Mineralogy, 20 Mineralogical Society of America, Chantilly, Virginia, USA.CrossRefGoogle Scholar
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=powdRGoogle Scholar
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.CrossRefGoogle Scholar
Brent, R. P. (1971). An algorithm with guaranteed convergence for finding a zero of a function. The Computer Journal, 14, 422425.CrossRefGoogle Scholar
Broyden, C. G. (1970). The convergence of a class of double-rank minimization algorithms 1. General considerations. IMA Journal of Applied Mathematics, 6, 7690.CrossRefGoogle 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, 4353.CrossRefGoogle Scholar
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, 413424.CrossRefGoogle ScholarPubMed
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.CrossRefGoogle ScholarPubMed
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, 7788.CrossRefGoogle 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, 744749.CrossRefGoogle Scholar
Clark, G. L., & Reynolds, D. H. (1936). Quantitative analysis of mine dusts: an X-ray diffraction method. Industrial & Engineering Chemistry Analytical Edition, 8, 3640.CrossRefGoogle Scholar
Costanzo, P. A., & Guggenheim, S. (2001). Baseline studies of the Clay Minerals Society Source Clays: preface. Clays and Clay Minerals, 49, 371371.CrossRefGoogle Scholar
Doebelin, N., & Kleeberg, R. (2015). Profex: a graphical user interface for the Rietveld refinement program BGMN. Journal of Applied Crystallography, 48, 15731580.CrossRefGoogle ScholarPubMed
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.Google Scholar
Fletcher, R. (1970). A new approach to variable metric algorithms. The Computer Journal, 13, 317322.CrossRefGoogle Scholar
Gates-Rector, S., & Blanton, T. (2019). The Powder Diffraction File: a quality materials characterization database. Powder Diffraction, 34, 352360.CrossRefGoogle Scholar
Goldfarb, D. (1970). A family of variable-metric methods derived by variational means. Mathematics of Computation, 24, 2326.CrossRefGoogle Scholar
Hillier, S. (1999). Use of an air brush to spray dry samples for X-ray powder diffraction. Clay Minerals, 34, 127135.CrossRefGoogle 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 importanceof sample preparation. Clay Minerals, 35, 291302.CrossRefGoogle 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, 213251.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.Google Scholar
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.Google Scholar
ICDD (2016). PDF-4+ 2016 (Database). International Center for Diffraction Data, Newtown Square, PA, USA.Google Scholar
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, 404415.CrossRefGoogle Scholar
Lawson, C. L. & Hanson, R. J. (1995). Solving least squares problems, volume 15. Siam.Google Scholar
Microsoft & Weston, S. (2017). foreach: Provides Foreach Looping Construct for R. R package version 1.4.4. URL: https://CRAN.R-project.org/package=foreachGoogle Scholar
Microsoft & Weston, S. (2018). doParallel: Foreach Parallel Adaptor for the ‘parallel’ Package. R package version 1.0.14. https://CRAN.R-project.org/package=doParallelGoogle Scholar
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=nnlsGoogle Scholar
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, 296302.CrossRefGoogle 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, 748760.CrossRefGoogle 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.CrossRefGoogle Scholar
Rietveld, H. M. (1969). A profile refinement method for nuclear and magnetic structures. Journal of Applied Crystallography, 2, 6571.CrossRefGoogle Scholar
Shanno, D. F. (1970). Conditioning of quasi-newton methods for function minimization. Mathematics of Computation, 24, 647656.CrossRefGoogle 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, 7377.CrossRefGoogle Scholar
Toby, B. H. (2006). R factors in Rietveld analysis: How good is good enough? Powder Diffraction, 21, 6770.CrossRefGoogle 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, 388400.CrossRefGoogle 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, 13691381.CrossRefGoogle Scholar
Supplementary material: File

Butler and Hillier supplementary material
Download undefined(File)
File 87.9 KB