Hostname: page-component-cd9895bd7-8ctnn Total loading time: 0 Render date: 2024-12-27T05:53:38.044Z Has data issue: false hasContentIssue false
  • English
  • Français

Comparison of Four Elemental Mass Balance Methods for Clay Mineral Quantification

Published online by Cambridge University Press:  28 February 2024

Randall K. Kolka ,
David A. Laird  and
Edward A. Nater
Randall K. Kolka
Affiliation:
Soil Science Department, 439 Borlaug Hall, University of Minnesota, St. Paul, Minnesota 55108-6028
David A. Laird
Affiliation:
USDA-ARS, Midwest Area, National Soil Tilth Laboratory, 2150 Pammel Drive, Ames, Iowa 50011
Edward A. Nater
Affiliation:
Soil Science Department, 439 Borlaug Hall, University of Minnesota, St. Paul, Minnesota 55108-6028
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

The quantification of the relative mineralogical composition of clay mixtures by powder X-ray diffraction or chemical mass balance methods has been severely hampered by a lack of representative standards. The recent development of elemental mass balance models that do not require standards for all minerals in the mixture may help circumvent this problem. These methods, which are based on the numerical optimization of systems of non-linear equations using the Marquardt algorithm, show promise for mineral quantification. The objective of this study is to make a preliminary assessment of the accuracy of these methods and to compare them to linear models that require standards for all mineral phases. Methods 1 and 2 are based on weighted average solutions to simultaneous linear equations solved for single samples with known standards. Solutions were achieved by a matrix decomposition algorithm and the Marquardt algorithm, respectively. Methods 3 and 4 are based on a set of simultaneous non-linear equations with reduced non-linearity solved by least squares optimization based on the Marquardt algorithm for multiple samples. Illite and halloysite compositions were fixed in Method 3, only the halloysite composition was fixed in Method 4. All models yielded relative weight fractions of the three mineral components; additionally, Methods 3 and 4 yielded compositions of smectite, and smectite and illite, respectively. Ten clay mixtures with varying proportions of the <0.2 μm size fraction of three different reference clays (Wyoming bentonite, Fithian illite, and New Bedford halloysite) were prepared gravi-metrically and analyzed by inductively coupled plasma-atomic emission spectroscopy. Accuracy of the four methods was evaluated by comparing the known mineralogical compositions of the mixtures with those predicted by the models. Relative errors of 5 and 10% (randomly +/-) were imposed on the elemental composition of the smectite standard to simulate errors due to lack of good standards. Not surprisingly, the accuracy of Methods 1 and 2 decreased rapidly with increasing error. Because Methods 3 and 4 optimized for the smectite composition and only used it for an initial guess, they were unaffected by the level of introduced error. They accurately quantified the mineralogical compositions of the mixtures and the elemental compositions of smectite, and smectite and illite, respectively.

Keywords

Elemental mass balanceMarquardt algorithmNon-linear modelsNumerical optimizationQuantification
Type
Research Article
Information
Clays and Clay Minerals , Volume 42 , Issue 4 , August 1994 , pp. 437 - 443
Copyright
Copyright © 1994, Clay Minerals Society

Footnotes

*

Published as a joint contribution of the USDA-ARS National Soil Tilth Laboratory and the Minnesota Agricultural Experiment Station, Scientific Journal Series Paper no. 20,539 of that station. Mention of a trademark, vendor, or proprietary product does not constitute a guarantee or warrant of the product by the University of Minnesota or the USDA and does not imply its approval to the exclusion of other products or vendors that may also be suitable.

References

Barak, P., Molina, J. A. E., Hadas, A., and Clapp, C. E., (1990) Optimization of an ecological model with the Marquardt algorithm: Ecol. Modell. 51, 251–263.CrossRefGoogle Scholar
Bevington, P. R., (1969) Data Reduction and Error Analysis for the Physical Sciences: McGraw-Hill, New York.Google Scholar
Braun, G. E., (1986) Quantitative analysis of mineral mixtures using linear programming: Clays & Clay Minerals 34, 330–337.CrossRefGoogle Scholar
Calvert, C. S., Palkowsky, D. A., and Pevear, D. R., (1989) A combined X-ray powder diffraction and chemical method for the quantitative mineral analysis of geologic samples: in Quantitative Mineral Analysis of Clays, Pevear, D. R., and Mumpton, F. A., eds., CMS Workshop Lectures 1, The Clay Minerals Society, 171 pp.Google Scholar
Hodgson, M., and Dudeney, A. W. L., (1984) Estimation of clay proportions in mixtures by X-ray diffraction and computerized chemical mass balance: Clays & Clay Minerals 32, 19–28.CrossRefGoogle Scholar
Hosterman, J. W., and Dulong, F. T., (1989) A computer program for semiquantitative mineral analysis by X-ray powder diffraction: in Quantitative Mineral Analysis of Clays, Pevear, D. R., and Mumpton, F. A., eds., CMS Workshop Lectures 1, The Clay Minerals Society, 171 pp.Google Scholar
Hussey, G. A. Jr. 1972() Use of simultaneous linear equations program for quantitative clay analysis and the study of mineral alterations during weathering: unpublished Ph.D. thesis, Pennsylvania State University, University Park, Pennsylvania.Google Scholar
Johnson, L. J., Chu, C. H., and Hussey, G. A., (1985) Quantitative clay mineral analysis using simultaneous equations: Clays & Clay Minerals 33, 107–117.CrossRefGoogle Scholar
Jones, R. C., (1989) A computer technique for X-ray diffraction curve fitting/peak decomposition: in Quantitative Mineral Analysis of Clays, Pevear, D. R., and Mumpton, F. A., eds., CMS Workshop Lectures 1, The Clay Minerals Society, 171 pp.Google Scholar
Kunze, G. W., and Dixon, J. B., (1986) Pretreatment for mineralogical analysis: in Methods of Soil Analysis. Part 2. Physical and Mineralogical Properties, 2nd ed., Klute, A., ed., Agronomy 9.Google Scholar
Laird, D. A., Barak, P., Nater, E. A., and Dowdy, R. H., (1991a) Chemistry of smectitic and illitic phases in inter-stratified soil smectite: Soil Sci. Soc. Am. J. 55, 1499–1504.CrossRefGoogle Scholar
Laird, D. A., Dowdy, R. H., and Munter, R. C., (1991b) Suspension nebulization analyses of clays by inductively coupled plasma-atomic emission spectroscopy: Soil Sci. Soc. Am. J. 55, 274–278.CrossRefGoogle Scholar
McNeal, B. L., and Sansoterra, T., (1964) Mineralogical examination of arid-land soils: Soil Science 97, 367–375.CrossRefGoogle Scholar
Moore, D., and Reynolds, R. C., (1989) X-ray Diffraction and the Identification and Analysis of Clay Minerals: Oxford University Press, Oxford, 332 pp.Google Scholar
Salyn, A. L., and Drits, V. A., (1972) Method of quantitative phase analysis of clays: Proc. Int. Clay Conf., Madrid, 1972, pp. 797–806.Google Scholar
Slaughter, M., (1989) Quantitative determination of clays and other minerals in rocks: in Quantitative Mineral Analysis of Clays, Pevear, D. R., and Mumpton, F. A., eds., CMS Workshop Lectures 1, The Clay Minerals Society, 171 pp.Google Scholar
Smith, D. K., (1989) Computer analysis of diffraction data. Ch. 7: in Modern Powder Diffraction, Bish, D. L., and Post, J. E., eds., Reviews in Mineralogy, 20, Mineralogical Society of America, 369 pp.Google Scholar
Zevin, L. S., (1977) Quantitative phase analysis without standards: J. Appl. Cryst. 10, 147–150.CrossRefGoogle Scholar