Abstract
A long-existing geochemical problem is the lack of a means of chemically defining non-stoichiometric complex minerals such as clays, which have no distinct composition and no clear compositional boundaries. We propose here a novel approach for describing the chemical nature of clay minerals using fuzzy logic. This non-conventional mathematical approach allows us to quantify compositional vagueness in such systems. We show that a clay mineral can be described in terms of how compositionally representative it is, of its own type ('belonging-ness') and to what extent it resembles other types (compositional overlap). Many clay minerals are seen to be far from the ideal, and most minerals are also to a lesser (and sometimes greater) extent, close to types other than their own. This has provided a means of grading such minerals, evaluating how 'good' a sample is, and defining the extent of transition to other phases. We have derived here the fundamental methodology for such computations, which could be a framework for the analysis of other complex chemical systems, especially in the fields of geology and metallurgy.
References
Dubois D, Prade H, Ughetto L (2002) A new perspective on reasoning with fuzzy rules. In: Pal NR, Sugeno M (eds) Advances in soft computing. Springer, Berlin Heidelberg New York, pp 1–11
Klir G, Yuan B (1997) Fuzzy sets and fuzzy logic. Prentice Hall, New Delhi, India
Meunier A, Velde B (1989) Solid solutions in I/S mixed layer minerals and illite. Am Mineral 74:1106–1112
Newman ACD, Brown G (1987) The chemical constitution of clays. In: Newman ACD (ed) Chemistry of clays and clay minerals. Wiley, New York, pp 1–128
Tardy Y, Duplay J (1994) Stability fields of smectites and illites including glauconites as a function of temperature and chemical composition. In: Wolf KH, Chilingarian GV (eds) Diagenesis IV: developments in sedimentology. Elsevier, Amsterdam, pp 95–132
Velde B (1985) Clay minerals: a physico-chemical explanation of their occurrence. Elsevier, Amsterdam
Weaver CE, Pollard LD (1973) The chemistry of clay minerals. (Developments in sedimentology 15) Elsevier, Amsterdam
Zadeh LA (1965) Fuzzy sets. Inf Control 8:338–353
Zimmerman AJ (ed) (1997) Proceedings of the fifth European congress on intelligent techniques and soft computing, EUFIT '97. Elite Foundation, Aachen, Germany
Acknowledgements
The authors are grateful to the Department of Science and Technology, Government of India, for financial support, and to Professor Kunal Ghosh for technical help.
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Varadachari, C., Mukherjee, G., Goswami, D.P. et al. Understanding clay minerals with fuzzy mathematics. Naturwissenschaften 90, 44–48 (2003). https://doi.org/10.1007/s00114-002-0387-y
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DOI: https://doi.org/10.1007/s00114-002-0387-y