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Understanding clay minerals with fuzzy mathematics.
Chandrika Varadachari1, Gargi Mukherjee, Damodar P Goswami
1Raman Centre for Applied and Interdisciplinary Sciences, 16A Jheel Road, Calcutta 700 075, India. rcais@cal3.vsnl.net.in
Die Naturwissenschaften
|January 25, 2003
Summary
This study introduces fuzzy logic to chemically define complex clay minerals, quantifying their compositional vagueness and relationships to other mineral types for better classification.
Area of Science:
- Geochemistry
- Mineralogy
- Applied Mathematics
Background:
- Non-stoichiometric complex minerals like clays lack distinct chemical compositions and clear boundaries.
- Existing methods struggle to chemically define minerals with variable compositions.
Purpose of the Study:
- To propose a novel fuzzy logic approach for chemically defining clay minerals.
- To quantify compositional vagueness and inter-mineral relationships in complex systems.
Main Methods:
- Application of fuzzy logic to quantify compositional representativeness ('belonging-ness').
- Assessment of compositional overlap between different clay mineral types.
- Development of a fundamental methodology for fuzzy chemical analysis.
Main Results:
- Clay minerals can be described by their degree of belonging to a type and their resemblance to other types.
- Many clay minerals deviate significantly from ideal compositions.
- The approach allows for grading minerals and defining phase transition extents.
Conclusions:
- Fuzzy logic provides a robust framework for chemically characterizing complex, non-stoichiometric minerals.
- This methodology can be extended to analyze other complex chemical systems in geology and metallurgy.