Abstract
Structure-chemical formulae not only show the relative proportions of the various atoms in the composition of a mineral but also give information concerning its crystal structure. Many systems of notation have been devised, giving greater or lesser structural detail, including those by Hey (1950), Povarennykh (1972), Strunz (1982), and more recently Lima-de-Faria et al. (1990), the latter being recommended by a subcommittee of the International Union of Crystallography. The notation recommended would give for example, for pyrite: Fe[60]{g} [S2 [3;1]t], indicating Fe in sixfold octahedral coordination by sulfur and S tetrahedrally coordinated by 3Fe and 1S, and for Mg, Al spinel: [Mg[4t]Al2 [60]O4 [1,3;12CO]], indicating Mg in fourfold tetrahedral and Al in sixfold octahedral coordination, O with one Mg and 3A1 neighbors and selfcoordinated by a cubo-octahedron of oxygens. Lima-de-Faria et al. also give the so-called Bauverband description indicating structure types by a lattice-complex notation.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Bulakh AG (1969) Calculation of mineral formulas 2nd edn. Nedra, Leningrad (In Russian).
Bulakh AG (1970) Berechnung von Mineralformeln. VEB Deutscher Verlag für Grundstoffindustrie, Leipzig
Bulakh AG (1984) On errors in formulas of minerals recalculated from inaccurate chemical data. Mineral J (Kiev) 4: 87–92 (In Russian)
Deer WA, Howie RA, Zussman J (1962, 1963 ) Rock-forming minerals, vols 1–5. Longman
Deer WA, Howie RA, Zussman J (1992) An introduction to rock-forming minerals, 2nd edn. Longman
Dollase WA, Newman WI (1984) Statistically most probable stoichiometric formulae. Am Mineral 69: 553–556
Droop GTR (1987) A general equation for estimating Fe3+ concentrations in ferromagnesian silicates and oxides from microprobe analyses using stoichiometric criteria. Mineral Mag 51: 431–435
Hey MH (1939) On the presentation of chemical analyses of minerals. Mineral Mag 25: 402–412
Hey MH (1950) An index of mineral species and varieties arranged chemically. London, British Museum
Hey MH (1954) A further note on the presentation of chemical analyses of minerals. Mineral Mag 30: 481–497
Lima-de-Faria J, Hellner E, Liebau F, Makovicky E, Parthé E (1990) Nomenclature of inorganic structure types. Report of the International Union of Crystallography Commission on Crystallographic Nomenclature Subcommittee on the Nomenclature of Inorganic Structure Type, Acta Crystallogr A46: 1–11
Nicholls GD, Zussman J (1954) The structural formula of a hydrous amphibole. Mineral Mag 30: 717–722
Povarennykh AS (1972) Crystal chemical classification of minerals, vols 1 and 2. Plenum Press, New York
Robinson P, Spear FS, Schumacker JC, Laird J, Klein C, Evans BW, Doolan BL (1982) Phase relations of metamorphic amphiboles; natural occurrence and theory. In: Vehlen DR, Ribbe PH (eds) Reviews in Mineralogy, 9B, pp 1–227, Min. Soc. America
Rock NMS, Carroll GW (1990) MINTAB: A general-purpose mineral recalculation and tabulation program for Macintosh microcomputers. Am Mineral 75: 424–430
Strunz H (1982) Mineralogische Tabellen, 8 Aufl. Akad Verlag, Leipzig
Aitchison J (1986) The statistical analysis of compositional data. Methuen, New York, 405 pp
Aitchison J (1990) Relative variation diagrams for describing patterns of compositional variability. Math geol 22 (4): 487–511
Anderson TW (1984) An introduction to multivariate statistical analysis, 2nd edn. Wiley and Sons, New York, 665 pp
Bezdek JC (1981) Pattern recognition with fuzzy objective functions. Plenum Press, New York, 256 pp
Bezdek JC, Coray C, Gunderson R, Watson J (1981a) Detection and characterization of cluster substructure. I. Linear structure: fuzzy c-lines. SIAM J. Appl Math 40: 339–357
Bezdek JC, Coray C, Gunderson R, Watson J (1981b) Detection and characterization of cluster substructure. II. Fuzzy c-varieties and convex combinations thereof. SIAM J Appl Math 40: 358–372
Conover WJ (1980) Practical nonparametric statistics. 2d edn. Wiley and Sons, New York, 485 pp
Eisenbeis RA, Avery RB (1972) Discriminant analysis and classification procedures: theory and applications. Lexington Books, Lexington, Massachusetts, 250 pp
d Ed., Marcel Dekker, Inc., 398 p.
Good IJ (1977) The botryology of botryology. In: van Ryzin J (ed) Classification and clustering. Academic Press, London, pp 73–94
Granath, G (1984) Application of fuzzy clustering and fuzzy classification to evaluate the provenance of glacial till. Math Geol 16 (3): 283–301
Granath G (1988) Pattern recognition in geochemical hydrocarbon exploration: a fuzzy approach. Math Geol 20 (6): 673–691
Greenacre MJ (1984) Theory and applications of correspondence analysis. Academic Press, London, 357 pp
Hand DJ (1981) Discrimination and classification. Wiley and Sons, Chichester, Great Britain, 209 pp
Haux R (ed) (1986) Expert systems in statistics. Gustav Fischer, Stuttgart, 190 pp
Hendrickson RG (1984) A survey of sensitivity analysis methodology. National Bureau of Standards, NBSIR 84-28114, Washington DC, 83 pp
James M (1985) Classification algorithms. Wiley-Interscience, New York, 220 pp
Jolliffe IT (1986) Principal component analysis. Springer Series in Statistics. Springer, Berlin Heidelberg New York, 271 pp
Kacewicz M (1989) On the problem of fuzzy searching for hard workability rocks in open-pit mine exploration. Math Geol 21 (3): 309–318
Kleijnen JPC (1987) Statistical tools for simulation practitioners. Marcel Dekker, New York, 407 pp
Lausen B, Vach W (1986) Estimation, graphical representation and judgement of evolutionary trees in expert systems. In: Haux R (ed) Expert systems in statistics. Gustav Fischer, Stuttgart, Germany, pp 61–74
Negoita CV (1985) Expert systems and fuzzy systems. Benjamin/Cummings, Menlo Park, California, 183 pp
Romesburg HC (1984) Cluster analysis for researchers. Lifetime learning Pubi, Belmont, California, 329 pp
Serra J (1982) Image analysis and mathematical morphology. Academic Press, London, 601 pp
Serra J (ed) (1988) Image analysis and mathematical morphology, vol 2: Theoretical advances. Academic Press, London, 405 pp
Urmantsev Yu A (1986) Symmetry of system and system of symmetry. Comput Math Appi 12B: 379–405
van Rijckevorsel (1987) The application of fuzzy coding and horseshoes in multiple correspondence analysis. DSWO Press, Leiden, 271 pp
van Ryzin J (ed) (1977) Classification and clustering. Academic Press, London, 458 pp
Yager RR, Ovchinnikov S, Tong RM, Nguyen HT (1987) Fuzzy sets and applications: selected papers by Zadeh LA. Wiley and Sons, New York, 684 pp
Zadeh LA (1977) Fuzzy sets and their applications to pattern classification and clustering analysis, pp 251–299 In: van Ryzin J (ed) ( 1977 ) Classification and clustering. Academic Press, London, pp 251–299
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1994 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Bulakh, A.G., Zussman, J., Mann, C.J., Ryakhovsky, V.M. (1994). Treatment of Chemical Composition Data for Minerals. In: Marfunin, A.S. (eds) Advanced Mineralogy. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-78523-8_2
Download citation
DOI: https://doi.org/10.1007/978-3-642-78523-8_2
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-78525-2
Online ISBN: 978-3-642-78523-8
eBook Packages: Springer Book Archive