Treatment of Chemical Composition Data for Minerals

  • A. G. Bulakh
  • J. Zussman
  • C. John Mann
  • V. M. Ryakhovsky


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.


Expert System Multivariate Statistical Analysis Math Geol Mineral Formula Nickel Sulphide 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Bulakh AG (1969) Calculation of mineral formulas 2nd edn. Nedra, Leningrad (In Russian).Google Scholar
  2. Bulakh AG (1970) Berechnung von Mineralformeln. VEB Deutscher Verlag für Grundstoffindustrie, LeipzigGoogle Scholar
  3. Bulakh AG (1984) On errors in formulas of minerals recalculated from inaccurate chemical data. Mineral J (Kiev) 4: 87–92 (In Russian)Google Scholar
  4. Deer WA, Howie RA, Zussman J (1962, 1963 ) Rock-forming minerals, vols 1–5. LongmanGoogle Scholar
  5. Deer WA, Howie RA, Zussman J (1992) An introduction to rock-forming minerals, 2nd edn. LongmanGoogle Scholar
  6. Dollase WA, Newman WI (1984) Statistically most probable stoichiometric formulae. Am Mineral 69: 553–556Google Scholar
  7. Droop GTR (1987) A general equation for estimating Fe3+ concentrations in ferromagnesian silicates and oxides from microprobe analyses using stoichiometric criteria. Mineral Mag 51: 431–435CrossRefGoogle Scholar
  8. Hey MH (1939) On the presentation of chemical analyses of minerals. Mineral Mag 25: 402–412CrossRefGoogle Scholar
  9. Hey MH (1950) An index of mineral species and varieties arranged chemically. London, British MuseumGoogle Scholar
  10. Hey MH (1954) A further note on the presentation of chemical analyses of minerals. Mineral Mag 30: 481–497CrossRefGoogle Scholar
  11. 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: 1–11Google Scholar
  12. Nicholls GD, Zussman J (1954) The structural formula of a hydrous amphibole. Mineral Mag 30: 717–722CrossRefGoogle Scholar
  13. Povarennykh AS (1972) Crystal chemical classification of minerals, vols 1 and 2. Plenum Press, New YorkGoogle Scholar
  14. 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. AmericaGoogle Scholar
  15. Rock NMS, Carroll GW (1990) MINTAB: A general-purpose mineral recalculation and tabulation program for Macintosh microcomputers. Am Mineral 75: 424–430Google Scholar
  16. Strunz H (1982) Mineralogische Tabellen, 8 Aufl. Akad Verlag, LeipzigGoogle Scholar
  17. Aitchison J (1986) The statistical analysis of compositional data. Methuen, New York, 405 ppCrossRefGoogle Scholar
  18. Aitchison J (1990) Relative variation diagrams for describing patterns of compositional variability. Math geol 22 (4): 487–511CrossRefGoogle Scholar
  19. Anderson TW (1984) An introduction to multivariate statistical analysis, 2nd edn. Wiley and Sons, New York, 665 ppGoogle Scholar
  20. Bezdek JC (1981) Pattern recognition with fuzzy objective functions. Plenum Press, New York, 256 ppGoogle Scholar
  21. 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: 339–357Google Scholar
  22. 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: 358–372Google Scholar
  23. Conover WJ (1980) Practical nonparametric statistics. 2d edn. Wiley and Sons, New York, 485 ppGoogle Scholar
  24. Eisenbeis RA, Avery RB (1972) Discriminant analysis and classification procedures: theory and applications. Lexington Books, Lexington, Massachusetts, 250 ppGoogle Scholar
  25. d Ed., Marcel Dekker, Inc., 398 p.Google Scholar
  26. Good IJ (1977) The botryology of botryology. In: van Ryzin J (ed) Classification and clustering. Academic Press, London, pp 73–94Google Scholar
  27. Granath, G (1984) Application of fuzzy clustering and fuzzy classification to evaluate the provenance of glacial till. Math Geol 16 (3): 283–301CrossRefGoogle Scholar
  28. Granath G (1988) Pattern recognition in geochemical hydrocarbon exploration: a fuzzy approach. Math Geol 20 (6): 673–691CrossRefGoogle Scholar
  29. Greenacre MJ (1984) Theory and applications of correspondence analysis. Academic Press, London, 357 ppGoogle Scholar
  30. Hand DJ (1981) Discrimination and classification. Wiley and Sons, Chichester, Great Britain, 209 ppGoogle Scholar
  31. Haux R (ed) (1986) Expert systems in statistics. Gustav Fischer, Stuttgart, 190 ppGoogle Scholar
  32. Hendrickson RG (1984) A survey of sensitivity analysis methodology. National Bureau of Standards, NBSIR 84-28114, Washington DC, 83 ppGoogle Scholar
  33. James M (1985) Classification algorithms. Wiley-Interscience, New York, 220 ppGoogle Scholar
  34. Jolliffe IT (1986) Principal component analysis. Springer Series in Statistics. Springer, Berlin Heidelberg New York, 271 ppGoogle Scholar
  35. Kacewicz M (1989) On the problem of fuzzy searching for hard workability rocks in open-pit mine exploration. Math Geol 21 (3): 309–318CrossRefGoogle Scholar
  36. Kleijnen JPC (1987) Statistical tools for simulation practitioners. Marcel Dekker, New York, 407 ppGoogle Scholar
  37. 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 61–74Google Scholar
  38. Negoita CV (1985) Expert systems and fuzzy systems. Benjamin/Cummings, Menlo Park, California, 183 ppGoogle Scholar
  39. Romesburg HC (1984) Cluster analysis for researchers. Lifetime learning Pubi, Belmont, California, 329 ppGoogle Scholar
  40. Serra J (1982) Image analysis and mathematical morphology. Academic Press, London, 601 ppGoogle Scholar
  41. Serra J (ed) (1988) Image analysis and mathematical morphology, vol 2: Theoretical advances. Academic Press, London, 405 ppGoogle Scholar
  42. Urmantsev Yu A (1986) Symmetry of system and system of symmetry. Comput Math Appi 12B: 379–405CrossRefGoogle Scholar
  43. van Rijckevorsel (1987) The application of fuzzy coding and horseshoes in multiple correspondence analysis. DSWO Press, Leiden, 271 ppGoogle Scholar
  44. van Ryzin J (ed) (1977) Classification and clustering. Academic Press, London, 458 ppGoogle Scholar
  45. Yager RR, Ovchinnikov S, Tong RM, Nguyen HT (1987) Fuzzy sets and applications: selected papers by Zadeh LA. Wiley and Sons, New York, 684 ppGoogle Scholar
  46. 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 251–299Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1994

Authors and Affiliations

  • A. G. Bulakh
  • J. Zussman
  • C. John Mann
  • V. M. Ryakhovsky

There are no affiliations available

Personalised recommendations