Physics and Chemistry of Minerals

, Volume 1, Issue 1, pp 83–94 | Cite as

Temperature, pressure and composition: Structurally analogous variables

  • Robert M. Hazen
Article

Abstract

Changes in temperature, pressure and composition cause changes in the ratios of polyhedral sizes in oxygen-based minerals. Polyhedra with large, high-coordination, low-valence cations expand and compress more than polyhedra with small, low-coordination, high-valence cations. Changes in cation composition alter the ratios of polyhedral sizes by changing mean cation radii. Thus temperature, pressure and composition are structurally analogous variables. Since temperature, pressure and composition change structures in similar ways, it is possible to construct isostructural surfaces in P-T-X space. For structures in which stability is limited to specific ranges of polyhedral size ratios (e.g. octahedral-tetrahedral layers in mica), certain P-T-X isostructural surfaces may coincide with phase boundaries. If geometrical constraints on mineral stability are known, then phase equilibria may be predicted. Examples of stability limit calculations are given for several major oxygen-based mineral groups.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Akimoto, S., Fujisawa, H., Katsura, T.: The olivine-spinel transition in Fe2SiO4 and Ni2SiO4. J. Geophys. Res. 70, 1969–1977 (1965)Google Scholar
  2. Anderson, D. L., Anderson, O. L.: The bulk modulus-volume relationship for oxides. J. Geophys. Res. 75, 3494–3500 (1970).Google Scholar
  3. Cameron, M., Sueno, S., Prewitt, C. T., Papike, J. J.: High-temperature crystal chemistry of acmite, diopside, hedenbergite, jadeite, spodumene, and ureyite. Am. Mineral. 58, 594–618 (1973)Google Scholar
  4. Carron, M. K., Mrose, M. E., Murata, K. J.: Relation of ionic radius to structures of rare-earth phosphates, arsenates, and vanadates. Am. Mineral. 43, 985–989 (1958)Google Scholar
  5. Dachille, F., Roy, R.: High pressure studies of the system Mg2GeO4 – Mg2SiO4 with special reference to the olivine-spinel transition. Am. J. Sci. 258, 225–246 (1960)Google Scholar
  6. Dempsey, M. J., Strens, R. G. J.: Modelling crystal structures. In: Physics and Chemistry of Minerals and Rocks, Strens, R. G. J. (ed.). New York, Wiley and Sons, 443–458 (1976)Google Scholar
  7. Hazen, R. M.: Sanidine: predicted and observed monoclinic-to-triclinic reversible transformation at high pressure. Science 194, 105–107 (1976a)Google Scholar
  8. Hazen, R. M.: Effects of temperature and pressure on the crystal structure of forsterite. Am. Mineral. 61, in press (1976 b)Google Scholar
  9. Hazen, R. M., Burnham, C. W.: The crystal structures of one-layer phlogopite and annite. Am. Mineral. 58, 889–900 (1973)Google Scholar
  10. Hazen, R. M., Prewitt, C. T.: Effects of temperature and pressure on interatomic distances in oxides and silicates. Am. Mineral. 62, in press (1977)Google Scholar
  11. Hazen, R. M., Wones, D. R.: The effect of cation substitutions on the physical properties of trioctahedral micas. Am. Mineral. 57, 103–129 (1972)Google Scholar
  12. Huggins, F.: Mössbauer studies of iron minerals under pressures of up to 200 kilobars. Ph. D. Thesis, Massachusetts Institute of Technology, 358 p. (1974)Google Scholar
  13. Kamb, B.: Structural basis of the olivine-spinel relation. Am. Mineral. 53, 1439–1455 (1968)Google Scholar
  14. Megaw, H. D.: Crystal structures and thermal expansion. Mater. Res. Res. Bull. 6, 1007–1018 (1971)Google Scholar
  15. Pauling, L.: The nature of the chemical bond. Ithaca, New York: Cornell University Press, 644 p. (1960)Google Scholar
  16. Prewitt, C. T., Sueno, S., Papike, J. J.: The crystal structures of high albite and monalbite at high temperatures. Am. Mineral. 61, in press (1976)Google Scholar
  17. Shannon, R. D.: Revised effective ionic radii and systematic studies of interatomic distances in halides and chalcogenides. Acta Crystallogr., in press (1976)Google Scholar
  18. Shannon, R. D., Prewitt, C. T.: Effective ionic radii in oxides and fluorides. Acta Crystallogr. B25, 925–945 (1969)Google Scholar
  19. Wyllie, P. J.: The Dynamic Earth. New York; John Wiley and Sons, 416 p. (1971)Google Scholar

Copyright information

© Springer-Verlag 1977

Authors and Affiliations

  • Robert M. Hazen
    • 1
  1. 1.Department of Mineralogy and PetrologyUniversity of CambridgeCambridgeEngland
  2. 2.Carnegie Institution of WashingtonGeophysical LaboratoryWashington, DC

Personalised recommendations