Physics and Chemistry of Minerals

, Volume 3, Issue 3, pp 237–249 | Cite as

A novel technique for characterizing thermal expansion in minerals

  • George A. Lager


When a crystalline solid is subjected to a temperature increase, its constituent polyhedra may change in size and shape and rotate relative to one another. If the deformation can be approximated by a linear transformation of atomic coordinates, these changes can be quantitatively described in terms of second rank tensors. An iterative least-squares method is used to calculate strain and rotation tensors given the positions of the coordinating atoms of a polyhedron at two temperatures. The method is applied to polyhedral thermal expansions in silicate and oxide minerals.


Oxide Silicate Thermal Expansion Temperature Increase Mineral Resource 
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. Birle, J.D., Gibbs, G.V., Moore, P.B., Smith, J.V.: Crystal structures of natural olivines. Am. Mineral.53, 807–824 (1968)Google Scholar
  2. Bjerhammer, A.: Theory of Errors and Generalized Matrix Inverses. New York: Elsevier Scientific Publishing Co. 1973Google Scholar
  3. Bloss, F.D.: Crystallography and Crystal Chemistry. New York: Holt, Rinehart and Winston 1971Google Scholar
  4. Brown, G.E., Prewitt, C.T.: High-temperature crystal chemistry of hortonolite. Am. Mineral.58, 577–587 (1973)Google Scholar
  5. 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
  6. Clark, J.R., Appleman, D.E., Papike, J.J.: Crystal-chemical characterization of clinopyronenes based on eight new structure refinements. Mineral. Soc. Am. Spec. Paper2, 31–50 (1969)Google Scholar
  7. Dollase, W.A.: A method of determining the distortion of coordination polyhedra. Acta. Cryst.A30, 513–517 (1974)Google Scholar
  8. Finger, L., Ohashi, Y.: The thermal expansion of diopside to 800°C and a refinement of the crystal structure at 700°C. Am. Mineral.61, 303–310 (1976)Google Scholar
  9. Golub, G., Riensch, C.: Singular value decomposition and least squares solutions. Numer. Math.14, 403–420 (1970)Google Scholar
  10. Hazen, R.M.: Effects of temperature and pressure on the crystal structure of forsterite. Am. Mineral.61, 1280–1293 (1976a)Google Scholar
  11. Lager, G.A.: A comparison of the structural changes in olivines as a function of chemical substitution and temperature. (abstr.) Geol. Soc. Am. Abstr. Progr.8, 1156 (1976)Google Scholar
  12. Lager, G.A., Meagher, E.P.: The crystal structure of Ni-olivine (Ni2SiO4) at high temperatures. (abstr.) EOS5, 350 (1974)Google Scholar
  13. Lager, G.A., Meagher, E.P.: High temperature structural study of six olivines. Am. Mineral.63, 365–377 (1978)Google Scholar
  14. Mase, G.E.: Schaum's Outline of Theory and Problems of Continuum Mechanics. New York: McGraw-Hill Book Co. 1970Google Scholar
  15. Noll, W.: The Foundations of Mechanics and Thermodynamics: Selected Papers. Berlin Heidelberg New York: Springer 1974Google Scholar
  16. Nye, J.F.: Physical Properties of Crystals. London: Oxford University Press 1957Google Scholar
  17. Ohashi, Y., Burnham, C.W.: Clinopyroxene lattice deformation: The roles of chemical substitution and temperature. Am. Mineral.58, 843–849 (1973)Google Scholar
  18. Papike, J.J., Prewitt, C.T., Sueno, S., Cameron, M.: Pyroxenes: Comparisons of real and ideal structural topologies. Z. Krist.69, 254–273 (1973)Google Scholar
  19. Pauling, L.: The Nature of the Chemical Bond. New York: Cornell University Press 1939Google Scholar
  20. Rajamani, V., Brown, G.E., Prewitt, C.T.: Cation ordering in Ni-Mg olivine. Am. Mineral.60, 292–299 (1975)Google Scholar
  21. Robinson, K., Gibbs, G.V., Ribbe, P.H.: Quadratic elongation: A quantitative measure of distortion in coordination polyhedra. Science172, 567–570 (1971)Google Scholar
  22. Shinno, I., Hayashi, M., Kuroda, Y.: Mössbauer studies of natural olivines. Mineral. J. Japan7, 344–358 (1974)Google Scholar
  23. Smyth, J.R., Hazen, R.M.: The crystal structures of forsterite and hortonolite at several temperatures up to 900°C. Am. Mineral.58, 588–593 (1973)Google Scholar
  24. Smyth, J.R.: High temperature crystal chemistry of fayalite. Am. Mineral.60, 1092–1097 (1975)Google Scholar
  25. Sueno, S., Cameron, M., Papike, J.J., Prewitt, C.T.: The high temperature crystal chemistry of tremolite. Am. Mineral.58, 649–664 (1973)Google Scholar
  26. Wayman, C.M.: Introduction to the Crystallography of Martensitic Transformations. New York: Macmillan Co. 1964Google Scholar

Copyright information

© Springer-Verlag 1978

Authors and Affiliations

  • George A. Lager
    • 1
  1. 1.Department of GeosciencesRider CollegeLawrencevilleU.S.A.

Personalised recommendations