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Symmetry–entropy–volume relationships in polymorphism

Published online by Cambridge University Press:  14 March 2018

R. G. J. Strens
R. G. J. Strens*
Affiliation:
Department of Earth Sciences, The University, Leeds 2
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Summary

Group theoretical analysis of the normal vibrations of isolated molecules and of macroscopic crystals indicates that the principal effect of symmetry reduction is to remove the degeneracy of the normal vibrations, thus reducing the number of microscopic complexions of the phonon distribution, and reducing the entropy. This mechanism is effective only in point groups containing a rotation axis of order 3 or greater, and may play a part in the high-low cordierite transition.

Two other symmetry-related entropy contributions are discussed : the first is the loss of positional degeneracy in systems in which the number of available positions exceeds the number of atoms, as in high-low quartz, vlasovite, and many ferroelectrics. The second is the loss of positional degeneracy in a solid solution, which leads to unmixing, as in high-low albite, microcline-sanidine, and high-low cordierite transitions. These mechanisms are effective in all point groups down to 1 = C1, and can proceed even within C1 by a change in the unit cell volume.

Consideration of entropy-volume relationships suggests that the glaucophane I–II transition has less order-disorder character than previously supposed. It is suggested that zoisite-clinozoisite, anthophyllite-cummingtonite and enstatite-clinoenstatite relationships are polytypic rather than polymorphic in the usual sense, and the mechanisms responsible for producing the stacking order are discussed.

The implications of the differences between the behaviour of the classical double oscillator (often used as a model for displacive transitions) and its quantized analogue are discussed.

Type
Research Article
Information
Mineralogical magazine and journal of the Mineralogical Society , Volume 36 , Issue 280 , December 1967 , pp. 565 - 577
Copyright
Copyright © The Mineralogical Society of Great Britain and Ireland 1967

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References

Bailey, (S. W.) and Taylor, (W. H.), 1955. Acta Cryst., vol. 8, p. 621.Google Scholar
Brickmann, (J.) and Zimmermann, (H.), 1966. Ber. Bunsengesell. phys. chem., Bd. 70, Heft 2, p. 157.Google Scholar
Buerger, (M. J.), 1945. Amer. Min., vol. 30, p. 469.Google Scholar
Clark, (S. P.), 1966. Handbook of physical constants. Geol. Soc. Amer. Memoir 97.Google Scholar
Cole, (W. F.), Sorum, (H.), and Kennard, (O.), 1949. Acta Cryst. vol. 2, p. 280.CrossRefGoogle Scholar
Cotton, (F. A.), 1963. Chemical applications of group theory. Wiley, New York.Google Scholar
Deer, (W. A.), Howie, (R. A.), and Zussman, (J.), 1962. Rock-forming minerals. Longmans, London.Google Scholar
Denbigh, (K. G.), 1961. Principles of chemical equilibrium. Cambridge University Press.Google Scholar
Ernst, (W. G.), 1963. Amer. Min., vol. 48, p. 241.Google Scholar
Ferguson, (R. B.), Traill, (R. J.), and Taylor, (W. H.), 1958. Acta Cryst., vol. 11, p. 331.Google Scholar
Fleet, (S. G.) and Cann, (J. R.), 1967. Min. Mag., vol. 36, p. 233.Google Scholar
Fyfe, (W. S.), Turner, (F. J.), and Verhoogen, (J.), 1958. Metamorphic reactions and metamorphic facies. Geol. Soc. Amer. Mere. 73.Google Scholar
Gibbs, (G. V.), 1966. Amer. Min., vol. 51, p. 1068.Google Scholar
Haas, (C.), 1965a. Journ. Phys. Chem. Solids, vol. 26, p. 1225.Google Scholar
Gibbs, (G. V.), 1965b. Phys. Rev., vol. 140A, p. 863.Google Scholar
Ito, (T.), 1950. X-ray studies on polymorphism. Maruzen Co., Tokyo.Google Scholar
Jaffe, (H. H.) and Orchin, (M.), 1965. Symmetry in chemistry. Wiley, New York.Google Scholar
Kanzig, (W.), 1957. Ferroelectrics and antiferroelectrics. Academic Press, New York.Google Scholar
Kittel, (C.), 1956. Introduction to solid state physics. Wiley, New York.Google Scholar
Knox, (R. S.), 1966. Solid State Comnlun., vol. 4, p. 453.Google Scholar
Krishna, (P.) and Verma, (A. P.), 1966. Physica Status Solidi, vol. 17, p. 437.Google Scholar
Landau, (L. D.), 1937a. Phys. Zeits. Sowjet., vol. 11, p. 26.Google Scholar
Landau, (L. D.), 1937b. Ibid., p. 545.Google Scholar
McConnell, (J. D. C.) and Fleet, (S. G.), 1963. Nature, vol. 199, p. 586.CrossRefGoogle Scholar
MacDonald, (D. K. C.), 1963. Introductory statistical mechanics for physicists. Wiley, New York.Google Scholar
Mckie, (D.), and McConnell, (J. D. C.), 1963. Min. Mag., vol. 33, p. 581.Google Scholar
Mott, (N. F.) and Gurney, (R. W.), 1948. Electronic processes in ionic crystals. Oxford University Press.Google Scholar
Powell, (J. I.) and Crasemann, (B.), 1961. Quantum mechanics. Addison-Wesley, Reading, Mass., U.S.A. Google Scholar
Sato, (H.), Toth, (R. S.), and Honjo, (G.), 1966. Solid State Commun., vol. 4, p. 103.CrossRefGoogle Scholar
Schneer, (C. J.), 1955. Acta Cryst., vol. 8, p. 279.Google Scholar
Venkatesh, (V.), 1954. Amer. Min., vol. 39, p. 636.Google Scholar
Wilsdorf, (D. K.), 1965. Phys. Rev., vol. 140A, p. 1599.Google Scholar