Symmetry-Entropy-Volume Relationships in Polymorphism

R. G. J. Strens1
Department of Earth Sciences, The University, Leeds 2
1Present address: School of Physics, The University, Newcastle Upon Tyne 1

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.

Mineralogical Magazine; December 1967 v. 36; no. 280; p. 565-577; DOI: 10.1180/minmag.1967.036.280.09
© 1967, The Mineralogical Society
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