Negative thermal expansion in beta-quartz |
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Authors: | P R L Welche V Heine M T Dove |
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Institution: | (1) Theory of Condensed Matter, Cavendish Laboratory, Madingley Road, Cambridge CB3 0HE, UK, GB;(2) Dept. of Earth Sciences, University of Cambridge, Downing Street, Cambridge CB2 3EQ, UK, GB |
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Abstract: | Computer modelling and theoretical analysis are used to explain the nearly zero and slightly negative coefficients of thermal
expansion in β-quartz well above the α-β phase transition temperature. Quartz was selected for study as an archetypal material with a framework structure of stiff
units, namely SiO4 tetrahedra, linked through shared oxygen atoms as very flexible hinges. The contributions of the soft mode, the Vallade mode,
the TAz phonon branch and the phonon spectrum as a whole are discussed in detail. The results fully support and illustrate a recent
theory of the negative contribution to thermal expansion in framework structures. It is a geometrical effect due to the rotation
of the tetrahedral units, folding together as they vibrate. The very rapid increase in the lattice parameters for about 20 K
above the transition temperature is well accounted for within quasiharmonic theory, and is therefore not evidence for critical
fluctuations or fluctuating patches of α
+, α
− structure.
Received August 14 1997 / Revised, accepted January 26 1998 |
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