Rigid Unit Modes in Framework Silicates

Martin T. Dove1, Volker Heine2 and Kenton D. Hammonds1
1 Department of Earth Sciences, University of Cambridge, Downing Street, Cambridge CB2 3EQ, UK
2 Cavendish Laboratory, University of Cambridge, Madingley Road, Cambridge CB3 OHE, UK

Abstract: We describe a model for framework silicates in which the SiO4 (and AlO4) tetrahedra are treated as perfectly rigid and freely jointed. From this model we are able to identify low-energy modes of distortion of the structure, which we call Rigid unit modes. These modes can act as soft modes to allow easy distortions at phase transition. We discuss three forces that will operate at a phase transition in conjunction with the candidate soft modes to determine which of the rigid unit modes will actually precipitate a phase transition, and illustrate these ideas by detailed discussions of the phase transitions in quartz, leucite and cristobalite. The model can also be used to estimate the transition temperature, and the theory highlights an important role for the stiffness of the tetrahedra.

Keywords: rigid unit modes • phase transitions • quartz • leucite • cristobalite

Mineralogical Magazine; December 1995 v. 59; no. 397; p. 629-639; DOI: 10.1180/minmag.1995.059.397.07
© 1995, The Mineralogical Society
Mineralogical Society (www.minersoc.org)