Hostname: page-component-cd9895bd7-lnqnp Total loading time: 0 Render date: 2024-12-26T13:04:35.136Z Has data issue: false hasContentIssue false
  • English
  • Français

Rigid unit modes in framework silicates

Published online by Cambridge University Press:  05 July 2018

Martin T. Dove ,
Volker Heine  and
Kenton D. Hammonds
Martin T. Dove
Affiliation:
Department of Earth Sciences, University of Cambridge, Downing Street, Cambridge CB2 3EQ, UK
Volker Heine
Affiliation:
Cavendish Laboratory, University of Cambridge, Madingley Road, Cambridge CB3 OHE, UK
Kenton D. Hammonds
Affiliation:
Department of Earth Sciences, University of Cambridge, Downing Street, Cambridge CB2 3EQ, UK
Get access Rights & Permissions [Opens in a new window]

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 modesphase transitionsquartzleucitecristobalite
Type
Research Article
Information
Mineralogical Magazine , Volume 59 , Issue 397 , December 1995 , pp. 629 - 639
Copyright
Copyright © The Mineralogical Society of Great Britain and Ireland 1995

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Berge, B., Bachheimer, J.P., Dolino, G., Vallade, M, and Zeyen, C.M.E. (1986) Inelastic neutron scattering study of quartz near the incommensurate phase transition. Ferroelectrics, 66, 73–84.CrossRefGoogle Scholar
Bethke, J., Dolino, G., Eckold, G., Berge, B., Vallade, M, Zeyen, C.M.E., Hahn, T., Arnold, H. and Moussa, F. (1987) Phonon dispersion and mode coupling in high-quartz near the incommensurate phase transition. Europhysics Letters, 3, 207–12.CrossRefGoogle Scholar
Boy sen, H. (1990) Neutron scattering and phase transitions in leucite. In Phase transitions in ferroelastic and co-elastic crystals (Salje, E.K.H., ed.). Cambridge University Press, 334-49.Google Scholar
Bruce, A.D.and Cowley, R.A. (1981) Structural Phase Transitions. Taylor and Francis, London.CrossRefGoogle Scholar
Carpenter, M.A. (1988) Thermochemistry of aluminium/ silicon ordering in feldspar minerals. In Physical properties and thermodynamic behaviour of minerals (Salje, E.K.H., ed.). Dordrecht, Holland: D. Reidel, 265–323.CrossRefGoogle Scholar
Dolino, G., Berge, B., Vallade, M. and Moussa, F. (1989) Inelastic neutron scattering study of the origin of the incommensurate phase of quartz. Physica, B156, 15–16.CrossRefGoogle Scholar
Dolino, G., Berge, B., Vallade, M. and Moussa, F. (1992) Origin of the incommensurate phase of quartz: I. Inelastic neutron scattering study of the high temperature b phase of quartz. Journal De Physique I. 2, 1461-80.CrossRefGoogle Scholar
Dove, M.T. (1993) Introduction to Lattice Dynamics. Cambridge University Press, Cambridge.CrossRefGoogle Scholar
Dove, M.T. and Heine, V. (1995) Anatomy of a structure phase transition: theoretical analysis of the displacive phase transition in quartz and other silicates, (in preparation).Google Scholar
Dove, M.T., Giddy, A.P. and Heine, V. (1992) On the application of mean-field and Landau theory to displacive phase transitions. Ferroelectrics, 136, 33–49.CrossRefGoogle Scholar
Dove, M.T., Giddy, A.P. and Heine, V. (1993) Rigid unit mode model of displacive phase transitions in framework silicates. Trans. Amer. Crystallogr. Assoc, 27, 65–74.Google Scholar
Dove, M.T., Chen, X., Giddy, A.P., Hammonds, K.D. and Heine, V. (1995a) Simplicity in complexity: Structural phase transitions in silicate framework structures. Phys. Rev. Letters (in press).Google Scholar
Dove, M.T., Hammonds, K.D., Heine, V., Withers, R.L., Xiao, Y. and Kirkpatrick, R.J. (19956) Rigid Unit Modes in the High-Temperature Phase of SiO2 Tridymite: Calculations and Electron Diffraction. Phys. Chem. Minerals (submitted).Google Scholar
Giddy, A.P., Dove, M.T., Pawley, G.S. and Heine, V. (1993) The determination of rigid unit modes as potential soft modes for displacive phase transitions in framework crystal structures. Ada Crystallogr., A49, 697–703.CrossRefGoogle Scholar
Grimm, H. and Dorner, B. (1975) On the mechanism of the xP phase transformation of quartz. Phys. Chem. Solids, 36, 407–13.CrossRefGoogle Scholar
Hammonds, K.D., Dove, M.T., Giddy, A.P. and Heine, V. (1994) CRUSH: A FORTRAN program for the analysis of the rigid unit mode spectrum of a framework structure. Amer. Mineral, 79, 1207–9.Google Scholar
Hammonds, K.D., Dove, M.T., Giddy, A.P., Winkler, B. and Heine, V. (1995) Rigid unit phonon modes and structural phase transitions in framework silicates. Amer. Mineral, (submitted).CrossRefGoogle Scholar
Hatch, D.M. and Ghose, S. (1991) The a.-b phase transition in cristobalite, SiO2 . Phys. Chem. Minerals, 17, 554–62.CrossRefGoogle Scholar
Hazen, R.M. and Finger, L.W. (1982) Comparative crystal chemistry: temperature, pressure, composition and the variation of crystal structure. Chichester: Wiley.Google Scholar
Hua, G.L., Welberry, T.R., Withers, R.L. and Thompson, J.G. (1988) An electron diffraction and lattice-dynamical study of the diffuse scattering in P-cristobalite, SiO2 . J. Applied Crystallogr., 21, 458–65.CrossRefGoogle Scholar
Lasaga, A.C. and Gibbs, G.V. (1988) Quantum mechanical potential surfaces and calculations of minerals and molecular clusters. Phys. Chem. Minerals, 16, 29–41.CrossRefGoogle Scholar
Megaw, H.D. (1973) Crystal structures: a working approach. Philadelphia: W.B. Saunders.Google Scholar
Palmer, D.C. (1990) Volume anomaly and the impure ferroelastic phase transition in leucite. In Phase transitions in ferroelastic and co-elastic crystals (Salje, E.K.H., ed.). Cambridge University Press, 350-66.Google Scholar
Pawley, G.S. (1972) Analytic formulation of molecular lattice dynamics based on pair potentials. Physica Status Solidi, 49b, 475–88.CrossRefGoogle Scholar
Phillips, B.L., Thompson, J.G., Xiao Y. and Kirkpatrick, R.J. (1993) Constraints on the structure and dynamics of the P-cristobalite polymorphs of SiO2and A1PO4 from 31P, 27A1 and 29Si NMR spectro-scopy to 770 K. Phys. Chem. Minerals, 20, 341–52.CrossRefGoogle Scholar
Sanders, M.J., Leslie, M. and Catlow, C.R.A. (1984) Interatomic potentials for SiO2. J. Chem. Soc: Chemical Communications, 1271-3.CrossRefGoogle Scholar
Schmahl, W.W., Swainson, I.P., Dove, M.T. and Graeme-Barber, A. (1992) Landau free energy and order parameter behaviour of the ab phase transition in cristobalite. Zeits. Kristallogr., 201, 125–45.CrossRefGoogle Scholar
Sollich, P., Heine, V. and Dove, M.T. (1994) The Ginzburg interval in soft mode phase transitions: Consequences of the Rigid Unit Mode picture. J. Phys.: Condensed Matter, 6, 3171–96.Google Scholar
Stokes, H.T. and Hatch, D.M. (1988) hotropy Subgroups of the 230 Crystallographic Space Groups. World Scientific, Singapore.Google Scholar
Swainson, I.P. and Dove, M.T. (1993a) Low-frequency floppy modes in P-cristobalite. Phys. Rev. Letters, 71, 193–6.CrossRefGoogle Scholar
Swainson, I.P. and Dove, M.T. (1993fo) Comment on 'First-Principles Studies on Structural Properties of P-cristobalite'. Phys. Rev. Letters, 71, 3610.CrossRefGoogle Scholar
Tautz, F.S., Heine, V., Dove, M.T. and Chen, X. (1991) Rigid unit modes in the molecular dynamics simulation of quartz and the incommensurate phase transition. Phys. Chem. of Minerals, 18, 326–36.CrossRefGoogle Scholar
Vallade, M., Berge, B. and Dolino, G. (1992) Origin of the incommensurate phase of quartz: II. Interpretation of inelastic neutron scattering data. Journal De Physique I. 2, 1481–95.CrossRefGoogle Scholar
Welberry, T.R., Hua, G.L. and Withers, R.L. (1989) An optical transform and Monte Carlo study of the disorder in P-cristobalite SiO2 . J. Appl. Crystallogr., 22, 87–95.CrossRefGoogle Scholar
Withers, R.L., Thompson, J.G. and Welberry, T.R. (1989) The structure and microstructure of oc-cristobalite and its relationship to P-cristobalite. Phys. Chem. Minerals, 16, 517–23.CrossRefGoogle Scholar
Withers, R.L., Thompson, J.G., Xiao, Y. and Kirkpatrick, R.J. (1995) An electron diffraction study of the polymorphs of SiO2-tridymite. Phys. Chem. Minerals, 21, 421–33.Google Scholar
Wright, A.F. and Leadbetter, A.J. (1975) The structures of the P-cristobalite phases of SiO2 and A1PO4 . Phil. Mag., 31, 1391–1401.CrossRefGoogle Scholar