Hostname: page-component-cd9895bd7-dk4vv Total loading time: 0 Render date: 2024-12-23T14:43:50.081Z Has data issue: false hasContentIssue false

Amorphous silica from the Rigid Unit Mode approach

Published online by Cambridge University Press:  05 July 2018

M. T. Dove*
Affiliation:
Mineral Physics group, Department of Earth Sciences, University of Cambridge, Downing Street, Cambridge, CB2 3EQ, UK
K. D. Hammonds
Affiliation:
Mineral Physics group, Department of Earth Sciences, University of Cambridge, Downing Street, Cambridge, CB2 3EQ, UK
M. J. Harris
Affiliation:
ISIS Facility, Rutherford Appleton Laboratory, Chilton, Didcot, Oxfordshire, OX11 0QX, UK
V. Heine
Affiliation:
Cavendish Laboratory, University of Cambridge, Madingley Road, Cambridge, CB3 0HE, UK
D. A. Keen
Affiliation:
ISIS Facility, Rutherford Appleton Laboratory, Chilton, Didcot, Oxfordshire, OX11 0QX, UK
A. K. A. Pryde
Affiliation:
Mineral Physics group, Department of Earth Sciences, University of Cambridge, Downing Street, Cambridge, CB2 3EQ, UK
K. Trachenko
Affiliation:
Mineral Physics group, Department of Earth Sciences, University of Cambridge, Downing Street, Cambridge, CB2 3EQ, UK
M. C. Warren
Affiliation:
Mineral Physics group, Department of Earth Sciences, University of Cambridge, Downing Street, Cambridge, CB2 3EQ, UK
*

Abstract

We apply the Rigid Unit Mode model, which was initially developed for crystalline silicates, to the study of the flexibility of silica glass. Using a density-of-states approach we show that silica glass has the same flexibility against infinitesimal displacements of crystalline phases. Molecular dynamics simulations also show that parts of the silica structure are able to undergo large spontaneous changes through reorientations of the SiO4 tetrahedra with no energy cost.

Type
Research Article
Copyright
Copyright © The Mineralogical Society of Great Britain and Ireland 2000

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, J., Vallade, M. and Zeyen, C. (1986) Inelastic neutron scattering study of quartz near the incommensurate phase transition. Ferroelectrics., 66, 73–84.CrossRefGoogle Scholar
Boysen, H. (1990) Neutron scattering and phase transitions in leucite. Pp. 334–47 in: Ferroelastic and Co-elastic Crystals. (Salje, E.K.H., editor). Cambridge University Press.Google Scholar
Buchenau, M., Prager, N., Nucker, N., Dianoux, A.J., Ahmad, N. and Philips, W.A. (1986) Low frequency modes in vitreous silica. Phys. Rev. B, 34, 5665–73.CrossRefGoogle ScholarPubMed
Buchenaue, M., Zhou, H.M., Nucker, N., Gilroy, K.S., and Philips, W.A. (1988) Structural relaxation in vitreous silica. Phys. Rev. Lett., 60, 1318–21.CrossRefGoogle Scholar
Dove, M.T. (1997 a) Silicates and soft modes. Pp. 349–83 in : Amrphous Insulators and Semiconductors., (Thorpe, M.F. and Mitkova, M.I., editors). NATO ASI series, 3., Amsterdam. High Technology, 23.CrossRefGoogle Scholar
Dove, M.T. (1997 b) The theory of displacive phase transitions: A review. Amer. Mineral., 82, 213–44.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, 6574.Google Scholar
Dove, M.T., Hammonds, K.D., Heine, V.,Withers, R.L., Xiao, Y. and Kirkpatrick, R.J. (1995 a) Rigid unit modes in the high-temperature phase of SiO2 tridymite: Calculations and electron diffraction. Phys. Chem. Min., 23, 5662.Google Scholar
Dove, M.T., Heine, V. and Hammonds, K.D. (1995 b) Rigid unit modes in framework silicates. Minerall. Mag., 59, 629–39.CrossRefGoogle Scholar
Dove, M.T., Harris, M.J., Hannon, A.C., Parker, J.M., Swainson, I.P. and Gambhir, M. (1997 a) Floppy modes in crystalline and amorphous silicates. Phys. Rev. Lett., 78, 1070–3.CrossRefGoogle Scholar
Dove, M.T., Keen, D.A., Hannon, A.C. and Swainson, I.P. (1997 b) Direct measurement of the Si-O bond length and orientational disorder in β-cristobalite. Phys. Chem. Min., 24, 311–7.CrossRefGoogle Scholar
Dove, M.T., Heine, V. and Hammonds, K.D., Ghambhir, M. and Pryde, A.K.A. (1998) Short-range disorder and long-range order: implications of the ‘Rigid Unit Mode’ model. Pp. 253–72 in: Local Structure from Diffraction., (Thorpe, M.F. and Billinge, S., editors). Plenum, New York.Google Scholar
Dove, M.T., Gambhir, M. and Heine, V. (1999) Anatomy of a structural phase transition: Theoretical analysis of the displacive phase transition in quartz and other silicates. Phys. Chem. Min., 26, 344–53.CrossRefGoogle Scholar
Dove, M.T., Pryde, A.K.A. and Keen, D.A. (2000) Phase transitions in tridymite studied using ‘Rigid Unit Mode’ theory, Reverse Monte Carlo methods and molecular dynamics simulations. Minerall. Mag., 64, 267–83.CrossRefGoogle Scholar
Foret, M., Courtens, , Vacher, R. and Suck, J.B. (1996) Scattering investigation of acoustic localization in fused silica. Phys. Rev. Lett., 77, 3831–5.CrossRefGoogle ScholarPubMed
Gambhir, M., Heine, V. and Dove, M.T. (1997) A one-parameter model of a rigid-unit structure. Phase Transitions, 61, 125–39.CrossRefGoogle Scholar
Gambhir, M., Dove, M.T. and Heine, V. (1999) Rigid Unit Modes and dynamic disorder: SiO2 cristobali te and quartz. Phys. Chem. Min., 26, 484–95.CrossRefGoogle 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. Acta Crystallogr., A49, 697703.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., Heine, V. and Winkler, B. (1996) Rigid unit phonon modes and structural phase transitions in framework silicates. Amer. Mineral., 81, 1057–79.CrossRefGoogle Scholar
Hammonds, K.D., Deng, H., Heine, V. and Dove, M.T. (1997 a) How floppy modes give rise to adsorption sites in zeolites. Phys. Rev. Lett., 78, 3701–4.CrossRefGoogle Scholar
Hammonds, K.D., Heine, V. and Dove, M.T. (1997 b) Insights into zeolite behaviour from the rigid unit mode model. Phase Transitions, 61, 155–72.CrossRefGoogle Scholar
Hammonds, K.D., Bosenick, A., Dove, M.T. and Heine, V. (1998 a,) Rigid unit modes in crystal structures with octahe drally-coord inated atoms. Amer. Mineral., 83, 476–9.CrossRefGoogle Scholar
Hammonds, K.D., Heine, V. and Dove, M.T. (1998 b) Rigid Unit Modes and the quantitative determination of the flexibility possessed by zeolite frameworks. J. Phys. Chem. B, 102, 1759–67.CrossRefGoogle Scholar
Harris, M.J., Bennington, S.M., Dove, M.T., and Parker, J.M. (1999) On the wavevector dependence of the Boson peak in silicate glasses and crystals. Physica B, 263, 357–60.CrossRefGoogle Scholar
Harris, M.J., Dove, M.T. and Parker, J.M. (2000) Floppy modes and the Boson peak in crystalline and amorphous silicates: an inelastic neutron scattering study. Minerall. Mag., 64, 435–40.CrossRefGoogle Scholar
Hatch, D.M. and Ghose, S. (1991) The α-β transition in cristobalite, SiO2 . Phys. Chem. Min., 17, 554–62.CrossRefGoogle Scholar
Heine, V., Welche, P.R.L. and Dove, M.T. (1999) Geometrical origin and theory of negative thermal expansion in framework structures. J. Amer. Ceramic Soc., 82, 1793–802.CrossRefGoogle Scholar
Keen, D.A. and Dove, M.T. (1999) Comparing the local structures of amorphous and crystalline polymorphs of silica. J. Phys.: Cond. Matter., 11, 9263–73.Google Scholar
Keen, D.A. and Dove, M.T. (2000) Total scattering studies of silica polymorphs: similarities in glass and disordered crystalline local structure. Minerall. Mag., 64, 447–57.CrossRefGoogle Scholar
Levelut, C., Terki, F., Scheyer, Y., and Pelous, J. (1997) Vibrational dynamics in glasses. Pp. 385403 in: Amorphous Insulators and Semiconductors, (Thorpe, M.F. and Mitkovao, M.I., editors). NATO ASI series 3. High Technology, 23. Kluwer, Amsterdam.CrossRefGoogle Scholar
Maxwell, J.C. (1864) On the calculation of the equilibrium and stiffness of frames. Phil. Mag., 27, 294–9.CrossRefGoogle Scholar
Phillips, J.C. (1979) Topology of covalent non-crystalline solids I: Short range order in chalcogenide alloys. J. Non-Cryst. Solids, 34, 153–81.CrossRefGoogle Scholar
Pryde, A.K.A. and Dove, M.T. (1998) The dynamic behaviour of tridymite - molecular dynamics simulations. Phys. Chem. Min. submitted)Google Scholar
Pryde, A.K.A., Hammonds, K.D., Dove, M.T., Heine, V., Gale, J.D. and Warren, M.C. (1996) Origin of the negative thermal expansion in ZrW2O8 and ZrV2O7 . J. Phys.: Cond. Matter., 8, 10973–82.Google Scholar
Sanders, M.J., Leslie, M. and Catlow, C.R.A. (1984) Interatomic potentials for SiO2. J. Chem. Soc.: Chem. Comm., 1271–3.CrossRefGoogle Scholar
Smith, W. and Forester, T.R. (1996) DL_POLY_2.0 Ñ A general purpose parallel molecular dynamics simulation package. J. Mol. Graphics, 14, 136–41.CrossRefGoogle Scholar
Swainson, I.P. and Dove, M.T. (1993) Low-frequency floppy modes in β-cristobalite. Phys. Rev. Lett., 71, 193–6.CrossRefGoogle ScholarPubMed
Swainson, I.P. and Dove, M.T. (1995) Molecular dynamics simulation of a-cristobalite and β-cristobalite. J. Phys.: Cond. Matter, 7, 1771–88.Google Scholar
Thorpe, M.F. (1983) Continuous deformations in random networks. J. Non-Cryst. Solids, 57, 355–70.CrossRefGoogle Scholar
Thorpe, M.F., Djordjevic, B.R. and Jacobs, D.J. (1997) The structure and mechanical properties of networks. Pp. 289328 in: Amorphous Insulators and Semiconductors. (Thorpe, M.F. and Mitkova, M.I., editors). NATO ASI series 3. Kluwer, Amsterdam, High Technology, 23.CrossRefGoogle Scholar
Tsuneyuki, S., Tsukada, M., Aoki, H. and Matsui, Y. (1988) First principles interatomic potential of silica applied to molecular dynamics. Phys. Rev. Lett., 61, 869–72.CrossRefGoogle ScholarPubMed
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
Welche, P.R.L., Heine, V. and Dove, M.T. (1998) Negative thermal expansion in β-quartz. Phys. Chem. Min., 26, 63–77.CrossRefGoogle Scholar
Wooten, F. and Weaire, D. (1987) Modelling tetra-hedrally bonded random networks by computer. Solid State Phys., 40, 1–42.CrossRefGoogle Scholar
Wooten, F., Winer, K. and Weaire, D. (1985) Computer generation of structural models of amorphous Si and Ge. Phys. Rev. Lett., 54, 1392–5.CrossRefGoogle ScholarPubMed
Wright, A.F. and Leadbetter, A.J. (1975) The structures of the β-cristobalite phases of SiO2 and AlPO4 . Phil. Mag., 31, 1391–401.CrossRefGoogle Scholar
Zeller, R.C. and Pohl, R.O. (1971) Thermal conductivity and specific heat of noncrystalline solids. Phys. Rev. B 4, 2029–41.CrossRefGoogle Scholar