Skip to main content
SpringerLink
Log in

Simple covalent potential models of tetrahedral SiO2: Applications to α-quartz and coesite at pressure

  • Published:
Physics and Chemistry of Minerals Aims and scope Submit manuscript

Abstract

We present a covalent potential model of tetrahedrally coordinated SiO2. The interactions include covalent effects in the form of a Si-O bond-stretching potential, O-Si-O and Si-O-Si angle-bending potentials, and oxygen-oxygen repulsion. Calculated equations of state of α-quartz and coesite agree well with experiment (calculated densities within 1 percent of experiment up to 6 GPa). The calculated α-quartz-coesite transition pressure agrees with the experimental value of ≈2 GPa. Furthermore, the compression mechanisms predicted by the model (i.e. pressure induced changes in Si-O bond lengths and O-Si-O and Si-O-Si angles) are accurate.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Akimoto S, Yagi Y, Inoue K (1977) High temperature-pressure phase boundaries in silicate systems using in situ X-ray diffraction. In: Akimoto S, Manghnani MH (eds) High pressure research in geophysics. Center for Academic Publications, Tokyo, Japan

    Google Scholar 

  • Anderson OL (1968) Some results on the volume dependence of the Grüneisen parameter γ. J Geophys Res 73:5187–5194

    Google Scholar 

  • Anderson OL (1974) The determination of the volume dependence of the Grüneisen parameter. J Geophys Res 79:1153–1155

    Google Scholar 

  • Bass JD (1987) Mineral and melt physics. Rev Geophys 25:1215–1276

    Google Scholar 

  • Birch F (1978) Finite strain isotherms and velocities for single-crystal and polycrystalline NaCl at high pressures and 300° K. J Geophys Res 83:1257–1268

    Google Scholar 

  • Boehler R (1982) Adiabats of quartz, coesite, olivine and magnesium oxide to 50 kbar and 1000 K, and the adiabatic gradient in the Earth's mantle. J Geophys Res 87:5501–5506

    Google Scholar 

  • Boehler R, Skoropanov A, O'Mara D, Kennedy GC (1979) Grüneisen parameter of quartz, quartzite and fluorite. J Geophys Res 84:3527–3531

    Google Scholar 

  • Born M, Huang K (1954) Dynamical theory of crystal lattices. Oxford University Press, pp 420

  • Busing WR (1981) WMIN. A computer program to model molecules and crystals in terms of potential energy functions. Oak Ridge National Laboratory, Oak Ridge

    Google Scholar 

  • Dolino G, Bachheimer JP, Berge B, Zeyen CME, Van Tendeloo G, Van Landuyt J, Amelinckx S (1984) Incommensurate phase of quartz: III. Study of the coexistence state between the incommensurate and the α-phases by neutron scattering and electron microscopy. J Physique 45:901–912

    Google Scholar 

  • Erikson RL, Hosteler CJ (1987) Application of empirical ionic models to SiO2 liquid: potential model approximations and integration of SiO2 polymorph data. Geochim Cosmochim Acta 51:1209–1218

    Google Scholar 

  • Gibbs GV (1982) Molecules as models for bonding in silicates. Am Mineral 67:421–450

    Google Scholar 

  • Grimm H, Dorner B (1975) On the mechanism of the α-β quartz phase transformation of quartz. J Phys Chem Solids 36:407–413

    Google Scholar 

  • Hazen RM, Finger LW (1978) Crystal chemistry of silicon-oxygen bonds at high pressure: implications for the Earth's mantle mineralogy. Science, 201:1122–1123

    Google Scholar 

  • Hemley RJ, Mao HK, Bell PM, Mysen BO (1986) Raman spectroscopy of SiO2 glass at high pressure. Phys Rev Lett 57:747–750

    Google Scholar 

  • Hess AC, McMillan PF, O'Keeffe M (1986) Force fields for SiF4 and H4SiO4: ab initio molecular orbital calculations. J Phys Chem 90:5661–5665

    Google Scholar 

  • Hostetler CJ (1982) Equilibrium properties of some silicate materials: a theoretical study. Ph D dissertation, Univ. Arizona

  • Jeanloz R, Thompson AB (1983) Phase transitions and mantle dicontinuities. Revs Geophys and Space Phys 21:51–74

    Google Scholar 

  • Jorgensen JD (1978) Compression mechanisms in α-quartz structures -SiO2 and GeO2. J Appl Phys 49:5473–5478

    Google Scholar 

  • Kieffer SW (1979) Thermodynamics and lattice vibrations of minerals: 3. lattice dynamics and an approximation for minerals with application to simple substances and framework silicates. Revs Geophys and Space Phys 17:35–59

    Google Scholar 

  • Lager GA, Jorgensen JD, Rotella FJ (1982) Crystal structure and thermal expansion of α-quartz SiO2 at low temperatures. J Appl Phys 53:6751–6756

    Google Scholar 

  • Lasaga AC, Gibbs GV (1987) Applications of quantum mechanical potential surfaces to mineral physics calculations. Phys Chem Minerals 14:107–117

    Google Scholar 

  • Levien L, Prewitt CT, Weidner DJ (1980) Structure and elastic properties of quartz at pressure. Am Mineral 65:920–930

    Google Scholar 

  • Levien L, Prewitt CT (1981) High-pressure crystal structure and compressibility of coesite. Am Mineral 66:324–333

    Google Scholar 

  • Liu L, Bassett WA (1986) Elements, oxides, silicates; high pressure phases with implications for the Earth's interior. Oxford University Press, pp 250

  • Matsui Y, Kawamura K, Syono Y (1982) Molecular dynamics calculations applied to silicate systems: molten and vitreous MgSiO3 and Mg2SiO4 under low and high pressures. Adv Earth Planet Sci 12:511–524

    Google Scholar 

  • Mirwald PW, Massonne HF (1980) The low-high quartz and quartz-coesite transition to 40 kbar between 600-degrees-C and 1600-degrees-C and some reconnaissance data on the effect of NaAlO2 component on the low quartz-coesite transition. J Geophys Res 85:6983–6990

    Google Scholar 

  • Mitra SK (1982) Molecular dynamics simulation of silicon dioxide glass. Phil Mag B 45:529–548

    Google Scholar 

  • Morse PM (1929) Diatomic molecules according to the wave mechanics. II. Vibrational levels. Phys Rev 43:57–67

    Google Scholar 

  • O'Keeffe M, Newton MD, Gibbs GV (1980) Ab initio calculation of interatomic force constants in H6Si2O7 and the bulk modulus of α quartz and α cristobalite. Phys Chem Minerals 6:305–312

    Google Scholar 

  • O'Keeffe M, McMillan PF (1986) The Si-O-Si force field: ab initio MO calculations. J Phys Chem 90:541–542

    Google Scholar 

  • Pauling L (1980) The nature of silicon-oxygen bonds. Am Mineral 65:321–323

    Google Scholar 

  • Price GD, Parker SC (1984) Computer simulations of the structural and physical properties of the Olivine and Spinel polymorphs of Mg2SiO4. Phys Chem Minerals 10:209–216

    Google Scholar 

  • Robie RA, Hemingway BS, Fisher JR (1978) Thermodynamic properties of minerals and related substances at 298.15 K and one bar (105 pascals) pressure and at high temperatures. US Geol Surv Bull 1452

  • Sanders MJ, Leslie M, Catlow CRA (1984) Interatomic potentials for SiO2. J Chem Soc, Chem Commun 1271–1274

  • Skinner BJ (1962) Thermal expansion of ten minerals. US Geol Surv Prof Paper 450D:109–112

    Google Scholar 

  • Smyth JR, Smith JV, Artioli G, Kvick A (1987) Crystal structure of coesite, a high-pressure form of SiO2 at 15 and 298 K from single-crystal neutron and x-ray diffraction data: test of bonding models. J Phys Chem 91:988–992

    Google Scholar 

  • Soules TF (1979) A molecular dynamic calculation of the structure of sodium silicate glasses. J Chem Phys 71:4570–4578

    Google Scholar 

  • Striefler ME, Barsch GR (1975) Lattice Dynamics of a quartz. Phys Rev B 12:4553–4566

    Google Scholar 

  • Wallace D (1972) Thermodynamics of crystals. J Wiley and Sons, Inc., New York, p 357

    Google Scholar 

  • Watanabe H (1982) Thermochemical properties of synthetic high-pressure compounds relevant to the Earth's mantle. In: Akimoto S, Manghnani MH (eds) High pressure research in geophysics. Center for Academic Publications, Tokyo, Japan

    Google Scholar 

  • Weidner DJ, Carleton HR (1977) Elasticity of coesite. J Geophys Res 82:1334–1346

    Google Scholar 

  • Williams Q, Jeanloz R (1988) Spectroscopic evidence for pressure-induced coordination changes in silicate glasses and melts. Science 239:902–905

    Google Scholar 

  • Woodcock LV, Angell CA, Cheeseman P (1976) Molecular dynamics studies of the vitreous state: simple ionic systems and silica. J Chem Phys 65:1565–1577

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Geology and Geophysics, University of California, 94720, Berkeley, CA, USA

    Lars Stixrude & M. S. T. Bukowinski

Authors
  1. Lars Stixrude
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. S. T. Bukowinski
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Stixrude, L., Bukowinski, M.S.T. Simple covalent potential models of tetrahedral SiO2: Applications to α-quartz and coesite at pressure. Phys Chem Minerals 16, 199–206 (1988). https://doi.org/10.1007/BF00203204

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00203204

Keywords

Search

Navigation