The structural properties of silica using classical and quantum interatomic forces

Tsuneyuki, S., Tsukada, M., Aoki, H., and Matsui, Y. (1988) First principles interatomic potential of silica applied to molecular dynamics, Phys. Rev. Lett., 61, 869–872.Google Scholar

Lasaga, A.C., and Gibbs, G.V. (1987) Applications of quantum mechanical potential surfaces to mineral physics calculations, Phys. Chem. Mineral., 14, 107–117.Google Scholar

Stixrude, L., and Bukowinski, M.S.T. (1991) Atomic structure of SiO₂ glass and its response to pressure, Phys. Rev., B44, 2523–2533.Google Scholar

Chelikowsky, J.R., King Jr., H.E., and Glinnemann, J. (1990) Interatomic potentials and the structural properties of silicon dioxide under pressure, Phys. Rev., B41, 10866–10871.Google Scholar

Kohn, W., and Sham, L. (1965) Self-consistent equations including exchange and correlation, Phys. Rev., A140, 1133–1143.CrossRefGoogle Scholar

Hohenberg, P., and Kohn, W. (1964) Inhomogeneous electron gas, Phys. Rev., 136, 864–872.CrossRefGoogle Scholar

Lundqvist, S., and March, N.H. (1987) Theory of the Inhomogeneous Electron Gas, Plenum, New York.Google Scholar

Chelikowsky, J.R., and Cohen, M.L. (1992) Ab initio pseudopotentials for semiconductors, in P.Landsberg, (ed.), Handbook on Semiconductors, Vol. 1, Elsevier, Amsterdam, p. 59.Google Scholar

Troullier, N., and Martins, J.L. (1991) Efficient pseudopotentials for plane wave calculations, Phys. Rev., B43, 1993–2006.CrossRefGoogle Scholar

Troullier, N., and Martins, J.L. (1991) Efficient pseudopotentials for plane wave calculations II. operators for fast iterative diagonalization, Phys. Rev., B43, 8861–8869.Google Scholar

Chelikowsky, J.R., King Jr., H.E., Troullier, N., Martins, J.L., and Glinnemann, J. (1990) Structural properties of α-quartz near the amorphous transition,, Phys. Rev. Lett., 65, 3309–3312.Google Scholar

Chelikowsky, J.R., Troullier, N., Martins, J.L., and King Jr., H.E. (1991) Pressure dependence of the structural properties of α-Quartz near the amorphous transition, Phys. Rev., B44, 489–497.Google Scholar

Binggeli, N., Troullier, N., Martins, J.L., and Chelikowsky, J.R. (1991) Electronic properties of α-quartz under pressure, Phys. Rev., B44, 4771–4778.Google Scholar

Binggeli, N.,, and Chelikowsky, J.R. (1991) Structural transformation of quartz at high pressures, Nature, 353, 344–346.Google Scholar

Keskar, N.R., and Chelikowsky, J.R. (1992) Structural properties of nine silica polymorphs, Phys. Rev., B46, 1.Google Scholar

Chelikowsky, J.R., Binggeli, N., and Keskar, N.R. (1993) First principles methods for structural trends in oxides: Applications to Crystalline Silica, J. of Compounds and Alloys, 197, 137–144.Google Scholar

Martins, J.L., and Cohen, M.L. (1988) Diagonalization of large matrices in pseudopotential calculations: dual space formalism, Phys. Rev., B37, 6134–6138.Google Scholar

Martins, J.L., Troullier, N., and Wei, D.S.-H. (1991) Pseudopotential calculations for ZnS, Phys. Rev., B43, 2213–2217.Google Scholar

Ihm, J., Zunger, A., and Cohen, M.L. (1979) Momentum space formalism for the total energy of solids, J. Phys. C, 12 4409–4422.Google Scholar

Keskar, N.R., Troullier, N., Martins, J.L., and Chelikowsky, J.R. (1991) Structural properties of SiO₂ in the stishovite structure, Phys. Rev., B44, 4081–4086.Google Scholar

Cohen, R.E. (1991) Bonding and elasticity of stishovite (SiO₂) at high pressurelinearized augmented plane wave calculations, Amer. Mineral., 76, 733–742.Google Scholar

Tsuneyuki, S., Matsui, Y., Aoki, H., and Tsukada, M. (1989) New pressure induced structural transformations in silica obtained by computer simulation, Nature, 339, 209–211.Google Scholar

Levien, L., and Prewitt, C.T. (1980) Structural and elastic properties of quartz at pressure, Amer. Mineral., 65, 920–930.Google Scholar

Bass, J.D., Libermann, R.C., Weidner, D.J., and Finch, S.J. (1981) Elastic properties from acoustic and volume compressibility experiments, Phys. Earth Planet. Inter., 25, 140–158.Google Scholar

Zubov, V.G., and Firsova, M.M. (1956) The elastic properties of high β-quartz, Kristallographia, 1, 546–552.Google Scholar

Ross, N.L., Shu, J., Hazen, R.M., and Gasparik, T. (1990) High pressure crystal chemistry of stishovite, Amer. MIneral., 75, 739–747.Google Scholar

Sugiyama, M., Endo, S., and Koto, K. (1987) Crystal structure of stishovite under pressure up to 6 GPa, Mineral. J., 13, 455–460.Google Scholar

Wyckoff, W.G. (1974) Crystal Structures, 4th edition, Interscience, New York.Google Scholar

Pluth, J.J., Smith, J.V., and Faber Jr., J. (1985) Crystal structure of low cristobalite at 10, 293 and 473 K: variation of framework geometry with temperature, J. Appl. Phys., 57, 1045–1049.Google Scholar

Barron, T.H.K., and Klein, M.L. (1965) Second order elastic constants of a solid under stress, Proc. Phys. Soc., 85, 523–533.Google Scholar

Fedorov, F.I. (1968) Theory of Elastic Waves in Crystals, Plenum, New York.Google Scholar

Smagin, A.G., and Mil'shtein, B.G. (1975) Internal friction of in quartz crystals at low temperatures, Sov. Phys. Crystal., 19, 514–516.Google Scholar

Yeganeh-Haeri, A., Weidner, D.J., and Parise, J.B. (1992) Elasticity of α-cristobalite-a silicon dioxide with a negative poisson ratio, Science, 257, 650–652.Google Scholar

Williams, Q., Hemley, R.J., Kruger, M.B., and Jeanloz, R. (1993) High pressure infrared spectra of α-quartz, coesite, stishovite, and silica glass, J. Geophys. Res., 98, 22157–22170.Google Scholar

Hazen, R.M., Finger, L.W., Hemley, R.J., and Mao, H.-K. (1988) High pressure crystal chemistry and amorphization of α-quartz, Solid State Commun., 72, 507–511.Google Scholar

Hemley, R.J., Jephcoat, A.P., Mao, H.-K., Ming, L.C., and Manghnani, M.H. (1988) Pressure induced amorphization of crystalline silica, Nature, 334, 52–54.Google Scholar

Tsuchida, Y., and Yagi, T. (1990) New pressure-induced transformations of silica at room temperature, Nature, 347, 267–269.Google Scholar

Sowa, H. (1988) The oxygen packing of low quartz and ReO₃ under high pressure, Z. Kristallogr., 184, 257–268.Google Scholar

Tse, J.S., and Klug, D.D. (1991) High pressure desification of amorphous silica, Phys. Rev., B46, 5933–5938.Google Scholar

Tse, J.S., Klug, D.D., and LePage, Y. (1992) Novel high pressure phase of silica, Phys. Rev. Lett., 69, 3647–3649.Google Scholar

Navrotsky, A., Geisinger, K.L., McMillan, P., and Gibbs, G.V. (1985) The tetrahedral framework in glasses and melts-inferences from molecular orbital calculations and implications for structure, thermodynamics, and physical properties, Phys. Chem. Mineral., 11, 284–298.Google Scholar

Hemley, R.J. (1987) Pressure dependence of Raman spectra of SiO₂ polymorphs: α-quartz, coesite, and stishovite, in M.H.Manghnani, and Y.Syono, (eds.), High Pressure Research in Minearl Physics, Terra Scientific Publishing Company (TERRAPUB), Tokyo, pp. 347–359.Google Scholar

Glinnemann, J., King Jr., H.E., Schulz, H., Hahn, T., Lapaca, S.J., and Dcaol, F. (1992) Crystal structure of the low temperature quartz type phases of SiO₂ and GeO₂ at elevated pressure, Z. Kristall., 198, 177–212.Google Scholar

Zemann, J. (1986) The shortest known Interpolyhedral O-O distance in a silicate, Z. für Kristall., 175, 299–303.Google Scholar

Kingma, K., Hemley, R.J., Mao, H.-K., and Veblen, D.R. (1993) New high pressure transformation in α-quartz, Phys. Rev. Lett., 70, 3927–3931.Google Scholar

Kingma, K., Meade, C., Hemley, R.J., Mao, H.-K., and Veblen, D.R. (1993) Microstructural observations of α-quartz amorphization, Science, 259, 666–669.Google Scholar

Chaplot, S.L., and Sikka, S.K. (1993) Molecular-dynamics simulation of pressure induced crystalline-to-amorphous transition in some corner-linked polyhedral compounds, Phys. Rev., B47, 5710–5715.Google Scholar

vanBeest, B.W.H., Kramer, G.J., and vanSanten, R.A. (1990) Force fields for silicas and aluminophospates based on ab initio calculations, Phys. Rev. Lett., 64, 1955–1958.CrossRefGoogle Scholar

Binggeli, N., and Chelikowsky, J.R. (1993) Is simulated ‘amorphous’ silica really amorphous?, in S.C. Schmidt, J.W. Shaner, G.A. Samara, and M. Ross, (eds.), Proceedings of the AIRAPT/APS High Pressure Science and Technology Conference, High Pressure Science and Technology 1993, American Institute of Physics, Woodbury, New York, p. 397–400.Google Scholar

Maradudin, A., Montroll, E.W., Weiss, G.H., and Ipatova, I.P. (1971) Theory of Lattice Dynamics in the Harmonic Approximation, Academic Press, New York.Google Scholar

Bruesch, P. (1982) Phonons: Theory and Experiment I., Springer-Verlag, Berlin.Google Scholar

Catlow, C.R.A., and Mackrodt, W.C., (eds.) (1982) Computer Simulations of Solids, Springer-Verlag, Berlin.Google Scholar

Ciccotti, G., Frenkel, McDonald, I.R., (eds.) (1987) Simulation of Liquids and Solids, North Holland, Amsterdam.Google Scholar

Allen, M.P., and Tildesley, D.J. (1987) Computer Simulations of Liquids, Oxford Press, Oxford.Google Scholar

Lee, C., and Gonze, X. (1994) Lattice dynamics and dielectric properties of SiO₂ stishovite, Physical Review Letters, 72, 1686–1689.Google Scholar

Barron, T.H.K., Huang, C.C., and Pasternak, A. (1976) Interatomic forces and lattice dynamics of α-quartz, J Phys C, 9, 3925–3940.Google Scholar

Hemley, R.J., Mao, H.-K., and Chao, E.C.T. (1986) Raman spectrum of natural and synthetic stishovite, Phys. Chem. Minerals, 13, 285–290.Google Scholar

Vigasina, M.F., Gusea, E.V., and Orlov, R.Y. (1989) Vibrational spectrum of stishovite and analysis of its crystal lattice dynamics, Soviet Physics-Solid State, 31, 747–749.Google Scholar

Hofmeister, A.M., Xu, J., and Akimoto, S. (1990) Infrared spectroscopy of synthetic and natural stishovite, Am. Mineral., 75, 951–955.Google Scholar

Lam, P., Chou, M.Y., and Cohen, M.L. (1984) Temperature and pressure induced crystal transitions in Be, J. Phys. C, 17: 2065–2073.Google Scholar

Akaogi, M., and Navrotsky, A. (1984) The quartz-coesite-stishovite transformations: new calorimetric measurements and calculation of phase diagrams, Phys Earth Planet. Int., 36, 124–134.Google Scholar

Richet, P., Bottinga, Y., Denielou, L., Petitet, J.P., and Tequi, C. (1982) Thermodynamic properties of quartz, cristobalite, and amorphous SiO₂: Drop calorimetry measurements between 1000K and 1800K and review from 0 to 2000K. Geochim. Cosmochim. Acta, 46, 2639–2658.Google Scholar

Holm, J.L., Kleppa, O.J., and Westrum, E.F. (1967) Thermodynamics of polymorphic transformations in silica: Thermal properties from 5–1070 K and pressure-temperature stability fields for coesite and stishovite, Geomchim. Cosmochim. Acta, 31, 2289–2307.Google Scholar

Robie, R.A., Hemingway, J.R., and Fisher, J.R. (1978) Thermodynamic properties of minerals and related substances at 298.15K and 1b pressure and higher temperatures, Geol Surv Bull, 1452, 216–221.Google Scholar

Navrotsky, A. (1980) Lower mantle phase transitions may generally have negative pressure temperature slope, Geophys. Res. Lett., 7, 709–711.Google Scholar

Cohen, L.H., and Klement, W. (1967) High-low quartz inversion: Determination to 35 Kbar, J. Geophys. Res., 72, 4245–4253.Google Scholar