Skip to main content
Log in

Ab initio potentials for the calculation of the dynamical and elastic properties of α-quartz

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

Abstract

Ab initio LDF theory has been used to derive interatomic potentials for the Si-O and O-O interaction in α-quartz. The potentials have been used to study the lattice dynamical properties of α-quartz from 1 atm to 12.5 Gpa pressure. The results are compared with other calculated and experimentally derived potentials.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Bachelet GB, Hammann DR, Schlüter M (1982) Pseudopotentials that work: from H to Pu. Phys Rev B26:3114–3117

    Google Scholar 

  • Beest BWH van, Kramer GJ, Santen RA van (1990) Force fields for silicas and aluminophosphates based on it ab initio calculations. Phys Rev Lett 16:1955–1958

    Google Scholar 

  • Briddon PR, Jones R (1990) Ab initio calculations on the passivation of shallow impurities in GaAs. Phys Rev Lett 64:2535–2538

    Google Scholar 

  • Catlow CRA, Norgett MJ (1976) Lattice structure and stability of ionic materials. United Kingdom Atomic Energy Authority Report, AEREM 2963

  • Catlow CRA, Stoneham AM (1983) Ionicity in solids. J Phys C16:4321–4338

    Google Scholar 

  • Catlow CRA, Price GD (1990) Computer modelling of solid-state inorganic materials. Nature 347:243–248

    Google Scholar 

  • Chelikowsky JR, Troullier N, Martins JL, King HE (1991) Pressure dependence of the structural properties of α-quartz near the amorphous transition. Phys Rev 844:489–497

    Google Scholar 

  • Cochran W (1973) The dynamics of atoms in crystals. Struct Prop Solids 3 London: Edward Arnold

    Google Scholar 

  • Cohen RE (1991) Bonding and elasticity of stishovite SiO2 at high pressure: linearized augmented plane wave calculations. Am Mineral 76:733–742

    Google Scholar 

  • Dean KJ, Sherman WF, Wilkinson GR (1982) Temperature and pressure dependence of the Raman active modes of vibration of α-quartz. Spectrochim Acta 38A:1105–1108

    Google Scholar 

  • Dick BG, Overhauser AW (1958) Theory of the dielectric constants of alkali halide crystals. Phys Rev 112:90–113

    Google Scholar 

  • Dorner B, Grimm H, Rzany (1980) Phonon dispersion branches in α-quartz. J Phys C13:6607–6612

    Google Scholar 

  • Elcombe MM (1967) Some aspects of the lattice dynamics of quartz. Proc Phys Soc 91:947–958

    Google Scholar 

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

    Google Scholar 

  • Hazen RM, Finger LW, Hemley RJ, Mao HK (1989) High-pressure crystal chemistry and amorphisation of α-quartz. Solid State Commun 72:507–511

    Google Scholar 

  • Hemley RJ (1987) Pressure dependence of Raman spectra of SiO2 polymorphs: α-quartz, coesite and stishovite. In: Manghnani MH, Syono Y (eds) High pressure research in mineral physics. American Geophysical Union, Washington, DC, pp 347–359

    Google Scholar 

  • Jackson RA, Catlow CRA (1988) Computer simulation studies of zeolite structure. Mol Sim 1:207–224

    Google Scholar 

  • Jayaraman A, Wood DL, Maines RG (1987) High-pressure Raman study of the vibrational modes in AlPO4 and SiO2 (α-quartz). Phys Rev B35:8316–8321

    Google Scholar 

  • Jones R (1987a) Ab initio calculation of the phonon frequencies in silicon using small atomic clusters. J Phys C20:271–273

    Google Scholar 

  • Jones R (1987b) Local density functional calculations of the structure and vibratory modes of the substitutional carbon impurity in silicon. J Phys C20:713–716

    Google Scholar 

  • Jones R, Öberg S, Heggie MI, Tole P Ab initio calculation of the structure of molecular water in quartz. Phys Chem Minerals (submitted)

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

    Google Scholar 

  • Lasaga AC, Gibbs GV (1988) Quantum mechanical potential surfaces and calculations on minerals and molecular clusters 1. STO-3G and 6–31G* results. Phys Chem Minerals 16:29–41

    Google Scholar 

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

    Google Scholar 

  • McMillan PF, Hess AC (1990) Ab initio valence force field calculations for quartz. Phys Chem Minerals 17:97–107

    Google Scholar 

  • McSkimin HJ, Andreatch P, Thurston RN (1965) Elastic moduli of quartz versus hydrostatic pressure at 25 and-195.8° C. J Applied Phys 36:1625–1632

    Google Scholar 

  • Nada R, Catlow CRA, Dovesi R, Pisani C (1990) An ab initio Hartree-Fock study of α-quartz and stishovite. Phys Chem Minerals 17:353–362

    Google Scholar 

  • Parker SC, Price GD (1989) Computer modelling of phase transitions in minerals. Adv Solid State Chem 1:295–327

    Google Scholar 

  • Perdew J, Zunger A (1981) Self-interaction correction to density functional approximations for many electron systems. Phys Rev B23:5048–5079

    Google Scholar 

  • Pulay P (1969) Ab initio calculation of force constants and equilibrium geometries in polyatomic molecules. 1. Theory. Mol Phys 17:197–204

    Google Scholar 

  • Pulay P (1983) Second and third derivatives of variational energy expressions: application to multiconfiguration self-consistent field wavefunctions. J Chem Phys 78:5043–5051

    Google Scholar 

  • Purton J, Jones R, Heggie MI, Öberg S, Catlow CRA (1992) LDF pseudopotential calculations of the α-quartz structure and hydrogarnet defect. Phys Chem Minerals 18:389–392

    Google Scholar 

  • Sanders MJ, Leslie M, Catlow CRA (1984) Interatomic potentials for SiO2. J Chem Soc Chem Commun 1271–1273

  • Sato RK, McMillan PF (1987) An infrared and Raman study of the isotopic species of α-quartz. J Phys Chem 91:3494–3498

    Google Scholar 

  • Silvi B, D'Arco P, Saunders VR, Dovesi R (1991) Periodic Hartree-Fock study of minerals: tetracoordinated silica polymorphs. Phys Chem Minerals 17:674–680

    Google Scholar 

  • Teter MP, Allen DC (1987) Non-local pseudopotential molecular dynamical density functional theory: applications to SiO2. Phys Rev Lett 59:1136–1139

    Google Scholar 

  • Tosi MP (1964) Cohesion of ionic solids in the Born model. Solid State Phys 16:1–120

    Google Scholar 

  • Tsuneyuki S, Tsukada M, Aoki H, Matsui Y (1988) First principles interatomic potential of silica applied to molecular dynamics. Phys Rev Lett 7:869–872

    Google Scholar 

  • Winkler B, Dove MT, Leslie M (1991) Static lattice energy minimisation and lattice dynamics calculations on aluminosilicate minerals. Am Mineral 76:313–331

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Purton, J., Jones, R., Catlow, C.R.A. et al. Ab initio potentials for the calculation of the dynamical and elastic properties of α-quartz. Phys Chem Minerals 19, 392–400 (1993). https://doi.org/10.1007/BF00202976

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00202976

Keywords

Navigation