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.
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
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
Briddon PR, Jones R (1990) Ab initio calculations on the passivation of shallow impurities in GaAs. Phys Rev Lett 64:2535–2538
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
Catlow CRA, Price GD (1990) Computer modelling of solid-state inorganic materials. Nature 347:243–248
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
Cochran W (1973) The dynamics of atoms in crystals. Struct Prop Solids 3 London: Edward Arnold
Cohen RE (1991) Bonding and elasticity of stishovite SiO2 at high pressure: linearized augmented plane wave calculations. Am Mineral 76:733–742
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
Dick BG, Overhauser AW (1958) Theory of the dielectric constants of alkali halide crystals. Phys Rev 112:90–113
Dorner B, Grimm H, Rzany (1980) Phonon dispersion branches in α-quartz. J Phys C13:6607–6612
Elcombe MM (1967) Some aspects of the lattice dynamics of quartz. Proc Phys Soc 91:947–958
Gibbs GV (1982) Molecules as models for bonding in silicates. Am Mineral 67:421–450
Hazen RM, Finger LW, Hemley RJ, Mao HK (1989) High-pressure crystal chemistry and amorphisation of α-quartz. Solid State Commun 72:507–511
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
Jackson RA, Catlow CRA (1988) Computer simulation studies of zeolite structure. Mol Sim 1:207–224
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
Jones R (1987a) Ab initio calculation of the phonon frequencies in silicon using small atomic clusters. J Phys C20:271–273
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
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
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
Levien L, Prewitt CT, Weidner DJ (1980) Structure and elastic properties of quartz at pressure. Am Mineral 65:920–930
McMillan PF, Hess AC (1990) Ab initio valence force field calculations for quartz. Phys Chem Minerals 17:97–107
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
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
Parker SC, Price GD (1989) Computer modelling of phase transitions in minerals. Adv Solid State Chem 1:295–327
Perdew J, Zunger A (1981) Self-interaction correction to density functional approximations for many electron systems. Phys Rev B23:5048–5079
Pulay P (1969) Ab initio calculation of force constants and equilibrium geometries in polyatomic molecules. 1. Theory. Mol Phys 17:197–204
Pulay P (1983) Second and third derivatives of variational energy expressions: application to multiconfiguration self-consistent field wavefunctions. J Chem Phys 78:5043–5051
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
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
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
Teter MP, Allen DC (1987) Non-local pseudopotential molecular dynamical density functional theory: applications to SiO2. Phys Rev Lett 59:1136–1139
Tosi MP (1964) Cohesion of ionic solids in the Born model. Solid State Phys 16:1–120
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
Winkler B, Dove MT, Leslie M (1991) Static lattice energy minimisation and lattice dynamics calculations on aluminosilicate minerals. Am Mineral 76:313–331
Author information
Authors and Affiliations
Rights 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
Received:
Revised:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF00202976