Molecular force constants in dynamical model of ?-quartz

Abstract

Ab initio force constants of structural fragments of e-quart, Si-O-Si bridge and SiO4 tetrahedron, are calculated by the gradient (force) method for molecules accessible to spectroscopic investigation, disiloxane and tetramethoxysilane respectively. The comparison of theoretical frequencies with experimental ones enables the empirical scaling of quantum chemical force constants. A generalized approach to the inverse vibrational problem in spectroscopy of solids is outlined. It consists of a joint treatment of vibrational spectra and properties of a crystal related to its homogeneous deformation, namely compressibility and elastic constants. The importance of analyzing the microscopic structure of compressibility for testing the force field model is emphasized. The scaled molecular force constants complemented by the force constants of nonbonded O... O interactions at shortest distances after slight empirical correction are found to be sufficient to reproduce all mechanical properties of e-quartz accessible to experimental determination. A discussion of results in terms of structure and bonding including the analysis of various versions of a force field model is presented. The calculated shapes of normal coordinates and uniform strains are validated by satisfactory reproduction of IR intensities and piezoelectric constants.

Experimental and theoretical aspects of electric-field-assisted positron kinetics in metal-oxide-silicon systems

“…For positrons in quasiequilibrium we have The maximum energy loss per collision at Eϭ2.5 MV/cm field is ␦ ϭ5.1 meV. This value is within the energy range of the available acoustic phonons and significantly less than the energy of the transverse optical ͑TO͒ phonons in quartz ͑20-23 meV͒, 24 which dominate the energy loss spectrum. Therefore, the limit at which wϭ ϩ E no longer holds occurs at fields that are several times larger than the maximum achieved in our experiments.…”

High-pressure twisting of tetrahedra and amorphization inα-quartz

“…The force field of ␣-quartz crystal is described in Ref. 20 using the scaled force constants K qi,q j 0 of molecular silicate clusters, calculated by quantum-chemical methods.…”

Thermal parameters for α-quartz: a lattice-dynamical calculation

“…Empirical force fields have also been extensively used in modelling the crystal structure (Sanders, Leslie & Catlow, 1984;Urusov et al, 1986;Jackson & Gordon, 1988;Lazarev & Mirgodsky, 1991), including phase transformations (Tautz, Heine, Dove & Chen, 1991).…”

“…At the same time, ab initio calculations have been performed at various levels of sophistication on silicate groups to derive several properties, including valence force-field (VFF) parameters (Lasaga & Gibbs, 1987, 1991McMillan & Hess, 1990;Kubicki & Sykes, 1993). Empirical force fields have also been extensively used in modelling the crystal structure (Sanders, Leslie & Catlow, 1984;Urusov et al, 1986;Jackson & Gordon, 1988;Lazarev & Mirgodsky, 1991), including phase transformations (Tautz, Heine, Dove & Chen, 1991).…”