Ab initio valence force field calculations for quartz     

Paul F. McMillan  Anthony C. Hess 《Physics and Chemistry of Minerals》1990,17(2):97-107

We have derived valence force constants for the tetrahedral SiO₄ unit and the inter-tetrahedral SiOSi linkage from previous ab initio molecular orbital calculations on H₄SiO₄ and H₆Si₂O₇ using a split-valence polarized Gaussian basis set (6-31G^*), and used these to calculate the infrared and Raman active vibrational modes of α-quartz. The calculation gives frequencies approximately 15% greater than experiment, as expected from harmonic force constants obtained at this level of Hartree-Fock theory, but the calculation gives the correct distribution of modes within each frequency range. Calculated 28–30 Si and 16–18 O isotope shifts and pressure shifts to 6 GPa are also in reasonable agreement with experiment. We have also used our ab initio force field to calculate the vibrational spectrum for β-quartz. The results suggest either that inclusion of a torsional force constant is important for determining the stability of this high temperature polymorph, or that the β-quartz has a disordered structure with lower symmetry (P6₂) domains, as suggested by earlier diffraction studies.  相似文献   

Single-crystal structure and Raman spectroscopy of synthetic titanite analog CaAlSiO<Subscript>4</Subscript>F     

Hannes Krüger  Daniel M. Többens  Peter Tropper  Udo Haefeker  Volker Kahlenberg  Martin R. Fuchs  Vincent Olieric  Ulrike Troitzsch 《Mineralogy and Petrology》2015,109(5):631-641

Synthetic CaAlSiO₄F, the Al-F analog of titanite, has been investigated using single-crystal synchrotron diffraction experiments at Beamline X06DA (Swiss Light Source, Paul Scherrer Institute, Villigen, Switzerland) and Raman spectroscopy. The presented structural model with 40 parameters was refined against 506 unique reflections to a final R _{o b s} of 0.026 (space group A2/a, a = 6.9120(11), b = 8.5010(10), c = 6.435(2) Å, β = 114.670(11)°, and Z = 4) and exhibits less distorted coordination polyhedra than earlier models from powder data. Vibrational spectra were calculated in harmonic approximation at the Γ point from fully relaxed energy optimisations of the crystal structure, using 3D-periodic density functional theory with Gaussian basis sets and the software CRYSTAL06. The lattice parameters of the fully relaxed structure were in good agreement with the experimental values, with the calculated values 0.8 ± 0.4 % too large; the monoclinic angle was calculated 0.4° too large. The agreement of the calculated Raman frequencies with the observed ones was very good, with standard deviation ±3 cm^?1 and maximum deviations of ±7 cm^?1. Furthermore, a detailed discussion of the atomic displacements associated with each Raman mode is given.  相似文献   

Optimization of CNDO for molecular orbital calculation on silicates     

Antonio C. Lasaga 《Physics and Chemistry of Minerals》1982,8(1):36-46

The use of approximate molecular orbital (MO) calculations [particularly complete neglect of differential overlap (CNDO)] as a tool in understanding chemical bonding in silicates is investigated. This requires first a detailed analysis of the parametrization employed by the CNDO theory when third row atoms are involved. The accuracy of the CNDO calculations is tested by calculations on the equilibrium bond lengths, orbital energies, and bond stretching force constants of simple third row molecules, for which we have experimental data and/or ab initio results. The effects of an optimization of the parameters in the theory on the calculated properties are then analyzed. The theory is subsequently applied to a sequence of silicate prototypes: silicic acid, H₄SiO₄, disiloxane, (SiH₃) - O - (SiH₃), and disilicic acid, (SiO₃H₃) - O - (SiO₃H₃). With proper tuning of the parameters, the CNDO method can be useful in further elucidating the details of the bonding in silicates.  相似文献   

Structural phase transition in titanite,CaTiSiO5: A ramanspectroscopic study     

Ekhard Salje  Claudia Schmidt  Ulrich Bismayer 《Physics and Chemistry of Minerals》1993,19(7):502-506

The structural phase transition in titanite is correlated with a strong temperature dependence of Raman scattering cross sections and, to a somewhat lesser extent, with shifts of the phonon frequencies. Their quantitative temperature evolution in the low-symmetry phase (P2₁/a) is compatible with a nearly 2D Ising behaviour with β≈0.12 and T _c = 497 K. At temperatures above 860 K, the phonon signals agree with A 2/a symmetry but not in the temperature interval between 497 K and 860 K. In this temperature range new structural states give rise to additional phonon signals. A model based on mobile APBs between slabs of P2₁/a material, first proposed by van Heurck et al. (1991), is in qualitative agreement with our experimental observations.  相似文献   

The tetrahedral framework in glasses and melts — inferences from molecular orbital calculations and implications for structure,thermodynamics, and physical properties     

A. Navrotsky  K. L. Geisinger  P. McMillan  G. V. Gibbs 《Physics and Chemistry of Minerals》1985,11(6):284-298

Results of ab initio molecular orbital (MO) calculations provide a basis for the interpretation of structural and thermodynamic properties of crystals, glasses, and melts containing tetrahedrally coordinated Si, Al, and B. Calculated and experimental tetrahedral atom-oxygen (TO) bond lengths are in good agreement and the observed average SiO and AlO bond lengths remain relatively constant in crystalline, glassy, and molten materials. The TOT framework geometry, which determines the major structural features, is governed largely by the local constraints of the strong TO bonds and its major features are modeled well by ab initio calculations on small clusters. Observed bond lengths for non-framework cations are not always in agreement with calculated values, and reasons for this are discussed in the text. The flexibility of SiOSi, SiOAl, and AlOAl angles is in accord with easy glass formation in silicates and aluminosilicates. The stronger constraints on tetrahedral BOB and BOSi angles, as evidenced by much deeper and steeper calculated potential energy versus angle curves, suggest much greater difficulty in substituting tetrahedral B than Al for Si. This is supported by the pattern of immiscibility in borosilicate glasses, although the occurrence of boron in trigonal coordination is an added complication. The limitations on glass formation in oxysulfide and oxynitride systems may be related to the angular requirements of SiSSi and Si(NH)Si groups. Although the SiO and AlO bonds are the strongest ones in silicates and aluminosilicates, they are perturbed by other cations. Increasing perturbation and weakening of the framework occurs with increasing ability of the other atom to compete with Si or Al for bonding to oxygen, that is, with increasing cation field strength. The perturbation of TOT groups, as evidenced by TO bond lengthening predicted by MO calculations and observed in ordered crystalline aluminosilicates, increases in the series Ca, Mg and K, Na, Li. This perturbation correlates strongly with thermochemical mixing properties of glasses in the systems SiO₂-M ₁ ^n/n+ AlO₂ and SiO₂-M ⁿ⁺O _n/2 (M=Li, Na, K, Rb, Cs, and Mg, Ca, Sr, Ba, Pb), with tendencies toward immiscibility in these systems, and with systematics in vibrational spectra. Trends in physical properties, including viscosity at atmospheric and high pressure, can also be correlated.  相似文献   

High-temperature Raman spectroscopy and quasi-harmonic lattice dynamic simulation of diopside     

Varghese Swamy  Leonid S. Dubrovinsky  Masanori Matsui 《Physics and Chemistry of Minerals》1997,24(6):440-446

We investigated the lattice vibrational properties and lattice dynamical behaviour of diopside by combining laser micro-Raman spectroscopic measurements with quasi-harmonic lattice dynamic simulation using a transferable interatomic potential. We obtained polarized Raman spectra from a Fe-poor natural diopside and the temperature dependencies of the Raman modes to 1125?K from high-temperature Raman spectra of a Fe-poor and a Fe-rich natural diopside. The various modes display different temperature dependencies: from ?0.021?cm^?1/K to ?0.004?cm^?1/K. The temperature shift of low frequency modes is generally higher. A comparison of experimentally determined frequencies and symmetries of vibrational modes of the optical type (Raman and infrared) obtained in this and earlier studies with those calculated by us suggests that a consistent characterization of the vibrational properties was achieved. The good agreement between the experimental and simulated data on the temperature-dpendencies of the Raman modes (within 5%), crystal structure (2%), bulk modulus (5%), volume thermal expansivity (6%), and constant volume heat capacity (0.2%) testifies to the applicability of the transferable interatomic potential and the lattice dynamic model to predicting the vibrational, physical, and thermodynamic properties. The simulated properties from the lattice dynamic calculations are very similar to those obtained by molecular dynamic calculations with the same potential model.  相似文献   

Phonon density of states in iron at high pressures and high temperatures     

G. ?ShenEmail author  W. ?Sturhahn  E. E. ?Alph  J. ?Zhao  T. S. ?Tollenner  V. B. ?Prakapenka  Y. ?Meng  H.-R. ?Mao 《Physics and Chemistry of Minerals》2004,31(6):353-359

The phonon density of states (DOS) in iron has been measured in situ by nuclear resonance inelastic X-ray scattering (NRIXS) at high pressures and high temperatures in a resistively heated diamond anvil cell. The DOS data provide a variety of thermodynamic and elastic parameters essential for characterizing iron at depth in the Earth interior, such as average sound velocity, Debye temperature, atomic mean square displacement, average kinetic energy, vibrational entropy and specific heat. The NRIXS data were collected at 6, 20, and 29 GPa and at temperatures up to 920 K. Temperatures were directly determined from the measured spectra by the ratio of intensities of the phonon creation/annihilation side bands that are determined only by the Boltzmann factor. The change of the DOS caused by the structural transition from -Fe to -Fe is small and not resolvable within the experimental precision. However, the phonon energies in -Fe are clearly shifted to lower values with respect to - and -Fe. The temperature dependence of derived thermodynamic parameters is presented and compared with those obtained by Debyes model. The Debye temperatures that best describe the data decrease slightly with increasing temperature.  相似文献