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1.
Pseudopotential periodic Hartree-Fock calculations have been performed on the three polymorphs of Mg2SiO4 with a polarized split valence basis set. The energy differences between polymorphs at their experimental geometries are correctly predicted. The olivine to modified spinel and olivine to spinel phase transition pressures have been estimated and agree within a few GPa with their experimental values. The bonding in Mg2SiO4 is discussed from the point of view of the, band structures, projected density of states, electron density and electron localization function (ELF) curves. It is concluded that both Mg-O and Si-O bonds are highly ionic. 相似文献
2.
Different polymorphs of silica and the opals exhibit significant variations in densities. The paper discusses and correlates
the variations in the molar refraction with density. It emerges that in different polymorphs of silica, the increase in density
involves a corresponding increase in the characteristic dispersion frequencies leading to a decrease in the molar refraction.
The variation of the molar refraction with density can be represented in terms of an elementary formula. The variation of
the molar refraction of opals with the water content in them is also accounted for. 相似文献
3.
K. R. Rao S. L. Chaplot Narayani Choudhury Subrata Ghose J. M. Hastings L. M. Corliss D. L. Price 《Physics and Chemistry of Minerals》1988,16(1):83-97
Magnesium-rich olivine (Mg0.9Fe0.1)2SiO4 is considered to be a major constituent of the Earth's upper mantle. Because of its major geophysical importance, the temperature and pressure dependence of its crystal structure, elastic and dielectric constants, long-wavelength phonon modes and specific heat have been measured using a variety of experimental techniques. Theoretical study of lattice dynamics provides a means of analyzing and understanding a host of such experimental data in a unified manner. A detailed study of the lattice dynamics of forsterite, Mg2SiO4, has been made using a crystal potential function consisting of Coulombic and short-range terms. Quasiharmonic lattice dynamical calculations based on a rigid molecular-ion model have provided theoretical estimates of elastic constants, long-wavelength modes, phonon dispersion relation for external modes along the three high symmetry directions in the Brillouin zone, total and partial density of states and inelastic neutron scattering cross-sections. The neutron cross-sections were used as guides for the coherent inelastic neutron scattering experiment on a large single crystal using a triple axis spectrometer in the constant Q mode. The observed and predicted phonon dispersion relation show excellent agreement. The inelastically scattered neutron spectra from a powder sample have been analyzed on the basis of a phonon density of states calculated from a rigid-ion model, which includes both external and internal modes. The experimental data from a powder sample show good agreement with the calculated spectra, which include a multiphonon contribution in the incoherent approximation. The computed phonon densities of states are used to calculate the specific heat as a function of temperature using both the rigid molecular-ion and rigid ion models. These results are in very good agreement with the calorimetric measurement of the specific heat. The interatomic potential developed here can be used with some confidence to study physical properties of forsterite as a function of pressure and temperature. 相似文献
4.
Subrata Ghose Narayani Choudhury S. L. Chaplot C. Pal Chowdhury S. K. Sharma 《Physics and Chemistry of Minerals》1994,20(7):469-477
Enstatites (Mg2Si2O6) are important rock forming silicates of the pyroxene group whose structures are characterised by double MgO6 octahedral bands and single silicate chains. Orthoenstatite transforms to protoenstatite above 1273 K with a doubling of the a axis and a rearrangement of the silicate chains with respect to the Mg2+ ions. Lattice dynamical calculations based on a rigid-ion model in the quasi-harmonic approximation provide theoretical estimates of elastic constants, long wavelength phonon modes, phonon dispersion relations, total and partial density of states and inelastic neutron scattering cross-sections of protoenstatite. The computed elastic constants are in good agreement with experimental data. The computed density of states of a chain silicate such as protoenstatite is distinct from that of olivines (forsterite, Mg2SiO4 and fayalite, Fe2-SiO4) with isolated silicate tetrahedra. The band gaps in the density of states in forsterite are largely due to the separation in the frequency ranges of the external and internal vibrations of the isolated silicate group, whereas in protoenstatite these gaps are filled by the vibrations of the bridging oxygens of the silicate chain. The computed density of states is used to calculate the specific heat, the mean square atomic displacements and temperature factors. Validity of these calculations are supported by Raman scattering measurements. Polarised and unpolarised Raman spectra are obtained from small single crystals of protoenstatite (Li,Sc)0.6Mg1.4Si2O6 stable at room temperature using the 488 nm or 514.5 nm lines of an Ar+ ion laser and a micro-Raman spectrometer with backscattering geometry. The Raman spectra were analysed and interpreted based on the lattice dynamical model. The experimental Raman frequencies and mode assignments (based on polarised single crystal spectra) are in good agreement with those obtained from lattice dynamical calculations. 相似文献
5.
6.
Geoffrey D. Price Stephen C. Parker Maurice Leslie 《Physics and Chemistry of Minerals》1987,15(2):181-190
We use an approach based upon the Born model of solids, in which potential functions represent the interactions between atoms in a structure, to calculate the phonon dispersion of forsterite and the lattice dynamical behaviour of the beta-phase and spinel polymorphs of Mg2SiO4. The potential used (THB1) was derived largely empirically using data from simple binary oxides, and has previously been successfully used to model the infrared and Raman behaviour of forsterite. It includes ‘bond bending’ terms, that model the directionality of the Si-O bond, in addition to the pair-wise additive Coulombic and short range terms. The phonon dispersion relationships of the Mg2SiO4 polymorphs predicted by THB1 were used to calculate the heat capacities, entropies, thermal expansion coefficients and Gruneisen parameters of these phases. The predicted heat capacities and entropies are in outstandingly good agreement with those determined experimentally. The predicted thermodynamic data of these phases were used to construct a phase diagram for this system, which has Clausius-Clapeyron slopes in very close agreement with those found by experiment, but which has predicted transformation pressures that show less close agreement with those inferred from experiment. The overall success, however, that we have in predicting the lattice dynamical and thermodynamic properties of the Mg2SiO4 polymorphs shows that our potential THB1 represents a significant step towards finding the elusive quantitative link between the microscopic or atomistic behaviour of minerals and their macroscopic properties. 相似文献
7.
Doklady Earth Sciences - Temperature relations of β-factors for 18O/16O fractionations in TiO2 polymorphs have been determined using the density functional theory:... 相似文献
8.
An empirical model for investigating the behaviour of CaCO3 polymorphs incorporating a shell model for oxygen has been created. The model was constructed by fitting to: the structure of aragonite and calcite; their elastic, static and high-frequency dielectric constants; phonon frequencies at the wave vectors [&frac; 0 2] and [0 0 0] of calcite; and vibrational frequencies of the carbonate deformation modes of calcite. The high-pressure phase transition between calcite I and II is observed. The potentials for the CO3 group were transferred to other carbonates, by refitting the interaction between CO3 and the cation to both the experimental structures and their bulk modulus, creating a set of potentials for calculating the properties of a wide range of carbonate materials. Defect energies of substitutional cation defects were analyzed for calcite and aragonite phases. The results were rationalized by studying the structure of calcite and aragonite in greater detail. 相似文献
9.
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
10.
Periodic Hartree-Fock STO-3G calculations have been performed on several tetracoordinated silica polymorphs: low and high quartz, low and idealized high cristobalite and prototype tridymite. The optimized structural parameters are in overall good agreement with experimental data. In the particular case of -quartz, the SiO4 tetrahedra are found to be irregular. The optimized values of the two different SiO bond lengths are respectively 1.608 Å and 1.613 Å. The potential energy versus tilt angle curves suggest a picture of the high temperature phases in terms of delocalized oxygen atoms which is consistent with a disordered structure. Finally, the bonding in silica polymorphs is discussed from electron density maps and Mulliken population analysis. 相似文献
11.
G. V. Gibbs D. F. Cox N. L. Ross T. D. Crawford J. B. Burt K. M. Rosso 《Physics and Chemistry of Minerals》2005,32(3):208-221
The electron localization function, ELF, generated for a number of geometry-optimized earth materials, provides a graphical representation of the spatial localization of the probability electron density distribution as embodied in domains ascribed to localized bond and lone pair electrons. The lone pair domains, displayed by the silica polymorphs quartz, coesite and cristobalite, are typically banana-shaped and oriented perpendicular to the plane of the SiOSi angle at ~0.60 Å from the O atom on the reflex side of the angle. With decreasing angle, the domains increase in magnitude, indicating an increase in the nucleophilic character of the O atom, rendering it more susceptible to potential electrophilic attack. The Laplacian isosurface maps of the experimental and theoretical electron density distribution for coesite substantiates the increase in the size of the domain with decreasing angle. Bond pair domains are displayed along each of the SiO bond vectors as discrete concave hemispherically-shaped domains at ~0.70 Å from the O atom. For more closed-shell ionic bonded interactions, the bond and lone pair domains are often coalesced, resulting in concave hemispherical toroidal-shaped domains with local maxima centered along the bond vectors. As the shared covalent character of the bonded interactions increases, the bond and lone pair domains are better developed as discrete domains. ELF isosurface maps generated for the earth materials tremolite, diopside, talc and dickite display banana-shaped lone pair domains associated with the bridging O atoms of SiOSi angles and concave hemispherical toroidal bond pair domains associated with the nonbridging ones. The lone pair domains in dickite and talc provide a basis for understanding the bonded interactions between the adjacent neutral layers. Maps were also generated for beryl, cordierite, quartz, low albite, forsterite, wadeite, åkermanite, pectolite, periclase, hurlbutite, thortveitite and vanthoffite. Strategies are reviewed for finding potential H docking sites in the silica polymorphs and related materials. As observed in an earlier study, the ELF is capable of generating bond and lone pair domains that are similar in number and arrangement to those provided by Laplacian and deformation electron density distributions. The formation of the bond and lone pair domains in the silica polymorphs and the progressive decrease in the SiO length as the value of the electron density at the bond critical point increases indicates that the SiO bonded interaction has a substantial component of covalent character. 相似文献
12.
B. Marler 《Physics and Chemistry of Minerals》1988,16(3):286-290
Five different refraction formulas were applied to SiO2 polymorphs in order to determine the most suitable refractive index-density relation. 13 SiO2 polymorphs with topological different tetrahedral frameworks are used in this study including eight new low density SiO2 polymorphs — so called “guest free porosils”. These SiO2 polymorphs cover a density range from 1.76 to 2.92 g/cm3. The mean refractive indices (ovn) of the porosils have been determined by the immersion method, the densities (ρ) were calculated from the unit cell parameters. Assuming the polarizability (α) of all SiO2 polymorphs to be constant the general refractivity formula $$\{ 2\overline {11} 0\} \langle 0001\rangle $$ turned out to be the most suitable for SiO2 polymorphs. Regression analysis yields an electronic overlap parameter b=1.2(1). 相似文献
13.
Many oxides tend to form different structures (polymorphs) for small particles. High temperature oxide melt solution calorimetry has been used to measure the enthalpy as a function of polymorphism and surface area for oxides of Al, Ti, and Zr. The results confirm crossovers in polymorph stability at the nanoscale. The energies of internal and external surfaces of zeolitic silicas with open framework structures are an order of magnitude smaller than those of oxides of normal density. 相似文献
14.
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
15.
Igor R. Shein Konstantin I. Shein Alexander L. Ivanovskii 《Physics and Chemistry of Minerals》2006,33(8-9):545-552
The structural, electronic properties and stability of thorium orthosilicate ThSiO4 polymorphs: thorite and huttonite are investigated by means of the full-potential linearized augmented-plane-wave method with the generalized gradient approximation for the exchange-correlation potential (FLAPW-GGA). The forbidden gaps of thorite and huttonite are estimated at about 7.8 and 7.6 eV, respectively. It is found that Th5f states in ThSiO4 partially overlap with occupied O2p bands. The data obtained showed that thorite is more stable than huttonite; in turn both ThSiO4 polymorphs are unstable with respect to their constituent binary oxides (thorianite ThO2 and α-quartz SiO2) in agreement with the experiments. The theoretical shapes of X-ray emission (XES) (Si,O)Kα,β spectra for thorite, huttonite as well as for SiO2 and ThO2 are calculated and discussed. We show that the XES spectroscopy near the (Si,O)K edge may be very useful technique not only for detailed investigation of the bulk-electronic structure of Th silicates but also for the phase analysis of complex mineral samples containing these species. 相似文献
16.
Raman spectra of the two high-pressure polymorphs of SiO2 (coesite and stishovite) were investigated in the temperature range 105–875 K at atmospheric pressure. Coesite remained intact after the highest temperature run, but stishovite became amorphous at temperatures above about 842～872 K. Most Raman modes exhibit a negative frequency shift with temperature for these polymorphs, but positive trends were also observed for some modes. Except for some weak modes, nonlinear temperature variation were established for these polymorphs within the experimental uncertainty and temperature range spanned. The slopes of the variation (δvi/δT)P for these polymorphs were compared with the published values. When compared with quartz and stishovite, the four-membered rings of SiO4-tetrahedra in coesite exhibit very little change with both temperature and pressure. It is also suggested that temperature and pressure should have opposite effects on the Raman shift of each vibrational mode. 相似文献
17.
We have used density functional theory to investigate the stability of MgAl2O4 polymorphs under pressure. Our results can reasonably explain the transition sequence of MgAl2O4 polymorphs observed in previous experiments. The spinel phase (stable at ambient conditions) dissociates into periclase and
corundum at 14 GPa. With increasing pressure, a phase change from the two oxides to a calcium-ferrite phase occurs, and finally
transforms to a calcium-titanate phase at 68 GPa. The calcium-titanate phase is stable up to at least 150 GPa, and we did
not observe a stability field for a hexagonal phase or periclase + Rh2O3(II)-type Al2O3. The bulk moduli of the phases calculated in this study are in good agreement with those measured in high-pressure experiments.
Our results differ from those of a previous study using similar methods. We attribute this inconsistency to an incomplete
optimization of a cell shape and ionic positions at high pressures in the previous calculations. 相似文献
18.
《地学前缘(英文版)》2023,14(1):101458
Plagioclase is the major rock-forming mineral constituting the Earth’s crust, whereas anorthite (CaAl2Si2O8) is a common minerals in lunar highlands crust, meteorites, possibly in some comets and on Mercury. Besides anorthite, two high-temperature polymorphs of CaAl2Si2O8 are known: dmisteinbergite and svyatoslavite, which are found in burnt coal dumps, meteorites and pseudotachylytes. Here we present the results of detailed studies (quenching experiments, elemental analysis, Raman spectroscopy and in situ high temperature single crystal X-ray diffraction (up to 1000 °C)) on naturally co-occurring CaAl2Si2O8 polymorphs (anorthite, dmisteinbergite and svyatoslavite) from a burnt coal dump in Kopeisk, Russia. New polymorphs were found in all natural samples and obtained upon heating of dmisteinbergite (unquenchable β-dmisteinbergite and quenchable γ-dmisteinbergite). It was shown that Ca coordination differs significantly in CaAl2Si2O8 polymorphs, resulting in a different capacity to host Ba and possibly other large ion lithophile elements. Combining our data on natural samples with the previously published data on natural and synthetic compounds, we propose a new scheme of CaAl2Si2O8 polymorphs stability. Our results indicate that CaAl2Si2O8 polymorphs could be used for temperature estimations for both Earth and planetary sciences. 相似文献
19.
Atransmission electron microscope (TEM) study of quartz-coesite inclusions in garnet in crustal rocks from the Western Alps is presented. Coesite shows a low dislocation density (<107 cm?2), and quartz a higher density of defects, Brasil twins (104 cm?1) and dislocations (108 cm?2). It is concluded that coesite has been not or only slightly plastically deformed and that the yield strength of coesite is higher than that of quartz. The large scale deformation implications are briefly discussed. TEM observations show no systematic topotactic relationship between the two polymorphs and their boundaries have a scalloped morphology which suggests that growth of quartz from coesite was controlled by a diffusion process. 相似文献
20.
Anne R. Remsberg James N. Boland Tibor Gasparik Robert C. Liebermann 《Physics and Chemistry of Minerals》1988,15(5):498-506
An experiment conducted in a 2000-ton uniaxial split-sphere apparatus (USSA-2000) utilizes large sample volume and a substantial temperature gradient to synthesize intergrowths of the olivine and spinel polymorphs of Co2SiO4. The olivine starting material consists of a finegrained fraction (<20μm) which records the stable polymorphs along the length of the sample plus large olivine grains (100–500 μm) which help decipher the mechanism of the phase transformation. At conditions near equilibrium, the olivine-spinel transformation in the large grains occurs by inward growth of a few large single crystals of spinel nucleated on the surfaces of the olivine. The overall rate of transformation is governed by the mobility of the interphase boundary, whose morphology is crystallographically controlled by the spinel. No renucleation of spinel is observed in the host olivine crystal, even in the region immediately adjacent to the olivine/spinel interface; analysis of this region with transmission electron microscopy reveals an extremely high density of dislocations induced by plastic flow accommodating the volume change associated with the phase transformation. 相似文献