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1.
G. V. Gibbs D. F. Cox T. D. Crawford M. B. Boisen Jr M. Lim 《Physics and Chemistry of Minerals》2002,29(5):307-318
The electron localization function, η, evaluated for first-principles geometry optimized model structures generated for quartz and coesite, reveals that the oxide anions are coordinated by two hemispherically shaped η-isosurfaces located along each of the SiO bond vectors comprising the SiOSi angles. With one exception, they are also coordinated by larger banana-shaped isosurfaces oriented perpendicular to the plane centered in the vicinity of the apex of each angle. The hemispherical isosurfaces, ascribed to domains of localized bond-pair electrons, are centered ～0.70 Å along the bond vectors from the oxide anions and the banana-shaped isosurfaces, ascribed to domains of localized nonbonding lone-pair electrons, are centered ～0.60 Å from the apex of the angle. The oxide anion comprising the straight SiOSi angle in coesite is the one exception in that the banana-shaped isosurface is missing; however, it is coordinated by two hemispherically shaped isosurfaces that lie along the bond vectors. In the case of a first-principles model structure generated for stishovite, the oxide anion is coordinated by five hemispherically shaped η-isosurfaces, one located along each of the three SiO bond vectors (ascribed to domains of bonding-electron pairs) that are linked to the anion with the remaining two (ascribed to domains of nonbonding-electron pairs) located on opposite sides of the plane defined by three vectors, each isosurface at a distance of ～0.5 Å from the anion. The distribution of the five isosurfaces is in a one-to-one correspondence with the distribution of the maxima displayed by experimental Δρ and theoretical ??2ρ maps. Isosurface η maps calculated for quartz and the (HO) 3 SiOSi(OH) 3 molecule also exhibit maxima that correspond with the (3,?3) maxima displayed by distributions of ??2ρ. Deformation maps observed for the SiOSi bridges for the silica polymorphs and a number of silicates are similar to that calculated for the molecule but, for the majority, the maxima ascribed to lone-pair features are absent. The domains of localized nonbonding-electron pair coordinating the oxide anions of quartz and coesite provide a basis for explaining the flexibility and the wide range of the SiOSi angles exhibited by the silica polymorphs with four-coordinate Si. They also provide a basis for explaining why the SiO bond length in coesite decreases with increasing angle. As found in studies of the interactions of solute molecules with a solvent, a mapping of η-isosurfaces for geometry-optimized silicates is expected to become a powerful tool for deducing potential sites of electrophilic attack and reactivity for Earth materials. The positions of the features ascribed to the lone pairs in coesite correspond with the positions of the H atoms recently reported for an H-doped coesite crystal. 相似文献
2.
This study examines the electron localization function (ELF) isosurfaces of the Al2SiO5 polymorphs kyanite, sillimanite, and andalusite to see how differences in coordination and geometry of the cations and anions affect the ELF isosurfaces. Examination of the ELF isosurfaces indicates that their shapes are dependent on the coordination and geometry of the oxygen atoms and are not sensitive to coordination of the surrounding cations. Of the 18 crystallographically distinct oxygen atoms in the Al2SiO5 polymorphs, 13 are bonded to two aluminum atoms and one silicon atom (Al2–O–Si) and are associated with two different ELF isosurface shapes. The shape of the ELF isosurface is dependent on the distance at which the oxygen atom lies from a plane defined by the three surrounding cations: at a distance greater than 0.2 Å the ELF can be defined as horseshoe-shaped and at a distance less then 0.2 Å it can be described as concave hemispherical. This feature is also seen in the ELF isosurfaces for the oxygens bonded to three aluminum atoms (Al3–O) where the isosurfaces can be defined as trigonally toroidal and uniaxially trigonally toroidal. The changes in the ELF isosurfaces for the three coordinated oxygens are also indicative of changes in hybridization. The ELF isosurface for the two-fold coordinated oxygen (Al–O–Si) has a large mushroom-shaped isosurface along the Al–O bond and a concave hemispherical isosurface along the Si–O. The four-fold coordinated oxygen (Al4–O) contains two concave hemispherical isosurfaces along the shorter Al–O bonds and a banana-shaped isosurface, which encompasses the longer Al–O bonds. In addition, this study shows the homeomorphic relationship between the ELF isosurfaces and electron density difference maps with respect to number and arrangement of domains. 相似文献
3.
4.
Several computer models of quartz were developed and tested. A simple model based on a potential energy function, derived in large part from quantum mechanical calculations on the molecule H6Si2O7, was found to reproduce the compressibility curve for quartz up to pressures of 8 GPa. The potential includes quadratic expressions for the SiO bond lengths, the OSiO angles and a parameter spanning the SiOSi angle together with an exponential OO repulsion term for non co-dimer O atoms. The variations in the cell edges and in the SiOSi angle, as a function of pressure, parallel observed trends when the bond lengths and angles calculated for the molecule are used as rgressor values. Poisson ratios calculated using the model match those observed. Two configurations for quartz related by the Dauphiné twin law are generated as minimum energy structures of the model with about equal frequencies as observed in nature. It is shown that the model, devised for quartz, can also be applied to the silica polymorph cristobalite, giving reasonable estimates of its compressibility curve, structural parameters and its negative Poisson ratio. When the observed bond lengths and angles are used as regressor values, the model generates the absolute coordinates of the atoms and the cell dimensions for quartz to within 0.005 Å and those of cristobalite to within 0.001 Å, on average, both at zero pressure. When applied to coesite, the model yields a zero pressure structure that is close to that observed but which is significantly softer than observed. The resulting SiO bond lengths are linearly correlated with f
s
(O), as observed for coesite, despite the use of a single bond length and a single SiOSi angle as regressor values in the calculation. When the structures are optimized assuming P1 space group symmetry and triclinic cell dimensions, the resulting frameworks of silicate tetrahedra exhibit the translational, rotational and reflection symmetries observed for quartz, cristobalite and coesite. The fact that the resulting frameworks exhibit observed space group symmetries is evidence that the symmetry adopted by the silica polymorphs can be explained by short ranged forces. 相似文献
5.
Ab initio STO-3G molecular orbital theory has been used to calculate energy-optimized Si-O bond lengths and angles for molecular orthosilicic and pyrosilicic acids. The resulting bond length for orthosilicic acid and the nonbridging bonds for pyrosilicic acid compare well with Si-OH bonds observed for a number of hydrated silicate minerals. Minimum energy Si-O bond lengths to the bridging oxygen of the pyrosilicic molecule show a close correspondence with bridging bond length data observed for the silica polymorphs and for gas phase and molecular crystal siloxanes when plotted against the SiOSi angle. In addition, the calculations show that the mean Si-O bond length of a silicate tetrahedron increases slightly as the SiOSi angle narrows. The close correspondence between the Si-O bond length and angle variations calculated for pyrosilicic acid and those observed for the silica polymorphs and siloxanes substantiates the suggestion that local bonding forces in solids are not very different from those in molecules and clusters consisting of the same atoms with the same coordination numbers. An extended basis calculation for H4SiO4 implies that there are about 0.6 electrons in the 3d-orbitals on Si. An analysis of bond overlap populations obtained from STO-3G* calculations for H6Si2O7 indicates that Si-O bond length and SiOSi angle correlations may be ascribed to changes in the hybridization state of the bridging oxygen and (d – p) π-bonding involving all five of the 3d AO's of Si and the lone-pair AO's of the oxygen. Theoretical density difference maps calculated for H6Si2O7 show a build-up of charge density between Si and O, with the peak-height charge densities of the nonbridging bonds exceeding those of the bridging bonds by about 0.05 e Å?3. In addition, atomic charges (+1.3 and ?0.65) calculated for Si and O in a SiO2 moiety of the low quartz structure conform reasonably well with the electroneutrality postulate and with experimental charges obtained from monopole and radial refinements of diffraction data recorded for low quartz and coesite. 相似文献
6.
M. B. Boisen Jr. G. V. Gibbs M. S. T. Bukowinski 《Physics and Chemistry of Minerals》1994,21(5):269-284
A simulated annealing technique was used to search for global and local minimum energy structures of a potential energy model for silica. The model is based on ab initio SCF MO calculations on the disilicic acid molecule, H6Si2O7. Starting with 4 SiO2 units, with the atoms randomly distributed in the unit cell, 23 distinct silica tetrahedral framework structures were found, with a variety of space group symmetries and cell dimensions. Despite the assumption of P 1 space group symmetry for the starting structure, only 7 of the local minimum energy structures were found to possess triclinic symmetry with the remainder exhibiting symmetries ranging from P c to
to within 0.001 Å. Although the interaction potential for the disilicic acid molecule has a single minimum energy SiO bond length and SiOSi angle, the local minimum energy structures exhibit angles that range between 105° and 180° and bond lengths that range between 1.55 and 1.68 Å. The correlation observed for coesite and the other silica polymorphs between SiO bond length and fs(O) is reproduced. The generated structures show a wide variety of coordination sequences, ring sizes and framework densities, the later ranging from 19.8 to 35.5 Si/1000 Å3. The energies of these structures correlate with their framework densities, particularly for higher energy structures. 相似文献
7.
CNDO/2 MO calculations on H12Si5O16 clusters modeling silicate tetrahedral linkage in the silica polymorphs show total energy minima at bent SiOSi angles and a correlation between the Si-O bond lengths, d(Si-O), used in the calculation and the minimum energy value of the SiOSi angle. Calculations on hydrogen saturated Si5O16 clusters isolated from the structures of low quartz, low cristobalite and coesite which were adjusted by DLS methods so that all d(Si-O) equal 1.61 Å and all L OSiO equal 109.47° yield Mulliken bond overlap populations, n(Si-O), and Si-O two-center energies, E(Si-O), which correlate with observed bond lengths; shorter bonds involve larger n(Si-O) values and more negative E(Si-O) values.
相似文献8.
Bond critical point properties of electron density distributions calculated for representative Si5O16 moieties of the structure of coesite are compared with those observed and calculated for the bulk crystal. The values calculated
for the moieties agree with those observed to within ∼5%, on average, whereas those calculated for the crystal agree to within
∼10%. As the SiOSi angles increase and the SiO bonds shorten, there is a progressive build-up in the calculated electron density
along the bonds. This is accompanied by an increase in both the curvatures of the electron density, both perpendicular and
parallel to each bond, and the Laplacian of the electron density distribution at the bond critical points. The cross sections
of the bonds at the critical points become more circular as the angle approaches 180o. Also, the bonded radius of the oxide
anion decreases about twice as much as that of the Si cation as the SiO bond length decreases and the fraction of s-character of the bond is indicated to increase. A knowledge of electron density distributions is central to our understanding
of the forces that govern the structure, properties, solid state reactions, surface reactions and phase transformations of
minerals. The software (CRYSTAL95 and TOPOND) used in this study to calculate the bond critical properties of the electron
density and Laplacian distributions is bound to promote a deeper understanding of crystal chemistry and properties.
Received: 23 February 1998 / Revised, accepted: 16 July 1998 相似文献
9.
G. V. Gibbs M. B. Boisen F. C. Hill O. Tamada R. T. Downs 《Physics and Chemistry of Minerals》1998,25(8):574-584
The topological properties of the electron density distributions for more than 20 hydroxyacid, geometry optimized molecules
with SiO and GeO bonds with 3-, 4-, 6- and 8-coordinate Si and Ge cations were calculated. Electronegativities calculated
with the bond critical point (bcp) properties of the distributions indicate, for a given coordination number, that the electronegativity
of Ge (∼1.85) is slightly larger than that of Si (∼1.80) with the electronegativities of both atoms increasing with decreasing
bond length. With an increase in the electron density, the curvatures and the Laplacian of the electron density at the critical
point of each bond increase with decreasing bond length. The covalent character of the bonds are assessed, using bond critical
point properties and electronegativity values calculated from the electron density distributions. A mapping of the (3, −3)
critical points of the valence shell concentrations of the oxide anions for bridging SiOSi and GeOGe dimers reveals a location
and disposition of localized nonbonding electron pairs that is consistent with the bridging angles observed for silicates
and germanates. The bcp properties of electron density distributions of the SiO bonds calculated for representative molecular
models of the coesite structure agree with average values obtained in X-ray diffraction studies of coesite and danburite to
within ∼5%.
Received: 18 August 1997 / Revised, accepted: 19 February 1998 相似文献
10.
11.
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
12.
Employing first-principles methods, the docking sites for H were determined and H, Al, and vacancy defects were modeled with an infinite periodic array of super unit cells each consisting of 27 contiguous symmetry nonequivalent unit cells of the crystal structure of stishovite. A geometry optimization of the super-cell structure reproduces the observed bulk structure within the experimental error when P1 translational symmetry was assumed and an array of infinite extent was generated. A mapping of the valence electrons for the structure displays mushroom-shaped isosurfaces on the O atom, one on each side of the plane of the OSi3 triangle in the nonbonded region. An H atom, placed in a cell near the center of the super cell, was found to dock upon geometry optimization at a distance of 1.69 Å from the O atom with the OH vector oriented nearly perpendicular to the plane of the triangle such that the OH vector makes a angle of 91° with respect to [001]. However, an optimization of a super cell with an Al atom replacing Si and an H atom placed nearby in a centrally located cell resulted in an OH distance of 1.02 Å with the OH vector oriented perpendicular to [001] as observed in infrared studies. The geometry-optimized position of the H atom was found to be in close agreement with that (0.44, 0.12, 0.0) determined in an earlier study of the theoretical electron density distribution. The docking of the H atom at this site was found to be 330 kJ mol–1 more stable than a docking of the atom just off the shared OO edge of the octahedra as determined for rutile. A geometry optimization of a super cell with a missing Si generated a vacant octahedra that is 20% larger than that of the SiO6 octahedra. The valence electron density distribution displayed by the two-coordinate O atoms that coordinate the vacant octahedral site is very similar to those displayed by the bent SiOSi angles in coesite. The internal distortions induced by the defect were found to diminish rather rapidly with distance, with the structure annealing to that observed in the bulk crystal to within about three coordination spheres. 相似文献
13.
Accurate interatomic potentials have been employed to compute the phonon density of states of αquartz, stishovite and coesite polymorphs of silica. The temperature variation of several thermodynamic properties is calculated by using the phonon density of states to describe the vibrational entropy contribution to the free energy. Results for these polymorphs are in surprisingly good agreement with available experimental data. Moreover, the microscopic origin of quantitative differences in the heat capacity behavior of low and high density polymorphs is established. 相似文献
14.
Ab-Initio quantum mechanical calculations on molecular clusters are used to obtain potential surfaces for the SiO bond in silicates. These potential surfaces form the basis for extracting the key parameters in various commonly employed potential functions. Applications to the usual ionic model demonstates a close relation between the ab-initio derived ionic potential and those empirically dervied. The ionic model is then used to predict structures and elastic properties of orthosilicates and of the silica polymorphs. The deficiencies in the ionic model lead to the application of the quantum results to covalent models. These latter models are then used in theoretical calculations of the properties of silica polymorphs. 相似文献
15.
Deep-sea biogenic silica: new structural and analytical data from infrared analysis - geological implications 总被引：1，自引：0，他引：1
François Fröhlich 《地学学报》1989,1(3):267-273
The main parameters of infrared spectra have been investigated for marine siliceous skeletons and for silica polymorphs. From infrared (IR)data, the mean values for the Si-O bond length (1.62 Å) and for the Si-O-Si angle (about 142°6) are inferred for biogenic silica. A model is proposed for the molecular structure of biogenic, amorphous silica, which consists of a discontinuous, three-dimensional framework of short chains of [SiO4 ] tetrahedra, bounded with apical hydroxyls. According to the relationship between the structure of the silica polymorphs and their infrared spectra, it is shown that a quantitative analysis of biogenic silica seems to be possible in quartz-rich sediments. Some geological implications of these data are emphasized, including the processes of siliceous skeleton sedimentation and diagenetic evolution. 相似文献
16.
蛇绿岩地幔岩中自由SiO2的发现及其地质意义 总被引：1，自引：0，他引：1
自由SiO_2系指石英及其同质多型物(polymorphs)柯石英、斯石英等。石英广泛分布于地壳中的各种岩石中,柯石英和斯石英只存在于超高压岩石和陨石坑中。由于石英和非饱和SiO_2的橄榄石不能共生,因此在地幔橄榄岩和超镁铁岩中不存在原生石英。最近笔者在西藏罗布莎蛇绿岩的地幔岩(方辉橄榄岩)的豆荚状铬铁矿中发现了自由SiO_2和柯石英相。根据高温高压相平衡实验资料,橄榄石、辉石这样的硅酸盐矿物在地幔深部的压力条件下可以分解成简单氧化物,如FeO(方铁矿)、MgO(方镁石)以及SiO_2(斯石英)等。由此推测,西藏蛇绿岩地幔岩中自由SiO_2可能是来自于下地幔的矿物,是地幔柱作用将其搬运到上地幔浅部。 相似文献
17.
G. V. Gibbs N. L. Ross D. F. Cox K. M. Rosso B. B. Iversen M. A. Spackman 《Physics and Chemistry of Minerals》2014,41(1):17-25
The power law regression equation, <R(M–O)> = 1.46(<ρ(r c)>/r)?0.19, relating the average experimental bond lengths, <R(M–O)>, to the average accumulation of the electron density at the bond critical point, <ρ(r c)>, between bonded pairs of metal and oxygen atoms (r is the row number of the M atom), determined at ambient conditions for oxide crystals, is similar to the regression equation R(M–O) = 1.41(ρ(r c)/r)?0.21 determined for three perovskite crystals at pressures as high as 80 GPa. The pair are also comparable with the equation <R(M–O)> = 1.43(<s>/r)?0.21 determined for oxide crystals at ambient conditions and <R(M–O)> = 1.39(<s>/r)?0.22 determined for geometry-optimized hydroxyacid molecules that relate the geometry-optimized bond lengths to the average Pauling bond strength, <s>, for the M–O bonded interactions. On the basis of the correspondence between the equations relating <ρ(r c)> and <s> with bond length, it seems plausible that the Pauling bond strength might serve a rough estimate of the accumulation of the electron density between M–O bonded pairs of atoms. Similar expressions, relating bond length and bond strength hold for fluoride, nitride and sulfide molecules and crystals. The similarity of the expressions for the crystals and molecules is compelling evidence that molecular and crystalline M–O bonded interactions are intrinsically related. The value of <ρ(r c)> = r[(1.41)/<R(M–O)>]4.76 determined for the average bond length for a given coordination polyhedron closely matches the Pauling’s electrostatic bond strength reaching each the coordinating anions of the coordinated polyhedron. Despite the relative simplicity of the expression, it appears to be more general in its application in that it holds for the bulk of the M–O bonded pairs of atoms of the periodic table. 相似文献
18.
Volker Stähle Rainer Altherr Mario Koch Lutz Nasdala 《Contributions to Mineralogy and Petrology》2008,155(4):457-472
The microtextures of stishovite and coesite in shocked non-porous lithic clasts from suevite of the Ries impact structure
were studied in transmitted light and under the scanning electron microscope. Both high-pressure silica phases were identified
in situ by laser-Raman spectroscopy. They formed from silica melt as well as by solid-state transformation. In weakly shocked
rocks (stage I), fine-grained stishovite (≤1.8 μm) occurs in thin pseudotachylite veins of quartz-rich rocks, where it obviously
nucleated from high-pressure frictional melts. Generally no stishovite was found in planar deformation features (PDFs) within
grains of rock-forming quartz. The single exception is a highly shocked quartz grain, trapped between a pseudotachylite vein
and a large ilmenite grain, in which stishovite occurs within two sets of lamellae. It is assumed that in this case the small
stishovite grains formed by the interplay of conductive heating and shock reverberation. In strongly shocked rocks (stages
Ib–III, above ∼30 GPa), grains of former quartz typically contain abundant and variably sized stishovite (<6 μm) embedded
within a dense amorphous silica phase in the interstices between PDFs. The formation of transparent diaplectic glass in adjacent
domains results from the breakdown of stishovite and the transformation of the dense amorphous phase and PDFs to diaplectic
glass in the solid state. Coesite formed during unloading occurs in two textural varieties. Granular micrometre-sized coesite
occurs embedded in silica melt glass along former fractures and grain boundaries. These former high-pressure melt pockets
are surrounded by diaplectic glass or by domains consisting of microcrystalline coesite and earlier formed stishovite. The
latter is mostly replaced by amorphous silica. 相似文献
19.
An ab initio Hartree–Fock study of spodumene structure has been performed, and the wave function was used for a topological analysis of the electron density. The three non-equivalent oxygen atoms (O1, O2 and O3) of spodumene differed mainly in their valence shell charge concentration (VSCC). In particular, O1 shows a maximum of charge concentration along the Si–O bond path, and two other maxima, which can be regarded as lone pairs, point in the opposite direction with respect to the silicon position. O2 shows a torus of local charge concentration, whose axis is parallel to the Al–Si direction, with a bulge on the external side of the Si–O2–Al angle; even if no maximum exists in the Si direction, the valence shell of O2 appears to be strongly polarized toward the silicon; a slight polarization also exists along the Al–O bond path. A similar situation is displayed by O3, whose charge concentration has a torus-like shape, with the axis parallel to the Si–Si direction, and a bulge on the external side of the Si–O3–Si angle; as in the case of O2, a significant polarization of the valence shell of O3 is observed, towards the two Si directions. By recasting the calculated electron distribution in terms of the valence bond theory, a correlation has been found between structural details (bond lengths) and the hybridization state of the oxygen atoms. 相似文献
20.
Timing of Himalayan ultrahigh-pressure metamorphism: sinking rate and subduction angle of the Indian continental crust beneath Asia 总被引：28，自引：0，他引：28
Y. Kaneko I. Katayama H. Yamamoto K. Misawa M. Ishikawa H. U. Rehman A. B. Kausar K. Shiraishi 《Journal of Metamorphic Geology》2003,21(6):589-599
Coesite relics were discovered as inclusions in clinopyroxene in eclogite and as inclusions in zircon in felsic and pelitic gneisses from Higher Himalayan Crystalline rocks in the upper Kaghan Valley, north‐west Himalaya. The metamorphic peak conditions of the coesite‐bearing eclogites are estimated to be 27–32 kbar and 700–770 °C, using garnet–pyroxene–phengite geobarometry and garnet–pyroxene geothermometry, respectively. Cathodoluminescence (CL) and backscattered electron (BSE) imaging distinguished three different domains in zircon: inner detrital core, widely spaced euhedral oscillatory zones, and thin, broadly zoned outermost rims. Each zircon domain contains a characteristic suite of micrometre‐sized mineral inclusions which were identified by in situ laser Raman microspectroscopy. Core and mantle domains contain quartz, apatite, plagioclase, muscovite and rutile. In contrast, the rim domains contain coesite and minor muscovite. Quartz inclusions were identified in all coesite‐bearing zircon grains, but not coexisting with coesite in the same growth domain (rim domain). 206Pb/238U zircon ages reveal that the quartz‐bearing mantle domains and the coesite‐bearing rim were formed at c. 50 Ma and 46.2 ± 0.7 Ma, respectively. These facts demonstrate that the continental materials were buried to 100 km within 7–9 Myr after initiation of the India–Asia collision (palaeomagnetic data from the Indian oceanic floor supports an initial India‐Asia contact at 55–53 Ma). Combination of the sinking rate of 1.1–1.4 cm year?1 with Indian plate velocity of 4.5 cm year?1 suggests that the Indian continent subducted to about 100 km depth at an average subduction angle of 14–19°. 相似文献