Ab initio calculated geometries and charge distributions for H4SiO4 and H6Si2O7 compared with experimental values for silicates and siloxanes

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.     

Raman scattering and lattice vibrations of Ni2SiO4 spinel at elevated temperature

Raman spectra of Ni₂SiO₄ spinel (O _h ⁷ Z=8) have been measured in the temperature range from 20 to 600 °C and the Raman active vibrations (A _1g +E _g +3F _2g ) have been assigned. A calculation of the optically active lattice vibrations of this spinel has been made, assuming a potential function which combines general valence and short range force constants. The values of the force constants at 20 and 500 °C have been calculated from the vibrational frequencies of the observed Raman spectra and infrared (IR) spectral data. The Ni spinel at 20 °C has a prominently small Si-O bond stretching force constant of K(SiO)=2.356 ～ 2.680 md/Å and a large Ni-O bond stretching constant of K(NiO)=0.843 ～ 1.062 md/Å and these force constants at 500 °C decrease to K(SiO)=2.327 ～ 2.494 md/Å and K(NiO)=0.861 ～ 0.990 md/Å. The Si-O bond is noticeably weakened at high temperatures, despite the small thermal expantion from 1.657 Å (20 °C) to 1.660 Å (500 °C). These changes of the interatomic force constants of the spinel at high temperatures are in accord with the thermal structure changes observed by X-ray diffraction study. The weakened Si-O bond is consistent with the fact that Si atoms in the spinel lattice can diffuse at significant rates at elevated temperature.     

The lattice dynamics and thermodynamics of the Mg2SiO4 polymorphs

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.     

Computer simulations of the structural and physical properties of the olivine and spinel polymorphs of Mg2SiO4

The aim of the work presented is to develop a computer simulation technique which will predict the structure and physical properties of forsterite and ringwoodite, the major mantle-forming polymorphs of Mg₂SiO₄. The technique is based upon energy minimization, in which all structural parameters are varied until the configuration with the lowest energy is achieved. The lattice energy and physical properties (e.g. elasticity and dielectric constants) are calculated from interatomic potentials, which generally include electrostatic and short-range terms. We investigate several types of traditional potential models, and present a new type of model which includes partial ionic charges and a Morse potential to describe the effect of covalency on the Si-O bond. This new form of potential model is highly successful, and not only reproduces the zero-pressure structural, elastic and dielectric properties of forsterite and ringwoodite, but also accurately describes their pressure dependence.     

A molecular orbital study of bond length and angle variations in framework structures

Molecular orbital calculations on a variety of silicate and aluminosilicate molecules have been used to explore the bonding forces that govern tetrahedral bond length variations, r(TO), in framework silicates and aluminosilicates. Not only do the calculations provide insight into the variety of structural types and the substitution limits of one tetrahedral atom for another, but they also provide an understanding of the interrelationships among r(TO) and linkage factors, bond strength sum, coordination number, and angles within and between tetrahedra. A study of these interrelationships for a theoretical data set shows that r(SiO) and r(AlO) are linearly correlated with (1) p _o, the bond strength sum to a bridging oxygen, (2) f _s(O), the fractional s-character of a bridging oxygen, and (3) f _s (T), the fractional s-character of the T atom. In a multiple linear regression analysis of the data, 92% of the variation of r(SiO) and 99% of the variation of r(AlO) can be explained in terms of a linear dependence on p _o, f _s (O), and f _s (T). Analogous regression analyses completed for observed r(Al, SiO) bond length data from a number of silica polymorphs and ordered aluminosilicates account for more than 75% of the bond length variation. The lower percentage of bond length variation explained is ascribed in part to the random and systematic errors in the experimental data which have a negligible effect on the theoretical data. The modeling of more than 75% of the variation of r(Al, SiO) in the framework silicates using the same model used for silicate and aluminosilicate molecules strengthens the viewpoint that the bonding forces that govern the shapes of such molecules are quite similar to the forces that govern the shapes of chemically similar groups in solids. The different regression coefficients calculated for f _s (T) indicate that SiO and AlO bond length variations in framework structures should not be treated as a single population in estimating the average Al, Si content of a tetrahedral site.     

Simple covalent potential models of tetrahedral SiO2: Applications to α-quartz and coesite at pressure

We present a covalent potential model of tetrahedrally coordinated SiO₂. The interactions include covalent effects in the form of a Si-O bond-stretching potential, O-Si-O and Si-O-Si angle-bending potentials, and oxygen-oxygen repulsion. Calculated equations of state of α-quartz and coesite agree well with experiment (calculated densities within 1 percent of experiment up to 6 GPa). The calculated α-quartz-coesite transition pressure agrees with the experimental value of ≈2 GPa. Furthermore, the compression mechanisms predicted by the model (i.e. pressure induced changes in Si-O bond lengths and O-Si-O and Si-O-Si angles) are accurate.     

Some physical properties of amorphous SiO2 synthesized by shock compression of α quartz

The amorphous phase of SiO₂ produced upon recovery of shock-compressed quartz demonstrates a wide range of refractive indices which can be correlated to the shock state. Both infra-red absorption spectra and X-ray diffraction patterns indicate that the shock-produced amorphous SiO₂ has a statistically more-random atomic distribution and longer Si-O and shorter Si-Si separation than does fused silica. By accounting for phase transformation, the calculated values of the shock and residual temperature are much higher than those obtained by Wackerle (1962) to a pressure of 700 kbar. Our results are consistent with experimental ones.     

Vibrational spectroscopy of beryllium aluminosilicates: Heat capacity calculations from band assignments

Far-infrared, mid-IR, and Raman powder spectra were measured on six phases (bromellite, chrysoberyl, phenakite, bertrandite, beryl, and euclase) in the system BeO-Al₂O₃-SiO₂-H₂O. A single-crystal absorption spectrum of IR fundamentals in beryl is also presented, which more closely resembles the powder absorption spectrum than it does absorption spectra calculated from single-crystal reflection data. Assignments of the SiO₄ and BeO₄ internal vibrations are made in accordance with each mineral's symmetry and composition and by comparison to structural analogs. Heat capacities C _v calculated for these partial band assignments agree with C _v derived from experimental C _p for all six phases, provided that Kieffer's (1979c) model is slightly modified to correctly enumerate both Si-O and Be-O stretching modes in the high frequency region (>750 cm^?1). Si-O stretching bands were found to out-number Be-O stretching modes in the high-energy region of the vibrational spectra with two exceptions: (1) For those phases containing oxygen ions not coordinated to silicon, vibrations occurring at v>1,080 cm^?1 that are attributable to Be-O (H) stretching must be treated separately in the model in order to calculate C _v accurately. (2) Minerals consisting entirely of interlocking Si and Be tetrahedra (i.e., phases without Al or OH) can be modeled by one optic continuum representing all optical modes. These results, along with the occurrence of very low energy lattice vibrations for Be-silicates within Al, suggests that although Be-O bonds are generally weaker than neighboring Si-O bonds, Be mimics the network-forming characteristic of Si to a limited extent.     

Ab initio calculation of interatomic force constants in H6Si2O7 and the bulk modulus of α quartz and α cristobalite

Ab initio force constants calculated for Si-O stretch and Si...Si non-bonded interactions in H₆Si₂O₇ are found comparable with experimental values derived from the lattice dynamics of α quartz. The bulk moduli of α quartz and α cristobalite are calculated using the molecular Si...Si force constant and assuming rigid regular SiO₄ tetrahedra. In the case (α quartz) where data are available the calculation agrees well with experiment.     

Application of empirical ionic models to SiO2 liquid: Potential model approximations and integration of SiO2 polymorph data

Structural and thermodynamic properties of crystalline SiO₂ and SiO₂ liquid have been examined with Monte Carlo (MC), molecular dynamics (MD), and energy minimization (EM) calculations using several ionic potential models obtained from the literature. The MC and MD methods calculate the same structural and thermodynamic properties for liquids when the same potential model is used. The Ewald (1921) method of calculating coulomb interactions reproduced most successfully the structure of liquid silica. Approximating the coulomb interaction by eliminating the inverse lattice sum results in predicted bond distances that are too short and an average 〈Si-O-Si〉 angle of approximately 180°. Introduction of a cut-off in the potential energy function produces irregular tetrahedra and inconsistencies in predicted Si-O coordination in silica liquid. The system internal energies show that liquid structures derived from random starting configurations can be metastable relative to structures calculated from crystalline starting configurations.The static lattice properties of the polymorphs alpha-quartz, coesite, and stishovite were used to evaluate further the accuracy of different sets of repulsive parameters for the full Ewald ionic model. Most of the models studied reproduced poorly the measured structures and elastic constants of the polymorphs. The major weakness of the ionic model is the unreasonably large Si-O bond strength (120 × 10⁻¹² ergs/bond) when formal ionic charges are used. Fractional charge models with a small Si-O bond strength (30 × 10⁻¹² ergs/bond) improve the agreement with experimental data. However, further improvement of the ionic model should include reducing the Si-O bond strength to values in better agreement with published estimates (7 × 10^{− 12} to 13 × 10⁻¹² ergs/bond). By using additional information to constrain the parameterization of the ionic model, such as estimated bond strengths and static properties of the silica polymorphs, a model more representative of the interparticle interactions may be obtained.     

Optimization of CNDO for molecular orbital calculation on silicates

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.     

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

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.     

A MEG study of the olivine and spinel forms of Mg2SiO4

In this paper we present a theoretical investigation of the structures and relative stability of the olivine and spinel phases of Mg₂SiO₄. We use both a purely ionic model, based on the Modified Electron Gas (MEG) model of intermolecular forces, and a bond polarization model, developed for low pressure silica phases, to investigate the role of covalency in these compounds. The standard MEG ionic model gives adequate structural results for the two phases but incorrectly predicts the spinel phase to be more stable at zero pressure. This is mainly because the ionic modeling of Mg₂SiO₄ only accounts for 95 percent of the lattice energy. The remainder can be attributed to covalency and many-body effects. An extension of the MEG ionic model using “many-body” pair potentials corrects the phase stability error, but predicts structures which are in poorer agreement with experiment than the standard ionic approach. In addition, calculations using these many-body pair potentials can only account for 10 percent of the missing lattice energy. This model predicts an olivine-spinel phase transition of 8 GPa, below the experimental value of 20 GPa. Therefore, in order to understand more fully the stability of these structures we must consider polarization. A two-shell bond polarization model enhances the stability of both structures, with the olivine structure being stabilized more. This model predicts a phase transition at about 80 GPa, well above the observed value. Also, the olivine and spinel structures calculated with this approach are in poorer agreement with experiment than the ionic model. Therefore, based on our investigations, to properly model covalency in Mg₂SiO₄, a treatment more sophisticated than the two-shell model is needed.     

Phonon spectra and rigid-ion model calculations on andalusite

Polarised Raman and infrared spectra of (ir) andalusite (Al₂SiO₅) single crystals have been measured and interpreted on the basis of a rigid-ion model calculation. The Al-O bond strength is found to be about 70% ionic in character whereas the mainly covalently bound SiO₄ tetrahedra show ca. 40% ionicity. The interatomic short range forces are strongest between silicon and oxygen and rather weak around the fivefold coordinated aluminium. Thermal soft modes appear above 200°C and are correlated with a weakening of the Al-O bonds.     

Application of infrared spectroscopy to studies of silicate glass structure: Examples from the melilite glasses and the systems Na2O-SiO2 and Na2O-Al2O3-SiO2

Infrared (IR) and Raman spectroscopic methods are important complementary techniques in structural studies of aluminosilicate glasses. Both techniques are sensitive to small-scale (<15 Å) structural features that amount to units of several SiO₄ tetrahedra. Application of IR spectroscopy has, however, been limited by the more complex nature of the IR spectrum compared with the Raman spectrum, particularly at higher frequencies (1200–800 cm^?1) where strong antisymmetric Si-O and Si-O-Si absorptions predominate in the former. At lower frequencies, IR spectra contain bands that have substantial contributions from ‘cage-like’ motions of cations in their oxygen co-ordination polyhedra. In aluminosilicates these bands can provide information on the structural environment of Al that is not obtainable directly from Raman studies. A middle frequency envelope centred near 700 cm^?1 is indicative of network-substituted AlO₄ polyhedra in glasses with Al/(Al+Si)>0·25 and a band at 520–620cm^?1 is shown to be associated with AlO₆ polyhedra in both crystals and glasses. The IR spectra of melilite and melilite-analogue glasses and crystals show various degrees of band localization that correlate with the extent of Al, Si tetrahedral site ordering. An important conclusion is that differences in Al, Si ordering may lead to very different vibrational spectra in crystals and glasses of otherwise gross chemical similarity.     

Interdiffusion of hydrous dacitic and rhyolitic melts and the efficacy of rhyolite contamination of dacitic enclaves

Effective binary diffusion coefficients of Si during the interdiffusion of hydrous, 3 and 6% H₂O, dacitic and rhyolitic melts have been determined at 1.0 GPa, 1100°–1400°C. Water is shown to enhance diffusivities by one to two orders of magnitude above dry Si diffusivities in the same compositional system for SiO₂ compositions 65–75wt%. The effect of silica content on diffusion is small and typically within experimental error. With 3% H₂O in the melts the Arrhenius equation for Si diffusion at 70% SiO₂ is: $${\text{D = }}2.583\operatorname{x} 10^{ - {\text{ }}8} {\text{ }}\exp ( - 126.5/R{\text{T}})$$ where D is the diffusivity in m²/s, the activation energy (126.5) is in kJ/mol, R is in J/mol and T in Kelvin. Although less-well constrained, the Si diffusivity at 70% SiO₂ with 6% H₂O in the melts can be described by: $${\text{D = }}2.692\operatorname{x} 10^{ - {\text{ }}7} {\text{ }}\exp ( - 131.4/R{\text{T}})$$ The activation energies for diffusion are substantially below the activation energy of 236.4kJ/mol measured during anhydrous interdiffusion in the same system (Baker 1990). The decrease in activation energy with the initial addition of 3% water and the relative insensitivity of the activation energy to the additional water is related to the abundance of OH species in the melt, and the reduction of (Si,Al)-O bond strengths due to the interaction of hydroxyls with the (Si,Al)-O network. Changes in the pre-exponential factor of Arrhenius equations are attributed to the abundance of H₂O species in the melts. No decoupling of non-alkalies from SiO₂ during interdiffusion of the two melts was observed, although alkalies diffuse much more rapidly than non-alkalies (but were not measured quantitatively in this study) and can become decoupled. Interdiffusion of Si and all non-alkalies is demonstrated to be predictable, at least to within a factor of ten, by the Eyring equation. Using the diffusion data of this study for nonalkalies and of other studies for alkalies and Sr isotopes the contamination of a host rhyolitic magma by dacitic enclaves, 5 and 50 cm radius, has been modeled for temperatures of 1000°, 900°, and 800° C with water contents of 3 and 6%. Even when the effects of phenocrysts on diffusion in the dacitic enclaves are estimated the results of the modeling demonstrate that significant contamination is possible in the case of small enclaves, and even large enclaves have the potential to affect the composition of their host magma in geologically short times.     

Crystal structures of Ni2SiO4 and Fe2SiO4 as a function of temperature and heating duration

X-ray structure refinements of Ni₂SiO₄ and Fe₂SiO₄ spinels have been made as a function of temperature and heating duration by intensity measurements at high temperatures and room pressure. The lattice parameters of Ni₂SiO₄ spinel linearly increased with temperature up to 1,000° C. However, Fe₂SiO₄ spinel exhibited a nonlinear thermal expansion and was converted to a polycrystalline mixture of spinel and olivine by heating of less than one-hour at 800° C. The ratios between the octahedral and tetrahedral bond lengths D _oct/D _tetr and between the shared and unshared edge distances (O-O)_sh/(O-O)_unsh in Fe₂SiO₄ spinel were both much larger than those in Ni₂SiO₄. These ratios increase with temperature. The Fe₂SiO₄ spinel more readily approached a activation state which facilitated the transition to the olivine structure than the Ni₂SiO₄ spinel. The lattice parameter of Ni₂SiO₄ spinel decreased with heating period at constant temperatures of 700° C and 800° C. The parameter of the quenched sample after heating for 52 h at 700° C was smaller than that of the nonheated sample. The refinements of the site occupancies at each heating duration indicated an increase in the cation deficiency in both tetrahedral and octahedral sites. Electron microprobe analysis, however, proved no significant difference in the chemical compositions between the quenched and nonheated samples. Si and Ni atoms displaced from normally occupied spinel lattice sites are assumed to settle in vacant sites defined by the cubic close packed oxygen sublattice in a manner which preserves the electric neutrality of the bulk crystal.     

The thermodynamics of substances at very high pressures and temperatures and some mineral reactions in the earth's mantle

The thermodynamic properties of 25 substances (elements, compounds, modifications) are calculated on the basis of an extrapolation of their caloric values and compressibilities into the region of pressures up to 2mbar and temperatures up to 4,000K. The extrapolation methods are described. The ratio of molar volumes is used to predict the thermodynamic properties of the high pressure modifications. It is inferred that water vapour and oxides of Mg, Fe, and Si ought to be stable in the entire mantle. In the lower mantle garnet should be more stable than the perovskite-type phase of MgSiO₃ (in presence of Al₂O₃ or Fe₂O₃). ‘Perovskite’ phase plus MgO are more stable here than forsterite, Mg₂SiO₄. Pyrrhotite, FeS, reveals astonishing stability in the entire mantle and in the outer core as well. Carbon dioxide, CO₂, may exist only in the upper mantle, whereas methane, CH₄, remains stable in the entire mantle.