Energy gap and density in SiO2 polymorphs

A relationship between the energy gap (E _G) and density (ρ) for pure SiO₂ polymorphs is derived from atomic weights and first ionization potentials of free silicon and oxygen atoms. Theoretical considerations are based on the Lorentz electron theory of solids. The eigenfrequency v₀ of elementary electron oscillators, in energy units h v₀, is identified with the energy gap of a solid. The numerical relation is expressed as \(E_G = \sqrt {139.24 - 13.8327\rho } \) is in eV. For low-quartz with a density of 2.65 g/cm³ and also for stishovite with a density of 4.28 g/cm³, the energy gap E _G=10.1 eV and 8.9 eV, respectively. From laboratory measurements for low-quartz E _G=10.2 eV. The energy gap-density relation suggests a critical density value of ρ_x ≈ 10.1 g/cm³ for an SiO₂ phase when the energy gap vanishes (E _G=0), which is consistent with estimated densities for a high pressure silica polymorph with the fluorite structure.     

ELF isosurface maps for the Al2SiO5 polymorphs

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.     

Dislocation strain energy in the Al2SiO5 polymorphs

Molar elastic strain energy arising from dislocations in andalusite and sillimanite were calculated using equations derived from a non-core, linear elasticity model. For perfect (unit) c screw dislocations in these polymorphs, minimum dislocation densities of about 10¹⁰/cm² are necessary to significantly perturb the andalusite=sillimanite equilibrium boundary in P-T space. Compared to unit c dislocations, smaller energy perturbations arise from dissociated c screw dislocations, which are commonly observed in kyanite and sillimanite. A low computed value of stacking fault energy (～30 ergs/cm²) in these polymorphs is compatible with the large separations of dissociated dislocations in these phases. Dislocation densities in naturally occurring Al₂SiO₅ polymorphs are typically <10⁸/cm². Assuming that these densities are representative of those existing during metamorphism, as is supported by the lack of microtextures indicative of strong recovery, it is concluded that molar strain energies corresponding to observed dislocation densities (<10⁸/cm²) result in insignificant perturbation of P-T phase equilibrium boundaries of the Al₂SiO₅ polymorphs.     

Elasticity of the olivine and spinel polymorphs of Ni2SiO4

The single-crystal elastic moduli, c _ij x, of the olivine (α) and spinel (γ) polymorphs of nickel orthosilicate have been measured at atmospheric pressure and 20° C by Brillouin spectroscopy. The results are (Mbar), Ni₂SiO₄ olivine: c ₁₁=3.40(2), c ₂₂=2.38(2), c ₃₃=2.53(2), c ₄₄=0.71(1), c ₅₅=0.87(1), c ₆₆=0.78(1), c ₁₂=1.09(2), c ₁₃=1.10(4), c ₂₃=1.13(3), Ni₂SiO₄ spinel: c ₁₁=3.66(3), c ₄₄=1.06(1), c ₁₂=1.55(3). In comparing these results with extant elasticity data for olivine- and spinel-type compounds we find distinctive elastic characteristics related to crystal structure, and systematic trends due only to compositional variation. For silicate olivines, the longitudinal moduli decrease in the order c ₁₁>c ₃₃>c ₂₂, regardless of composition. The moduli c ₅₅ and c ₆₆ are approximately equal, and greater than c ₄₄. The former relationship is related to differences in polyhedral linkages along the crystallographic axes, whereas the latter may result from rotational freedom of SiO₄ tetrahedra in response to different directions of shear. Composition affects elasticity most directly through the relative magnitudes of \(\bar c_{12} > \; = (c_{12} + c_{13} + c_{23} )/3\) and \(\bar c_{44} = (c_{44} + c_{55} + c_{66} )/3\) . When transition-metal cations are six-coordinated by oxygen \(\bar c_{12} > \bar c_{44}\) , and when alkaline-earth cations are six-coordinated \(\bar c_{44} > \bar c_{12}\) . The longitudinal moduli along and normal to the close-packed directions of spinels are similar, reflecting the framework-like arrangement of octahedra. These longitudinal moduli exhibit little compositional dependence upon tetrahedral cations but vary dramatically with octahedral substitution. Our data indicate that tetrahedral cations affect elastic properties more as the oxygen positional parameter, u, decreases. The u parameter is also directly related to elastic anisotropy. While γ-Ni₂SiO₄ (u=0.244) is elastically isotropic, anisotropy increases rapidly as u approaches a limiting value near 0.27, and may be related to mechanical stability of the spinel structure. The longitudinal wave velocities along close-packed directions in α and γ Ni₂SiO₄ are equal. Thus, for an α-γ polymorphic pair, the assumptions of elastic isotropy of the γ phase and equal velocities in close-packed directions of α and γ allows the c _ij's and shear modulus of a spinel-structure silicate to be estimated from c ₁₁ of the corresponding α phase and the bulk modulus of the γ phase.     

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.     

On the Relationship between Refractive Index and Density for SiO2-polymorphs

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).     

GeO2 vs SiO2: Glass transitions and thermodynamic properties of polymorphs

Relative-enthalpy measurements have been made on the hexagonal, tetragonal, glass and liquid phases of GeO₂. The glass transition is very sensitive to the impurity content, with a T _g ranging from 980 K for a pure product to 780 K for a Li-doped sample with 0.06 mol % Li. The relative C _p change at T _g of about 5% increases with the impurity content as a result of lower glass transition temperatures. Above 298 K the derived heat capacities are similar for all forms, with slightly higher values for the amorphous phases and two C _p cross-overs at 400 and 1000 K between the hexagonal and tetragonal modifications. For both GeO₂ and SiO₂ the coordination state markedly affects C _p and the entropy below 300 K, where the properties are much lower for the tetragonal than for the hexagonal modifications, i.e., S ₂₉₈ = 39.7 vs 55.3 J/mole K and 27.8 vs 41.4 J/ mole K for GeO₂ and SiO₂, respectively. The high-temperature C _p's of coesite and stishovite are likely similar to those of the low-pressure SiO₂ forms. Finally, these results, low-temperature C _p data and enthalpy-of-solution measurements have been used to derive a consistent set of thermodynamic properties for the GeO₂ modifications.     

Raman spectra of high-pressure polymorphs of SiO2 at various temperatures

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 (δv_i/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.     

Electronic structure and electric field gradient calculations of Al2SiO5 polymorphs

 The electronic structure of the three polymorphs of Al₂SiO₅, andalusite, sillimanite, and kyanite, is studied by linearized-augmented-plane-wave (LAPW) calculations using the WIEN code. Total energy calculations verify, in agreement with recent pseudopotential calculations, that andalusite is the most stable phase, followed by sillimanite and kyanite.We determine the electronic charge density distribution and find strong polarizations on all oxygen ions. We identify different polarizations due to Al or Si neighbors which depend on their respective distances to the oxygen atom. The chemical bonding is not purely ionic in nature but has important covalent contributions. Electric field gradients (EFGs) at all sites are calculated and agree well (within 10%) with available experimental data on Al. We identify the origin of the EFGs and demonstrate its relation to the nearest-neighbor coordination and the resulting anisotropy of the electronic charge distribution. Received: 22 March 2000 / Accepted: 3 August 2000     

Raman spectra from the Al2SiO5 polymorphs at high pressures and room temperature

Raman spectra of the three Al₂SiO₅ polymorphs; andalusite, sillimanite and kyanite were recorded as a function of pressure at room temperature. All the Raman active bands which could be observed from the high-pressure cell showed a linear pressure dependence for each of the three Al₂SiO₅ polymorphs and no phase changes were observed over the pressure ranges used in this study. In andalusite and to a lesser extent in sillimanite, vibrations which could be correlated with internal motions of the SiO₄ tetrahedra were generally well separated from the lattice modes and showed a greater pressure dependence than that observed for other modes. The distinct pressure dependence of the internal SiO₄ modes is less evident in kyanite, probably due to the lack of continuous tetrahedral chains and the fact that the rigid SiO₄ tetrahedra now form an integral part of the structural network. At ambient pressure, kyanite also exhibits two fluorescence bands at 705 and 706.2 nm which are due to small amounts of Cr³⁺ in the kyanite crystals. These fluorescence bands showed a non-linear frequency shift as pressure was increased.     

Influence of high pressure on the refractive index and density of tholeiite basalt glass

The pressure dependence of the refractive index of tholeiite basalt glass was studied in the range 0–5.0 GPa with an interference-polarization microscope and a diamond anvil cell. The non-linear change of the refractive index of basalt glass, with a kink around 2.0–2.5 GPa, is similar to the behaviour of the refractive index, density and elastic properties of silica glass under pressure. The comparison of data for glasses with continuous silicon-oxygen frameworks shows that the strain-polarizability potential Λ (photoelasticity theory), describing the change of refraction R with increasing density ρ: (Λ=–ΔR ρ/R₀Δρ) is nearly constant. Using the value Λ=0.21 and the refractive index data, the compressibility of the investigated basalt glass under pressure up to 5.0 GPa was calculated by the equation: Δρ/ρ=6nΔn/(n²–1)(n²+2)(1–Λ). The results of the calculation agree with the compressibility of tholeiite basalt glass determined by measurement of the sizes of glass samples under pressure using photographic equipment. The compressibility of basalt glass is higher than that for plagioclases, resulting in the possibility of relative density inversion of deep-seated basalt melts and plagioclase crystals. These data reinforce the model of anorthositec crust generation on the Earth and on the Moon by inverse plagioclase crystal fractionation at high degrees of melting of basic rocks.     

The SiO2 polymorphs: The equations of state and thermodynamic properties of phase transformations

Thermal equations of state have been derived for polymorphic forms of SiO₂ and values of \(\mathop \smallint \limits_0^P\) V _T dP have been tabulated. Available experimental data on the phase equilibria at high pressures and temperatures have been used with these equations to calculate the standard thermodynamic functions for the α-quartz-coesite and coesite-stishovite transformations. A study of sensitivity of calculated thermodynamical properties to uncertainties of phase equilibria data, initial data for elastic constants and equations of state has been carried out. The discrepancies between standard thermodynamic properties of these transformations calculated from phase equilibria data and solution calorimetry data still persist.     

Distinction between six- and fourfold coordinated silicon in SiO2 polymorphs via electron loss near edge structure (ELNES) spectroscopy

Si K-, L- and O K-edge ELNES spectra of natural α-quartz and synthetic coesite on one side and synthetic stishovite on the other show characteristic differences that can be related, by comparison with multiple-scattering (MS) calculations, to the fourfold vs. sixfold coordination of Si in these polymorphs of SiO₂. It is shown by MS calculations on large clusters that the outer shells contribute relatively little to the overall topologies of the spectra. Therefore, distinction between fourfold- and sixfold-coordinated Si is possible even on a nm scale and probably also in amorphous substances.     

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.     

Pseudopotential periodic Hartree-Fock study of Mg2SiO4 polymorphs: Olivine,modified spinel and spinel

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.     

遥感异常与地球化学指标间的映射关系模型探索

采用改进的遥感异常提取方法,以甘肃金川地区的LandSat 8遥感影像数据为基础,结合主成份分析方法及低通滤波后期处理,得到空间规律性较强的烃基及铁染异常;进而对测区的土壤地球化学取样分析数据,利用统计学方法寻找不同元素异常(或地球化学指标)的内在关联,并建立土壤地球化学指标比值与遥感异常之间的关系模型.继续构建出基于...     

黄土的湿陷性与击实试验指标关系研究

进行了黄土的击实试验,提出了击实率的概念,拓展了CART(classification and regression trees)决策树算法的功能。将其用于相关性挖掘,进行了原状黄土湿陷性与击实率等指标的相关性挖掘,结果表明,击实率与湿陷系数具有相关性,击实率与最优含水率状态的击实率呈显著负相关性。根据试验及分析结果提出黄土在击实过程中的变形特性可反映黄土的湿陷性,黄土的击实效果同其湿陷性具相关性。这一研究为黄土湿陷性的评价提出了一条新的思路,同时成果具有实用性。     

Interaction between fluorine and silica in quenched melts on the joins SiO2-AlF3 and SiO2-NaF determined by raman spectroscopy

The solubility mechanism of fluorine in quenched SiO₂-NaF and SiO₂-AlF₃ melts has been determined with Raman spectroscopy. In the fluorine abundance range of F/(F+Si) from 0.15 to 0.5, a portion of the fluorine is exchanged with bridging oxygen in the silicate network to form Si-F bonds. In individual SiO₄-tetrahedra, one oxygen per silicon is replaced in this manner to form fluorine-bearing silicate complexes in the melt. The proportion of these complexes is nearly linearly correlated with bulk melt F/(F+Si) in the system SiO₂-AlF₃, but its abundance increases at a lower rate and nonlinearly with increasing F/(F+Si) in the system SiO₂-NaF. The process results in the formation ofnonbridging oxygen (NBO), resulting in stabilization of Si₂O ₅ ^2? units as well as metal (Na⁺ or Al³⁺) fluoride complexes in the melts. Sodium fluoride complexes are significantly more stable than those of aluminum fluoride.