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).     

Decomposition of fayalite (Fe2SiO4) in an oxygen potential gradient at 1,418 K

The decomposition of fayalite (Fe₂SiO₄) in oxygen potential gradients is studied at T=1,418 K. The compound will be decomposed into its component oxides wüstite, Fe_1?δO, and silica, SiO₂, by the simultaneous action of two different oxygen partial pressures, exceeding a critical ratio, despite the fact that fayalite is stable at both the lower and the higher oxygen potential. A quantitative analysis of the decomposition process caused by defect fluxes within the bulk Fe₂SiO₄ is given.     

Electrical conductivity measurements on olivines and pyroxenes under defined thermodynamic activities as a function of temperature and pressure

Electrical conductivities of Ni₂SiO₄, Fe₂SiO₄, and MgSiO₃ were measured on synthetic powders in the temperature range 340° to 1,100° C and at pressures up to 20 kbars. For ternary compounds such as olivines and pyroxenes the control of two further variables, like the chemical activities of two components are needed, besides temperature and pressure. The activities of the corresponding binary oxides were controlled by equilibrating the samples with their neighbour-phases. Control of the oxygen partial pressure was achieved by buffer techniques. From the slopes of the lg σ vs. 1/T lines the activation energies were calculated for 10 kbar: 0.56 eV and 2.7 eV for Ni₂SiO₄ in equilibrium with SiO₂ and Ni/NiO-buffer for the temperature range 500°–800°C and 800°–1,000°C resp. 0.52 eV for Fe₂SiO₄ in equilibrium with SiO₂ and metallic iron, and 0.38 eV in equilibrium with SiO₂ and magnetite; 1.11 eV for MgSiO₃ in equilibrium with SiO₂, and 1.25 eV in equilibrium with Mg₂SiO₄.     

Infrared vibrational spectra of Beta-Phase Mg2SiO4 and Co2SiO4 to Pressures of 27 GPa

Infrared absorption spectra of the high-pressure polymorphs β-Mg₂SiO₄ and β-Co₂SiO₄ have been measured between 0 and 27 GPa at room temperature. Grüneisen parameters determined for 11 modes of β-Mg₂SiO₄ (frequencies of 300 to 1,050 cm^?1) and 5 modes of β-Co₂SiO₄ (490 to 1,050 cm^?1) range between 0.8 and 1.9. Averaging the mid-infrared spectroscopic data for β-Mg₂SiO₄ yields an average Grüneisen parameter of 1.3 (±0.1), in good agreement with the high-temperature thermodynamic value of 1.35. Similarly, we find a value of 1.05 (±0.2) for the average spectroscopic Grüneisen parameter of β-Co₂SiO₄.     

Synthetic Mn3+-kyanite and viridine, (Al2-xMn x 3+ ) SiO5, in the system Al2O3-MnO-MnO2-SiO2

Experiments on the join Al₂SiO₅-“Mn₂SiO₅” of the system Al₂O₃-SiO₂-MnO-MnO₂ in the pressure/temperature range 10–20 kb/900–1050° C with gem quality andalusite, Mn₂O₃, and high purity SiO₂ as starting materials and using /_O2-buffer techniques to preserve the Mn³⁺ oxidation state had following results: At 20 kb/1000°C orange-yellow kyanite mixed crystals are formed. The kyanite solid solubility is limited at about (Al_1.88Mn _0.12 ³⁺ )SiO₅ and, thus, equals approximately that on the join Al₂SiO₅-“Fe₂SiO₅” (Langer and Frentrup, 1973) indicating that there is no Jahn-Teller stabilisation of Mn³⁺ in the kyanite matrix. 5 mole % substitution causes the kyanite lattice constants a _o, b _o, c _o, and V _o to increase by 0.015, 0.009, 0.014 Å, and 1.6 ų, resp., while α, β, γ, remain unchanged. Between 10 and 18 kb/900°C, Mn³⁺-substituted, strongly pleochroitic (emeraldgreen-yellow) andalusite_ss (viridine) was obtained. At 15 kb/900°C, the viridine compositional range is about (Al_1.86Mn _0.14 ³⁺ )SiO₅-(Al_1.56Mn _0,44 ³⁺ )SiO₅. Thus, Al→Mn³⁺ substitutional degrees are appreciably higher in andalusite than in kyanite, proving a strong Jahn-Teller effect of Mn³⁺ in the andalusite structure, which stabilises this structure type at the expense of kyanite and sillimanite and, thus, enlarges its PT-stability range extremely. 17 mole % substitution cause the andalusite constants a _o, b _o, c _o, and V _o to increase by 0.118, 0.029, 0.047 Å and 9.4 ų, resp. At “Mn₂SiO₅”-contents smaller than about 7 mole %, viridine coexists with Mn-poor kyanite. At “Mn₂SiO₅”-concentrations higher than the maximum kyanite or viridine miscibility, braunite (tetragonal, ideal formula Mn²⁺Mn³⁺[O₈/Si0₄]), pyrolusite and SiO₂ were found to coexist with the Mn³⁺-saturated ky _ss or and _ss, respectively. In both cases, braunites were Al-substituted (about 1 Al for 1 Mn³⁺). Pure synthetic braunites had the lattice constants a _o 9.425, c _o, 18.700 Å, V _o 1661.1 ų (ideal compn.) and a _o 9.374, c _o 18.593 ų, V _o 1633.6 ų (1 Al for 1 Mn³⁺). Stable coexistence of the Mn²⁺-bearing phase braunite with the Mn⁴⁺-bearing phase pyrolusite was proved by runs in the limiting system MnO-MnO₂-SiO₂.     

The lattice energy of forsterite. Charge distribution and formation enthalpy of the SiO 4 4− ion

In the lattice energy expression of forsterite, based on a Born-Mayer (electrostatic+repulsive+dispersive) potential, the oxygen charge z _o, the hardness parameter ρ and the repulsive radii r _Mg and r _Si appear as unknown parameters. These were determined by calculating the first and second partial derivatives of the energy with respect to the cell edges, and equalizing them to quantities related to the crystal elastic constants; the overdetermined system of equations was solved numerically, minimizing the root-mean-square deviation. To test the results obtained, the SiO ₄ ^4? ion was assumed to move in the unit-cell, and the least-energy configuration was sought and compared with the experimental one. By combining the two methods, the optimum set of parameters was: z _o=?1.34, ρ=0.27 Å, r _Mg=0.72 Å, r _Si=0.64 Å. The values ?8565.12 and ?8927.28 kJ mol^?1 were obtained, respectively, for the lattice energy E _Land for its ionic component E _L ⁰ ,which accounts for interactions between Mg²⁺ and SiO ₄ ^4? ions only. The charge distribution calculated on the SiO ₄ ^4? ion was discussed and compared with other results. Using appropriate thermochemical cycles, the formation enthalpy and the binding energy of SiO ₄ ^4? were estimated to be: ΔH _f(SiO ₄ ^4? )=2117.6 and E(SiO ₄ ^4? )=708.6 kJ mol^?1, respectively.     

Infrared spectra of olivine polymorphs: α, β phase and spinel

Infrared (IR) absorption spectra are presented for olivine (α) and spinel (γ) phases of A₂SiO₄ (A=Fe, Ni, Co) and Mg₂GeO₄. IR spectra of β phase (“modified spinel”) Co₂SiO₄ and of α Mg₂SiO₄ are also included. These results provide reference spectra for the identification of olivine high-pressure polymorphs. Isostructural and isochemical correlations are used to support a general interpretation of the spectra and to predict the spectrum of γ Mg₂SiO₄. A γ Mg₂GeO₄ sample equilibrated at 1,000° C shows evidence of partial inversion, but one equilibrated at 730° C does not. This suggests that partial inversion could occur in silicate spinels at elevated temperatures and pressures, however no evidence of inversion is seen in the ir spectra of the silicates in this study.     

The effect of crystal field stabilization on the olivine→spinel transition in the system Mg2SiO4 - Fe2SiO4

Crystal field stabilization (CFS) plays a significant role in determining equilibrium phase boundaries in olivine→spinel transformations involving transition-metal cations, including Fe²⁺ which is a major constituent of the upper mantle. Previous calculations for Fe₂SiO₄ ignored pressure and temperature dependencies of crystal field stabilization enthalpies (CFSE) and the electronic configurational entropy (S _CFS). We have calculated free energy changes (ΔG _CFS) due to differences of crystal field splittings between Fe₂SiO₄ spinel and fayalite from: ΔG _CFS=?ΔCFSE?TΔS _CFS, as functions of P and T, for different energy splittings of t _2g orbital levels of Fe²⁺ in spinel. The results indicate that ΔG _CFS is always negative, suggesting that CFS always promotes the olivine→spinel transition in Fe₂SiO₄, and expands the stability field of spinel at the expense of olivine. Because of crystal field effects, transition pressures for olivine→spinel transformations in compositions (Mg_1?x Fe _x )₂SiO₄ are lowered by approximately 50x kbar, which is equivalent to having raised the olivine→spinel boundary in the upper mantle by about 15 km.     

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.     

Factors effecting the stability field of Ca-poor pyroxene and the origin of the Ca-poor minimum in Ca-rich pyroxenes from tholeiitic intrusions

Ca-poor pyroxene ceases to crystallise towards the end of fractionation in tholeiitic intrusions and is usually replaced by Fe-rich olivine. Using the data of Nicholls et al. (1971), the \(a_{{\text{SiO}}_2 }\) at which olivine and pyroxene can coexist has been calculated at different temperatures and pressures. From these calculations it is clear that the Fe/Mg ratio of the last Ca-poor pyroxene to crystallise from a melt is increased by raising the temperature or pressure of crystallisation. The Ca-poor pyroxene-Fe-rich olivine relationship is also dependent on the \(a_{{\text{SiO}}_2 }\) of the melt. In magmas which crystallise Fe-rich olivine before quartz, inicreasing their \(a_{{\text{SiO}}_2 }\) will raise the Fe/Mg ratio of the last Ca-poor pyroxene to crystallise. If the \(a_{{\text{SiO}}_2 }\) of the magma is so high that SiO₂ saturation is reached before the appearance of cumulus Fe-rich olivine, any further increase in the \(a_{{\text{SiO}}_2 }\) of the melt will not influence the stability field of Ca-poor pyroxene. The replacement of Ca-poor pyroxene by Fe-rich olivine requires the magma to reach a high level of a _FeO late in its fractionation. If a magma fractionates with an FeO depletion trend, Ca-poor pyroxene is replaced by Ca-rich pyroxene. The reaction is initiated by the appearance of cumulus K-feldspar which results in a marked reduction in the amount of anorthite crystallising from the magma. This increases the a _CaO of the melt so that Ca-poor pyroxene is replaced by Ca-rich pyroxene.     

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.     

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.     

Study of pocyclic aromatic hydrocarbons at a pressure of 6–9 GPa with X-ray diffraction and synchrotron radiation

This work is one of the stages of study of the deep C-O-H fluid and investigates the behavior of polycyclic aromatic hydrocarbons (PAHs) under conditions of the Earth’s mantle. The composition of the C-O-H fluid in the upper mantle is estimated as a mixture of H₂O and CH₄ with a minor amount of H₂ and heavier hydrocarbons. Some theoretical calculations show that the stability of heavy hydrocarbons (alkanes, alkenes, and PAHs) increases with an increase in temperature. This paper presents the results of an XRD study of PAHs stability in multianvil presses on a Spring-8 accelerator (Japan). The primary compositions were chosen according to the abundance of PAHs in nature. In situ diffraction spectrums were recorded to determine the PAHs stability field. It was established that the PAHs become unstable at a pressure of 6–9 GPa and a temperature of 873–1073 K.     

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.     

Exoelectron spectroscopy of traps in surface layers of phenakite and quartz

The possibilities of exoelectron spectroscopy to investigate defects in dielectrics are demonstrated for phenakite Be₂SiO₄, its structural analogs Zn₂ SiO₄, Be₂GeO₄, solid solutions Be₂Si_1?x Ge _x O₄ (x=0÷1) and α-quartz. Emission maxima at 330 and 670 K in phenakite have been found to be due to [GeO₄]^5? andE' centers, respectively. Structural disturbances in the silicon and oxygen positions have been shown to control the exoemission activity of the crystals. Radiation induced decrease of exoemission activity connected with generation ofE' centers by neutron irradiation has been discovered. The energy level scheme of active centers in the subsurface region of Be₂SiO₄ has been established.     

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.     

Thermodynamic properties of the forsterite-fayalite (Mg2SiO4-Fe2SiO4) solid solution. determination of heat of formation

A high temperature calorimetric solution method involving the use of a sodium and lithium metaborate (NaBO₂+LiBO₂) molten bath at 1,180 K, has been developed in order to measure the enthalpy of formation of the forsterite-fayalite (Mg₂SiO₄-Fe₂SiO₄) system. The samples used for these measurements have been obtained by synthesis. They have been carefully controlled by chemical and X-ray analysis and Mössbauer spectroscopy. The results obtained for forsterite and fayalite agree closely with the data commonly found in the literature. Owing to the uncertainty of the experimental results, it is not possible to determine conclusively whether an enthalpy of mixing exists in this system.     

Charge distribution from least-energy structure in Ca - Mg orthosilicates

Calcium-olivine, γ-Ca₂SiO₄, larnite, β-Ca₂SiO₄, merwinite, Ca₃Mg(SiO₄)₂, and monticellite, CaMgSiO₄, are considered. According to a rigid oxyanion scheme, eulerian orientation angles of the SiO₄ tetrahedra and translation coordinates of Ca and Si atoms are specified as structural variables τk. All derivatives of the static energy (Born model) contain atomic charges and repulsive parameters as unknowns; the minimum energy conditions ?E _L/?τ_k=0 yield 34 equations which are solved by a least-squares method. The set of energy parameters fitting structural properties of all four phases together is: z _Ca=1.50, z _o=?1.10 e, r _Ca=1.05, ρ=0.25 Å; the Mg charge was fixed at 1.38 e, from a previous study on forsterite. An average shift of 0.04 Å is observed between experimental and least-energy calculated atomic positions. Results are compared with those of Mg₂SiO₄, where the fit was based both on thermoelastic and on structural properties. If no charge values were fixed “a priori”, just ratios between charges could be determined by fitting them to structural data only.     

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.