Thermal expansion of fayalite,Fe2SiO4

Thermal expansion of single-crystal fayalite has been measured by a dilatometric method at temperatures between 25 °C and 850 °C. The results show the presence of anomalous expansion in the b axis, which is correlated to the anomalous variation of elastic moduli with temperature. Grüneisen's parameter is 1.10 and the thermal Debye temperature is 565 K, which is close to the acoustic Debye temperature of 511 K.     

Single-crystal infrared reflectivity of pure Mg2SiO2 forsterite and (Mg0.86,Fe0.14)2SiO4 olivine

New polarized infrared reflectance spectra of pure synthetic forsterite and natural Fo₈₆-olivine have been recorded from 5000 to 100cm^-1. Out of the 35 expected infrared active modes, 33 have been observed (8 B_1u, 12 B_2u, 13 B_3u). The observed frequency shift from pure forsterite to Fo₈₆-olivine is consistent with the higher mass of the substituted iron. The substitution of only 14% of iron also reduces the overal far-infrared reflectivity of olivine as compared to pure forsterite. Several discrepancies associated with previous studies of forsterite are explained by our investigation. We suggest that some of the previous investigations were complicated by polarization mixing.     

Electric field gradient calculation in forsterite,Mg2SiO4

The electric field gradient (EFG) in Mg₂SiO₄ is calculated on the basis of the extended point ion model, including the local term of the overlap contribution. The agreement with experimental data deduced from the quadrupole coupling constants and principal axes at the Mg sites is quite good. The results of the present calculation exhibit a small overlap contribution to the EFG at M1 and a clearly bigger one at M2, whereas the lattice contribution to the EFG at M1 and M2 is reversed. The distinct overlap effects are assumed to be due to the particular Mg₂SiO₄ crystal structure and the different point symmetry at M1 and M2. The oxygen polarizability and charge used to calculate the EFG tensor were found to be smaller than the theoretical polarizability and formal charge, respectively. The sign of the Mg quadrupole coupling constants at M1 and M2, which has not been determined experimentally, results from the EFG calculation as positive.     

Oxidation kinetics of fayalite (Fe2SiO4)

Single crystals of fayalite (Fe₂SiO₄) have been oxidized either in the hematite or the magnetite stability field to investigate the kinetics and mechanisms of oxidation. For samples heated in air at 770° C, a two-phase region composed of fine-grained iron oxide and silica phases formed as the reaction front moved into the sample, and an iron oxide layer formed external to this two-phase region. The presence of the single-phase oxide layer coating the specimens indicates that oxidation occurs by the migration of iron from the fayalite to the gas-solid interface rather than by the movement of oxygen in the opposite direction. For oxidation in air, the kinetics followed a parabolic growth law, with the rate of oxidation limited by the diffusion of iron from the internal reaction front to the gas-solid interface through the iron oxide. When fayalite was oxidized in the magnetite stability field, using a CO/CO₂ gas mixture at 1030° C, oxidation was controlled by the reaction at the gas-solid interface, yielding an oxidation rate considerably slower than that predicted for diffusion-controlled growth of the oxide layer.     

Polarized optical absorption spectra of synthetic chromium doped Mg2SiO4 (forsterite)

Polarized optical absorption measurements were carried out on three single crystals of Mg₂SiO₄ (forsterite), differently doped with Cr. Two crystals containing average 0.013 and 0.027 weight% Cr, respectively, were pulled from the melt in air, whereas one crystal containing average 0.08 weight% Cr was pulled from the melt in an argon atmosphere. The absorption spectra of the three crystals agree with each other although the intensity of single absorption bands varies significantly. In all -polarized patterns a sharp absorption line around 18000cm^-1 (550 nm) appears. Conjectures are presented to assign this line to the lasing center in Cr doped forsterite which very likely exists as Cr⁴⁺ at the fourfold coordinated Si site.     

The pressure and temperature dependence of the elastic properties of single-crystal fayalite Fe2SiO4

The nine adiabatic elastic stiffness constants of synthetic single-crystal fayalite, Fe₂SiO₄, were measured as functions of pressure (range, 0 to 1.0 GPa) and temperature (range, 0 to 40° C) using the pulse superposition ultrasonic method. Summary calculated results for a dense fayalite polycrystalline aggregate, based on the HS average of our single-crystal data, are as follows: V_p = 6.67 km/s; V_s = 3.39km/s; K= 127.9 GPa; μ = 50.3 GPa; (?K/?P)_T = 5.2; (?μ/?P)_T=1.5;(?K/?T)_P= ?0.030 GPa/K;and,(?/?T)_P =-0.013 GPa/K (the pressure and temperature data are referred to 25° C and 1 atm, respectively). Accuracy of the single-crystal results was maintained by numerous cross and redundancy checks. Compared to the single-crystal elastic properties of forsterite, Mg₂SiO₄, the fayalite stiffness constants, as well as their pressure derivatives, are lower for each of the on-diagonal (C _ij for which i=j) values, and generally higher for the off-diagonal (C _ij for which i≠j) data. As a result, the bulk moduli (K) and dK/dP for forsterite and fayalite are very similar, but the rigidity modulus (μ) and dμ/dP for polycrystalline fayalite are much lower than their forsterite counterparts. The bulk compression properties derived from this study are very consistent with the static-compression x-ray results of Yagi et al. (1975). The temperature dependence of the bulk modulus of fayalite is somewhat greater (in a negative sense) than that of forsterite. The rigidity dependencies are almost equivalent. Over the temperature range relevant to this study, the elastic property results are generally consistent with the data of Sumino (1978), which were obtained using the RPR technique. However, some of the compressional modes are clearly discrepant. The elastic constants of fayalite appear to be less consistent with a theoretical HCP model (Leibfried 1955) than forsterite, reflecting the more covalent character of the Fe-O bonding in the former.     

Electron spin resonance of trivalent chromium in forsterite,Mg2SiO4

The electron spin resonance (ESR) spectrum of Cr³⁺ in a synthetic single crystal of forsterite doped with Cr₂O₃ was studied at room temperature in the X-band frequency range. The dependence of the observed spectra on the crystal orientation with respect to the applied magnetic field was investigated. The ESR spectra are described by the spin Hamiltonian \(H = \beta HgS + D(S_Z^{\text{2}} - {\text{1/3}}S{\text{(}}S{\text{ + 1)) + }}E{\text{(}}S_x^{\text{2}} - S_y^{\text{2}} {\text{)}}\) with S=3/2. The spin resonance reveals that the chromium ions are located at both the M1 and M2 positions. Other possible substitutional or interstitial Cr³⁺ positions may be possible, but were not observed. The site occupancy numbers of Cr³⁺ at M1 and M2 are roughly 1.2×10^?4 and 0.8×10^?4, respectively, assuming that chromium is oxidized completely. The preference of the chromium ions for M1 was interpreted qualitatively in terms of crystal field criteria. The rhombic and axial spin Hamiltonian parameters, D and E, and the directions of the magnetic axes obtained for M1 and M2 are consistent with the respective oxygen coordination polyhedra.     

First principles simulations of the stability and structure of grain boundaries in Mg2SiO4 forsterite

Our understanding of how grain boundaries (GBs) can dramatically influence key mineral properties such as creep and diffusion depends on knowledge of their detailed atomic and electronic structures. For this purpose, we simulate different types of tilt GBs, (0l1)/[100], (1l0)/[001] and (012)/[100] modeled with stepped and non-stepped surfaces in Mg₂SiO₄ forsterite using a first-principles approach based on density functional theory. Our results suggest that several configurations arising from Mg-terminated planes with tilt angles ranging from 16° to 67° are energetically competitive over the entire pressure regime (0–17 GPa) studied. At the ambient pressure, the predicted important features of the boundaries include distorted bonds (Si–O and Mg–O distances changed by 1 and 4 %, respectively), coordination defects (four and fivefold Mg–O coordination), and void spaces (0.2–0.9 × 10^?10 m³/m²). Also, the interface induces splitting of electronic states from the conduction band and kinks at the top of the valence band. These structural and electronic features continue to exist at higher pressures. The formation enthalpy and excess volume for each boundary configuration studied were shown to systematically increase and decrease, respectively, with pressure. The predicted energy range (0.8–1.7 J/m² at zero pressure) widens by a factor of two at 17 GPa (1.1–2.8 J/m²). The presence of low-density and structurally distorted regions imply that these GBs can serve as primary impurity segregation sites, fast diffusion pathways, and electron-trapped regions, which all are relevant for mantle rheology.     

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.     

Elastic properties of a single-crystal forsterite Mg2SiO4, up to 1,200 K

Elastic moduli of forsterite were measured between 300 and 1,200 K (? 1.6 times the Debye temperature) by the Rectangular Parallelepiped Resonance method. All the moduli decrease regularly with temperature. A summary of the results is as follows:

Iron local structure in tektites and impact glasses by extended X-ray absorption fine structure and high-resolution X-ray absorption near-edge structure spectroscopy

The local structure of iron in three tektites has been studied by means of Fe K-edge extended X-ray absorption fine structure (EXAFS) and high-resolution X-ray absorption near-edge structure (XANES) spectroscopy in order to provide quantitative data on <Fe-O> distance and Fe coordination number. The samples studied are a moldavite and two australasian tektites. Fe model compounds with known Fe oxidation state and coordination number were used as standards in order to extract structural information from the XANES pre-edge peak. EXAFS-derived grand mean <Fe-O> distances and Fe coordination numbers for the three tektite samples are constant within the estimated error (<Fe-O > =2.00 Å ± 0.02 Å, CN = 4.0 ± 0.4). In contrast to other data from the literature on Fe-bearing silicate glasses, the tektites spectra could not be fitted with a single Fe-O distance, but rather were fit with two independent distances (2 × 1.92 Å and 2 × 2.08 Å). High-resolution XANES spectra of the three tektites display a pre-edge peak whose intensity is intermediate between those of staurolite and grandidierite, thus suggesting a mean coordination number intermediate between 4 and 5. Combining the EXAFS and XANES data for Fe, we infer the mean coordination number to be close to 4.5.Comparison of the tektites XANES spectra with those of a suite of different impact glasses clearly shows that tektites display a relatively narrow range of Fe oxidation state and coordination numbers, whereas impact glasses data span a much wider range of Fe oxidation states (from divalent to trivalent) and coordination numbers (from tetra-coordinated to esa-coordinated). These data suggest that the tektite production process is very similar for all the known strewn fields, whereas impact glasses can experience a wide variety of different temperature-pressure-oxygen fugacity conditions, leading to different Fe local structure in the resulting glasses. These data could be of aid in discriminating between tektite-like impact glasses and impact glasses sensu strictu.     

Electron density distribution and bond critical point properties for forsterite, Mg2 SiO4, determined with synchrotron single crystal X-ray diffraction data

A generalized X-ray scattering factor model experimental electron density distribution has been generated for the orthosilicate forsterite, using an essentially extinction and absorption free set of single crystal diffraction data recorded with intense, high energy synchrotron X-ray radiation (E=100.6 keV). A refinement of the model converged with an R(F)=0.0061. An evaluation of the bond critical point, bcp, properties of the distribution at the (3, –1) stationary points for the SiO and MgO bonded interactions, yielded values that agree typically within ~5%, on average, with theoretical values generated with quantum chemical computational strategies, using relatively robust basis sets. On the basis of this result, the modeling of the experimental distribution is considered to be adequate. As the bcp properties increase in magnitude, the MgO and SiO bonds decrease in length as calculated for a number of rock forming silicates. As asserted by Coppens (X-ray charge densities and chemical bonding. Oxford University Press, Oxford, 1997), large negative ²(r_c) values, characteristic of shared interactions involving first row atoms, may not be characteristic of closed shell covalent bonded interactions involving second row Si, P and S atoms bonded to O. This study adds new evidence to the overall relatively good agreement between theoretical bcp properties generated with computational quantum strategies, on the one hand, and experimental properties generated with single crystal high energy synchrotron diffraction data on the other. The similarity of results not only provides a basis for using computational strategies for studying and modeling structures, defects and the reactivity of representative structures, but it also provides a basis for improving our understanding of the crystal chemistry of earth materials and the character of the SiO bonded interaction.     

Back transformation and oxidation of (Mg,Fe)2SiO4 spinels at high temperatures

Based on the in situ and temperature-quench X-ray measurements, the back transformation in the (Mg, Fe)₂SiO₄-spinels has been characterized in terms of the transformation temperature (T _r ),mechanism and kinetics of the transformation, and of the end product(s), with specific emphasis on the effect of oxygen on this transformation. The in situ measurements were conducted to 900° C in vacuum (10^-4 to 10^-5 torr) and to 600° C in air using synchrotron radiation (SR) at Stanford Synchrotron Radiation Laboratory (SSRL). In the quench-type measurements, samples were heated in air to 1100° C, quenched and examined at ambient conditions using the conventional X-ray diffraction facilities. Important results are (1) in vacuum, all the spinels convert back into the olivine phase, with their T _r decreasing with increasing iron content; (2) the spinel olivine back transformation is a nucleation and growth type of transformation and can be described quantitatively using the Avrami equation; (3) in air, the (Mg, Fe)₂SiO₄-spinels with 0.2 mole fraction Fe or more are all oxidized, and the composition and phase of the end products depend upon the temperature and the starting composition; and (4) the oxidation of the iron-rich (Mg, Fe)₂SiO₄-spinels in air occurs at 350–400° C, which is significantly lower than its T _r ( 300° C) in vacuum.     

Atomic structures and energies of grain boundaries in Mg2SiO4 forsterite from atomistic modeling

Grain boundaries influence many physical and chemical properties of crystalline materials. Here, we perform molecular dynamics simulations to study the structure of a series of [100] symmetric tilt grain boundaries in Mg₂SiO₄ forsterite. The present results show that grain boundary energies depend significantly on misorientation angle. For small misorientation angles (up to 22°), grain boundary structures consist of an array of partial edge dislocations with Burgers vector $\frac{1}{2}[001]$ associated with stacking faults and their energies can be readily fit with a model which adds the Peach-Koehler equation to the Read-Shockley dislocation model for grain boundaries. The core radius of partial dislocations and the spacing between the partials derived from grain boundary energies show that the transition from low- to high-angle grain boundaries occurs for a misorientation angle between 22° and 32°. For high misorientation angles (32.1° and 60.8°), the cores of dislocations overlap and form repeated structural units. Finally, we use a low energy atomic configuration obtained by molecular dynamics for the misorientation of 12.18° as input to simulate a high-resolution transmission electron microscopy (HRTEM) image. The simulated image is in good agreement with an observed HRTEM image, which indicates the power of the present approach to predict realistic atomic structures of grain boundaries in complex silicates.     

Modelling of structural and elastic changes of forsterite (Mg2SiO4) under stress

The method of crystal static deformation, including inner strain effects, was applied to calculate the structure configuration and the elastic constants of forsterite under anisotropic and isotropic pressure. A Born type interatomic potential is used, with optimized atomic charges and repulsive radii; SiO₄ tetrahedra are approximated as rigid units. Computations were carried out in the range 1–8 GPa, with steps of 1 GPa, for the three uniaxial stresses τ₁, τ₂, τ₃ and for pressure p. By interpolation of results, interatomic distances and elastic tensor components are shown to depend quadratically on stress. A non-linear behaviour generally appears above 4 GPa; the importance of inner strain and non-linear effects is analyzed. Mg-O bond lengths and O-O edges of coordination polyhedra respond differently to anisotropic and to isotropic stresses, according to the topological features of the structure. Elastic and structural results for hydrostatic pressure are compared to experimental literature data, discussing the range of validity of the rigid body approximation for SiO₄ groups.     

Chemical analysis for optimal synthesis of ferrihydrite-modified diatomite using soft X-ray absorption near-edge structure spectroscopy

Effects of process parameters such as concentrations of FeCl₂, NaOH, and drying temperature on the formation mechanism and chemical characteristics of ferrihydrite-modified diatomite are studied by using X-ray absorption near-edge structure spectroscopy. The spectra were recorded in total electron yield mode and/or fluorescence yield mode to investigate the chemical nature of Fe and Si on the surface and/or in the bulk of ferrihydrite-modified diatomite, respectively. It was found that only the surface SiO₂ was partially dissolved in the NaOH solution with stirring and heating, whereas the bulk of diatomite seemed to be preserved. The dissolved Si was incorporated into the structure of ferrihydrite to form the 2-line Si-containing ferrihydrite on the surface of diatomite. The crystalline degree of ferrihydrite increased with the increasing FeCl₂ concentration and the Brunauer–Emmett–Teller specific surface area of ferrihydrite-modified diatomite decreased with the increasing FeCl₂ concentration. The crystalline degree of ferrihydrite decreased with the increase of NaOH concentration. The high temperature calcination caused an energy shift in the Si L-edge spectra to the high energy side and a transformation of Si-containing ferrihydrite to crystallized hematite might occur when ferrihydrite-modified diatomite is calcined at 900°C. In this study, the optimal synthesis conditions for the ferrihydrite-modified diatomite with the least crystalline Si-containing ferrihydrite and the highest surface area were found to be as the follows: 0.5 M FeCl₂ solution, 6 M NaOH solution and drying temperature of 50°C.     

Temperature-dependent magnetic susceptibility behaviour of spinelloid and spinel solid solutions in the systems Fe2SiO4–Fe3O4 and (Fe,Mg)2SiO4–Fe3O4

The magnetic behaviour and Curie temperatures (T _C ) of spinelloids and spinels in the Fe₃O₄–Fe₂SiO₄ and Fe₃O₄–(Mg,Fe)₂SiO₄ systems have been determined from magnetic susceptibility (k) measurements in the temperature range –192 to 700 °C. Spinelloid II is ferrimagnetic at room temperature and the k measurements display a characteristic asymmetric hump before reaching a T _C at 190 °C. Spinelloid V from the Mg-free system is paramagnetic at room temperature and hysteresis loops at various low temperatures indicate a ferri- to superparamagnetic transition before reaching the T _{C .} The T _C shows a non-linear variation with composition between –50 and –183 °C with decreasing magnetite component (X _Fe3O₄). The substitution of Mg in spinelloid V further decreases T _C . Spinelloid III is paramagnetic over nearly the total temperature range. Ferrimagnetic models for spinelloid II and spinelloid V are proposed. The T _C of Fe₃O₄–Fe₂SiO₄ spinel solid solutions gradually decrease with increasing Si content. Spinel is ferrimagnetic at least to a composition of X _Fe3O₄=0.20, constraining a ferrimagnetic to antiferromagnetic transition to occur at a composition of X _Fe3O₄<0.20. A contribution of the studied ferrimagnetic phases for crustal anomalies on the Earth can be excluded because they lose their magnetization at relatively low temperatures. However, their relevance for magnetic anomalies on other planets (Mars?), where these high-pressure Fe-rich minerals could survive their exhumation or were formed by impacts, has to be considered.     

The electric field gradient in synthetic fayalite α-Fe2SiO4 at moderate temperatures

This work reports on the evaluation of the electric field gradient (efg) in synthetic fayalite α-Fe₂SiO₄ using three different procedures: (1) experimental, with single-crystal Mössbauer spectroscopy (SCMBS) on the three principal sections of an α-Fe₂SiO₄ sample for several temperatures in the range 20?°C?≤?T?≤?300?°C; (2) semiquantitative, with the on-line calculation of the efg from three-dimensional difference electron densities, and (3) a fully quantitative method with cluster molecular orbital calculations based on the density functional theory. The experimental efg is in good agreement with our previously published low-temperature data as well as with the results obtained by the fully quantitative approach. In the latter case, large cluster sizes (up to 97 atoms) are necessary to obtain quantitative agreement with experiment. This is also considered as being responsible for the lack of correspondence with the semiquantitative efg on M1. Previously reported symmetry violations on the M2 site are also confirmed by our SCMBS measurements.     

Compression and amorphization of (Mg,Fe)2SiO4 olivines: An X-ray diffraction study up to 70 GPa

The effect of (Mg,Fe) substitution on the compression and pressure-induced amorphization of olivines has been investigated up to more than 50 GPa in a diamond anvil cell through energy-dispersive X-ray diffraction experiments with synchrotron radiation. For the four (Mg_1–x , Fe _x )₂SiO₄ olivines studied, the compressibility is the highest along the b axis and the smallest along the a axis. For compositions with x = 0, 0.17, 0.66, and 1, the slope of the volume-pressure curves shows a rapid decrease at pressures of around 42, 34, 20 and 10 GPa, respectively. Assuming K₀ = 4, we obtained at lower pressures with a Birch-Murnaghan equation of state essentially the same room-pressure bulk modulus for all olivines, namely K ₀ = 131 ± 6 GPa, in agreement with previous single-crystal compression and ultrasonic measurements. At higher pressures, the compression becomes nearly isotropic and the materials very stiff. These changes could precede partial transformation of olivines to a high-pressure polymorph related to the spinel structure. Only a small fraction of olivines seems to transform actually to this phase, however, because most of the material undergoes instead pressure-induced amorphization which take place at considerably higher pressures for Mg-than for Fe-rich olivines.