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.     

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.     

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:

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.     

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.     

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.     

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.     

Theoretical analysis of X-ray absorption near-edge structure in forsterite, Mg2SiO4-Pbnm, and fayalite, Fe2SiO4-Pbnm, at room temperature and extreme conditions

We calculated the forsterite Mg K-edge and the fayalite Fe K-edge X-ray absorption spectra both for the M 1 and M 2 sites and for the overall edge by using the one-electron multiple-scattering theory. The validity of the theoretical model is well illustrated by comparison of calculations with experimental data at the Mg K-edge of MgO (periclase) and at the Mg and Fe K-edges spectra of forsterite and fayalite. Starting from these results at room conditions, we calculated the Mg and Fe K-edges X-ray absorption spectra of forsterite and fayalite at low and high temperatures and at high pressures as well. Variations of fine structures occur mostly in the intermediate multiple scattering (IMS) regions and as a result of the applied pressure. In order to demonstrate the capability of XAS to lead to deeper knowledge of structure relevant to Earth's upper mantle we also attempted calcuating the high-P edge for Fe ²⁺ in low-spin using a different occupation of valence electrons. If a change in spin state really occurs in fayalite, our simple model shows that XAS would evidence it easily even with low resolution.     

The vibrational frequencies of forsterite Mg2SiO4: an all-electron ab initio study with the CRYSTAL code

The vibrational spectrum of Mg₂SiO₄ olivine was calculated at the Γ point by using the periodic ab initio CRYSTAL program. An all electron localized Gaussian-type basis set and the B3LYP Hamiltonian were employed. The full set of frequencies (35 IR active, 36 Raman active, 10 “silent” modes) was computed and compared to experimental data from different sources (four for IR and four for Raman). A generally good agreement is observed with experiment (the mean absolute difference ranging from 7 to 10 cm⁻¹ for the various sets), when some of the experimental frequencies, whose attribution is uncertain or appears to be affected by large errors, are not taken into account. A small number of observed peaks are not consistent with calculated frequencies, and a few theoretical peaks do not correspond to measured values. The implications are discussed in detail. The full set of modes are characterized using different tools, namely isotopic substitution, direct inspection of the eigenvectors and graphical representation, so as to obtain a consistent mode assignment.     

Lattice dynamics and inelastic neutron scattering from forsterite,Mg2SiO4: Phonon dispersion relation,density of states and specific heat

Magnesium-rich olivine (Mg_0.9Fe_0.1)₂SiO₄ is considered to be a major constituent of the Earth's upper mantle. Because of its major geophysical importance, the temperature and pressure dependence of its crystal structure, elastic and dielectric constants, long-wavelength phonon modes and specific heat have been measured using a variety of experimental techniques. Theoretical study of lattice dynamics provides a means of analyzing and understanding a host of such experimental data in a unified manner. A detailed study of the lattice dynamics of forsterite, Mg₂SiO₄, has been made using a crystal potential function consisting of Coulombic and short-range terms. Quasiharmonic lattice dynamical calculations based on a rigid molecular-ion model have provided theoretical estimates of elastic constants, long-wavelength modes, phonon dispersion relation for external modes along the three high symmetry directions in the Brillouin zone, total and partial density of states and inelastic neutron scattering cross-sections. The neutron cross-sections were used as guides for the coherent inelastic neutron scattering experiment on a large single crystal using a triple axis spectrometer in the constant Q mode. The observed and predicted phonon dispersion relation show excellent agreement. The inelastically scattered neutron spectra from a powder sample have been analyzed on the basis of a phonon density of states calculated from a rigid-ion model, which includes both external and internal modes. The experimental data from a powder sample show good agreement with the calculated spectra, which include a multiphonon contribution in the incoherent approximation. The computed phonon densities of states are used to calculate the specific heat as a function of temperature using both the rigid molecular-ion and rigid ion models. These results are in very good agreement with the calorimetric measurement of the specific heat. The interatomic potential developed here can be used with some confidence to study physical properties of forsterite as a function of pressure and temperature.     

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.     

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.     

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.     

Calorimetric study of olivine solid solutions in the system Mg2SiO4-Fe2SiO4

Solution enthalpies of synthetic olivine solid solutions in the system Mg₂SiO₄-Fe₂SiO₄ have been measured in molten 2PbO·B₂O₃ at 979 K. The enthalpy data show that olivine solid solutions have a positive enthalpy of mixing and the deviation from ideality is approximated as symmetric with respect to composition, in contrast to the previous study. Applying the symmetric regular solution model to the present enthalpy data, the interaction parameter of ethalpy (W_H) is estimated to be 5.3±1.7 kJ/mol (one cation site basis). Using this W_h and the published data on excess free energy of mixing, the nonideal parameter of entropy (W_s) of olivine solid solutions is estimated as 0.6±1.5 J/mol·K.     

High pressure phase transformations in the joins Mg2SiO4-Ca2SiO4 and MgO-CaSiO3

High pressure phase transformations for all the mineral phases along the joins Mg₂SiO₄-Ca₂-SiO₄ and MgO-CaSiO₃ in the system MgO-CaO-SiO₂ were investigated in the pressure range between 100 and 300 kbar at about 1,000 °C, by means of the technique involving a diamond-anvil press coupled with laser heating. In addition to the four end-members, there are three stable intermediate mineral components in these two joins. Phase behaviour of all the end-member components at high pressure have been reported earlier and are reviewed here. Results of this study reveal that the three intermediate components are all unstable relative to the end-members at pressures greater than 200 kbar. Ultimately, monticellite (CaMgSiO₄) decomposes into CaSiO₃ (perovskite-type)+MgO; merwinite (Ca₃MgSi₂O₈) decomposes into Ca₂SiO₄(K₂NiF₄-type)+CaSiO₃ (perovskite-type)+MgO; and akermanite (Ca₂MgSi₂O₇) decomposes into CaSiO₃ (perovskite-type)+MgO. Note that the decomposition reactions of all phases studied here result in the formation of MgO. Intermediate Ca-Mg silicates transform to pure Ca-silicates plus MgO, while pure Mg₂SiO₄ transforms to MgSiO₃+MgO.     

A computer simulation study of OH defects in Mg2SiO4 and Mg2GeO4 spinels

Classical atomistic simulation techniques have been used to investigate the energies of hydrogen defects in Mg₂SiO₄ and Mg₂GeO₄ spinels. Ringwoodite (γ-Mg₂SiO₄) is considered to be the most abundant mineral in the lower part of the transition zone and can incorporate large amounts of water in the form of hydroxyls, whereas the germanate spinel (γ-Mg₂GeO₄) corresponds to a low-pressure structural analogue for ringwoodite. The calculated defect energies indicate that the most favourable mechanisms for hydrogen incorporation are coupled either with the reduction of ferric iron or with the creation of tetrahedral vacancies. Hydrogen will go preferentially into tetrahedral vacancies, eventually leading to the formation of the hydrogarnet defect, before associating with other negatively charged point defects. The presence of isolated hydroxyls is not expected. The same trend is observed for germanate, and thus γ-Mg₂GeO₄ could be used as a low-pressure analogue for ringwoodite in studies of water-related defects and their effect on physical properties.     

Electrical conductivity measurements on olivines Mg2SiO4-Fe2SiO4 under defined thermodynamic conditions

The isobaric (P=10 kb) temperature dependence of the electrical conductivities of forsterite, fayalite and forsterite-fayalite mixed crystals was measured with special regard to the thermodynamics of point defects in these minerals. Measurements, taken at increasing and decreasing temperature, were performed on synthetic powders of the following compositions: Fo 100/Fa 0, Fo 90/Fa 10, Fo 80/Fa 20, Fo 60/Fa 40, and Fo 0/Fa100. Control of oxygen partial pressure was achieved with solid state buffers (Fa/Q/M, Fa/Q/I, and Fe/FeO). Activities of the binary components were controlled by equilibrating the sample with its neighbouring phases. All values for σ, obtained with controlled pO₂ and fixed activities of the binary components, agree well upon either heating or cooling. From the gradient of lg σ vs. 1/T plots, the following activation energies were estimated: 2,461 eV (970°–1075°C) and 0.984 eV (522°–970°C) for Fo 100/Fa 0 equilibrated with MgO; 0.777 eV and 0.683 eV for Fo 90/Fa 10 and Fo 80/Fa 20 equilibrated with enstatite and pO₂ controlled by Fe/FeO buffer; 0.622 eV, 0.528 eV, and 0.479 eV for Fo 90/Fa 10, Fo 80/Fa 20, and Fo 60/Fa 40 equilibrated with enstatite and pO₂ controlled by Fa/Q/M buffer; and 0.524 eV and 0.383 eV for Fo 0/Fa 100 equilibrated with Q/I and Q/M respectively.     

Olivine flotation and settling experiments on the join Mg2SiO4-Fe2SiO2

Some unusual density relations between olivine and coexisting liquid in the system fosterite-fayalite are reported. At 1 atmosphere pressure olivine floats on its coexisting liquid for intermediate compositions on this binary because of extreme partitioning of Fe into the melt phase. At 20 kilobars the usual behavior of olivine settling occurs because the partitioning of Fe in the melt is reduced, aided possibly by the dissolution of CO₂ in the melt from use of a graphite container. Olivine flotation and settling are rapid in a time period of only a few hours because viscosities are a little greater than that of paraffin oil at room temperature. Some adcumulate textures with good triple junction grain boundaries are developed. General observations of differentiated magmatic systems on a number of scales and experimental data indicate that the mechanisms by which magmas can differentiate vary considerably in the ultramafic to tholeiitic compositional range.     

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.