Thermodynamics and behavior of γ-Mg2SiO4 at high pressure: Implications for Mg2SiO4 phase equilibrium

Raman spectra of γ-Mg₂SiO₄ taken to 200 kbar were used to calculate entropy and heat capacity at various P-T conditions. These new thermodynamic data on γ-MgSiO₄, similar data on MgSiO₃ perovskite (pv), previous data on β-MgSiO₄ and MgO (mw), and previous volumetric data of all phases were used to calculate the phase boundaries in the Mg₂SiO₄ phase diagram. Our resulting slope for the β→γ transition (50±4 bar K^-1) is in excellent agreement with recent multi-anvil studies. The slopes for the β→pv+MgO and γ→pv+MgO are-7±3 and -25±4 bar K^-1, respectively, and are consistent with our CO₂ laser heated diamond anvil studies. These slopes result in a β-γ-MgO+pv triple point at approximately 229 kbar and 2260 K for the iron free system.     

High pressure phase transformations in aragonite-type carbonates

High-temperature and high-pressure experiments conducted in a diamond-anvil cell revealed phase transformations in the aragonite-type carbonates of strontianite (SrCO₃), cerussite (PbCO₃), and witherite (BaCO₃) at pressures below 4 GPa and ～1000?°C. The powder X-ray diffraction patterns of these high-pressure phases can be reasonably indexed with the same type of orthorhombic cell having a space group of P2₁22 (17). By assuming 16 MCO₃ (M=Sr, Ba or Pb) molecules in a unit cell, the transition from the aragonite form to a new phase was concomitant with a volume contraction of 4.23, 2.38, and 2.34% for SrCO₃, PbCO₃, and BaCO₃, respectively. If the same phase transition were to occur in CaCO₃, it has been estimated that the transition would accompany a 7% volume contraction.     

The system Mg2SiO4-Ca2SiO4-CaAl2O4-NaAlSiO4-SiO2: one atmosphere liquidus equilibria of analogs of alkaline mafic lavas

One atmosphere liquidus relationships in the system Mg₂SiO₄ (Fo)–Ca₂SiO₄ (La)–NaAlSiO₄ (Ne)–CaAl₂O₄ (CA)–SiO₂ (Sil) are presented as analogs for alkaline mafic lavas. Liquidus diagrams are constructed from electron microprobe analyses of quenched liquids and coexisting mineral phases produced in melting experiments and they are depicted in terms of sub-projections within the pseudo-quaternary system Fo–La–[Ne,CA]–Sil. The Ne and CA components are combined to create a normative feldspathoid component defined as Ne#=Ne/[Ne+CA]. Liquidus relations at Ne#=0.5 from this study are compared to relations at Ne#=0.0 and 1.0 from previous studies. In general, liquidus temperatures decrease and positions of liquidus boundaries involving feldspathic phases shift toward the [Ne, CA] component as Ne# increases. The pseudoinvariant points fo+di+pl+mel+l and fo+pl+mel+sp+l exist at Ne#=0.5. These equilibria between forsterite-plagioclase-melilite-liquid are not present in the system when Ne#=1.0 because a boundary curve (fo+di+ne+l) separates the plagioclase and melilite liquidus fields. The liquidus diagrams provide useful analogs for the crystallization sequences of natural primary alkali olivine basalts, basanitoids, basanites, olivine nephelinites, olivine-melilite nephelinites and olivine melilitites.     

Molecular dynamics simulations of pressure and temperature effects on MgSiO3 and Mg2SiO4 melts and glasses

Ab-initio interionic potentials for Mg²⁺, Si⁴⁺, and O^2– have been used in molecular dynamics (MD) simulations to investigate diffusivity changes, pressure-induced structural transitions, and temperature effects on polymerization in MgSiO₃ and Mg₂SiO₄ melts and glasses. The potential gives reasonable agreement with the 0.1 MPa radial distribution function of MgSiO₃ glass. Maxima in the diffusion coefficients of Si⁴⁺ and O^2– occur as pressure is increased on the MgSiO₃ melt. The controlling structural mechanism for this behavior is the Q¹ species of SiO₄ tetrahedra. Mg²⁺ diffusion coefficients decrease monotonically with pressure in both melt compositions. Increasing Mg²⁺ coordination number and population of 3- and 4-membered SiO₄ rings with pressure combine to hinder translation of the Mg²⁺ ions. The dominant changes in structure with pressure are a decrease in the intertetrahedral (Si-O--Si) angle up to approximately 4 g/cm³ and coordination changes of the ions above this density. Temperature effects on viscosity in these simulated melts are indirectly studied by analyzing polymerization changes with temperature. Polymerization and coordination numbers increase with decreasing temperature and a small quench rate effect is observed. Fair agreement is found between the MD simulations and experimental equation of state for Mg₂SiO₄, but the equation of state predictions for MgSiO₃ melts are much less accurate. The zero pressure volume, V ₀, is significantly higher and K ₀ is lower in the simulations than empirical values. The inadequacies reflect error in using the ionic approximation for polymerized systems and a need to collect more data for a variety of molecular configurations in the development of ab-initio potentials.     

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 elasticity and phase transformation in brucite, Mg(OH)2

The first pressure derivatives of the second-order elastic constants have been calculated for brucite, Mg(OH)₂ from the second- and third-order elastic constants. The deformation theory and finite strain elasticity theory have been used to obtain the second- and third-order elastic constants of Mg(OH)₂ from the strain energy of the lattice. The strain energy ϕ is calculated by taking into account the interactions up to third nearest neighbors in the Mg(OH)₂ lattice. ϕ is then compared with the strain dependent lattice energy from continuum model approximation to obtain the expressions of elastic constants. The complete set of six second-order elastic constants C _IJ of brucite exhibits large anisotropy. Since C ₃₃ (= 21.6 GPa), which corresponds to the strength of the material along the c-axis direction, is less than the longitudinal mode C ₁₁ (= 156.7 GPa), the interlayer binding forces are weaker than the binding forces along the basal plane of Mg(OH)₂. The 14 nonvanishing components of the third-order elastic constants, C _IJK , of brucite have been obtained. All the C _IJK of brucite are negative except the values of C ₁₁₄ (= 230.36 GPa), C ₁₂₄ (= 75.45 GPa) and C ₁₃₄ (= 36.98 GPa). The absolute values of the C _IJK are, in general, one order of magnitude greater than the C _IJ ’s in the Mg(OH)₂ system as usually expected for a crystalline material. To our knowledge, no previous data are available to compare the pressure derivatives of brucite. The pressure derivatives of the two components viz., C ₁₄ and C ₃₃ become negative indicating an elastic instability in brucite while under pressure. This may be related to the phase transition of brucite largely involving rearrangements of H atoms revealed in the Raman spectroscopic, powder neutron diffraction and synchrotron X-ray diffraction studies.     

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.     

A study of the polymorphic transformations in Co2SiO4

The olivine-beta phase transformation in Co₂SiO₄ has been studied in a large-volume high-pressure apparatus (USSA-2000). The experimental conditions straddle the univariant phase boundaries due to the presence of a substantial temperature gradient (150–200° C over the 3-mm length of the sample). At conditions close to equilibrium, the transformation mechanism is one of limited nucleation with rapid growth of large crystals of the beta phase. Transmission electron microscopy (TEM) analysis shows that the cation stacking faults in Co₂SiO₄-spinel are identical to those seen in numerous spinels. The 010 faults in beta-Co₂SiO₄ are found to be identical to those seen in beta-(Mg,Fe)₂SiO₄ found in shocked veins in meteorites.     

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.     

High-pressure phase transformations in the MgFe2O4 and Fe2O3–MgSiO3 systems

 The crystal structure of MgFe₂O₄ was investigated by in situ X-ray diffraction at high pressure, using YAG laser annealing in a diamond anvil cell. Magnesioferrite undergoes a phase transformation at about 25 GPa, which leads to a CaMn₂O₄-type polymorph about 8% denser, as determined using Rietveld analysis. The consequences of the occurrence of this dense MgFe₂O₄ form on the high-pressure phase transformations in the (MgSi)_0.75(Fe^III)_0.5O₃ system were investigated. After laser annealing at about 20 GPa, we observe decomposition to two phases: stishovite and a spinel-derived structure with orthorhombic symmetry and probably intermediate composition between MgFe₂O₄ and Mg₂SiO₄. At pressures above 35 GPa, we observe recombination of these products to a single phase with Pbnm perovskite structure. We thus conclude for the formation of Mg₃Fe₂Si₃O₁₂ perovskite. Received: 27 March 2000 / Accepted: 1 October 2000     

High pressure single-crystal synthesis, structure and compressibility of the garnet Mn2+ 3Mn3+ 2[SiO4]3

Single crystals of the garnet Mn²⁺ ₃Mn³⁺ ₂[SiO₄]₃ and coesite were synthesised from MnO₂-SiO₂ oxide mixtures at 1000°C and 9 GPa in a multianvil press. The crystal structure of the garnet [space group Ia3¯d, a=11.801(2) Å] was refined at room temperature and 100 K from single-crystal X-ray data to R1=2.36% and R1=2.71%, respectively. In contrast to tetragonal Ca₃Mn³⁺ ₂[GeO₄]₃ (space group I4₁/a), the high-pressure garnet is cubic and does not display an ordered Jahn-Teller distortion of octahedral Mn³⁺. A disordered Jahn-Teller distortion either dynamic or static is evidenced by unusual high anisotropic displacement parameters. The room temperature structure is characterised by following bond lengths: Si-O=1.636(4) Å (tetrahedron), Mn³⁺-O=1.995 (4) Å (octahedron), Mn²⁺-O=2.280(5) and 2.409(4) Å (dodecahedron). The cubic structure was preserved upon cooling to 100 K [a=11.788(2) Å] and upon compressing up to 11.8 GPa in a diamond-anvil cell. Pressure variation of the unit cell parameter expressed by a third-order Birch-Murnaghan equation of state led to a bulk modulus K ₀=151.6(8) GPa and its pressure derivatives K′=6.38(19). The peak positions of the Raman spectrum recorded for Mn²⁺ ₃Mn³⁺ ₂[SiO₄]₃ were assigned based on a calderite Mn²⁺ ₃Fe³⁺ ₂[SiO₄]₃ model extrapolated from andradite and grossular literature data.     

The phase boundary between wadsleyite and ringwoodite in Mg2SiO4 determined by in situ X-ray diffraction

The phase boundary between wadsleyite and ringwoodite in Mg₂SiO₄ has been determined in situ using a multi-anvil apparatus and synchrotron X-rays radiation at SPring-8. In spite of the similar X-ray diffraction profiles of these high-pressure phases with closely related structures, we were able to identify the occurrence of the mutual phase transformations based on the change in the difference profile by utilizing a newly introduced press-oscillation system. The boundary was located at ~18.9 GPa and 1,400°C when we used Shim’s gold pressure scale (Shim et al. in Earth Planet Sci Lett 203:729–739, 2002), which was slightly (~0.8 GPa) lower than the pressure as determined from the quench experiments of Katsura and Ito (J Geophys Res 94:15663–15670, 1989). Although it was difficult to constrain the Clapeyron slope based solely on the present data due to the kinetic problem, the phase boundary [P (GPa)=13.1+4.11×10⁻³×T (K)] calculated by a combination of a P–T position well constrained by the present experiment and the calorimetric data of Akaogi et al. (J Geophys Res 94:15671–15685, 1989) reasonably explains all the present data within the experimental error. When we used Anderson’s gold pressure scale (Anderson et al. in J Appl Phys 65:1535–1543, 1989), our phase boundary was located in ~18.1 GPa and 1,400°C, and the extrapolation boundary was consistent with that of Kuroda et al. (Phys Chem Miner 27:523–532, 2000), which was determined at high temperature (1,800–2,000°C) using a calibration based on the same pressure scale. Our new phase boundary is marginally consistent with that of Suzuki et al. (Geophys Res Lett 27:803–806, 2000) based on in situ X-ray experiments at lower temperatures (<1,000°C) using Brown’s and Decker’s NaCl pressure scales.     

High pressure Ca2SiO4, the silicate K2NiF4-isotype with crystalchemical and geophysical implications

The first silicate possessing a K₂NiF₄-type structure (Ca₂SiO₄) has been synthesized at loading pressures between 220 and 260 kbar and a temperature of about 1000° C in a diamond-anvil press coupled with a YAG laser heater. The lattice parameters for Ca₂SiO₄ (K₂NiF₄-type) area=3.564±0.002 andc=11.66±0.01 Å at room temperature and 1 bar pressure, and the molar volume is 44.57±0.05 cm³. The lattice parameter for the non-quenchable high-pressure perovskite modification of CaSiO₃ is estimated to be 3.56±0.03 Å at STP conditions. To date, A₂BX₄ compounds possessing the K₂NiF₄-type structure arein all cases less dense than their corresponding mixtures of ABX₃ and AX compounds possessing, respectively, the perovskite (or related structures) and rocksalt structures. Hence the K₂NiF₄ structure is unstable relative to the mixture perovskite plus rocksalt at high pressures. For example, in a preliminary experimental study Ca₂GeO₄ in the K₂NiF₄-type structure has been found to transform to an as-yet-undetermined phase or assemblage at pressures between 200 and 250 kbar and at about 1000° C. It is concluded that a similar phase transformation might also occur in Ca₂SiO₄ (K₂NiF₄ type) but that the K₂NiF₄-type structure would not be adopted by Mg₂SiO₄ in the earth's mantle.     

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.     

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.     

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.     

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.     

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.     

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.