CdGeO3-phase transformations at high pressure and temperature and structural refinement of the perovskite polymorph

Four polymorphs of CdGeO₃ were synthesized at high temperatures (600 ～ 1200° C) and high pressures up to 12 GPa. The pyroxenoid phase synthesized under ambient pressure transforms to garnet, ilmenite and perovskite phases with increasing pressure. The phase boundary of ilmenite-perovskite had a slightly negative P-T slope in contrast to the positive P-T slopes of the pyroxenoid-garnet and garnet-ilmenite transition boundaries. CdGeO₃III has the ilmenite structure with hexagonal lattice parameters, a=5.098 Å and c =14.883 Å. The c/a ratio of 2.919 is greater than that of any other ilmenite. CdGeO₃IV has a distorted perovskite structure with orthorhombic lattice parameters a = 5.209 Å, b = 5.253 Å and c = 7.434 Å. Synthesis of a CdGeO₃IV single crystal was successful and structural refinement revealed that the structure is isomorphic to GdFeO₃ with the space group Pbnm. The increase of density with the CdGeO₃III→CdGeO₃IV transformation is the largest (9.8%) for any ilmenite-perovskite transition studied so far.     

High-pressure transformations of ilmenite to perovskite, and lithium niobate to perovskite in zinc germanate

In-situ X-ray powder diffraction measurements conducted under high pressure confirmed the existence of an unquenchable orthorhombic perovskite in ZnGeO₃. ZnGeO₃ ilmenite transformed into perovskite at 30.0 GPa and 1300±150 K in a laser-heated diamond anvil cell. After releasing the pressure, the lithium niobate phase was recovered as a quenched product. The perovskite was also obtained by recompression of the lithium niobate phase at room temperature under a lower pressure than the equilibrium phase boundary of the ilmenite–perovskite transition. Bulk moduli of ilmenite, lithium niobate, and perovskite phases were calculated on the basis of the refined X-ray diffraction data. The structural relations among these phases are considered in terms of the rotation of GeO₆ octahedra. A slight rotation of the octahedra plays an important role for the transition from lithium niobate to perovskite at ambient temperature. On the other hand, high temperature is needed to rearrange GeO₆ octahedra in the ilmenite–perovskite transition. The correlation of quenchability with rotation angle of GeO₆ octahedra for other germanate perovskites is also discussed.     

Calorimetric study of high-pressure polymorphs of MnSiO3

With increasing pressure, MnSiO₃ rhodonite stable at atmospheric pressure transforms to pyroxmangite, then to clinopyroxene and further to tetragonal garnet, which finally decomposes into MnO (rocksalt) plus SiO₂ (stishovite). High temperature solution calorimetry of synthetic rhodonite, clinopyroxene and garnet forms of MnSiO₃ was used to measure the enthalpies of these transitions. ΔH ₉₇₄ ⁰ for the rhodonite-clinopyroxene and ΔH ₂₉₈ ⁰ for the clinopyroxene-garnet transition are 520±490 and 8,270±590 cal/mol, respectively. The published data on the enthalpy of the rhodonite-pyroxmangite transition, phase equilibrium boundaries, compressibility and thermal expansion data are used to calculate entropy changes for the transitions. The enthalpy, entropy and volume changes are very small for all the transitions among rhodonite, pyroxmangite and clinopyroxene. The calculated boundary for the clinopyroxene-garnet transition is consistent with the published experimental results. The pyroxene-garnet transition in several materials, including MnSiO₃, is characterized by a relatively small negative entropy change and large volume decrease, resulting in a small positiveP – T slope. The disproportionation of MnSiO₃ garnet to MnO plus stishovite and of Mn₂SiO₄ olivine to garnet plus MnO are calculated to occur at about 17–18 and 14–15 GPa, respectively, at 1,000–1,500 K.     

High-pressure behavior of MnGeO3 and CdGeO3 perovskites and the post-perovskite phase transition

The stability and high-pressure behavior of perovskite structure in MnGeO₃ and CdGeO₃ were examined on the basis of in situ synchrotron X-ray diffraction measurements at high pressure and temperature in a laser-heated diamond-anvil cell. Results demonstrate that the structural distortion of orthorhombic MnGeO₃ perovskite is enhanced with increasing pressure and it undergoes phase transition to a CaIrO₃-type post-perovskite structure above 60 GPa at 1,800 K. A molar volume of the post-perovskite phase is smaller by 1.6% than that of perovskite at equivalent pressure. In contrast, the structure of CdGeO₃ perovskite becomes less distorted from the ideal cubic perovskite structure with increasing pressure, and it is stable even at 110 GPa and 2,000 K. These results suggest that the phase transition to post-perovskite is induced by a large distortion of perovskite structure with increasing pressure.     

The ZnSiO3 clinopyroxene-ilmenite transition: Heat capacity,enthalpy of transition,and phase equilibria

ZnSiO₃ clinopyroxene stable above 3 GPa transforms to ilmenite at 10–12 GPa, which further decomposes into ZnO (rock salt) plus stishovite at 20–30 GPa. The enthalpy of the clinopyroxene-ilmenite transition was measured by high-temperature solution calorimetry, giving ΔH⁰=51.71 ±3.18 kJ/mol at 298 K. The heat capacities of clinopyroxene and ilmenite were measured by differential scanning calorimetry at 343–733 and 343–633 K, respectively. The C _p of ilmenite is 3–5% smaller than that of clinopyroxene. The entropy of transition was calculated using the measured enthalpy and the free energy calculated from the phase equilibrium data. The enthalpy, entropy and volume changes of the pyroxene-ilmenite transition in ZnSiO₃ are similar in magnitude to those in MgSiO₃. The present thermochemical data are used to calculate the phase boundary of the ZnSiO₃ clinopyroxene-ilmenite transition. The calculated boundary,

A transferable interatomic potential for crystalline phases in the system MgO—SiO2

A central interatomic potential model is presented for compounds in the binary system MgO-SiO₂. The potential, of a simple form which consists of a Coulombic term, a Born repulsive term, and a Van der Walls term for oxygen-oxygen interactions, is designed to predict the properties of magnesium silicates containing Si in octahedral and tetrahedral coordination. This is achieved by fitting simultaneously to forsterite and MgSiO₃ ilmenite crystal structure data, and fixing the partial ionic charges using elastic data for forsterite. The potential is found to transfer successfully to γ-Mg₂SiO₄ and MgSiO₃ perovskite. The potential results in local structural errors around the bridging oxygen ions in clinoenstatite and β-Mg₂SiO₄. The predicted structure for MgSiO₃ garnet is similar to the experimentally measured structure of the MnSiO₃ analogue. Calculated elastic constants average to K=2.41 Mbar and μ=1.44 Mbar for the bulk and shear moduli of MgSiO₃ perovskite, and K=1.87 Mbar and μ=1.10 Mbar for the bulk and shear moduli of MgSiO₃ garnet.     

Formation enthalpy of ThSiO4 and enthalpy of the thorite → huttonite phase transition

The standard enthalpy of formation of thorite and huttonite and the enthalpy of the phase transition between these polymorphs were determined using high-temperature oxide melt solution calorimetry and transposed temperature drop calorimetry. Standard enthalpies of formation of thorite and huttonite are reported for the first time and are −2117.6 ± 4.2 kJ/mol and −2110.9 ± 4.7 kJ/mol, respectively. Based on our measurements, thorite and huttonite are metastable relative to SiO₂ (quartz) and ThO₂ (thorianite) at standard conditions, but are presumably stabilized at high temperature by the entropy contribution. Based on the measured enthalpy of the thorite-huttonite phase transition of 6.7 ± 2.5 kJ/mol, a dP/dT slope for the transformation was calculated as −1.21 ± 0.45 MPa/K.     

Heat capacity calculations for Al2O3 corundum and MgSiO3 ilmenite

We have used Kieffer's vibrational model to calculate heat capacities and entropies for Al₂O₃ corundum and MgSiO₃ ilmenite, using available vibrational and elastic data for these phases. The calculated heat capacity for corundum is within 1–2 percent of the experimental values between 100 K and 1,800 K, while that for MgSiO₃ ilmenite is within 1–2 percent of the experimental data between 350 K and 500 K. We have calculated the heat capacity for MgSiO₃ ilmenite from 50 K to 1,800 K, which extends the range of available heat capacity data for this phase. The results of this calculation suggest that there may be differences in the vibrational properties of corundum and MgSiO₃ ilmenite. Finally, we have used the results of our calculation to obtain a transition entropy of near -18.8 J/mol.K for the MgSiO₃ pyroxene-ilmenite reaction.     

Low-temperature heat capacities,entropies and high-pressure phase relations of MgSiO<Subscript>3</Subscript> ilmenite and perovskite

Low-temperature isobaric heat capacities (C _p ) of MgSiO₃ ilmenite and perovskite were measured in the temperature range of 1.9–302.4 K with a thermal relaxation method using the Physical Properties Measurement System. The measured C _p of perovskite was higher than that of ilmenite in the whole temperature range studied. From the measured C _p , standard entropies at 298.15 K of MgSiO₃ ilmenite and perovskite were determined to be 53.7 ± 0.4 and 57.9 ± 0.3 J/mol K, respectively. The positive entropy change (4.2 ± 0.5 J/mol K) of the ilmenite–perovskite transition in MgSiO₃ is compatible with structural change across the transition in which coordination of Mg atoms is changed from sixfold to eightfold. Calculation of the ilmenite–perovskite transition boundary using the measured entropies and published enthalpy data gives an equilibrium transition boundary at about 20–23 GPa at 1,000–2,000 K with a Clapeyron slope of −2.4 ± 0.4 MPa/K at 1,600 K. The calculated boundary is almost consistent within the errors with those determined by high-pressure high-temperature in situ X-ray diffraction experiments.     

Phase boundary between ilmenite and perovskite structures in MnGeO3 determined by in situ X-ray diffraction measurements

In situ X-ray observations of the phase transition from ilmenite to perovskite structure in MnGeO₃ were carried out in a Kawai-type high-pressure apparatus interfaced with synchrotron radiation. The phase boundary between the ilmenite and perovskite structures in the temperature range of 700–1,400°C was determined to be P (GPa) = 16.5(±0.6) − 0.0034(±0.0006)T (°C) based on Anderson’s gold pressure scale. The Clapeyron slope, dP/dT, determined in this study is consistent with that for the transition boundary between the ilmenite and the perovskite structure in MgSiO₃.     

Thermodynamic data for phases in the FeO-MgO-SiO2 system and phase relations in the mantle transition zone

Based on the available experimental data on phase equilibria in the FeO -MgO -SiO₂ system the mixing properties of the solid solutions (olivine, β- and γ-spinel, pyroxene, majorite, ilmenite and perovskite and magnesiowustite), the enthalpies of FeO and fictive FeSiO₃ phases with ilmenite and majorite structures have been assessed. The entropies, temperature dependance of heat capacities for fictive FeSiO₃ end-members were estimated from structural analogies. The calculated phase diagrams for Mg₂SiO₄-Fe₂SiO₄ and MgSiO₃ — FeSiO₃ systems at pressures up to 30 GPa and temperatures between 1000 and 2100 K are quite consistent with the available experimental determinations except for the fine features of the phase diagram at 2073 K.     

Regression Modelling of Metamorphic Reactions in Metapelites, Snow Peak, Northern Idaho

The second of two periods of regional metamorphism that affectedpelitic rocks near Snow Peak caused complete re-equilibrationof mineral assemblages and resulted in a consistent set of metamorphicisograds. Metamorphic chlorite and biotite occur in the lowestgrade rocks. With increasing grade, garnet, staurolite, andkyanite join the assemblage, resulting in a transition zonecontaining all the above phases. At higher grade, chlorite,and finally staurolite disappear. Mass balance relations at isograds and among minerals of low-varianceassemblages have been modelled by a non-linear least-squaresregression technique. The progressive sequence can be describedin terms of schematic T-X_H2O relations among chlorite, biotite,garnet, staurolite, and kyanite at P_total above the KFMASH invariantpoint involving those phases. The first appearance of garnetwas the result of an Fe-Mg-Mn continuous reaction. As temperaturerose, the garnet zone assemblage encountered the stauroliteisograd reaction, approximated by the model reaction: 3?0 chlorite + 1?5 garnet + 3?3 muscovite + 05 ilmenite = 1?0staurolite + 3?1 biotite + 1?5 plagioclase + 3?3 quartz + 10?3H₂O. The staurolite zone corresponds to buffering along this reactionto the intersection where chlorite, biotite, garnet, staurolite,and kyanite coexist. The transition zone assemblage formed byreaction at this T–X _H2O intersection which migrates towardmore H2O-rich fluid composition with progressive reaction. Thenet reaction at the intersection is approximated by the transitionzone reaction: 1?0 chlorite +1?1 muscovite + 0?2 ilmenite = 2?7 kyanite + 1?0biotite + 0?4 albite + 4?2 H₂O. Chlorite was commonly the first phase to have been exhaustedand the remaining assemblage was buffered along a staurolite-outreaction, represented by the model reaction: 1?0 staurolite + 3?4 quartz + 0?4 anorthite + 1?4 garnet + 0?1ilmenite + 7?9 kyanite + 2?0 H₂O. Consumption of staurolite by this reaction resulted in the highestgrade assemblage, which contains kyanite, garnet, biotite, muscovite,quartz, plagioclase, ilmenite, and graphite.     

Thermodynamic properties of MgSiO3 ilmenite from vibrational spectra

Unpolarized infrared (IR) reflectance spectra for MgSiO₃ ilmenite taken from a single-crystal and from a densly packed polycrystalline sample possessed all eight peaks mandated by symmetry between 337 and 850 cm^?1. Polarizations were inferred from intensity differences between the two samples. IR peak positions differ by up to 250 cm^?1 from recent calculations, but on average are within 11%. Heat capacity C _p calculated from these data by using a Kieffer-type model are within the experimental uncertainty of calorimetric measurements from 170 to 700 K. Outside this range, calculated C _p is probably accurate within a few percent, based on recent results for garnets. Calculated entropy is only slightly less accurate, giving S ⁰ (298.15 K) as 54.1 ±0.5 J/ mol-K, which is 10% lower than recent estimates based on phase equilibria. The slope of the phase boundary between ilmenite and perovskite is used to predict S ⁰ (298.15 K) of perovskite as 58.7 ±1.4 J/mol-K, which is 10% lower than previous values.     

Computer simulation of the MgSiO3 polymorphs

Six polymorphs of MgSiO₃ have been studied using molecular dynamic (MD) simulation techniques, based on the empirical potential (MAMOK), which is composed of terms to describe pairwise additive Coulomb, van der Waals attraction, and repulsive interactions. Crystal structures, bulk moduli, volume thermal expansivities, and enthalpies were simulated for the known MgSiO₃ polymorphs; orthoenstatite, clinoenstatite, protoenstatite, garnet, ilmenite, and perovskite. The simulated values compare very well with the available experimental data, and the results are quite satisfactory in view of the diversity of the crystal structures of the six polymorphs, the wide range of simulated properties, and the simplicity of the MAMOK potential. MD simulation was further successfully used to study the possibile existence of a post-protoenstatite phase at high temperature, and a C2/c phase at high pressure, both phases being suggested or inferred previously from experimental works.     

MgSiO3 ilmenite: Heat capacity,thermal expansivity,and enthalpy of transformation

A new determination, using high temperature drop-solution calorimetry, of the enthalpy of transformation of MgSiO₃ pyroxene to ilmenite gives H ₂₉₈ = 59.03 ±4.26 kJ/mol. The heat capacity of the ilmenite and orthopyroxene phases has been measured by differential scanning calorimetry at 170–700 K; C_p of MgSiO₃ ilmenite is 4–10 percent less than that of MgSiO₃ pyroxene throughout the range studied. The heat capacity differences are consistent with lattice vibrational models proposed by McMillan and Ross (1987) and suggest an entropy change of -18 ± 3 J-K^-1 ·mol^-1, approximately independent of temperature, for the pyroxene-ilmenite transition. The unit cell parameters of MgSiO₃ ilmenite were measured at 298–876 K and yield an average volume thermal expansion coefficient of 2.44 × 10^-5 K^-1. The thermochemical data are used to calculate phase relations involving pyroxene, -Mg₂SiO₄ plus stishovite, Mg₂SiO₄ spinel plus stishovite, and ilmenite in good agreement with the results of high pressure studies.     

High-pressure transformations in silicates,germanates, and titanates with ABO3 stoichiometry

High-pressure phase transformations were investigated for two silicates, MgSiO₃ and ZnSiO₃; six germanates, MGeO₃ and six titanates, MTiO₃ (M=Ni, Mg, Co, Zn, Fe, and Mn) at about 1,000°C and pressures up to ca. 30 GPa. CoGeO₃ was found to assume the ilmenite form. The ilmenite phases were confirmed to transform in the following schemes: to perovskite in MgSiO₃ and MnGeO₃, to corundum in MgGeO₃ and ZnGeO₃, to rocksalt plus rutile in ZnSiO₃ and CoGeO₃ and to rocksalt plus TiO₂ (possibly of some denser structure) in NiTiO₃, MgTiO₃, CoTiO₃, ZnTiO₃ and FeTiO₃. In the case of FeTiO₃, the corundum form appeared as an intermediate phase. The possibility that the corundum type MnTiO₃ might transform to some denser modification could not be excluded. The compound NiGeO₃ was nonexistent throughout the pressure range studied. High-pressure phases of ABO₃ (A=Ni, Mg, Co, Zn, Fe, and Mn; B=Si, Ge and Ti) are summarized, and those stabilized at pressures higher than 20 GPa are discussed.     

Geochemical evolution of the Zadoi Alkaline-Ultramafic Massif,Cis-Sayan area,southern Siberia

The unaltered magmatic rocks of the Zadoi Massif were analyzed for Sr isotopic composition and concentrations of major oxides and trace elements by ICP MS. The evolution of the massif involved four phases: (i) perovskite and ilmenite clinopyroxenites, (ii) ijolites, (iii) nepheline syenites, and (iv) carbonatites. The perovskite clinopyroxenites have anomalously high Ce/Pb (223–1132) and Pr/Sr × 1000 (70–360) ratios at a low initial Sr isotopic ratio (⁸⁷Sr/⁸⁶Sr)₀ = 0.70247–0.70285. The ilmenite clinopyroxenites have Ce/Pb and Pr/Sr × 1000 ratios approaching those in basalts of oceanic islands (OIB) (decreasing to 39 and 30, respectively) at a simultaneous increase in the (⁸⁷Sr/⁸⁶Sr)₀ ratios (0.7030–0.7036). The ijolites and nepheline syenites have patterns of incompatible trace elements similar to those in OIB and the highest (⁸⁷Sr/⁸⁶Sr)₀ ratios (0.70346–0.70414). The carbonatites are complementarily enriched in incompatible elements of the nepheline syenites and have (⁸⁷Sr/⁸⁶Sr)₀ = 0.7029–0.7034, which is comparable with the range of analogous ratios for the ilmenite clinopyroxenites. Our geochemical data indicate that the carbonatites were formed as an immiscible liquid or fluid, which separated from the ijolite-nepheline syenite melt during its interaction with the source material of the perovskite and ilmenite clinopyroxenites.     

Computational model of the structural and elastic properties of the ilmenite and perovskite phases of MgSiO3

The structural and elastic properties of the ilmenite and perovskite phases of MgSiO₃ are investigated with a computational model based on energy minimization. The potential energies of these two crystals are approximated by the sum of Coulomb, van der Waals, and repulsion terms between atoms. Required energy parameters are derived by fitting the parameters to the observed crystal structures of these two phases as well as to the measured elastic constants of the ilmenite phase. The resulting potential model is applied to predicting the elastic constants of the perovskite phase. The calculated bulk modulus of the perovskite phase compares favorably with the data obtained from volume-compression experiments as well as the values estimated from empirical elasticity systematics of perovskite type compounds. The predicted shear modulus of the perovskite phase is also in reasonable agreement with the values proposed from similar empirical elasticity systematics. Subsequently, the model is used to simulate the high pressure behaviors of the crystal structures and elastic constants of these two phases.     

Structure and crystal chemistry of perovskite-type MgSiO3

Synthetic clinoenstatite (MgSiO₃) has been converted to a single phase with the perovskite structure in complete reactions at approx. 300 kbar in experiments that utilize the laser-heated diamond-anvil pressure apparatus. The structure of this phase after quenching was determined by powder X-ray diffraction intensity measurement to be similar to that of the distorted rare-earth, orthoferrite-type, orthorhombic perovskites, but it is suggested that such distortion from ideal cubic perovskite would diminish at high pressure. The unit cell dimensions and density of perovskite-type MgSiO₃ at ambient conditions (1 bar, 25°C) are a=4.780(1) Å, b=4.933(1) Å, c=6.902(1) Å, V=162.75 ų, and ρ=4.098(1) g/cm³. This phase is 3.1% denser than the isochemical oxide mixture [periclase (MgO)+stishovite (SiO₂)]. The small crystal-field stabilization energy of the cation site in the perovskite structure may play an important role in limiting the high-pressure stability field of perovskites that contain transition metal cations. Approximate calculations of the crystal-field effects indicate that perovskite of pure FeSiO₃ composition may become stable at 400–600 kbar; pressures greater than 800 kbar would be required to stabilize CoSiO₃ or NiSiO₃ perovskite.     

Phase equilibrium and calorimetric study of the transition of MnTiO3 from the ilmenite to the lithium niobate structure and implications for the stability field of perovskite

The phase boundary between MnTiO₃ I (ilmenite structure) and MnTiO₃ II (lithium niobate structure) has been determined by analysis of quench products from reversal experiments in a cubic anvil apparatus at 1073–1673 K and 43–75 kbar using mixtures of MnTiO₃ I and II as starting materials. Tight brackets of the boundary give P(kbar)=121.2−0.045 T(K). Thermodynamic analysis of this boundary gives ΔH^o=5300±1000 J·mol⁻¹, ΔS^o = 1.98 ±1J·K⁻¹· mol⁻¹. The enthalpy of transformation obtained directly by transposed-temperature-drop calorimetry is 8359 ±2575 J·mol⁻¹. Possible topologies of the phase relations among the ilmenite, lithium niobate, and perovskite polymorphs are constrained using the above data and the observed (reversible with hysteresis) transformation of II to III at 298 K and 20–30 kbar (Ross et al. 1989). The observed II–III transition is likely to lie on a metastable extension of the II–III boundary into the ilmenite field. However the reversed I–II boundary, with its negative dP/ dT does represent stable equilibrium between ilmenite and lithium niobate, as opposed to the lithium niobate being a quench product of perovskite. We suggest a topology in which the perovskite occurs stably at low T and high P with a triple point (I, II, III) at or below 1073 K near 70 kbar. The I–II boundary would have a negative P-T slope while the II–III and I–III boundaries would be positive, implying that entropy decreases in the order lithium niobate, ilmenite, perovskite. The inferred positive slope of the ilmenite-perovskite transition in MnTiO₃ is different from the negative slopes in silicates and germanates. These thermochemical parameters are discussed in terms of crystal structure and lattice vibrations.