Formation of a solid solution in the MgSiO3–MnSiO3 perovskite system

Experiments using laser-heated diamond anvil cells combined with synchrotron X-ray diffraction and SEM–EDS chemical analyses have confirmed the existence of a complete solid solution in the MgSiO₃–MnSiO₃ perovskite system at high pressure and high temperature. The (Mg, Mn)SiO₃ perovskite produced is orthorhombic, and a linear relationship between the unit cell parameters of this perovskite and the proportion of MnSiO₃ components incorporated seems to obey Vegard’s rule at about 50 GPa. The orthorhombic distortion, judged from the axial ratios of a/b and \( \sqrt{2}\,a/c, \) monotonically decreases from MgSiO₃ to MnSiO₃ perovskite at about 50 GPa. The orthorhombic distortion in (Mg_0.5, Mn_0.5)SiO₃ perovskite is almost unchanged with increasing pressure from 30 to 50 GPa. On the other hand, that distortion in (Mg_0.9, Mn_0.1)SiO₃ perovskite increases with pressure. (Mg, Mn)SiO₃ perovskite incorporating less than 10 mol% of MnSiO₃ component is quenchable. A value of the bulk modulus of 256(2) GPa with a fixed first pressure derivative of four is obtained for (Mg_0.9, Mn_0.1)SiO₃. MnSiO₃ is the first chemical component confirmed to form a complete solid solution with MgSiO₃ perovskite at the P–T conditions present in the lower mantle.     

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.     

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.     

Pressure dependence of electrical conductivity of (Mg,Fe)SiO<Subscript>3</Subscript> ilmenite

The electrical conductivity of (Mg_0.93Fe_0.07)SiO₃ ilmenite was measured at temperatures of 500–1,200 K and pressures of 25–35 GPa in a Kawai-type multi-anvil apparatus equipped with sintered diamond anvils. In order to verify the reliability of this study, the electrical conductivity of (Mg_0.93Fe_0.07)SiO₃ perovskite was also measured at temperatures of 500–1,400 K and pressures of 30–35 GPa. The pressure calibration was carried out using in situ X-ray diffraction of MgO as pressure marker. The oxidation conditions of the samples were controlled by the Fe disk. The activation energy at zero pressure and activation volume for ilmenite are 0.82(6) eV and −1.5(2) cm³/mol, respectively. Those for perovskite were 0.5(1) eV and −0.4(4) cm³/mol, respectively, which are in agreement with the experimental results reported previously. It is concluded that ilmenite conductivity has a large pressure dependence in the investigated P–T range.     

Determination of the phase boundary between ilmenite and perovskite in MgSiO3 by in situ X-ray diffraction and quench experiments

Determination of the phase boundary between ilmenite and perovskite structures in MgSiO₃ has been made at pressures between 18 and 24 GPa and temperatures up to 2000 °C by in situ X-ray diffraction measurements using synchrotron radiation and quench experiments. It was difficult to precisely define the phase boundary by the present in situ X-ray observations, because the grain growth of ilmenite hindered the estimation of relative abundances of these phases. Moreover, the slow reaction kinetics between these two phases made it difficult to determine the phase boundary by changing pressure and temperature conditions during in situ X-ray diffraction measurements. Nevertheless, the phase boundary was well constrained by quench method with a pressure calibration based on the spinel-postspinel boundary of Mg₂SiO₄ determined by in situ X-ray experiments. This yielded the ilmenite-perovskite phase boundary of P (GPa) = 25.0 (±0.2) – 0.003 T (°C) for a temperature range of 1200–1800 °C, which is generally consistent with the results of the present in situ X-ray diffraction measurements within the uncertainty of ∼±0.5 GPa. The phase boundary thus determined between ilmenite and perovskite phases in MgSiO₃ is slightly (∼0.5 GPa) lower than that of the spinel-postspinel transformation in Mg₂SiO₄. Received: 19 May 1999 / Accepted: 21 March 2000     

The transition of pyrope to perovskite

The stability field of Mg₃Al₂Si₃O₁₂-pyrope was examined for the first time under hydrostatic pressure conditions in a CO₂-laser heated diamond cell in the pressure range 21–30 GPa between 2300 and 3200 K. The phases were characterized using Raman and fluorescence spectroscopy. With increasing pressure pyrope transforms to an ilmenite phase above ∼21.5 GPa, to perovskite plus ilmenite above ∼24 GPa, and to perovskite above 29 GPa. The pressures of the first occurrence of perovskite in this study are about 2 GPa above the corresponding phase boundary between end-member MgSiO₃-ilmenite and perovskite. A small amount of Al₂O₃ coexists with perovskite up to 43 GPa, as evident from fluorescence spectra resembling those of ruby, but above 43 GPa the entire Al₂O₃ content of the pyrope starting material is accommodated in the perovskite structure. Received: 6 March 1997 / Revised, accepted: 23 July 1997     

Evolution of the distortion of perovskites under pressure: An EXAFS study of BaZrO3, SrZrO3 and CaGeO3

We have investigated the evolution of the distortion of several oxide perovskites with increasing pressure, using EXAFS in the diamond anvil cell. Cubic perovskite BaZrO₃ remains cubic up to 52 GPa. Orthorhombic perovskite CaGeO₃ becomes less distorted as pressure increases, becomes tetragonal at about 12 GPa and evolves toward cubic structure, still not obtained at 23 GPa. The distortion of orthorhombic perovskite SrZrO₃ first increases with pressure up to 8 GPa, then decreases until the perovskite becomes cubic at 25 GPa. The results are interpreted in terms of a systematics, relating the distortion to the ratio f of the volumes of the AO₁₂ dodecahedron and the BO₆ octahedron, and to the compressibilities of the polyhedra. For cubic perovskites, f=5, which may correspond to a situation where the compressibilities of octahedra and dodecahedra are equal.The behavior of SrZrO₃ offers a clue to predict the evolution of the distortion of MgSiO₃ at lower mantle pressures. It is suggested that the increase in distortion experimentally observed at lower pressures should stop above about 10 GPa, and the distortion decrease until the perovskite undergoes ferroelastic transitions to tetragonal and cubic phases, at pressures possibly below the pressure at the core-mantle boundary.     

Mg-Fe partitioning between silicate spinel and magnesiowüstite at high pressure: experimental determination and calculation of phase relations in the system Mg2SiO4-Fe2SiO4

 Mg-Fe partitioning experiments between (Mg,Fe)₂SiO₄ spinel and (Mg,Fe)O magnesiowüstite were carried out at pressures of 17–21.3 GPa at temperatures of 1400 and 1600 °C, using a multi-anvil apparatus, in order to determine interaction parameters of spinel and magnesiowüstite solid solutions and also to constrain the equilibrium boundaries of the postspinel transition in the Fe-rich side in the system Mg₂SiO₄-Fe₂SiO₄. The obtained values of the interaction parameters were 3.4 ± 1.5 and 13.9 ± 1.4 kJ mol⁻¹, respectively, for spinel and magnesiowüstite solid solutions at 19 GPa and 1600 °C. The partitioning data in the system Mg₂SiO₄-Fe₂SiO₄ at 1400 and 1600 °C showed that the transition boundary between spinel and the mixture of magnesiowüstite and stishovite has a negative dP/dT slope. Using the above interaction parameters and available thermodynamic data of the Mg₂SiO₄ and Fe₂SiO₄ end members, the transition boundaries of spinel to the mixture of magnesiowüstite and stishovite were calculated. Within the uncertainties of the data used, the calculated boundaries are in good agreement with the boundaries at 1400 and 1600 °C experimentally determined in this study. The dissociation boundary of Fe₂SiO₄ spinel to wüstite and stishovite, calculated from the thermodynamic data, has a negative slope of −1.5 ± 0.6 MPa K⁻¹. Received: 18 February 1998 / Revised, accepted: 18 October 1999     

Effect of KCl on melting in the Mg<Subscript>2</Subscript>SiO<Subscript>4</Subscript>–MgSiO<Subscript>3</Subscript>–H<Subscript>2</Subscript>O system at 5 GPa

To examine the effect of KCl-bearing fluids on the melting behavior of the Earth’s mantle, we conducted experiments in the Mg₂SiO₄–MgSiO₃–H₂O and Mg₂SiO₄–MgSiO₃–KCl–H₂O systems at 5 GPa. In the Mg₂SiO₄–MgSiO₃–H₂O system, the temperature of the fluid-saturated solidus is bracketed between 1,200–1,250°C, and both forsterite and enstatite coexist with the liquid under supersolidus conditions. In the Mg₂SiO₄–MgSiO₃–KCl–H₂O systems with molar Cl/(Cl + H₂O) ratios of 0.2, 0.4, and 0.6, the temperatures of the fluid-saturated solidus are bracketed between 1,400–1,450°C, 1,550–1,600°C, and 1,600–1,650°C, respectively, and only forsterite coexists with liquid under supersolidus conditions. This increase in the temperature of the solidus demonstrates the significant effect of KCl on reducing the activity of H₂O in the fluid in the Mg₂SiO₄–MgSiO₃–H₂O system. The change in the melting residues indicates that the incongruent melting of enstatite (enstatite = forsterite + silica-rich melt) could extend to pressures above 5 GPa in KCl-bearing systems, in contrast to the behavior in the KCl-free system.     

Pseudopotential periodic Hartree-Fock study of Mg2SiO4 polymorphs: Olivine,modified spinel and spinel

Pseudopotential periodic Hartree-Fock calculations have been performed on the three polymorphs of Mg₂SiO₄ with a polarized split valence basis set. The energy differences between polymorphs at their experimental geometries are correctly predicted. The olivine to modified spinel and olivine to spinel phase transition pressures have been estimated and agree within a few GPa with their experimental values. The bonding in Mg₂SiO₄ is discussed from the point of view of the, band structures, projected density of states, electron density and electron localization function (ELF) curves. It is concluded that both Mg-O and Si-O bonds are highly ionic.     

A MEG study of the olivine and spinel forms of Mg2SiO4

In this paper we present a theoretical investigation of the structures and relative stability of the olivine and spinel phases of Mg₂SiO₄. We use both a purely ionic model, based on the Modified Electron Gas (MEG) model of intermolecular forces, and a bond polarization model, developed for low pressure silica phases, to investigate the role of covalency in these compounds. The standard MEG ionic model gives adequate structural results for the two phases but incorrectly predicts the spinel phase to be more stable at zero pressure. This is mainly because the ionic modeling of Mg₂SiO₄ only accounts for 95 percent of the lattice energy. The remainder can be attributed to covalency and many-body effects. An extension of the MEG ionic model using “many-body” pair potentials corrects the phase stability error, but predicts structures which are in poorer agreement with experiment than the standard ionic approach. In addition, calculations using these many-body pair potentials can only account for 10 percent of the missing lattice energy. This model predicts an olivine-spinel phase transition of 8 GPa, below the experimental value of 20 GPa. Therefore, in order to understand more fully the stability of these structures we must consider polarization. A two-shell bond polarization model enhances the stability of both structures, with the olivine structure being stabilized more. This model predicts a phase transition at about 80 GPa, well above the observed value. Also, the olivine and spinel structures calculated with this approach are in poorer agreement with experiment than the ionic model. Therefore, based on our investigations, to properly model covalency in Mg₂SiO₄, a treatment more sophisticated than the two-shell model is needed.     

Solid solution behaviour of CaSiO<Subscript>3</Subscript> and MgSiO<Subscript>3</Subscript> perovskites

Using density functional simulations within the generalized gradient approximation and projector-augmented wave method together with thermodynamic modelling, the reciprocal solubilities of MgSiO₃ and CaSiO₃ perovskites were calculated for pressures and temperatures of the Earth’s lower mantle from 25 to 100 GPa and 0 to 6,000 K, respectively. The solubility of Ca in MgSiO₃ at conditions along a mantle adiabat is found to be less than 0.02 atoms per formula unit. The solubility of Mg in CaSiO₃ is even lower, and most important, the extent of solid solution decreases with pressure. To dissolve CaSiO₃ perovskite completely in MgSiO₃ perovskite, a solubility of 7.8 or 2.3 mol% would be necessary for a fertile pyrolytic or depleted harzburgitic mantle, respectively. Thus, for any reasonable geotherm, two separate perovskites will be present in fertile mantle, suggesting that Ca-perovskite will be residual to low degree melting throughout the entire mantle. At the solidus, CaSiO₃ perovskite might completely dissolve in MgSiO₃ perovskite only in a depleted mantle with <1.25 wt% CaO. These implications may be modified if Ca solubility in MgSiO₃ is increased by other major mantle constituents such as Fe and Al.     

Low Mantle Perovskite: Solid Solution,Spin State of Iron and Water Solubility

Silicate perovskites((Mg, Fe)SiO 3 and CaS iO 3) are believed to be the major constituent minerals in the lower mantle. The phase relation, solid solution, spin state of iron and water solubility related to the lower mantle perovskite are of great effect on the geodynamics of the Earth's interior and on ore mineralization. Previous studies indicate that a large amount of iron coupled with aluminum can incorporate into magnesium perovskite, but this is discordant with the disproportionation of(Mg,Fe)SiO 3 perovskite into iron-free MgS i O3 perovskite and hexagonal phase(Mg0.6Fe0.4)SiO 3 in the Earth's lower mantle. MnS iO 3 is the first chemical component confirmed to form wide range solid solution with Ca SiO 3 perovskite and complete solid solution with MgS i O3 perovskite at the P-T conditions in the lower mantle, and addition of Mn Si O3 will strongly affects the mutual solubility between Mg Si O3 and CaS iO 3. The spin state of iron is deeply depends on the site occupation of the Fe3+or Fe2+, the synthesis and the annealing conditions of the sample. It seems that the spin state of Fe2+ in the lower mantle perovskite can be settled as high spin, however, the existence of intermediate spin or low spin state of Fe2+ in perovskite has not been clarified. Moreover, different results have also been reported for the spin state of Fe3+ in perovskite. The water solubility of the lower mantle perovskite is related with its composition. In pure Mg SiO 3 perovskite, only less than 500 ppm water was reported. Al–Mg Si O3 perovskite or Al–Fe–MgS iO 3 perovskite in the lower mantle accommodates water of 1100 to 1800 ppm. Further experiments are necessary to clarify the detailed conditions for perovskite solid solution, to reliably analyze the valence and spin states of iron in the coexisting iron-bearing phases, and to compare the water solubility of different phases at different layers for deeply understanding the geodynamics of the Earth's interior and ore mineralization.     

Electronic state of Fe2+ in (Mg,Fe)(Si,Al)O3 perovskite and (Mg,Fe)SiO3 majorite at pressures up to 81 GPa and temperatures up to 800 K

Despite a large number of studies of iron spin state in silicate perovskite at high pressure and high temperature, there is still disagreement regarding the type and P–T conditions of the transition, and whether Fe²⁺ or Fe³⁺ or both iron cations are involved. Recently, our group published results of a Mössbauer spectroscopy study of the iron behaviour in (Mg,Fe)(Si,Al)O₃ perovskite at pressures up to 110 GPa (McCammon et al. 2008), where we suggested stabilization of the intermediate spin state for 8- to 12-fold coordinated ferrous iron (^[8–12]Fe²⁺) in silicate perovskite above 30 GPa. In order to explore the behaviour in related systems, we performed a comparative Mössbauer spectroscopic study of silicate perovskite (Fe_0.12Mg_0.88SiO₃) and majorite (with two compositions—Fe_0.18Mg_0.82SiO₃ and Fe_0.11Mg_0.88SiO₃) at pressures up to 81 GPa in the temperature range 296–800 K, which was mainly motivated by the fact that the oxygen environment of ferrous iron in majorite is quite similar to that in silicate perovskite. The ^[8–12]Fe²⁺ component, dominating the Mössbauer spectra of majorites, shows high quadrupole splitting (QS) values, about 3.6 mm s^?1, in the entire studied P–T region (pressures to 58 GPa and 296–800 K). Decrease of the QS of this component with temperature at constant pressure can be described by the Huggins model with the energy splitting between low-energy e _g levels of ^[8–12]Fe²⁺ equal to 1,500 (50) cm^?1 for Fe_0.18Mg_0.82SiO₃ and to 1,680 (70) cm^?1 for Fe_0.11Mg_0.88SiO₃. In contrast, for the silicate perovskite dominating Mössbauer component associated with ^[8–12]Fe²⁺ suggests the gradual change of the electronic properties. Namely, an additional spectral component with central shift close to that for high-spin ^[8–12]Fe²⁺ and QS about 3.7 mm s^?1 appeared at ~35 (2) GPa, and the amount of the component increases with both pressure and temperature. The temperature dependence of QS of the component cannot be described in the framework of the Huggins model. Observed differences in the high-pressure high-temperature behaviour of ^[8–12]Fe²⁺ in the silicate perovskite and majorite phases provide additional arguments in favour of the gradual high-spin—intermediate-spin crossover in lower mantle perovskite, previously reported by McCammon et al. (2008) and Lin et al. (2008).     

Tetrahedral compression in (Mg,Fe)SiO3 orthopyroxenes

Single-crystal structure determinations at pressure have shown that the structural response of synthetic (Mg_0.6Fe_0.4)SiO₃ orthopyroxene to compression is the same as that previously observed in MgSiO₃ orthoenstatite. At pressure below ～4?GPa there is no significant compression of the SiO₄ tetrahedra, while above ～4?GPa the tetrahedra decrease in volume as a result of Si?O bond shortening. A study of the compressional behaviour of synthetic FeSiO₃ orthoferrosilite also shows the same behaviour below 4?GPa, but studies at higher pressures are precluded due to the transformation of the sample to the higher density C2/c high-clinoferrosilite polymorph. A further single-crystal study to 6?GPa of a Ca²⁺-containing natural orthopyroxene shows that chemical substitution of, primarily, Al³⁺ and Ca²⁺ into the structure of orthopyroxene inhibits the initial rapid compression of the M2?O3 bonds observed in the synthetic samples, and no significant tetrahedral compression is observed in this sample. Raman data collected from synthetic MgSiO₃ orthoenstatite show that there is a change in the rate of change of frequency with pressure, δν/δP, between 3.5 and 6.0?GPa, but no changes in the number of observed bands. These observations indicate a non-symmetry-breaking change in the properties of the orthoenstatite, which is associated with the change in compression mechanism observed using X-ray diffraction techniques at this pressure.     

Low-temperature heat capacities,entropies and enthalpies of Mg<Subscript>2</Subscript>SiO<Subscript>4</Subscript> polymorphs,and α−β−γ and post-spinel phase relations at high pressure

The low-temperature isobaric heat capacities (C _p) of β- and γ-Mg₂SiO₄ were measured at the range of 1.8–304.7 K with a thermal relaxation method using the Physical Property Measurement System. The obtained standard entropies (S°₂₉₈) of β- and γ-Mg₂SiO₄ are 86.4 ± 0.4 and 82.7 ± 0.5 J/mol K, respectively. Enthalpies of transitions among α-, β- and γ-Mg₂SiO₄ were measured by high-temperature drop-solution calorimetry with gas-bubbling technique. The enthalpies of the α−β and β−γ transitions at 298 K (ΔH°₂₉₈) in Mg₂SiO₄ are 27.2 ± 3.6 and 12.9 ± 3.3 kJ/mol, respectively. Calculated α−β and β−γ transition boundaries were generally consistent with those determined by high-pressure experiments within the errors. Combining the measured ΔH°₂₉₈ and ΔS°₂₉₈ with selected data of in situ X-ray diffraction experiments at high pressure, the ΔH°₂₉₈ and ΔS°₂₉₈ of the α−β and β−γ transitions were optimized. Calculation using the optimized data tightly constrained the α−β and β−γ transition boundaries in the P, T space. The slope of α−β transition boundary is 3.1 MPa/K at 13.4 GPa and 1,400 K, and that of β−γ boundary 5.2 MPa/K at 18.7 GPa and 1,600 K. The post-spinel transition boundary of γ-Mg₂SiO₄ to MgSiO₃ perovskite plus MgO was also calculated, using the optimized data on γ-Mg₂SiO₄ and available enthalpy and entropy data on MgSiO₃ perovskite and MgO. The calculated post-spinel boundary with a Clapeyron slope of −2.6 ± 0.2 MPa/K is located at pressure consistent with the 660 km discontinuity, considering the error of the thermodynamic data.     

High-pressure crystal chemistry of MgSiO3 perovskite

A high-pressure single-crystal x-ray diffraction study of perovskite-type MgSiO₃ has been completed to 12.6 GPa. The compressibility of MgSiO₃ perovskite is anisotropic with b approximately 23% less compressible than a or c which have similar compressibilities. The observed unit cell compression gives a bulk modulus of 254 GPa using a Birch-Murnaghan equation of state with K set equal to 4 and V/V ₀ at room pressure equal to one. Between room pressure and 5 GPa, the primary response of the structure to pressure is compression of the Mg-O and Si-O bonds. Above 5 GPa, the SiO₆ octahedra tilt, particularly in the [bc]-plane. The distortion of the MgO₁₂ site increases under compression. The variation of the O(2)-O(2)-O(2) angles and bondlength distortion of the MgO₁₂ site with pressure in MgSiO₃ perovskite follow trends observed in GdFeO₃type perovskites with increasing distortion. Such trends might be useful for predicting distortions in GdFeO₃-type perovskites as a function of pressure.     

Electron microscopy of high-pressure phases synthesized from natural olivine in diamond anvil cell

The products of the transformation of natural (Mg_0.83Fe_0.17)₂SiO₄ olivine have been prepared at various high pressures (between 25 GPa and 90 GPa), and high temperature in a laser-heated diamond-anvil cell (DAC). Studies of the high-pressure phases have been made by transmission electron microscopy (TEM), and X-ray microanalysis. The olivine/spinel boundaries exhibit all the characteristics of a diffusionless shear transition, having a finely sheared structure and a constant orientation relationship between the close-packed planes of the two structures ((100)_ol∥(111)_sp). The TEM observations of zones where olivine (or spinel) transforms into post-spinel phases show that the transformation possesses the features of an eutectoïdal decomposition, leading to a lamellar intergrowth of magnesiowüstite (Mg,Fe)O and perovskite (Mg,Fe)SiO₃. With increasing temperature and/or decreasing pressure, the grain size of the high-pressure phases increases and obeys an Arrhenius law with an activation volume equal to zero. (Mg,Fe)O grains exhibit a very high density of dislocations (higher than 10¹¹cm^?2), whereas (Mg,Fe)SiO₃ grains exhibit no dislocations but systematic twinning. The composition plane of the twins is (112) of the GdFeO₃-type perovskite, corresponding to the {110} plane of the cubic lattice of ideal perovskite.     

Prediction of high-temperature oxygen isotope fractionation factors between mantle minerals

The increment method is adopted to calculate oxygen isotope fractionation factors for mantle minerals, particularly for the polymorphic phases of MgSiO₃ and Mg₂SiO₄. The results predict the following sequence of ¹⁸O-enrichment: pyroxene (Mg,Fe,Ca)₂Si₂O₆>olivine (Mg,Fe)₂SiO₄>spinel (Mg,Fe)₂SiO₄>ilmenite (Mg,Fe, Ca)SiO₃>perovskite (Mg,Fe,Ca)SiO₃. The calculated fractionations for the calcite-perovskite (CaTiO₃) system are in excellent agreement with experimental calibrations. If there would be complete isotopic equilibration in the mantle, the spinel-structured silicates in the transition zone are predicted to be enriched in ¹⁸O relative to the perovskite-structured silicates in the lower mantle but depleted in ¹⁸O relative to olivines and pyroxenes in the upper mantle. The oxygen isotope layering of the mantle would essentially result from differences in the chemical composition and crystal structure of mineral phases at different mantle depths. Assuming isotopic equilibrium on a whole earth scale, the chemical structure of the Earth's interior can be described by the following sequence of ¹⁸O-enrichment: uppr crust>lower crust>upper mantle>transition zone>lower mantle >core.