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1.
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.  相似文献   

2.
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 (Mg0.5, Mn0.5)SiO3 perovskite is almost unchanged with increasing pressure from 30 to 50 GPa. On the other hand, that distortion in (Mg0.9, Mn0.1)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 (Mg0.9, Mn0.1)SiO3. MnSiO3 is the first chemical component confirmed to form a complete solid solution with MgSiO3 perovskite at the PT conditions present in the lower mantle.  相似文献   

3.
Kankan diamonds (Guinea) II: lower mantle inclusion parageneses   总被引:3,自引:2,他引:1  
Frequent inclusions of ferropericlase, some coexisting with phases of MgSiO3, CaSiO3 and SiO2 composition, suggest that a large proportion of diamonds from Guinea are derived from the lower mantle. Low aluminium contents in MgSiO3 inclusions indicate derivation from the uppermost lower mantle, where Al solubility in perovskite is low. Trace element analyses (SIMS) of CaSiO3 inclusions reveal extreme degrees of LREE (200–2000 times chondritic) and Sr enrichment (70–1000 times chondritic) together with negative and positive Eu anomalies. This implies a highly enriched lower mantle source, possibly a product of a subducted oceanic slab. A number of phases that are only stable in the upper mantle are found to coexist with lower mantle phases and thereby indicate retrograde equilibration during slow exhumation within a rising plume or convection cell. In one case, however, an inclusion paragenesis of ferropericlase and olivine can be shown to have formed within the upper mantle, indicating that the occurrence of ferropericlase inclusions alone is an unreliable indicator of lower mantle origin. Received: 26 January 2000 / Accepted: 18 May 2000  相似文献   

4.
We have determined the partitioning of a wide range of trace elements between silicate melts and CaSiO3 and MgSiO3 perovskites using both laser ablation-ICPMS and ion microprobe techniques. Our results show that, with the exception of Sc, Zr, and Hf, all trace elements we considered are incompatible in MgSiO3 perovskite, from highly incompatible for U, Th, Ba, La, Sr and monovalent elements to slightly incompatible for heavy rare earth elements. MgSiO3 perovskite-melt partition coefficients increase slightly with Al content in the perovskite. These observations contrast strongly with partitioning between CaSiO3 perovskite and silicate melts. In the latter case, all rare earth elements are clearly compatible as are U and Th. Our data also suggest that, contrary to pressure and temperature, melt composition can significantly affect CaSiO3 perovskite-melt partitioning; partition coefficients for rare earth elements and U and Th increase with decreasing CaO melt content. The presence of ∼0.4 wt% water in melt makes little difference, however. Partitioning of trace elements into the large site of both MgSiO3 and CaSiO3 perovskites follows the near-parabolic dependence on ionic radius predicted from the lattice strain model. The peaks of the parabolae are much higher for the CaSiO3 phase, perhaps suggesting that the mechanisms of charge compensation for heterovalent substitution are different in the two cases. Our partitioning data have been used to assess the potential effect of perovskite fractionation into the lower mantle during early Earth history. Crystallisation of less than 8% of a mixture of CaSiO3 and MgSiO3 perovskites could have led to a ‘layer’ enriched in U and Th without disturbing the chondritic pattern of refractory lithophile elements in the primitive upper mantle. The resultant reservoir could have high Sm/Nd, U/Pb, Sr/Rb, Lu/Hf ratios similar to the HIMU component of ocean island basalts, but would not balance the observed depletion of the primitive upper mantle in Si and Nb.  相似文献   

5.
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 PT 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 (Fe0.12Mg0.88SiO3) and majorite (with two compositions—Fe0.18Mg0.82SiO3 and Fe0.11Mg0.88SiO3) 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 PT 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 Fe0.18Mg0.82SiO3 and to 1,680 (70) cm?1 for Fe0.11Mg0.88SiO3. 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).  相似文献   

6.
Semi-empirical and quantum chemical studies of Al atom energy in CaSiO3 and MgSiO3 with the perovskite-type structure at pressures and temperatures of the Earth’s mantle are reported. The phase diagram for CaSiO3 is reproduced and refined. Probable mechanisms of Al incorporation in the structures studied are considered. According to the results of the calculations, Al is preferably incorporated into MgSiO3, rather than into CaSiO3. Evaluation of the isomorphic capacity of perovskite phases in relation to Al shows that the Al content in MgSiO3 may reach 2.4 mol % at 120 GPa and 2400 K. CaSiO3 cannot be a source of Al atoms in the Earth’s mantle.  相似文献   

7.
High-pressure and temperature experiments (28–62 GPa, and 1,490–2,000 K, corresponding to approximately 770–1,500 km depth in the mantle) have been conducted on a MgCO3 + SiO2 mixture using a laser-heated diamond anvil cell combined with analytical transmission electron microscope observation of the product phases to constrain the fate of carbonates carried on the subducting basalt into the lower mantle. At these conditions, the decarbonation reaction MgCO3 (magnesite) + SiO2 (stishovite) → MgSiO3 (perovskite) + CO2 (solid) has been recognized. This indicates that above reaction takes place as a candidate for decarbonation of the carbonated subducting mid ocean ridge basalts in the Earth’s lower mantle.  相似文献   

8.
The molar volumes and bulk moduli of CaSiO3 perovskite are calculated in the temperature range from 300 to 2,800 K and the pressure range from 0 to 143 GPa using molecular dynamics simulations that employ the breathing shell model for oxygen and the quantum correction in addition to the conventional pairwise interatomic potential models. The performance of five equations of state, i.e., the Keane, the generalized-Rydberg, the Holzapfel, the Stacey–Rydberg, and the third-order Birch–Murnaghan equations of state are examined using these data. The third-order Birch–Murnaghan equation of state is found to have a clear tendency to overestimate the bulk modulus at very high pressures. The Stacey–Rydberg equation of state degrades slightly at very high pressures along the low-temperature isotherms. In comparison, the Keane and the Holzapfel equations of state remain accurate in the whole temperature and pressure range considered in the present study. K 0′ derived from the Holzapfel equation of state also agrees best with that calculated independently from molecular dynamics simulations. The adiabatic bulk moduli of CaSiO3 perovskite along lower mantle geotherms are further calculated using the Keane and the Mie-Grüneisen–Debye equations of state. They are found to be constantly higher than those of the PREM by ~5%, and also very similar to those of the MgSiO3 perovskite. Our results support the view that CaSiO3 perovskite remains invisible in the Earth’s lower mantle.  相似文献   

9.
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.  相似文献   

10.
We have determined the partition coefficients of a large number of trace elements between CaTiO3 perovskite and anhydrous silicate melts at atmospheric pressure and 3 GPa. Determination of the concentration limits of Henrys law behaviour in the CaO-Al2O3–SiO2–TiO2 system reveals that the incorporation of rare earth elements (REE) and tetravalent large ion lithophile elements (LILE4+ such as U and Th) at the Ca-site of CaTiO3 perovskite occurs with charge compensation through Ca-vacancy formation rather than by coupled substitution of Al for Ti. When melt composition is varied, we find that partition coefficients for REE and Th are strong functions of the CaO content of the melt. The observed trends are in excellent agreement with those predicted from the Ca-vacancy model. Given that they adopt the same crystal structure and have similar trace element partitioning behaviour, CaTiO3 perovskite and the deep mantle phase CaSiO3 perovskite can be considered analogous to one another. When the analogy is pursued in detail, we find that partitioning into both phases follows the composition-dependence predicted by the Ca-vacancy model. Thus, substitution of REE, U4+ and Th into CaSiO3 in the lower mantle also occurs with Ca-vacancy formation to balance charge. Furthermore when 2+, 3+ and 4+ partition coefficients for both phases are plotted as functions of CaO melt content, the trends for CaSiO3 and CaTiO3 appear to be continuous. This surprising result means that partitioning into Ca-perovskite is independent of pressure and temperature and also of whether or not the host is CaSiO3 or CaTiO3. One implication is that CaSiO3 crystallising from a peridotitic magma ocean may have partition coefficients for Th and U up to about 400. Crystallisation and sequestration of as little as 0.25 volume% of this phase in the lower mantle early in earth history would make a significant contribution to current mantle heat production.Electronic Supplementary Material Supplementary material is available for this article at  相似文献   

11.
Fifteen samples of (Mg,Fe)SiO3 majorite with varying Fe/Mg composition and one sample of (Mg,Fe)(Si,Al)O3 majorite were synthesized at high pressure and temperature under different conditions of oxygen fugacity using a multianvil press, and examined ex situ using X-ray diffraction and Mössbauer and optical absorption spectroscopy. The relative concentration of Fe3+ increases both with total iron content and increasing oxygen fugacity, but not with Al concentration. Optical absorption spectra indicate the presence of Fe2+–Fe3+ charge transfer, where band intensity increases with increasing Fe3+ concentration. Mössbauer data were used in conjunction with electron microprobe analyses to determine the site distribution of all cations. Both Al and Fe3+ substitute on the octahedral site, and charge balance occurs through the removal of Si. The degree of Mg/Si ordering on the octahedral sites in (Mg,Fe)SiO3 majorite, which affects both the c/a ratio and the unit cell volume, is influenced by the thermal history of the sample. The Fe3+ concentration of (Mg,Fe)(Si,Al)O3 majorite in the mantle will reflect prevailing redox conditions, which are believed to be relatively reducing in the transition zone. Exchange of material across the transition boundary to (Mg,Fe) (Si,Al)O3 perovskite would then require a mechanism to oxidize sufficient iron to satisfy crystal-chemical requirements of the lower-mantle perovskite phase.  相似文献   

12.
The crystal structure of ScAlO3 has been refined at temperatures up to 1100° C on the basis of x-ray powder diffraction data. The thermal expansion is adequately described by a Grüneisen-Debye model with the elastic Debye temperature and an effective Grüneisen parameter of 1.6. The volumetric thermal expansion of 3.0% between 10 and 1100° C, corresponding to a mean thermal expansion coefficient of 2.7 × 10−5 K−1, is entirely attributable to the expansion of the AlO6 octahedra. The interoctahedral angles, though not fixed by symmetry, do not vary significantly with temperature —indicating that the expansivities of the constituent AlO6 and distorted ScO8 polyhedra are well matched. Similar considerations of polyhedral expansivity suggest thermal expansion coefficients of ∼2 × 10−5K−1 for cubic CaSiO3 perovskite and a value between 2 × 10−5 K−1 and 4 × 10−5 K−1 for MgSiO3 perovskite. The lower value is consistent with the reconnaissance measurements for Mg0.9Fe0.1SiO3 (Knittle et al. 1986) below 350° C, with low-temperature measurements of single-crystal MgSiO3 (Ross and Hazen 1989), and with the results of some recent calculations. The markedly greater expansivity ∼4 × 10−5 K−1 measured at higher temperatures (350–570° C) by Knittle et al. is inconsistent with the simple Grüneisen-Debye quasiharmonic model and may reflect the marginal metastability of the orthorhombic perovskite phase. Under these circumstances, extrapolation of the measured expansivity is hazardous and may result in the under-estimation of lower mantle densities and the drawing of inappropriate inferences concerning the need for chemical stratification of the Earth's mantle.  相似文献   

13.
The postperovskite phase transition of Fe and Al-bearing MgSiO3 bridgmanite, the most aboundant mineral in the Earth's lower mantle, is believed to be a key to understanding seismological observations in the D″ layer, e.g., the discontinuous changes in seismic wave velocities. Experimentally reported phase transition boundaries of Fe and Al-bearing bridgmanite are currently largely controversial and generally suggest wide two-phase coexistence domains. Theoretical simulations ignoring temperature effects cannot evaluate correctly two-phase coexistence domains under high-temperature. We show high-pressure and high-temperature phase transition boundaries for various compositions with geophysically relevant impurities of Fe2+SiO3, Fe3+Fe3+O3, Fe3+Al3+O3, and Al3+Al3+O3 derived from the ab initio finite-temperature free energies calculated combining the internally consistent LSDA + U method and a lattice dynamics approach. We found that at ~ 2500 K, incorporations accompanied by Fe3+ expand the two-phase coexistence domains distinctly, implying that D″ seismic discontinuities likely arise from the phase transition of Fe2+-bearing bridgmanite.  相似文献   

14.
15.
Phase relations in the system CaTiO3-CaSiO3 were experimentally examined at 5.3–14.7 GPa and 1200–1600 °C with a 6–8 type multianvil apparatus. As pressure increases, stability field of perovskite solid solution extends from CaTiO3 to CaSiO3, and the perovskite becomes stable for the entire composition range above about 12.3 GPa. The stability field of Ca(Ti1?X, SiX)2O5 (0.78<x≦1) titanite solid solution +Ca2SiO4 larnite exists in the CaSiO3-rich composition range at 9.3–12.3 GPa and 1200 °C. Perovskite solid solutions containing CaSiO3 component of 0 to 66 mol% could be quenched to 1 atm. The composition-molar volume relationship of perovskite solid solution showed that molar volume of perovskite solid solution linearly reduces from the value of CaTiO3 to that of CaSiO3.  相似文献   

16.
Many rheological and transport properties of rocks are determined by the grain boundary structures of their constituent minerals. These grain boundaries often also hold a high concentration of dopant ions. Here, as a first step towards modelling the transport and rheological behaviour of the lower mantle, we report the results of lattice static simulations on the surface structures of Fe2+ and Ca2+-doped orthorhombic MgSiO3-perovskite. For all the surfaces we studied, the energies of the doped structures are lowered, sometimes by more than 1 J/m2, with respect to the pure surfaces. From our calculated crystal morphologies, we predict that the grains become more tabular as the concentration of Fe2+ ions increases, while under equilibrium conditions the grains are cubic. By calculating the replacement energies of Mg2+ by Fe2+ and Ca2+ ions in the six outermost surface layers, we conclude that these divalent ions would tend to segregate onto the crystal surfaces. We suggest, therefore, that the grain boundary structure and rheology of MgSiO3-perovskite dominated rocks will be strongly affected by the presence of minor elements in the lower mantle.  相似文献   

17.
We investigated the valence state and spin state of iron in an Al-bearing ferromagnesian silicate perovskite sample with the composition (Mg0.88Fe0.09)(Si0.94Al0.10)O3 between 1 bar and 100 GPa and at 300 K, using diamond cells and synchrotron Mössbauer spectroscopy techniques. At pressures below 12 GPa, our Mössbauer spectra can be sufficiently fitted by a “two-doublet” model, which assumes one ferrous Fe2+-like site and one ferric Fe3+-like site with distinct hyperfine parameters. The simplest interpretation that is consistent with both the Mössbauer data and previous X-ray emission data on the same sample is that the Fe2+-like site is high-spin Fe2+, and the Fe3+-like site is high-spin Fe3+. At 12 GPa and higher pressures, a “three-doublet” model is necessary and sufficient to fit the Mössbauer spectra. This model assumes two Fe2+-like sites and one Fe3+-like site distinguished by their hyperfine parameters. Between 12 and 20 GPa, the fraction of the Fe3+-like site, Fe3+/∑Fe, changes abruptly from about 50 to 70%, possibly due to a spin crossover in six-coordinate Fe2+. At pressures above 20 GPa, the fractions of all three sites remain unchanged to the highest pressure, indicating a fixed valence state of iron within this pressure range. From 20 to 100 GPa, the isomer shift between the Fe3+-like and Fe2+-like sites increases slightly, while the values and widths of the quadruple splitting of all three sites remain essentially constant. In conjunction with the previous X-ray emission data, the Mössbauer data suggest that Fe2+ alone, or concurrently with Fe3+, undergoes pressure-induced spin crossover between 20 and 100 GPa.  相似文献   

18.
The role of phase transformations in a mantle of pyrolite composition is reviewed in the light of recent experimental data. The pyroxene component of pyrolite transforms to the garnet structure at 300–350 km whilst olivine transforms to beta-Mg2SiO4 near 400 km. Between about 500 and 550 km, beta-Mg2SiO4 probably transforms to a partially inverse spinel structure whilst the CaSiO3 component of the complex garnet solid solution exsolves and transforms to the perovskite structure. The major seismic discontinuity near 650–700 km is probably caused by disproportionation of Mg2SiO4 spinel into periclase plus stishovite. At a slightly greater depth, the remaining magnesian garnet transforms to the corundum or ilmenite structure. Finally, at a depth probably in the vicinity of 800–1000 km, the (Mg,Fe)SiO3 component of the ilmenite phase transforms to a perovskite structure whilst stishovite and some of the periclase recombine to form perovskite also. The mineral assemblage so formed is about 4% denser than mixed oxides (MgO + FeO + A12O3 + CaO + stishovite) isochemical with pyrolite. The above sequence of phase transformations in pyrolite provides a satisfactory general explanation of the elastic properties and density distribution in the mantle. In particular, there is no evidence requiring an increase of FeO/(FeO + MgO) ratio with depth.The depths at which major phase transformations occur in subducted lithosphere differ from those in ‘normal’ mantle. These differences are caused by two factors: (1) Temperatures within sinking plates are much lower than in surrounding mantle to depths of 700 km or more. (2) Irreversible chemical differentiation of pyrolite occurs at oceanic ridges. Lithosphere plates so formed consist of a layer of basaltic rocks underlain successively by layers of harzburgite, lherzolite, and pyrolite slightly depleted in highly incompatible elements (e.g. La, Ba, Rb, U). The phase-transformation behaviour of the first three of these layers differs from that of pyrolite.The effects of these and other factors connected with phase transformations on the dynamics of plate subsidence are discussed. It appears quite likely that plates penetrate the 650–700 km discontinuity, largely because the slope of the spinel disproportionation is probably positive, not negative as generally supposed. The former basaltic oceanic crust probably sinks deeply into the lower mantle, whilst the former harzburgite component of the plate may collect above the perovskite transition boundary. Phase transformations may thus serve as a kind of filter, leading to increased and irreversible mantle heterogeneity with time.The possible roles of phase transformations in causing deep-focus earthquakes and introducing water into the mantle in subduction zones are also briefly discussed.  相似文献   

19.
In this paper I present results of IR spectroscopic measurements of water solubility in Al-bearing periclase and ferropericlase (Mg# = 88) synthesized at 25 GPa and 1400–2000 °C. The IR spectra of their crystals show narrow absorption peaks at 3299, 3308, and 3474 cm?1. The calculated H2O contents are 11–25 ppm in periclase (Al2O3 = 0.9–1.2 wt.%) and 14–79 ppm in ferropericlase (Al2O3 = 0.9–2.9 wt.%). Ferropericlase contains more H2O and Al2O3 than periclase at 1800–2000 °C. I suggest that addition of Al2O3 does not influence the solubility of water in ferropericlase but can favor the additional incorporation of Fe2O3 into the structure. The incorporation of Fe3+ into ferropericlase increases water solubility as a result of iron reduction to Fe2+. It is shown that water has limited solubility in ferropericlase from mantle peridotite; therefore, ferropericlase cannot be considered an important hydrogen-bearing mineral in the lower mantle.  相似文献   

20.
Magnesium silicate perovskite is the predominant phase in the Earth’s lower mantle, and it is well known that incorporation of iron has a strong effect on its crystal structure and physical properties. To constrain the crystal chemistry of (Mg, Fe)SiO3 perovskite more accurately, we synthesized single crystals of Mg0.946(17)Fe0.056(12)Si0.997(16)O3 perovskite at 26 GPa and 2,073 K using a multianvil press and investigated its crystal structure, oxidation state and iron-site occupancy using single-crystal X-ray diffraction and energy-domain Synchrotron Mössbauer Source spectroscopy. Single-crystal refinements indicate that all iron (Fe2+ and Fe3+) substitutes on the A-site only, where \( {\text{Fe}}^{ 3+ } /\Upsigma {\text{Fe}}\sim 20\,\% \) based on Mössbauer spectroscopy. Charge balance likely occurs through a small number of cation vacancies on either the A- or the B-site. The octahedral tilt angle (Φ) calculated for our sample from the refined atomic coordinates is 20.3°, which is 2° higher than the value calculated from the unit-cell parameters (a = 4.7877 Å, b = 4.9480 Å, c = 6.915 Å) which assumes undistorted octahedra. A compilation of all available single-crystal data (atomic coordinates) for (Mg, Fe)(Si, Al)O3 perovskite from the literature shows a smooth increase of Φ with composition that is independent of the nature of cation substitution (e.g., \( {\text{Mg}}^{ 2+ } - {\text{Fe}}^{ 2+ } \) or \( {\text{Mg}}^{ 2+ } {\text{Si}}^{ 4+ } - {\text{Fe}}^{ 3+ } {\text{Al}}^{ 3+ } \) substitution mechanism), contrary to previous observations based on unit-cell parameter calculations.  相似文献   

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