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.     

Single crystal X-ray diffraction study of MgSiO3 perovskite from 77 to 400 K

Single crystal X-ray diffraction study of MgSiO₃ perovskite has been completed from 77 to 400 K. The thermal expansion coefficient between 298 and 381 K is 2.2(8) × 10^-5 K^-1. Above 400 K, the single crystal becomes so multiply twinned that the cell parameters can no longer be determined.From 77 to 298 K, MgSiO₃ perovskite has an average thermal expansion coefficient of 1.45(9) × 10^-5 K^-1, which is consistent with theoretical models and perovskite systematics. The thermal expansion is anisotropic; the a axis shows the most expansion in this temperature range (_a = 8.4(9) × 10^-6 K^-1) followed by c(_c = 5.9(5) × 10^-6 K^-1) and then by b, which shows no significant change in this temperature range. In addition, the distortion (i.e., the tilting of the [SiO₆] octahedra) decreases with increasing temperature. We conclude that the behavior of MgSiO₃ perovskite with temperature mirrors its behavior under compression.     

Crystal morphology and surface structures of orthorhombic MgSiO3 perovskite

Orthorhombic MgSiO₃ perovskite is thought to be the most abundant mineral in the mantle of the Earth. Its bulk properties have been widely studied, but many geophysical and rheological processes are also likely to depend upon its surface and grain boundary properties. As a first step towards modelling these geophysical properties, we present here an investigation of the structures and energetics of the surfaces of MgSiO₃-perovskite, employing both shell-model atomistic effective-potential simulations, and density-functional-theory (DFT) calculations. Our shell-model calculations predict the {001} surfaces to be the energetically most stable surfaces: the calculated value of the surface energy being 2.2 J/m² for the MgO-terminated surface, which is favoured over the SiO₂-terminated surface (2.7 J/m²). Also for the polar surfaces {111}, {101} and {011} the MgO-terminated surfaces are energetically more stable than the Si-terminated surfaces. In addition we report the predicted morphology of the MgSiO₃ perovskite structure, which is dominated by the energetically most stable {001} and {110} surfaces, and which appears to agree well with the shape of grown single crystals.     

Modelling of Al impurity in perovskite and ilmenite structures of MgSiO3

A methodology based on the Hartree–Fock theory is used to study pure MgSiO₃ crystals as well as Al doping in perovskite and ilmenite modifications of this mineral. Atomic displacements in the neighbourhood of the defect are obtained for cases when the Al substitutes for either Mg or Si host atoms. The atomic relaxation is due to the changes produced upon the chemical bonding within the defective region and in some occasions obeys the Coulomb electrostatic interaction. Band structure properties are briefly revised for the pure and doped minerals. The occurrence of Al-bound hole polaron is predicted in the ilmenite mineral. The results of output are compared to the available reports on the same subject in both experimental and theoretical fields of the investigation.     

Thermodynamic properties of MgSiO3 perovskite derived from large scale molecular dynamics simulations

A molecular dynamics simulation study of MgSiO₃ has been performed using a large sample containing 4096 unit cells. Thermodynamic properties have been extracted using a semiclassical approximation to the correct quantum mechanical treatment, using the calculated density of states and the quantum harmonic formalism for thermodynamic functions. Simulations performed at different temperatures and volumes have given an estimate of the relative contributions due to thermal expansion (quasi-harmonic effects) and direct anharmonic interactions. Comparison of results for mean square atomic displacements with results on smaller samples have shown the limitations of smaller sample sizes.     

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.     

Effect of pressure on the crystal structure of perovskite-type MgSiO3

The crystal structure of perovskite-type MgSiO₃ has been studied up to 96 kbar, using a miniature diamondanvil pressure cell and by means of single-crystal four-circle diffractometry. The observed unit cell compression gives a bulk modulus of K _o=2.47 Mbar, assuming K′_o=4. The unit cell compression is controlled mainly by the tilting of SiO₆ octahedra. The effect of pressure is to change Mg polyhedron towards 8-fold coordination rather than 12-fold coordination. The polyhedral bulk moduli of SiO₆ and MgO₈ are 3.8 Mbar and 1.9 Mbar, respectively.     

A quantum-mechanical study of the relative stability under pressure of MgSiO3-ilmenite,MgSiO3-perovskite,and MgO-periclase+SiO2-stishovite assemblage

The relative stability of MgSiO₃-ilmenite, MgSiO₃-perovskite and (periclase+stishovite) assemblage phases as a function of the pressure is investigated with the periodic quantum mechanical ab initio HartreeFock program CRYSTAL. For the first time, the structure of MgSiO₃-ilmenite is fully optimized. Basis set effects are explored. It turns out that relatively small basis sets reproduce correctly experimental geometries. However, larger basis sets (triple zeta quality, plus polarization d functions) are needed to yield significant thermochemical results. All contributions to the 0 K enthalpy are discussed. On the basis of the present highest level calculations, it appears that in the explored range of pressure (0P< 60=" gpa)=" the=" mineralogical=" assemblage=" periclase+stishovite=" has=" higher=" enthalpy=" than=">₃-ilmenite or perovskite, and that ilmenite transforms to orthorhombic perovskite around to 29.4 GPa in good agreement with experimental data extrapolated down to 0 K.     

A high P-T single-crystal X-ray diffraction study of thermoelasticity of MgSiO3 orthoenstatite

P-V-T data of MgSiO₃ orthoenstatite have been measured by single-crystal X-ray diffraction at simultaneous high pressures (in excess of 4.5 GPa) and temperatures (up to 1000 K). The new P-V-T data of the orthoenstatite, together with previous compression data and thermal expansion data, are described by a modified Birch-Murnaghan equation of state for diverse temperatures. The fitted thermoelastic parameters for MgSiO₃ orthoenstatite are: thermal expansion ?α/?P with values of a=2.86(29)×10^-5 K^-1 and b=0.72(16)×10^-8 K^-2; isothermal bulk modulus K _{T o} =102.8(2) GPa; pressure derivative of bulk modulus K′=?K/?P=10.2(1.2); and temperature derivative of bulk modulus K=?K/?T=-0.037(5) GPa/K. The derived thermal Grüneisen parameter is γ _th=1.05 for ambient conditions; Anderson-Grüneisen parameter is δ _{T o} =11.6, and the pressure derivative of thermal expansion is ?α/?P=-3.5×10^-6K^-1 GPa^-1. From the P-V-T data and the thermoelastic equation of state, thermal expansions at two constant pressures of 1.5 GPa and 4.0 GPa are calculated. The resulting pressure dependence of thermal expansion is Δα/ΔP=-3.2(1)× 10^-6 K^-1 GPa^-1. The significantly large values of K′, K, δ _T and ?α/?P indicate that compression/expansion of MgSiO₃ orthoenstatite is very sensitive to changes of pressure and temperature.     

The site of Fe in Fe-bearing MgSiO3 enstatite and perovskite. a theoretical-, x-ray multiple-scattering study at Fe K-edge

Two polycrystalline-, Fe-bearing MgSiO₃ enstatite and perovskite have been probed by x-ray absorption near edge structure (XANES) spectroscopy at the Fe K-edge under ambient conditions. The perovskite sample was synthesized at 260 kbar and 1973 K in a multianvil apparatus. The experimental XANES spectrum has been compared to ab-initio-, x-ray multiple-scattering calculations (Feff 6 code). Calculations confirm that the Fe K-edge arises mainly from multiple scattering involving the first shell of oxygen neighbors around Fe. In Fe-enstatite, these calculations are consistent with Fe²⁺ as substituted in the M2 site of this orthopyroxene, in good agreement with crystal structure refinements and previous XANES studies. In perovskite, Feff 6 suggests that Fe is likely to be substituted to Mg within the (8+4)-coordinated sites of that perovskite. No evidences for 6-coordinated Fe were found. These results are consistent with a previous anharmonic analysis of the extended x-ray absorption fine structure (EXAFS) study that evidenced the presence of 8-coordinated Fe in the same perovskite sample.     

钙钛矿结构MgSiO3的分子动力学研究——体系大小对弹性性质与状态方程的影响

本文利用分子动力学模拟方法,研究了300~3000K、0.1~100GPa条件下,MgSiO3钙钛矿大小两个体系的平衡状况和热力学性质,并将大小两个体系的模拟结果与高温高压实验结果进行比较,验证体系大小对哪些物理性质有影响以及影响有多大,为后续工作选择合适的模拟体系进行模拟研究工作提供参考。研究发现,无论在模拟的平衡过程中还是利用模拟数据对状态方程参数的拟合中,大体系的拟合结果都比小体系的计算结果接近高温高压实验结果。大体系的各项模拟结果与高温高压实验结果相比,相差均在1%左右。因此,在计算条件允许的情况下,尽量模拟较大的体系有助于得到更精确的分子动力学研究结果。     

Ab initio study of MgSiO3 C2/c enstatite

We have used a newly developed ab initio constant-pressure molecular dynamics with variable cell shape technique to investigate the zero temperature behaviour of high pressure clinoenstatite (MgSiO₃-C2/c) from 0 up to 30 GPa. The optimum structure at 8 GPa, as well as structural trends under pressure, compare very well with experimental data. At this pressure, we find noticeable “fluctuations” in the chain configuration which suggests the structure is on the verge of a mechanical instability. Two distinct compressive behaviours then appear: one below and another above 8 GPa. This phenomenon may be related to the observed transition to a lower symmetry P2₁/c phase which involves a reconfiguration of the silicate chains, and suggests that the C2/c structure at low pressures found here, may be an artifact of the dynamical algorithm which preserves space group in the absence of symmetry breaking fluctuations. Comparison with calculations in other magnesium silicate phases, indicates that the size and shape of the silicate units (isolated and/or linked tetrahedra and octahedra) are generally well described by the local density approximation; however, the weaker linkages provided by the O-Mg-O bonds, are not as well described. This trend suggests that, as in the recently studied case of H₂O-ice, the structural properties of more inhomogeneous systems, like enstatite, may be improved by using gradientcorrected density functionals.     

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     

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.     

Phase changes and thermodynamic properties of CaTiO3. Spectroscopic data,vibrational modelling and some insights on the properties of MgSiO3 perovskite

The effect of pressure (up to 21 GPa at room temperature) and temperature (up to 1570 K at room pressure) on the Raman spectrum of CaTiO₃ is presented. No significant changes, which could be attributed to a major structural change, are observed in the spectra up to 22 GPa. The pressure shifts of the Raman modes can be related to a significant compression of the Ti-O bond. Discontinuous changes in the spectra upon heating may be related to phase changes observed by calorimetry and X-ray diffraction. The important temperature shifts of some low-frequency modes can be related to an increase in the Ti-O-Ti angle in agreement with the X-ray data showing a decrease of the structural distortion with increasing temperature. These data are compared to those available for MgSiO₃-perovskite and show that CaTiO₃ is a good structural analogue for MgSiO₃-perovskite. The present spectroscopic data are used to calculate the specific heat and entropy of CaTiO₃. The role of the low frequency modes in the calculations is emphasized. Good agreement is observed between calculated and experimentally determined values in the 0–1300 K temperature range. A similarly defined model is proposed for MgSiO₃-perovskite. It is found that the entropy lies between 57 and 64 J/mol/K at 298 K and between 190 and 200 J/mol/K at 1000 K in agreement with the values inferred from experimental equilibrium data. Finally we briefly discuss the values of the Grüneisen parameters of both perovskites inferred from macroscopic and microscopic data.     

High pressure study of ScAlO3 perovskite

The crystal structure of orthorhombic (Pbnm) ScAlO₃ perovskite has been refined to 5 GPa using single-crystal X-ray diffraction. The compression of the structure if anisotropic with β _a =1.39(3)×10⁻³ GPa⁻¹, β _b =1.14(3)×10⁻³ GPa⁻¹ and β _c =1.84(3)×10⁻³ GPa⁻¹. The isothermal bulk modulus of ScAlO₃, K _T , determined from fitting a Birch-Murnaghan equation of state (K ^′ _T =4) to the volume compression data is 218(1) GPa. The interoctahedral angles to not vary significantly with pressure, and the compression of the structure is entirely attributable to compression of the AlO₆ octahedra. The compressibilities of the constituent AlO₆ and ScO₁₂ are well matched: β_Al−O=1.6×10⁻³ GPa⁻¹ and β_Sc−O=1.5×10⁻³ GPa⁻¹. Therefore the distortion of the structure shows no significant change with increasing pressure. Received: 18 August 1997 / Revised, accepted: 11 November 1997     

SrTiO3基钙钛矿结构X射线衍射谱特征

通过对常规电子陶瓷工艺合成的Sr1-xCaxTiO3和Sr1-xPbxTiO3钙钛矿结构陶瓷进行研究X射线衍射谱特征、晶体结构和衍射强度I100/I110进行研究,并根据原子散射因子与衍射强度关系,提出用衍射强度I100/I110变化规律预测ABO3钙钛矿结构中置换A位离子种类的方法.     

Ab initio study of the high-pressure behavior of CaSiO3 perovskite

Using density functional simulations, within the generalized gradient approximation and projector-augmented wave method, we study structures and energetics of CaSiO₃ perovskite in the pressure range of the Earths lower mantle (0–150 GPa). At zero Kelvin temperature the cubic CaSiO₃ perovskite structure is unstable in the whole pressure range, at low pressures the orthorhombic (Pnam) structure is preferred. At 14.2 GPa there is a phase transition to the tetragonal (I4/mcm) phase. The CaIrO₃-type structure is not stable for CaSiO₃. Our results also rule out the possibility of decomposition into oxides.