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.     

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.     

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.     

Ion migration in MgSiO3-perovskite and olivine by molecular dynamics calculations

We applied molecular dynamics (MD) simulations to finding likely paths of atomic migration of the Mg ion in forsterite (Mg₂SiO₄) and the oxygen ion in MgSiO₃-perovskite to better understand atomic diffusion in minerals. Our simulations show that there exist two routes of Mg migration in the forsterite structure, that is, paths between the M1 and M2 sites and between the M1 and M1 sites. In the MgSiO₃-perovskite structure, some oxygen ions migrate to the next sites all together through the O1 vacant site showing co-operative movements. The O ions are relatively mobile mainly along the b axis in the perovskite structure. Meta-stable sites are often present between a stable site and another stable site on atomic migration. In spite of many assumptions, our MD simulations may show likely paths of atomic migration in crystal.     

A thermochemical data base for phase equilibria in the system Fe-Mg-Si-O at high pressure and temperature

A thermochemical data base for phases in the system Fe-Mg-Si-O at high pressures up to 300 kbar is established by supplementing the available calorimetric data with data calculated from experimental high pressure synthesis studies. Phases included in the data base are the SiO₂ polymorphs, rock salt solid solutions (Fe-Mg-O), Fe₂O₃, Fe₃O₄, (Mg, Fe)₂SiO₄ olivine, spinel, modified spinel and (Mg, Fe)SiO₃ perovskite and pyroxene. Phases not included are the MgSiO₃-ilmenite and -garnet. Fe-Mg solution properties of olivine, spinel, perovskite and wustite (rock salt) are estimated. The wüstite solid solution has been modeled as a nonideal solution of three end members; FeO, FeO_1.5 and MgO. The new data base is made consistent with most of the available information on high pressure phase studies. The data base is useful in generating phase diagrams of various different compositions for the purpose of planning new experiments and analysing existing phase synthesis data.     

The thermodynamics of substances at very high pressures and temperatures and some mineral reactions in the earth's mantle

The thermodynamic properties of 25 substances (elements, compounds, modifications) are calculated on the basis of an extrapolation of their caloric values and compressibilities into the region of pressures up to 2mbar and temperatures up to 4,000K. The extrapolation methods are described. The ratio of molar volumes is used to predict the thermodynamic properties of the high pressure modifications. It is inferred that water vapour and oxides of Mg, Fe, and Si ought to be stable in the entire mantle. In the lower mantle garnet should be more stable than the perovskite-type phase of MgSiO₃ (in presence of Al₂O₃ or Fe₂O₃). ‘Perovskite’ phase plus MgO are more stable here than forsterite, Mg₂SiO₄. Pyrrhotite, FeS, reveals astonishing stability in the entire mantle and in the outer core as well. Carbon dioxide, CO₂, may exist only in the upper mantle, whereas methane, CH₄, remains stable in the entire mantle.     

Electrical conductivity measurements on olivines and pyroxenes under defined thermodynamic activities as a function of temperature and pressure

Electrical conductivities of Ni₂SiO₄, Fe₂SiO₄, and MgSiO₃ were measured on synthetic powders in the temperature range 340° to 1,100° C and at pressures up to 20 kbars. For ternary compounds such as olivines and pyroxenes the control of two further variables, like the chemical activities of two components are needed, besides temperature and pressure. The activities of the corresponding binary oxides were controlled by equilibrating the samples with their neighbour-phases. Control of the oxygen partial pressure was achieved by buffer techniques. From the slopes of the lg σ vs. 1/T lines the activation energies were calculated for 10 kbar: 0.56 eV and 2.7 eV for Ni₂SiO₄ in equilibrium with SiO₂ and Ni/NiO-buffer for the temperature range 500°–800°C and 800°–1,000°C resp. 0.52 eV for Fe₂SiO₄ in equilibrium with SiO₂ and metallic iron, and 0.38 eV in equilibrium with SiO₂ and magnetite; 1.11 eV for MgSiO₃ in equilibrium with SiO₂, and 1.25 eV in equilibrium with Mg₂SiO₄.     

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.     

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.     

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.     

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.     

Raman spectra of MgSiO3·10% Al2O3-perovskite at various pressures and temperatures

Variations of Raman spectra of MgSiO₃·10% Al₂O₃-perovskite were investigated up to about 270 kbar at room temperature and in the range 108–425 °K at atmospheric pressure. Like MgSiO₃-perovskite, the Raman frequencies of MgSiO₃·10% Al₂O₃-perovskite increase nonlinearly with increasing pressure and decrease linearly with increasing temperature within the experimental uncertainties and the range investigated. A comparison of these data with those of MgSiO₃-perovskite suggests that MgSiO₃·10% Al₂O₃-perovskite is slightly more compressible than MgSiO₃-perovskite, and that the volume thermal expansion for MgSiO₃·10% Al₂O₃-perovskite is also slightly greater than that for MgSiO₃-perovskite.     

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.     

Rare earth element geochemistry of the Fen alkaline complex,Norway

Determination of rare earth element (REE) abundances in rocks of the Fen complex has shown that within rocks of the first magmatic series REE abundances increase in the order urtiteFen magmas are discussed and it is considered that parental magmas had relatively high La/Yb ratios (40–60). Utilizing petrological evidence from other alkaline complexes coupled with experimental studies it is considered that the parental magma was a carbonated nephelinite produced by limited (<10%) partial melting of the mantle. All the Fen rocks are placed in a petrogentic scheme in which a carbonated nephelinite magma undergoes liquid immiscibility, differentiation and volatile transport.     

Clinopyroxene on the join CaMgSi2O6-CaFe3+AlSiO6-CaTiAl2O6 at low oxygen fugacity

Subsolidus phase relations on the join CaMgSi₂O₆-CaFe³⁺ AlSiO₆-CaTiAl₂O₆ were studied by the ordinary quenching method at \(f_{O_2 } = 10^{ - 11} \) atm and 1,100°C. Crystalline phases encountered are clinopyroxene_ss (ss:solid solution) (Cpx_ss), melilite (Mel), perovskite (Pv), spinel_ss (Sp_ss), magnetite_ss (Mt_ss) and anorthite (An). There is no Cpx_ss single phase field, and the following assemblages were found; Cpx_ss+Mel, Cpx_ss+Mel+Sp_ss, Cpx_ss+Mel+Pv, Cpx_ss+Mel+Sp_ss+Pv, Cpx_ss+Pv+Sp_ss+An, Sp_ss+Pv+Mel+An+Cpx_ss, Mel+Mt_ss+An+Sp_ss+Cpx_ss+liquid and Mel+Mt_ss+An+Sp_ss+Cpx_ss+Pv. Mössbauer spectral study revealed that Cpx_ss contains both Fe²⁺ and Fe³⁺ in the octahedral site, and it was confirmed that the CaFe³⁺ AlSiO₆ content in the Cpx_ss at low \(f_{O_2 } \) is considerably less than that in the Cpx_ss crystallized in air, whereas the CaFe²⁺Si₂O₆ component increases. The maximum solubility of CaTlAl₂O₆ component in the Cpx_ss at low \(f_{O_2 } \) is higher than that in air. The decrease of CaFe³⁺ AlSiO₆ in the Cpx_ss at low \(f_{O_2 } \) may cause increase of CaTial₂O₆ in the Cpx_ss.     

Synthetic Mn3+-kyanite and viridine, (Al2-xMn x 3+ ) SiO5, in the system Al2O3-MnO-MnO2-SiO2

Experiments on the join Al₂SiO₅-“Mn₂SiO₅” of the system Al₂O₃-SiO₂-MnO-MnO₂ in the pressure/temperature range 10–20 kb/900–1050° C with gem quality andalusite, Mn₂O₃, and high purity SiO₂ as starting materials and using /_O2-buffer techniques to preserve the Mn³⁺ oxidation state had following results: At 20 kb/1000°C orange-yellow kyanite mixed crystals are formed. The kyanite solid solubility is limited at about (Al_1.88Mn _0.12 ³⁺ )SiO₅ and, thus, equals approximately that on the join Al₂SiO₅-“Fe₂SiO₅” (Langer and Frentrup, 1973) indicating that there is no Jahn-Teller stabilisation of Mn³⁺ in the kyanite matrix. 5 mole % substitution causes the kyanite lattice constants a _o, b _o, c _o, and V _o to increase by 0.015, 0.009, 0.014 Å, and 1.6 ų, resp., while α, β, γ, remain unchanged. Between 10 and 18 kb/900°C, Mn³⁺-substituted, strongly pleochroitic (emeraldgreen-yellow) andalusite_ss (viridine) was obtained. At 15 kb/900°C, the viridine compositional range is about (Al_1.86Mn _0.14 ³⁺ )SiO₅-(Al_1.56Mn _0,44 ³⁺ )SiO₅. Thus, Al→Mn³⁺ substitutional degrees are appreciably higher in andalusite than in kyanite, proving a strong Jahn-Teller effect of Mn³⁺ in the andalusite structure, which stabilises this structure type at the expense of kyanite and sillimanite and, thus, enlarges its PT-stability range extremely. 17 mole % substitution cause the andalusite constants a _o, b _o, c _o, and V _o to increase by 0.118, 0.029, 0.047 Å and 9.4 ų, resp. At “Mn₂SiO₅”-contents smaller than about 7 mole %, viridine coexists with Mn-poor kyanite. At “Mn₂SiO₅”-concentrations higher than the maximum kyanite or viridine miscibility, braunite (tetragonal, ideal formula Mn²⁺Mn³⁺[O₈/Si0₄]), pyrolusite and SiO₂ were found to coexist with the Mn³⁺-saturated ky _ss or and _ss, respectively. In both cases, braunites were Al-substituted (about 1 Al for 1 Mn³⁺). Pure synthetic braunites had the lattice constants a _o 9.425, c _o, 18.700 Å, V _o 1661.1 ų (ideal compn.) and a _o 9.374, c _o 18.593 ų, V _o 1633.6 ų (1 Al for 1 Mn³⁺). Stable coexistence of the Mn²⁺-bearing phase braunite with the Mn⁴⁺-bearing phase pyrolusite was proved by runs in the limiting system MnO-MnO₂-SiO₂.     

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 disproportionation of andalusite (Al2SiO5) to Al2O3 and SiO2 under shock compression

Shock-recovery experiments have been carried out on andalusite single crystals of gem quality in a pressure range from 300 up to 575 kbar. Infrared spectroscopic investigations indicate a progressive shock-induced transformation of andalusite into short-range-ordered Al₂O₃ and SiO₂ phases within a pressure interval from ～360 to ～575 kbar. Exposure to dynamic pressures of about 575 kbar results in andalusite breaking down into incoherently crystallized γ-Al₂O₃, well-crystallized α-Al₂O₃ and X-ray amorphous SiO₂. The shock disproportionation of andalusite is presumed to take place in three separate stages of reaction. The comparison of shock-induced reactions with results from static experiments on kyanite indicates significant differences in the transformation pressures and in the mechanism of the high pressure decomposition.     

Synthesis and physical properties of piemontite Ca2Al3-pMn p 3+ (Si2O7/SiO4/O/OH)

Mn³⁺-bearing piemontites and orthozoisites, Ca₂(Al_3-pMn³⁺ _p)-(Si₂O₇/SiO₄/O/OH), have been synthesized on the join Cz (p = 0.0)-Pm (p = 3.0) of the system CaO-Al₂O₃-(MnO·MnO₂)-SiO₂-H₂O atP = 15 kb,T= 800 °C, and \(f_{O_2 } \) of the Mn₂O₃/MnO₂ buffer. Pure Al-Mn³⁺-piemontites were obtained with 0.5≦p≦1.75, whereas atp=0.25 Mn³⁺-bearing orthozoisite (thulite) formed as single phase product. The limit of piemontite solid solubility is found near p=1.9 at the above conditions. Withp>1.9, the maximum piemontite coexisted with a new high pressure phase CMS-X1, a Ca-bearing braunite (Mn _0.2 ²⁺ Ca_0.8)Mn ₆ ³⁺ O₈(SiO₄), and quartz. Al-Mn³⁺-piemontite lattice constants (LC),b ₀,c ₀,V ₀, increase with increasingp:

Hydrothermal synthesis of pyroxenoids in the system MnSiO3-CaSiO3 at Pf=2 kb

Pyroxenoids on the join MnSiO₃-CaSiO₃ were synthesized from (Mn, Ca)-carbonate solid solutions and SiO₂ in CO₂-H₂O mixtures at a total pressure of 2 kb. The type of structure found (pyroxmangite, rhodonite, bustamite or wollastonite) is mainly dependent on the Mn/Ca ratio, but also to a lesser extent on temperature. Johannsenite-type structures were encountered at low temperatures over a wide compositional range. It has been possible to convert the pyroxenoids pyroxmangite → rhodonite, rhodonite → bustamite, bustamite → wollastonite, and johannsenite → bustamite or wollastonite with increase of temperature, but not the reverse. The compositional ranges of the synthetic pyroxenoids are very similar to those found in natural pyroxenoids.