Elasticity of MgSiO3 in the ilmenite phase

The single-crystal elastic moduli of the ilmenite phase of MgSiO₃ have been determined from Brillouin spectroscopy. They are: C₁₁ = 472, C₁₂ = 168, C₃₃ = 382, C₁₃ = 70, C₄₄ = 106, C₁₄ = ?27, C₆₆ = 152 and C₂₅ = ?24 in GPa. These elastic properties are consistent with a structural mechanical model where the silicon octahedra are very stiff under compression and shear. This latter property yields an unexpectedly high shear modulus for the magnesium silicate ilmenite as compared with analogue compounds. The further transformation to perovskite will probably be associated with a significant increase in elastic properties since the strong silicon polyhedra form a structural network in this phase. The transformation of spinel and stishovite to ilmenite is associated with a slight density increase and a slight decrease in acoustic velocities. This transformation will probably not produce a seismic discontinuity even if it does occur in the Earth's mantle.     

High-pressure phase equilibria in a garnet lherzolite,with special reference to Mg2+Fe2+ partitioning among constituent minerals

Phase equilibria in a natural garnet lherzolite nodule (PHN 1611) from Lesotho kimberlite and its chemical analogue have been studied in the pressure range 45–205 kbar and in the temperature range 1050–1200°C. Partition of elements, particularly Mg²⁺Fe²⁺, among coexisting minerals at varying pressures has also been examined. High-pressure transformations of olivine(α) to spinel(γ) through modified spinel(β) were confirmed in the garnet lherzolite. The transformation behavior is quite consistent with the information previously accumulated for the simple system Mg₂SiO₄Fe₂SiO₄. At pressures of 50–150 kbar, a continuous increase in the solid solubility of the pyroxene component in garnet was demonstrated in the lherzolite system by means of microprobe analyses. At 45–75 kbar and 1200°C, the Fe²⁺/(Mg + Fe²⁺) value becomes greater in the ascending order orthopyroxene, Ca-rich clinopyroxene, olivine and garnet. At 144–146 kbar and 1200°C, garnet exhibits the highest Fe²⁺/(Mg + Fe²⁺) value; modified spinel(β) and Ca-poor clinopyroxene follow it. When the modified spinel(β)-spinel(γ) transformation occurred, a higher concentration of Fe²⁺ was found in spinel(γ) rather than in garnet. As a result of the change in the Mg²⁺Fe²⁺ partition relation among coexisting minerals, an increase of about 1% in the Fe₂SiO₄ component in (Mg,Fe)₂SiO₄ modified spinel and spinel was observed compared with olivine.These experimental results strongly suggest that the olivine(α)-modified spinel(β) transformation is responsible for the seismic discontinuity at depths of 380–410 km in the mantle. They also support the idea that the minor seismic discontinuity around 520 km is due to the superposition effect of two types of phase transformation, i.e. the modified spinel(β)-spinel(γ) transformation and the pyroxene-garnet transformation. Mineral assemblages in the upper mantle and the upper half of the transition zone are given as a function of depth for the following regions: 100–150, 150–380, 380–410, 410–500, 500–600 and 600–650 km.     

Effects of cation disordering in a natural MgAl2O4 spinel observed by rectangular parallelepiped ultrasonic resonance and Raman measurements

At moderate temperatures, the elastic properties of natural MgAl₂O₄ spinel differ in several significant ways from properties of synthetic spinels. Below 1000 K, the ultrasonic resonant frequencies of an ordered natural spinel change significantly after heat treatment; at higher temperatures, both types of spinels have similar resonant responses. The temperature derivatives of the elastic constants of an ordered spinel also differ from those of disordered spinels at moderate temperatures; again, at higher temperatures, both types of spinels have similar behaviors. The Raman spectra also differ below 1000 K for ordered natural and disordered spinels and are similar at higher temperatures and after cooling to ambient temperature. We associate these changes in ultrasonic resonance and Raman spectra of spinel with cation disordering at high temperature which may be quenched by cooling. We deduce estimates of the inversion parameter from the relative intensities of the two A_1g Raman modes in very good agreement with estimates made from other measurements. We find thatC ₁₁ andC ₁₂ decrease by 4 and 8%, respectively, with 20% inversion in spinel;C ₄₄ is less sensitive to cation order. These results imply that previous measurements of the adiabatic elastic constants of spinels at ambient conditions have been affected by the state of cation disorder of the specimen.     

Elasticity of single-crystal SmAlO3, GdAlO3 and ScAlO3 perovskites

The adiabatic single-crystal elastic moduli of SmAlO₃, GdAlO₃ and ScAlO₃, all with the orthorhombic perovskite structure, have been measured by Brillouin spectroscopy under ambient conditions. These 3 compounds display various degrees of crystallographic distortion from the ideal cubic perovskite structure. We find that longitudinal moduli in directions parallel to the axes of a pseudocubic subcell are nearly equal and insensitive to distortions of the crystal structure from cubic symmetry, whereas, the moduli C₁₁ and C₂₂, parallel to the orthorhombic axes, display pronounced anisotropy with the exception of ScAlO₃. The shear moduli also correlate with distortion from cubic symmetry, as measured by rotation, or tilt angles, of the AlO₆ octahedra. Our data support the observations of Liebermann et al. that perovskite-structure compounds define consistent elasticity trends relating bulk modulus and molar volume, and sound speed and mean atomic weight. These relationships have been used to estimate bulk and shear moduli for the high-pressure polymorphs of CaSiO₃ and MgSiO₃ with the perovskite structure.     

Calorimetric study of the stability of high pressure phases in the systems CoOSiO2 and “FeO”SiO2, and calculation of phase diagrams in MOSiO2 systems

High temperature calorimetric measurements of the enthalpies of solution in molten if2 PbO · B₂O₃ of α- and γ-Fe₂SiO₄ and α-, β-, and γ-Co₂SiO₄ permit the calculation of phase relations at high pressure and temperature. The reported triple point involving α-, β-, and γ-Co₂SiO₄ is confirmed to represent stable equilibrium. The curvature in the α?β phase boundary in Co₂SiO₄ and of an α?γ boundary in Fe₂SiO₄ at high temperature is explained in part by the effects of compressibility and thermal expansion, but better agreement with the observed phase diagram is obtained when one considers the effect of small amounts of cation disorder in the spinel and/or modified spinel phases. The calculated ΔH⁰ and ΔS⁰ values for the α?β, α?γ, and β?γ transitions show that enthalpy and en changes both vary strongly in the series Mg, Fe, Co, and Ni, and are of equal importance in determining the stability relations. The disproportionation of Fe₂SiO₄ and Co₂SiO₄ spinel to rocksalt plus stishovite is calculated to occur in the 170–190 kbar region; cation disorder and/or changes in wüstite stoichiometry can affect the P?T slope. The calorimetric data for CoSiO₃ and FeSiO₃ are in good agreement with the observed phase boundary for pyroxene formation from olivine and quartz. The decomposition of pyroxene to spinel and stishovite at pressures near the coesite-stishovite transition is predicted in both iron and cobalt systems. The use of calorimetric data, obtained from small samples of high pressure phases, is very useful in predicting equilibrium phase diagrams in the 50–300 kbar range.     

Synthesis of γ-Mg2SiO4

Magnesium orthosilicate with spinel structure (γ-Mg₂SiO₄) was synthesized at about 250 kbar and 1000°C. Unit cell dimension was established to be 8.076 ± 0.001Å. X-ray powder diffraction pattern revealed a significant difference between γ-Mg₂SiO₄ and other γ-M₂SiO₄ spinels (M = Fe, Co, and Ni) in the intensities of (111) and (331) reflections, both of which are virtually absent in the Mg₂SiO₄ spinel. This feature could be thoroughly understood by the calculation of the intensities for several silicate spinels.     

High-temperature elasticity of the fluorite-structure compounds CaF2, SrF2 and BaF2

The elastic moduli of single-crystal CaF₂, SrF₂ and BaF₂ have been determined by the ultrasonic pulse superposition technique as a function of temperature from T = 298 to T = 650°K. These new data are consistent with other data obtained by ultrasonic pulse techniques in the region of room temperature and are superior to previous high-temperature data from resonance experiments. The elastic moduli (c) are represented by quadratic functions in T over the experimental temperature range with the curvature in the same sense for all the moduli. Evaluation of the temperature derivatives of the elastic moduli at constant volume indicates that the dominant temperature effect is extrinsic for (?K_S/?T)_P and intrinsic for (?μ/?T)_P, where K_S and μ are the isotropic bulk and shear moduli, respectively. For the series CaF₂SrF₂BaF₂, |(?c/?T)_p| decreases with increasing molar volume for all moduli; however there are no theoretical or empirical grounds on which to derive a simple relationship between (?c/?T)_P and crystallographic parameters.     

Disproportionation of Ni2SiO4 to stishovite plus bunsenite at high pressures and temperatures

Samples of Ni₂SiO₄ in both olivine and spinel phases have been compressed to pressures above 140 kbar in a diamond-anvil cell and heated to temperatures of 1400–1800°C using a continuous YAG laser. After quenching and releasing pressure, X-ray diffraction examination indicates that the samples disproportionate to a mixture of stishovite (SiO₂) and bunsenite (NiO) at pressures between 140 and 190 kbar. The exact disproportionation pressure is not certain due to transient increases in pressure during the local and rapid heating. However, thermodynamic calculations suggest that the transition pressure is about 192 ± 4 kbar at 1545°C and that the equation of the spinel-mixed oxides phase boundary isP(kbar) = 121 + (0.046 ± 0.020) T (°C).     

In situ measurements of sound velocities and densities across the orthopyroxene → high-pressure clinopyroxene transition in MgSiO3 at high pressure

Using acoustic measurement interfaced with a large volume multi-anvil apparatus in conjunction with in situ X-radiation techniques, we are able to measure the density and elastic wave velocities (V_P and V_S) for both ortho- and high-pressure clino-MgSiO₃ polymorphs in the same experimental run. The elastic bulk and shear moduli of the unquenchable high-pressure clinoenstatite phase were measured within its stability field for the first time. The measured density contrast associated with the phase transition OEN → HP-CEN is 2.6-2.9% in the pressure of 7-9 GPa, and the corresponding velocity jumps are 3-4% for P waves and 5-6% for S waves. The elastic moduli of the HP-CEN phase are K_S=156.7(8) GPa, G = 98.5(4) GPa and their pressure derivatives are K_S′=5.5(3) and G′ = 1.5(1) at a pressure of 6.5 GPa, room temperature. In addition, we observed anomalous elastic behavior in orthoenstatite at pressure above 9 GPa at room temperature. Both elastic wave velocities exhibited softening between 9 and 13-14 GPa, which we suggest is associated with a transition to a metastable phase intermediate between OEN and HP-CEN.     

High-pressure disproportionation of Co2SiO4 spinel and implications for Mg2SiO4 spinel

Co₂SiO₄ spinel has been found to disproportionate into its isochemically mixed oxides with rocksalt and rutile structures at pressures between 170 and 190 kbar and temperatures between 1400 and 1800°C in a diamond-anvil press. The exact disproportionation pressure is not certain due to transient increases in pressure during the local and rapid heating by a continuous YAG laser. The slope of the phase boundary between the spinel phase and the mixed oxides is calculated to be?33 ± 20bar/deg. This negative slope is consistent with the observed anomalously large entropy of CoO (relative to its isostructural oxides) in entropy vs.(MV)^?1/2 systematics, whereM is the formula weight andV the molar volume. The sign of the slope for a phase boundary in the disproportionation of spinel depends on the values of entropy of the rocksalt oxides as well as the inverse character exhibited in the spinel phases. The normal entropy of MgO suggests that the phase boundary for the disproportionation of Mg₂SiO₄ spinel has positive slope.     

Ni2SiO4-enthalphy of the olivine-spinel transition by solution calorimetry at 713°C

The high pressure spinel polymorph of Ni₂SiO₄ persists metastably at 713°C and atmospheric pressure. The enthalpy of the olivine-spinel transition was obtained by measuring the heats of solution of both polymorphs in a molten oxide solvent, 2PbO · B₂O₃, at that temperature. For Ni₂SiO₄(ol)→Ni₂SiO₄, ΔH₉₈₆⁰ = +1.4 ± 0.7kcal/mol. The heat content increments, H₉₈₆ ? H₂₉₇, were found to be: olivine, 25.73 ± 0.42kcal/mol, and spinel, 25.39 ± 0.20kcal/mol. The measured enthalpy of the transformation is consistent with the low slope of the phase boundary, ?P/?T = ～ 12b/deg, observed by Akimoto and others. The entropy of the olivine-spinel transition in Ni₂SiO₄ is accordingly about a factor of three smaller in magnitude (ΔS = ～ ?1cal/deg mol) than that for Co₂SiO₄,Fe₂SiO₄,Mg₂SiO₄or Mg₂GeO₄ (ΔS = ?3to?3.5cal/deg mol).     

Co2+ as a chemical analogue for Fe2+ in high-temperature experiments in basaltic systems

High-temperature experiments on ferromagnesian compositions have been hampered by the rapid absorption of up to 95% of the original iron by platinum and 40% by silver-palladium capsules. Molybdenum or iron capsule materials can decrease or alleviate iron loss, but restrict oxygen fugacities to values near the iron-wustite buffer. Because Co²⁺ is stable at f_O2 =HM and because the solubility of Co in platinum in this range of f_O2 is ～0.05% at temperatures to 1350°C, its use as an analogue for Fe²⁺ is possible. In addition, experiments simulating various Fe²⁺ ratios can be easily performed by choosing appropriate Co²⁺/Fe³⁺ ratios. The cobalt phases produced possess brilliant and distinctive colors which are valuable aids in optical identification of minute phases. The cobalt analogue hypothesis was tested with atmospheric pressure experiments in air on the cobalt analogue of the 1921 Kilauea basalt at three simulated Fe²⁺/Fe³⁺ ratios. The results were compared with those of R.E.T. Hill (1969) for the natural 1921 basalt. The phase relations were the same, with the cobalt system stability fields systematically shifted by about +50°C. Microprobe analysis of olivines and the coexisting glasses indicate that the distribution of Co²⁺ between olivine and melt is independent of temperature and liquid composition. Although the analogue liquid composition differs from the equilibrium composition of the natural system, it may be corrected be employing distribution coefficients (K_D = 0.61 for the Co system; K_D = 0.33 for the Fe system) to closely approximate what the natural system would yield if iron loss did not occur.     

High-temperature behaviour of the elastic moduli of LiF and NaF: Comparison with MgO and CaO

The elastic moduli of single-crystal LiF and NaF have been determined by the ultrasonic pulse superposition technique as a function of temperature from T = 298–650° K. These new data are consistent with low-temperature (T < 298° K) data obtained by other ultrasonic pulse techniques and are superior to previous high-temperature data from resonance experiments. The elastic moduli (c) are represented by quadratic functions in T over the experimental temperature range although the curvature is not in the same sense for all modes. For LiF, NaF, MgO and CaO, evaluation of the temperature derivatives of the elastic moduli at constant volume (V) indicates that the elastic moduli are only weakly dependent on T at constant volume. The fluoride—oxide analogue pair LiFMgO both exhibit high-temperature elastic behaviour at approximately the same absolute temperature. Mitskevich's theory and observed K_S-V systematics imply that (?c/?T)_P should be a function of the nearest neighbour distance for rocksalt fluorides and oxides; this result lends further support to a fluorideoxide modelling scheme based on similar ionic radii.     

Static and dynamic elastic moduli of organic-rich chalk

The elastic moduli and anisotropy of organic-rich rocks are of great importance to geoengineering and geoprospecting of oil and gas reservoirs. In this paper, we probe into the static and dynamic moduli of the Ghareb–Mishash chalk through laboratory measurements and new analytical approaches. We define a new anisotropy parameter, ‘hydrostatic strain ratio’ (Ω), which describes the differential contraction of anisotropic rocks consequent to hydrostatic compression. Ω depends on the C₁₁, C₁₂, C₁₃ and C₃₃ stiffness constants of a transversely isotropic material, and therefore enables a unique insight into the anisotropic behaviour of TI rocks. Ω proves more sensitive to anisotropy within the weak anisotropy range, when compared with Thomsen's ε and γ parameters. We use Ω to derive static moduli from triaxial compression tests performed on a single specimen. This is done by novel employment of a hydrostatic-deviatoric combination for transversely isotropic elastic stiffnesses. Dynamic moduli are obtained from acoustic velocities measurements. We find that the bedding-normal velocities are described well by defining kerogen as the load-supporting matrix in a Hashin–Shtrikman model (‘Hashin–Shtrikman (HS) kerogen’). The dynamic moduli of the Ghareb–Mishash chalk in dry conditions are significantly higher than the static moduli. The dynamic/static moduli ratio decreases from ∼4 to ∼2 with increasing kerogen content. Both the static and dynamic moduli decrease significantly with increasing porosity and kerogen content. The effect of porosity on them is two times stronger than the effect of kerogen.     

Geobarometry of ultramafic xenoliths from Loihi Seamount,Hawaii, on the basis of CO2 inclusions in olivine

Abundant fluid inclusions in olivine of dunite xenoliths (～1–3 cm) in basalt dredged from the young Loihi Seamount, 30 km southeast of Hawaii, are evidence for three coexisting immiscible fluid phases—silicate melt (now glass), sulfide melt (now solid), and dense supercritical CO₂ (now liquid + gas)—during growth and later fracturing of some of these olivine crystals. Some olivine xenocrysts, probably from disaggregation of xenoliths, contain similar inclusions.Most of the inclusions (2–10 μm) are on secondary planes, trapped during healing of fractures after the original crystal growth. Some such planes end abruptly within single crystals and are termed pseudosecondary, because they formed during the growth of the host olivine crystals. The “vapor” bubble in a few large (20–60 μm), isolated, and hence primary, silicate melt inclusions is too large to be the result of simple differential shrinkage. Under correct viewing conditions, these bubbles are seen to consist of CO₂ liquid and gas, with an aggregate ? = ～ 0.5–0.75 g cm^?3, and represent trapped globules of dense supercritical CO₂ (i.e., incipient “vesiculation” at depth). Some spinel crystals enclosed within olivine have attached CO₂ blebs. Spherical sulfide blebs having widely variable volume ratios to CO₂ and silicate glass are found in both primary and pseudosecondary inclusions, demonstrating that an immiscible sulfide melt was also present.Assuming olivine growth at ～ 1200°C and hydrostatic pressure from a liquid lava column, extrapolation of CO₂P-V-T data indicates that the primary inclusions were trapped at ～ 220–470 MPa (2200–4700 bars), or ～ 8–17 km depth in basalt magma of ? = 2.7 g cm^?3. Because the temperature cannot change much during the rise to eruption, the range of CO₂ densities reveals the change in pressure from that during original olivine growth to later deformation and rise to eruption on the sea floor. The presence of numerous decrepitated inclusions indicates that the inclusion sample studied is biased by the loss of higher-density inclusions and suggests that some part of these olivine xenoliths formed at greater depths.     

High-pressure phases of Co2GeO4, Ni2GeO4, Mn2GeO4 and MnGeO3: implications for the germanate-silicate modeling scheme and the Earth's mantle

In a diamond-anvil press coupled with YAG laser heating, the spinels of Co₂GeO₄ and Ni₂GeO₄ have been found to disproportionate into their isochemical oxide mixtures at about 250 kbar and 1400–1800°C in the same manner as their silicate analogues. At about the same P-T conditions MnGeO₃ transforms to the orthorhombic perovskite structure (space group Pbnm); the lattice parameters at room temperature and 1 bar are a₀ = 5.084 ± 0.002, b₀ = 5.214 ± 0.002, and c₀ = 7.323 ± 0.003Å with Z = 4 for the perovskite phase. The zero-pressure volume change associated with the ilmenite-perovskite phase transition in MnGeO₃ is ?6.6%. Mn₂GeO₄ disproportionates into a mixture of the perovskite phase of MnGeO₃ plus the rocksalt phase of MnO at P = 250kbar and T = 1400–1800°C. The concept of utilizing germanates as high-pressure models for silicates is valid in general. The results of this study support the previous conclusion that the lower mantle comprises predominantly the orthorhombic perovskite phase of ferromagnesian silicate.     

Electrical conductivity jump produced by the α-β-δ transformation in Mn2GeO4

The electrical conductivity of three polymorphs of Mn₂GeO₄ was measured under high pressures in the temperature range of 300–1200 K. It was found that the electrical conductivity increases discontinuously due to the transformation both from olivine structure (α) to modified spinel structure (β) and from β to strontium plumbate structure (δ). The amount of discontinuous change is about one half order of magnitude from α to β and one third order of magnitude from β to δ at 1200 K. In order to see the effect of the presence of iron ions, the electrical conductivity of the solid solution of (Mn_0.9Fe_0.1)₂GeO₄ was also measured. It was found that at low temperatures, where impurity conduction may be dominant, the solid solution is more conductive than the pure Mn₂GeO₄, but at high temperature no significant differences were observed between the solid solution and pure Mn₂GeO₄ in all polymorphs.A phase transformation from modified spinel structure to strontium plumbate structure is considered to be one of the plausible transformations occurring at a depth around 650 km in the earth's mantle. These experiments suggest that if this kind of transformation occurs in the mantle, some degrees of discontinuous change in electrical conductivity may be expected around 650 km.     

Elasticity of (Mg, Fe)(Si, Al)O3-perovskite at high pressure

The most abundant mineral on Earth has a perovskite crystal structure and a chemistry that is dominated by MgSiO₃ with the next most abundant cations probably being aluminum and ferric iron. The dearth of experimental elasticity data for this chemically complex mineral limits our ability to calculate model seismic velocities for the lower mantle. We have calculated the single crystal elastic moduli (c_ij) for (Mg, Fe^3 +)(Si, Al)O₃ perovskite using density functional theory in order to investigate the effect of chemical variations and spin state transitions of the Fe³⁺ ions. Considering the favored coupled substitution of Mg²⁺-Si^4 + by Fe³⁺-Al³⁺, we find that the effect of ferric iron on seismic properties is comparable with the same amount of ferrous iron. Ferric iron lowers the elastic moduli relative to the Al charge-coupled substitution. Substitution of Fe³⁺ for Al³⁺, giving rise to an Fe/Mg ratio of 6%, causes 1.8% lower longitudinal velocity and 2.5% lower shear velocity at ambient pressure and 1.1% lower longitudinal velocity and 1.8% lower shear velocity at 142 GPa. The spin state of the iron for this composition has a relatively small effect (< 0.5% variation) on both bulk modulus and shear modulus.     

Elasticity of (Mg0.83,Fe0.17)O ferropericlase at high pressure: ultrasonic measurements in conjunction with X-radiation techniques

The elasticity of ferropericlase with a potential mantle composition of (Mg_0.83,Fe_0.17)O is determined using ultrasonic interferometry in conjunction with in situ X-radiation techniques (X-ray diffraction and X-radiography) in a DIA-type cubic anvil high-pressure apparatus to pressures of 9 GPa (NaCl pressure scale) at room temperature. In this study, we demonstrate that it is possible to directly monitor the specimen length using an X-ray image technique and show that these lengths are consistent with those derived from X-ray diffraction data when no plastic deformation of the specimen occurs during the experiment. By combining the ultrasonic and X-ray diffraction data, the adiabatic elastic bulk (K_S) and shear (G) moduli and specimen volume can be measured simultaneously. This enables pressure scale-free measurements of the equation of state of the specimen using a parameterization such as the Birch-Murnaghan equation of state. The elastic moduli determined for (Mg_0.83,Fe_0.17)O are K_S0=165.5(12) GPa, G₀=112.4(4) GPa, and their pressure derivatives are K_S0′=4.17(20) and G₀′=1.89(6). If these results are compared with those for MgO, they demonstrate that K_S0 and K_S0′ are insensitive to the addition of 17 mol% FeO, but G₀ and G₀′ are reduced by 14% and 24%, respectively. We calculate that the P and S wave velocities of a perovskite plus ferropericlase phase assemblage with a pyrolite composition at the top of the lower mantle (660 km depth) are lowered by 0.8 and 2.3%, respectively, when compared with those calculated using the elastic properties of end-member MgO. Consequently, the magnitudes of the calculated wave velocity jumps across the 660 km discontinuity are reduced by about 11% for P wave and 20% for S wave, if this discontinuity is considered as a phase transformation boundary only (ringwoodite→perovskite+ferropericlase).     

High-pressure phase transformations in the system of MgSiO3-FeSiO3

Two synthetic pyroxenes (FeSiO₃, MgSiO₃) and five natural pyroxenes with compositions of about Fs₈₀En₂₀, Fs₆₀En₄₀, Fs₅₀En₅₀, Fs₄₀En₆₀, and Fs₂₀En₈₀ have been subjected to pressures up to250 ± 50kbars at a temperature of about1500 ± 200°C in a diamond anvil cell heated by an infrared laser beam. After quenching and unloading X-ray data analysis indicates that (1) those with Mg less than 50% undergo the following reactions: 2(Mg,Fe)SiO₃ (pyroxene) → (Mg,Fe)₂SiO₄ (spinel) + SiO₂ (stishovite) → 2(Mg,Fe)O (magnesiowu¨stite) + SiO₂ (stishovite) with increase of pressure, and (2) those with Mg higher than 60%, undergo the following reactions: 2(Mg,Fe)SiO₃ (pyroxene) → (Mg,Fe)₂SiO₄ (spinel) + SiO₂ (stishovite) → 2(Mg,Fe)SiO₃ (hexagonal phase) → 2(Mg,Fe)O (magnesiowu¨stite) + SiO₂ (stishovite) with increase of pressure.