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.     

Elasticity of MgO to 130 GPa: Implications for lower mantle mineralogy

The aggregate shear wave velocities of MgO (periclase) have been determined throughout Earth's lower mantle pressure regime approaching 130 GPa using Brillouin spectroscopy in conjunction with synchrotron X-ray diffraction technique in a diamond anvil cell apparatus. We found that the extrapolations of the high-pressure shear wave velocities and shear moduli to ambient pressure are highly consistent with earlier studies. However, the measurements over a wide pressure range revealed that the pressure derivative of the shear modulus (dG/dP = G₀′) of MgO is 1.92(2), which is distinctly lower than that of previous lower-pressure experiments. Compared with the previous results on (Mg,Fe)O ferropericlase, there is no clear correlation between iron content and G₀′. We calculate that the shear wave velocity profile of lower mantle along the adiabatic geotherm applied by the lower G₀′ value of periclase can remarkably well reproduce the global seismological 1-D velocity profile model with uniform composition model. The best-fitting result indicates the possibility of a lower mantle mineralogy with ~ 92 vol.% silicate perovskite phase, implying that the bulk composition of lower mantle is likely not to be pyrolitic but more chondritic. The present acoustic measurements performed over the large pressure range have thus led us to a better understanding of compositional model of the Earth's lower mantle.     

The effect of ferromagnetism on the equation of state of Fe3C studied by first-principles calculations

First-principles calculations have been used to determine the equation of state of Fe₃C in both its low-pressure magnetically ordered and high-pressure non-magnetically ordered states; at 0 K the ferromagnetic transition was found to occur at about 60 GPa. In the high pressure, non-magnetically ordered regime at 0 K the material may be described by a Birch-Murnaghan third-order equation of state with V₀=8.968(7) ų per atom, K₀=316.62(2) GPa and K′=4.30(2). At atmospheric pressure the ferromagnetic phase transition in Fe₃C occurs at ∼483 K; preliminary measurements of the thermal expansion by powder neutron diffraction show that this transition produces a large effect on thermoelastic properties. The volumetric thermal expansion coefficient in the paramagnetic phase was found to be 4.34×10⁻⁵ K⁻¹ at T∼550 K. By applying a thermal expansion correction to the calculated equation of state at 0 K, predicted values for the density and adiabatic incompressibility of this material at core pressures and temperatures were obtained. These results appear to be sufficiently different from seismological data so as to preclude Fe₃C as the major inner core-forming phase.     

Melting of forsterite Mg2SiO4 up to 15 GPa

The melting curve of forsterite has been studied by static experiment up to a pressure of 15 GPa. Forsterite melts congruently at least up to 12.7 GPa. The congruent melting temperature is expressed by the Kraut-Kennedy equation in the following form: T_m(K)=2163 (1+3.0(V₀ ? V)/V₀), where the volume change with pressure was calculated by the Birch-Managhan equation of state with the isothermal bulk modulus K₀ = 125.4 GPa and its pressure derivative K′ = 5.33. The triple point of forsterite-β-Mg₂SiO₄-liquid will be located at about 2600°C and 20 GPa, assuming that congruent melting persists up to the limit of the stability field of forsterite. The extrapolation of the previous melting data on enstatite and periclase indicates that the eutectic composition of the forsterite-enstatite system should shift toward the forsterite component with increasing pressure, and there is a possibility of incongruent melting of forsterite into periclase and liquid at higher pressure, although no evidence on incongruent melting has been obtained in the present experiment.     

Determination of phase transition pressures of ZnTe under quasihydrostatic conditions

Pressure behavior of ZnTe at room temperature was studied using an X-ray energy dispersive method on a DIA type cubic anvil apparatus (SAM-85) at NSLS-X17B1. By using powdered polyethylene, the sample and NaCl for a pressure scale were held under quasihydrostatic conditions, which were confirmed by X-ray diffraction method. Two high-pressure phase transitions were confirmed using X-ray powder diffraction simultaneously with electrical resistance measurements. The phase transition pressures under quasihydrostatic conditions were determined to be 9.6 GPa, at which the resistance increased, and 12.0 GPa, which was the midpoint of a large resistance decrease. Errors in the pressure determinations were estimated to be less than 0.2 GPa. These pressure values may depend on grain size and anisotropic stress effects on the calibrant. From X-ray observation of ZnTe, the bulk modulus of the zinc blende structure was calculated to beK ₀=51(3) GPa andK ₀ =3.6(0.8), and the first transition at 9.6 GPa was found to have about 9% volume change. It was consistent with an anomaly in the pressure generating curves.     

Compressibility of brownmillerite (Ca2Fe2O5): effect of vacancies on the elastic properties of perovskites

The evolution with pressure of the unit-cell parameters brownmillerite (Ca₂Fe₂O₅), a stoichiometric defect perovskite structure, has been determined to a maximum pressure of 9.46 GPa, by single-crystal X-ray diffraction measurements at room temperature. Brownmillerite does not exhibit any phase transitions in this pressure range. A fit of a third-order Birch–Murnaghan equation-of-state to the P–V data yields values of K_T0=127.0(5) GPa and K₀′=5.99(13). Analysis of the unit-cell parameter data shows that the structure compresses anisotropically. Compressional moduli for the axes are K_a0=141(1) GPa, K_b0=118(3) GPa and K_c0=122.2(2) GPa, with K_a0′=8.9(3), K_b0′=6.2(6) and K_c0′=4. The stiffest direction (i.e. along a) coincides with the direction of the FeO₄ tetrahedral chains. Comparison of these data with the elasticity systematics of Ca-perovskites shows that the presence of oxygen vacancies in the brownmillerite structure softens the structure by ∼25% and that the ordering of vacancies in the perovskite structure increases the anisotropy of compression.     

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.     

Compression and phase behavior of solid CO2 to half a megabar

CO₂ has been investigated up to 514 kbar at23 ± 2°C by both optical and in situ X-ray diffraction studies using a diamond-anvil pressure cell. CO₂ solidifies in an unknown structure in the pressure range 5 to 23 kbar, and transforms to ordinary dry-ice structure above 23 kbar at room temperature. Isothermal compression data for dry ice have been obtained above about 24 kbar. These appear to be the first data at room temperature known in the literature. The data fitted to the Birch equation of state yieldK₀ = 29.3 ± 1.0kbar andK₀^′ = 7.8 assuming the volume of the hypothetical dry ice at zero-pressure and room temperature is 31.4 ± 0.2 cm³/mole. The isothermal bulk modulus(K₀) thus derived is consistent with the compression data and compressibilities for dry ice obtained at low temperatures using dilatometry and ultrasonic techniques, respectively, reported in the literature. By comparing shock-wave data for relevant materials, it is suggested that CO₂ is not likely to transform to one of the crystalline forms of SiO₂ which is otherwise expected from empirical grounds, but may instead decompose into C (diamond) + O₂, at high pressures.     

Thermal equation of state of magnesiowüstite (Mg0.6Fe0.4)O

Volume measurements for magnesiowüstite (Mg_0.6Fe_0.4)O, were carried out up to pressures of 10.1 GPa in the temperature range 300–1273 K, using energy-dispersive synchrotron X-ray diffraction. These data allow reliable determination of the temperature dependence of the bulk modulus and good constraint on the thermal expansitivity at ambient pressure which was previously not known for magnesiowüstite. From these data, thermal and elastic parameters were derived from various approaches based on the Birch–Murnaghan equation of state (EOS) and on the relevant thermodynamic relations. The results from three different equations of state are remarkably consistent. With (∂K_T/∂P)_T fixed at 4, we obtained K₀=158(2) GPa, (∂K_T/∂T)_P=−0.029(3) GPa K⁻¹, (∂K_T/∂T)_V=−3.9(±2.3)×10⁻³ GPa K⁻¹, and α_T=3.45(18)×10⁻⁵+1.14(28)×10⁻⁸T. The K₀, (∂K_T/∂T)_P, and (∂K_T/∂T)_V values are in agreement with those of Fei et al. (1992) and are similar to previously determined values for MgO. The zero pressure thermal expansitivity of (Mg_0.6Fe_0.4)O is found to be similar to that for MgO (Suzuki, 1975). These results indicate that, for the compositional range x=0–0.4 in (Mg_1−xFe_x)O, the thermal and elastic properties of magnesiowüstite exhibit a dependence on the iron content that is negligibly small, within uncertainties of the experiments. They are consequently insensitive to the Fe–Mg partitioning between (Mg, Fe)SiO₃ perovskite and magnesiowüstite when applied to compositional models of the lower mantle. With the assumption that (Mg_0.6Fe_0.4)O is a Debye-like solid, a modified equation of heat capacity at constant pressure is proposed and thermodynamic properties of geophysically importance are calculated and tabulated at high temperatures.     

Thermal equation of state of majorite with MORB composition

In situ synchrotron X-ray diffraction experiments were conducted using the SPEED-1500 multi-anvil press at SPring-8 on majoritic garnet synthesized from natural mid-ocean ridge basalt (MORB), whose chemical composition is close to the average of oceanic crust, at 19 GPa and 2200 K. Pressure-volume-temperature data were collected using a newly developed high-pressure cell assembly to 21 GPa and 1273 K. Data were fit to the high-temperature Birch-Murnaghan equation of state, with fixed values for the ambient cell volume (V₀ = 1574.14(4) Å³) and the pressure derivative of the isothermal bulk modulus (K^′T = 4). This yielded an isothermal bulk modulus of K_T0 = 173(1) GPa, a temperature derivative of the bulk modulus (∂K_T/∂T)_P = −0.022(5) GPa K⁻¹, and a volumetric coefficient of thermal expansivity α = a + bT with values of a = 2.0(3) × 10⁻⁵ K⁻¹ and b = 1.0(5) × 10⁻⁸ K⁻². The derived thermoelastic parameters are very similar to those of pyrope. The density of subducted oceanic crust compared to pyrolitic mantle at the conditions in Earth's transition zone (410-660 km depth) was calculated using these results and previously reported thermoelastic parameters for MORB and pyrolite mineral assembledges. These calculations show that oceanic crust is denser than pyrolitic mantle throughout the mantle transition zone along a normal geotherm, and the density difference is insensitive to temperature at the pressures in lower part of the transition zone.     

Elastic anisotropy of ferromagnesian post-perovskite in Earth's D” layer

We report experimental observation of a sizable elastic anisotropy in a polycrystalline sample of ferromagnesian silicate in post-perovskite (ppv) structure. Using a novel composite X-ray transparent gasket to contain and synthesize ppv in a panoramic diamond-anvil cell along with oblique X-ray diffraction geometry, we observed the anisotropic lattice strain and {1 0 0} or {1 1 0} slip-plane texture in the sample at 140 GPa. We deduced the elasticity tensor (c_ij), orientation-dependent compressional wave velocities, polarization-dependent shear-wave velocities, and the velocity anisotropy of the silicate ppv. Our results are consistent with calculations and indicate that with sufficient preferred orientation, the elastic anisotropy of this phase can produce large shear-wave splitting.     

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.     

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-pressure phase transformations and isothermal compression in CaTiO3 (perovskite)

A polycrystalline CaTiO₃ (perovskite) was investigated under static pressures up to 38 GPa and temperatures up to 1000°C by using a diamond anvil pressure cell, a YAG laser, and the ruby fluorescence pressure calibration system. In situ x-ray diffraction data reveal that at room temperature, the orthorhombic CaTiO₃(I) transforms into a hexagonal CaTiO₃(II) at ∼ 10 GPa with a volume of change of 1.6%. At 1000°C, the orthorhombic CaTiO₃(I) first transforms into a tetragonal CaTiO₃(III) at 8.5 GPa and then transforms further into a hexagonal CaTiO₃(II′) at ∼ 15 GPa with molar volume changes of 0% and 1.6%, respectively. All three high-pressure polymorphs found in this study are nonquenchable.Isothermal compressibility of the orthorhombic CaTiO₃ was derived from measurements under truly hydrostatic environments (i.e., ⩽ 10.4 GPa). By assuming K^′₀ = 5.6 obtained ultrasonically on SrTiO₃ perovskite, the value of the bulk modulus (K₀) was calculated with the Birch-Murnaghan equation to be 210 ± 7 GPa.     

High-pressure phase transformations in vitreous and crystalline GeO2 (rutile)

Phase transformations in vitreous and crystalline GeO₂ (rutile) have been investigated up to ～50 GPa and ～1000°C by using a diamond anvil pressure cell coupled with a YAG laser heating system and in situ x-ray diffraction techniques. The results show that whereas the vitreous GeO₂ transforms into a hexagonal phase at pressures ～25 GPa, the crystalline GeO₂ transforms into an orthorhombic phase at ～28 GPa; the molar volume changes for the hexagonal and orthorhombic transformations are ? 1.0% (at 25 GPa) and ? 3.0% (at 28 GPa), respectively. When unloaded to 0.1 MPa, both the hexagonal and orthorhombic phases of GeO₂ are retained, and the zero-pressure molar volume is 0.7% larger and 4.5% smaller than that of the rutile-structured GeO₂, respectively. These results are in good agreement with previously published data.     

Equation of state of gold and its application to the phase boundaries near 660 km depth in Earth’s mantle

The pressure-volume-temperature equation of state (EOS) of gold is fundamental to high-pressure science because of its widespread use as an internal pressure standard. In particular, the EOS of gold has been used in recent in situ multi-anvil press studies for determination of phase boundaries related to the 660-km seismic discontinuity. These studies show that the boundaries are lower by 2 GPa than expected from the depth of the 660-km discontinuity. Here we report a new P-V-T EOS of gold based on the inversion of quasi-hydrostatic compression and shock wave data using the Mie-Grüneisen relation and the Birch-Murnaghan-Debye equation. The previously poorly constrained pressure derivative of isothermal bulk modulus and the volume dependence of Grüneisen parameter (q=d lnγ/d ln V) are determined by including both phonon and electron effects implicitly: K′_0T=5.0±0.2 and q=1.0±0.1. This combined with other accurately measured parameters enables us to calculate pressure at a given volume and temperature. At 660-km depth conditions, this new EOS yields 1.0±0.2 GPa higher pressure than Anderson et al.’s EOS which has been used in the multi-anvil experiments. However, after the correction, there still exists a 1.5-GPa discrepancy between the post-spinel boundary measured by multi-anvil studies and the 660-km discontinuity. Other potential error sources, such as thermocouple emf dependence on pressure or systematic errors in spectroradiometry, should be investigated. Theoretical and experimental studies to better understand electronic and anharmonic effects in gold at high P-T are also needed.     

A scaling law for K′0 for silicates with constant mean atomic mass

It is shown that Birch's formula for the isothermal pressure derivative of the isothermal bulk modulus, K′, can be used to generate reasonable values of K′₀ for a sequence of silicates with various ambient densities and constant mean atomic mass, m¯. The theory predicts values in fairly good agreement with experimental results, although there is a regrettable spread of experimental values of K′₀ for each solid. This first-order approximation theory for scaling between K′₀ and ?₀ is analogous to the law of corresponding states which scales K₀ and ?₀.     

The elastic properties of single-crystal fayalite as determined by dynamical measurement techniques

We present new elasticity measurements on single-crystal fayalite and combine our results with other data from resonance, pulse superposition interferometry, and Brillouin scattering to provide a set of recommended values for the adiabatic elastic moduliC _ij and their temperature variations. We use a resonance method (RPR) with specimens that were previously investigated by pulse superposition experiments. The nineC _ij of fayalite are determined from three new sets of measurements. One set of our newC _ij data is over the range 300–500 K. We believe that the relatively large discrep ncies found in someC _ij are due in large part to specimen inhomogeneities (chemical and microstructural) coupled with differences in the way various techniques sample, rather than only systematic errors associated with experimental procedures or in the preparations of the specimens.Our recommendeaC _ij's (GPa) and (C _ij/T) _p (GPa/K) are: The resulting values for the isotropic bulk and shear moduli,K _s and , and their temperature derivatives are:K _s=134(4) GPa; =50.7(0.3) GPa; (K _s/T) _p =–0.024(0.005) GPa/K; and (/T) _p =–0.013(0.001) GPa/K. An important conclusion is thatK _s increases as the Fe/(Fe+Mg) ratio in olivine is increased.     

High-pressure X-ray diffraction studies on β- and γ-Mg2SiO4

Pressure effects on the lattice parameters of β- and γ-Mg₂SiO₄ have been measured at room temperature and at pressures up to 100 kbar using a multi-anvil high-pressure X-ray diffraction apparatus. The volume changes (ΔV/V₀) at 90 kbar are 5.4 · 10^?2 and 4.2 · 10^?2 for β- and γ-Mg₂SiO₄, respectively. Isothermal bulk moduli at zero pressure have been calculated from least-square fits of the data to straight lines. They turn out to be 1.66 ± 0.4 and 2.13 ± 0.1 Mbar for β- and γ-Mg₂SiO₄, respectively. The α → γ transition obeys Wang's linear V_φ?ρ relation but the α → β transition does not.     

Shock behavior of zircon: phase transition to scheelite structure and decomposition

Both single-crystal and powdered specimens of zircon (ZrSiO₄) were shocked to peak pressures between 30 and 94 GPa using the gun method, and specimens recovered were studied by means of X-ray diffraction analysis, transmission electron microscopy and infrared spectroscopy. Transformation to the scheelite structure started above 30 GPa, and was completed above 53 GPa in the case of single crystal specimens. Tetragonal unit cell parameters of the scheelite type ZrSiO₄ at room condition are measured to bea = 4.7341(1)Å, c = 10.51(1)Å, c/a = 2.219(2) andV = 235.5(2)ų, which is smaller than that of the zircon type by 9.9%. The recovered scheelite-type ZrSiO₄ reverts to the zircon type after rapid heating to 1200°C at room pressure. This transformation from the zircon type to the scheelite type is unique in that it is fast, displacive-like, but does not reverse. Tetragonal ZrO₂ was detected as decomposition product in the single-crystal specimen shocked to 94 GPa, and further confirmed in a powdered specimen shocked to 53 GPa where enhancement of temperature is expected because of high porosity. Decomposition behavior of zircon observed in natural shock events is discussed on the basis of present experimental results.