Melting of enstatite from 13 to 18 GPa under hydrous conditions

Experiments on MgSiO₃ enstatite were conducted in the pressure range from 13 to 18 GPa under hydrous conditions in order to clarify the effect of water on the melting phase relations of enstatite at pressures corresponding to the Earth’s mantle transition zone. In some previous experiments [Geol. Soc. Am. Bull. 79 (1968) 1685; Phys. Earth Planet. Inter. 85 (1994) 237], incongruent melting behavior to form Mg₂SiO₄ forsterite and SiO₂ enriched liquid up to 5 GPa was observed, and congruent melting behavior at pressures up to 12 GPa was observed. Under hydrous conditions, we found that the melting reaction changes from congruent to incongruent at around 13.5 GPa. Liquid formed above 13.5 GPa is enriched in MgO component relative to MgSiO₃ because it coexists with stishovite (SiO₂). Moreover, the solidus temperature decreases drastically at around 13.5 GPa, in unison with the change in the melting reaction. The solidus temperature is about 1400 °C at 13 GPa, but approximately 900 °C at 15 GPa. Our results show that the liquidus phase changes from clinoenstatite to stishovite with increasing pressure and water content above 13.5 GPa. MgSiO₃ enstatite is one of the major constituent minerals in the Earth’s mantle, and it is expected that MgO-enriched liquid will be generated in the transition zone if water is present.     

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.     

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.     

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 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.     

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.     

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.     

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.     

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.     

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.     

Elastic properties from acoustic and volume compression experiments

Hydrostatic compression data for a number of high-pressure phases of oxides and silicates, which have been studied independently by acoustic techniques, have been analyzed by least-squares fitting of the Birch-Murnaghan equation of state to determine the zero-pressure bulk modulus K₀ and its pressure derivative K′₀ for each material. The standard deviations of K₀ and K′₀ so determined are generally underestimated unless the experimental errors in the measurements of volume and pressure are explicitly included. When the values of K₀ determined from the acoustic and compression techniques are consistent, test results for quartz and rutile demonstrate that constraining K₀ to be equal to the acoustic value significantly improves both the accuracy and the precision of K′₀ obtained from the compression data. Similar analyses for high-pressure phases (e.g., pyrope garnet and silicate spinels) indicate that by combining the acoustic and P-V data, the standard deviation of K′₀ is typically reduced by a factor of three. Thus, we conclude that this approach does allow precise determinations of K′₀ even when neither technique alone is able to resolve this parameter. For some materials, however, the P-V and acoustic experiments do not define mutually consistent values of K₀, invalidating any combination of these data. The compression data for stishovite clearly exhibit run to run effects, and we infer that systematic errors are present in some of the P-V data which are responsible for many of the interlaboratory inconsistencies. Such systematic biases in the P-V data can at least be partially compensated for by performing several duplicate experimental runs.     

Melting of Mg2GeO4 under pressure

Melting point of germanate forsterite, Mg₂GeO₄, was raised by compression at the rate of 30°C/GPa. The triple point, at which three phases of olivine- and spinel-type solids and liquid coexisted, was fixed at 1950°C and 3.5GPa. Wen these results are combined with the thermodynamical data of forsterite, Mg₂SiO₄, it is estimated that the triple point of forsterite lies in a region ranging from 2700° to 3000°C in temperature and from 20 to 30GPa in pressure.     

The use of sintered diamond anvils in the MA8 type high-pressure apparatus

A new multi-anvil type high-presure apparatus has been developed using sintered diamond anvils to generate pressures over 30 GPa and temperatures up to about 2000°C. A maximum sample volume of about 1 mm³ is available in this system. The pressure was confirmed by dissociation of forsterite into Mg-perovskite and periclase. The basic techniques and problems in utilizing sintered diamond in the MA8 type high-pressure apparatus are discussed with an emphasis on the future prospect of incorporating simultancous X-ray diffraction observation.     

Mechanisms and kinetics of the post-spinel transformation in Mg2SiO4

Mechanisms and kinetics of the post-spinel transformation in Mg₂SiO₄ were examined at 22.7–28.2 GPa and 860–1200 °C by in situ X-ray diffraction experiments using synchrotron radiation combined with microstructural observations of the recovered samples. The post-spinel phases nucleated on spinel grain boundaries and grew with a lamellar texture. Under large overpressure conditions, reaction rims were formed along spinel grain boundaries at the initial stage of the transformation, whereas under small overpressure conditions, the transformation proceeded without formation of reaction rims. Mg₂SiO₄ spinel metastably dissociated into MgSiO₃ ilmenite and periclase, and stishovite and periclase as intermediate steps in the transformation into the stable assemblage of MgSiO₃ perovskite and periclase. Topotactic relationships were found in the transformation from spinel into ilmenite and periclase. Kinetic parameters in the Avrami rate equation, time taken to 10% completion, and the growth rate were estimated by analysis of the kinetic data obtained by in situ X-ray observations. The empirical activation energy for 10% transformation decreases with increasing pressure because the activation energy for nucleation becomes smaller at larger overpressure conditions. Extrapolations of the 10% transformation to ∼700 °C, which is the lowest temperature expected for the cold slabs at ∼700 km depth, suggest that overpressure of more than ∼1 GPa is needed for the transformation. Because the growth rate is estimated to be large even at low-temperatures of ∼700 °C and overpressures of 1 GPa, the depth of the post-spinel transformation in the cold slabs is possibly controlled by nucleation kinetics.     

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.     

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.     

Stability relation of (Mg,Fe)SiO3 garnets, major constituents in the Earth's interior

High-pressure and high temperature experiments at 20 GPa on (Mg,Fe)SiO₃ have revealed stability fields of two types of aluminium-free ferromagnesian garnets; non-cubic garnet and cubic garnet (majorite). Majorite garnet is stable only within a limited compositional variation, 0.2 < Fe/(Mg + Fe)< 0.4, and in the narrow temperature interval of 200°C around 2000°C, while the stability of non-cubic garnet with more iron-deficient compositions persists up to higher temperatures. These two garnets show fractional melting into iron-deficient garnet and iron-rich liquid, and the crystallization field of cubic garnet extends over Fe/(Mg + Fe)= 0.5. The assemblage silicate spinel and stishovite is a low-temperature phase, which also occurs in the iron-rich portion of the MgSiO₃—FeSiO₃ system. The sequence as given by the Fe/(Mg + Fe) value for the coexisting phases with the two garnets at 2000°C and 20 GPa is: silicate modified spinel aluminium-free garnets silicate spinel.Natural majorite in shock-metamorphosed chondrites is clarified to be produced at pressures above 20 GPa and temperatures around 2000°C. Similar shock events may cause the occurrence of non-cubic garnet in iron-deficient meteorites. Non-cubic garnet could be a stable phase in the Earth's mantle if a sufficiently low concentration of aluminium is present in the layer corresponding to the stable pressure range of non-cubic garnet. The chemical differentiation by melting in the deep mantle is also discussed on the basis of the present experimental results and the observed coexistence of majorite garnet with magnesiowüstite in chondrites.     

Shock temperature in calcite (CaCO3) at 95-160 GPa

The temperatures induced in crystalline calcite (CaCO₃) upon planar shock compression (95-160 GPa) are reported from two-stage light gas gun experiments. Temperatures of 3300-5400 K are obtained by fitting six-channel optical pyrometer radiances in the 450-900 nm range to the Planck gray-body radiation law. Thermodynamic calculations demonstrate that these temperatures are some 400-1350 K lower than expected for vibronic excitations of the lattice with a 3R/mole-atom specific heat (R is gas constant). The temperature deficit along the Hugoniot is larger than that expected from only melting. In addition to melting, it appears likely that shock-induced decomposition of calcite occurs behind the shock front. We modeled disproportionation of calcite into CaO (solid) plus CO₂ (gas). For temperature calculations, specific heat at constant volume for 1 mole of CO₂ is taken to be 6.7R as compared to 9R in the solid state; whereas a mole of calcite and a mole of CaO have their solid state values 15R and 6R, respectively. Calculations suggest that the calcite decomposes to CaO and CO₂ at ∼110±10 GPa along the Hugoniot. Recent reanalysis of earlier VISAR measurements of particle velocity profiles [1] indicates that calcite shocked to 18 GPa undergoes disproportionation at much lower pressures upon isentropic expansion.     

Phase relations of titan-phlogopite,K2Mg4TiAl2Si6O20(OH)4: a refractory phase in the upper mantle?

Experimental data on the stability of titan-phlogopite [K₂Mg₄TiAl₂Si₆O₂₀(OH)₄] are presented which show it to be stable to substantially higher temperatures than normal phlogopite [K₂Mg₆Al₂Si₆O₂₀(OH)₄]. A qualitative model to explain the role of titan-phlogopite during magma generation is put forward. Breakdown of titan-phlogopite during melting at depth (> 150km) on subducted lithospheric slabs is believed responsible for the concomitant increase of K and Ti observed in magmas erupted during orogenic volcanism. At lower pressures (up to about 10 kbar) beneath mid-oceanic ridges, titan-phlogopite is predicted to behave as a refractory phase during partial melting in the mantle, especially if H₂O-excess conditions pertain, although at higher pressures in this environment it would almost certainly behave as a low-melting component.