Zero-pressure Density Research Articles

Phase transition and compression behavior of phase D up to 46 GPa using multi-anvil apparatus with sintered diamond anvils

A thermal equation of state of phase D with a Mg1.02Si1.73H3.03O6 composition has been derived from in situ X-ray diffraction experiments using synchrotron radiation and multianvil apparatus with sintered diamond anvils at pressures up to 46 GPa and temperatures up to 1300 K. The refined unit-cell parameters at ambient conditions are: a=4.7643(7) Å, c=4.346(2) Å, and V 0=85.43(4)Å3 and the zero-pressure density of ρ0=3.357(2) g/cm3 (Z=1; formula weight=172.70 g/mol). At room temperature, the unit-cell parameters show anisotropic compression behavior up to ∼35 GPa, where the c-axis is more compressible than the a-axis. Above 35 GPa, however, the c-axis becomes less compressible than the a-axis. This change of the axial compression behavior tends to start at higher pressure with increasing temperature. The change of the linear compressibilities may be related to the hydrogen-bond symmetrization in phase D, as suggested by recent first-principles calculations.

Hugoniot Data for Helium in the Ionization Regime

Hugoniot data were obtained for fluid He in the 100 GPa pressure range by shock compression of samples statically precompressed in diamond-anvil cells. The initial (precompressed) He density (rho_(1)) for each experiment was tuned to a value between rho_(0L)<rho_(1)<3.3rho_(0L), where rho_(0L) is the zero-pressure density of the cryogenic liquid (rho_(0L)=0.123 g/cm(3)). The maximum observed shock-compression ratios range from rho/rho_(1)=6 for rho_(1)=rho_(0L) to rho/rho_(1)=4 for rho_(1)> or =3rho_{0L} (i.e., rho/rho_(0L)> or =12). Data show an increase in compressibility at the onset of ionization, similar to theoretical predictions.

Elastic wave velocities and Raman shift of MORB glass at high pressures — Reply

The elastic wave velocities of MORB glass were measured up to 18.7 GPa at 27 °C using an ultrasonic technique combined with in situ high-pressure X-ray diffraction and imaging. High-pressure Raman spectroscopy using a diamond anvil cell was also employed to study the local structure of the glass sample up to 20 GPa. Both the elastic wave velocities and Raman frequency at ∼ 1600 cm-1 show significant changes in their pressure dependences at ∼ 10 GPa. The pressure derivatives of the P-wave and bulk sound velocities gradually increase with pressure above ∼ 10 GPa, whereas the S-wave velocity is almost constant below 10 GPa, above which it increases significantly. The plot of apparent change in the Raman frequency shift versus pressure suggests that these notable changes in elastic properties may be attributed to the local structural changes in the MORB glass. Our observations demonstrate that both the density and adiabatic bulk modulus of the MORB glass increase continuously at pressures above ∼ 10 GPa. These apparently conflicting tendencies can be reasonably explained if the zero-pressure density is increased continuously above ∼ 10 GPa accompanied by structural modification. Since the fundamental structure of silicate glass is analogous to that of melt, the results are important and aid in understanding the elastic properties of silicate melt at high pressures.

High-temperature and high-pressure equation of state for the hexagonal phase in the system NaAlSiO4 – MgAl2O4

Thermal equation of state of an Al-rich phase with Na1.13Mg1.51Al4.47Si1.62O12 composition has been derived from in situ X-ray diffraction experiments using synchrotron radiation and a multianvil apparatus at pressures up to 24 GPa and temperatures up to 1,900 K. The Al-rich phase exhibited a hexagonal symmetry throughout the present pressure–temperature conditions and the refined unit-cell parameters at ambient condition were: a=8.729(1) A, c=2.7695(5) A, V0=182.77(6) A3 (Z=1; formula weight=420.78 g/mol), yielding the zero-pressure density ρ0=3.823(1) g/cm3 . A least-square fitting of the pressure-volume-temperature data based on Anderson’s pressure scale of gold (Anderson et al. in J Appl Phys 65:1534–543, 1989) to high-temperature Birch-Murnaghan equation of state yielded the isothermal bulk modulus K0=176(2) GPa, its pressure derivative K0′=4.9(3), temperature derivative (∂KT/∂T)P=−0.030(3) GPa K−1 and thermal expansivity α(T)=3.36(6)×10−5+7.2(1.9)×10−9T, while those values of K0=181.7(4) GPa, (∂KT/∂T)P=−0.020(2) GPa K−1 and α(T)=3.28(7)×10−5+3.0(9)×10−9T were obtained when K0′ was assumed to be 4.0. The estimated bulk density of subducting MORB becomes denser with increasing depth as compared with earlier estimates (Ono et al. in Phys Chem Miner 29:527–531 2002; Vanpeteghem et al. in Phys Earth Planet Inter 138:223–230 2003; Guignot and Andrault in Phys Earth Planet Inter 143–44:107–128 2004), although the difference is insignificant (<0.6%) when the proportions of the hexagonal phase in the MORB compositions (∼20%) are taken into account.

Effects of CO 2 on the phase behavior of the enstatite–forsterite system at high pressures and temperatures

The effect of CO 2 on the various phase transitions in the enstatite (MgSiO 3)–forsterite (Mg 2SiO 4) system observed at high pressures and high temperatures is investigated on the basis of the available experimental results and the zero-pressure density data for all the phases. Except for the coexistence with magnesite and stishovite, the high-pressure phase transition scheme for the MgSiO 3–CO 2 system remains very much the same as for pure enstatite when CO 2 <30.48 wt.%. The transformation scheme for the Mg 2SiO 4–CO 2 system, however, becomes rather complicated when minute amounts of CO 2 are present. Not only the ordinary high-pressure modifications of Mg 2SiO 4 (e.g., β-phase and spinel modification) are present, but those of MgSiO 3 and SiO 2 plus magnesite are also present in the Mg 2SiO 4–CO 2 system. It has also been found that all the high-pressure phase transitions known in MgSiO 3 should not occur when CO 2 ≥30.48 wt.%, and that all those known in Mg 2SiO 4 should not occur when CO 2 ≥38.48 wt.%. With the presence of a small amount of CO 2, the number of high-pressure phase transitions in the Mg 2SiO 4–CO 2 system is about twice as that found in forsterite, and the increase in density associated with each transition in both forsterite and enstatite is reduced.

Limits to resolution in composition and density in ultra high-pressure experiments on natural mantle-rock samples

We compressed and analyzed an undepleted natural peridotite—thought to be representative of the Earth’s upper mantle—from ∼25 to 110 GPa and heated to 2000–2500 K. Scatter in zero-pressure unit-cell volumes observed for high-pressure phases synthesized from peridotite, of ±0.4% for orthorhombic perovskite and ±0.8% for magnesiowüstite, can be ascribed to compositional heterogeneity in the natural starting material and its transformation products (calcium perovskite was also observed at high pressures, but does not quench to zero pressure). The scatter is larger than the measurement uncertainties, which are as little as ±0.1%, but is less than would be expected from the variation in composition among distinct minerals if the starting material had failed to equilibrate upon transformation to the high-pressure assemblage (e.g., up to ±0.6–0.8% in volume for orthorhombic perovskite). The equilibrium unit-cell volume of orthorhombic perovskite calculated from an average of electron microprobe analyses on the quenched samples, 163.3 (±0.6) Å 3 , agrees to within 0.4% with the average value measured from the same samples by X-ray diffraction at zero pressure (163.9±0.7 Å 3 ). Similarly, values of zero-pressure density for the whole-rock assemblage of high-pressure phases are identical (4.13±0.03 g/cm 3 ), whether derived from electron microprobe or X-ray diffraction measurements.

Limits to resolution in composition and density in ultra high-pressure experiments on natural mantle-rock samples

We compressed and analyzed an undepleted natural peridotite—thought to be representative of the Earth’s upper mantle—from ∼25 to 110 GPa and heated to 2000–2500 K. Scatter in zero-pressure unit-cell volumes observed for high-pressure phases synthesized from peridotite, of ±0.4% for orthorhombic perovskite and ±0.8% for magnesiowüstite, can be ascribed to compositional heterogeneity in the natural starting material and its transformation products (calcium perovskite was also observed at high pressures, but does not quench to zero pressure). The scatter is larger than the measurement uncertainties, which are as little as ±0.1%, but is less than would be expected from the variation in composition among distinct minerals if the starting material had failed to equilibrate upon transformation to the high-pressure assemblage (e.g., up to ±0.6–0.8% in volume for orthorhombic perovskite). The equilibrium unit-cell volume of orthorhombic perovskite calculated from an average of electron microprobe analyses on the quenched samples, 163.3 (±0.6) Å 3, agrees to within 0.4% with the average value measured from the same samples by X-ray diffraction at zero pressure (163.9±0.7 Å 3). Similarly, values of zero-pressure density for the whole-rock assemblage of high-pressure phases are identical (4.13±0.03 g/cm 3), whether derived from electron microprobe or X-ray diffraction measurements.

Ab initio simulation of the ice II structure

We have carried out ab initio simulations on the high-pressure polymorph of solid water, ice II, a phase for which there is a surprising lack of experimental data. We report our calculated third-order Birch–Murnaghan equation of state for ice II: the zero pressure and temperature density, ρ0=1240.27±0.62 kg m−3, bulk modulus, K0=16.18±0.12 GPa, with the first pressure derivative of the bulk modulus, K0′, fixed equal to 6.0. These parameters, the unit cell dimensions, and the atomic positions are in good agreement with experimental values. We also describe the way in which the change in unit cell volume is accommodated within the structure, primarily by contraction of the distance between neighboring hexagonal tubes—the principal structural element of ice II. This is in agreement with existing experimental data.

The compressibility of hexagonal Al-rich NAL phase: similarities and differences with calcium ferrite-type (CF) phase with implications for the lower mantle

We have determined the equation of state of a hexagonal Al-rich type NAL phase [K 0.07Na 0.81Ca 0.12] Σ1.01[Mg 1.62Fe 0.38] Σ2.00[Al 4.98Fe 0.10Ti0 .05Si 0.88] Σ6.01O 12, an aluminum host mineral that is likely to occur in subducted oceanic crusts (mid-oceanic ridge basaltic (MORB)) in the Earth’s lower mantle. Angle-dispersive X-ray powder diffraction experiments were conducted up to 36 GPa at room temperature at the BL04-B2 at Spring-8. Fitting a third-order Birch–Murnaghan equation of state to the data gives a bulk modulus of K 0=214 (±2) GPa with K 0′=3 (±0.1) , a volume V 0=184.55(6) Å 3 and a zero-pressure density of ρ 0=4 g/cm 3. When K 0′ is fixed at 4, the value of K 0=202.3 (±0.9) GPa. These values are comparable to those for similar anhydrous hexagonal aluminous phases reported previously by Ono et al. [Phys. Chem. Minerals 29 (2002a) 527]. The density of NAL phase is lower than that of other minerals (excluding the CF phase) co-existing in the subducted oceanic crust, such as Mg-perovskite, Ca-perovskite and stishovite. We find that the elastic properties of the hexagonal Al-rich phase do not change despite substantial variations in Si, Al, Fe, Mg, Na and K content in the NAL chemical composition.

Finite strain, thermodynamics and the earth’s core

A critical appraisal of finite strain theories used in geophysics, emphasising the importance of derivative properties, especially K′=d K/d P (K is bulk modulus and P is pressure), leaves only two survivors, Keane’s equation and the reciprocal K′ equation, by which 1/ K′ varies linearly with P/ K. The two most used relationships, by Birch and Rydberg, are fundamentally flawed, as is the argument that the infinite pressure asymptote, K ∞′, should have the value 5/3, corresponding to a Thomas–Fermi gas. A study of the PREM data for the core restricts K ∞′ for core material to a value close to 3.0, confirming an earlier suggestion. Extrapolation of core data to P=0 gives zero pressure values of K′, K and density, ρ at the foot of the core adiabat: 5.2≤ K 0′≤5.4, 108 GPa≤K 0 ≤123 GPa , 6420 kg m −3≤ρ 0≤6570 kg m −3 . These values do not agree well with reports on K 0′ and K 0 for laboratory liquid iron. At least part of the explanation appears to be a structural difference between liquid iron at core pressures and P=0, mirroring the different structures of the solid. This limits the accuracy with which equations of state can, at present, be fitted to outer core data. Inner core properties, apart from density, must be very similar to those of ε-iron but comparison with high pressure measurements on iron reveals an incompatibility in bulk moduli that is most easily explained as pressure calibration errors in the laboratory data. This means that the equation of state for platinum, used as a reference standard to estimate pressure, requires reconsideration. This could involve comparison of laboratory data for iron with seismological data for the core, where pressure is more precisely known. The estimated zero pressure density for inner core material is 7850 kg m −3 , at least 5% less than the extrapolated density of ε-iron, indicating a light element content more than half of that in the outer core.

Structure type and bulk modulus of Fe3S, a new iron-sulfur compound

We performed a series of experiments in the system Fe-FeS at a pressure of 21 GPa and temperatures between 950 and 1400 °C, and we found two new iron-excess iron-sulfur compounds, Fe3S and Fe2S, formed at subsolidus temperatures. Powder X-ray diffraction data revealed that Fe3S has a tetragonal cell, isostructural with Fe3P (space group I 4). The tetragonal unit-cell dimensions for Fe3S are a = 9.144(2) A and c = 4.509(2) A, with a zero-pressure density of 7.033 g/cm3. Static compression experiments on Fe3S were carried out in a diamond-anvil cell, using synchrotron X-ray diffraction technique. A least-squares fit to the experimental data at room temperature yielded bulk modulus K = 170 ± 8 GPa with a corresponding pressure derivative K ′ = 2.6 ± 0.5 or K = 150 ± 2 GPa with fixed K ′ = 4.

Effect of irreversible phase change on shock-wave propagation

New release adiabat data for vitreous GeO 2 are reported up to ∼25 GPa using the VISAR technique. Numerical modeling of isentropic release wave induced dynamic states achieved from one dimensional strain–stress waves is consistent with a phase change that induce an increase in zero-pressure density from 3.7–6.3 Mg/m 3 starting at ∼8 GPa. The first release adiabat data for SiO 2 ( fused quartz) are presented (obtained with immersed foil technique) . Above 10 GPa, the SiO 2 release isentropes, in analogy with GeO 2, are steeper than the Hugoniot in the volume-pressure space, indicating the presence of an irreversible phase transition (to a stishovite-like phase) . We simulate propagation of shock-waves in GeO 2, in spherical and planar symmetries, and predict enhanced attenuation for shock pressures ( p) above the phase change initiation pressure (8 GPa) . The pressure from a spherical source decays with propagation radius r, p ∼ r x, where x is the decay coefficient. Modeling hysteresis of the phase change gives x = −2.71, whereas without the phase change, x = −1.15. An analytical model is also given.

Hydrogen in strong magnetic fields in neutron star surfaces

In magnetic fields of very much more than G, polyatomic hydrogen molecules, in the form of long chains, are stable. In neutron star surfaces, fields of G are commonplace and G has been reported. Liquid hydrogen can form at the higher field with a zero-pressure density of about . At these densities, hydrogen can burn to helium by pycnonuclear reactions even at low temperatures - the `real cold fusion'.

A new unquenchable high-pressure polymorph of Ca 3Al 2Si 3O 12

A perovskite structured new high-pressure polymorph of Ca 3Al 2Si 3O 12 grossular garnet was synthesized using a diamond anvil cell combined with laser heating at 30.2 GPa and about 1000–1500°C. This high-pressure phase is unquenchable on release of pressure, and the in situ X-ray diffraction analysis indicates that the new phase is slightly distorted from a cubic symmetry. It can be indexed by a Pbnm orthorhombic structure which is isostructural with MgSiO 3 perovskite. The bulk modulus calculated from the compression curve using the Birch-Murnaghan equation of state is 283 ± 7 GPa, when its pressure derivative is fixed at four. The estimated zero-pressure density is 11% larger than that of grossular garnet. The volume difference between this phase and CaSiO 3 perovskite is less than 1%, which indicates that, in perovskite structure, the substitution of two Al 3+ for Ca 2+ and Si 4+ does not change the volume significantly.

Phase transformations in subducted oceanic crust and buoyancy relationships at depths of 600–800 km in the mantle

Phase transformations in a representative oceanic crust composition (MORB) have been studied at pressures up to 28 GPa, at 1200°C and 1500°C using a multi-anvil apparatus. The assemblage of majorite + CaSiO 3-rich perovskite + stishovite which is displayed by the MORB composition at pressures above 20 GPa was found to transform further into an assemblage containing a new aluminous phase at pressures above 25 GPa. This Al-phase has a complex composition and is also relatively sodium rich. Its X-ray diffraction pattern is similar to that observed for MgAl 2O 4 (calcium ferrite type), and is tentatively indexed on the basis of an orthorhombic cell, yielding a zero-pressure density of 3.87(2) g/cm 3. Majorite garnet was found to remain as the most abundant phase at the highest pressure studied (28 GPa) and does not appear likely to transform to perovskite until pressures exceed 29–30 GPa. These results imply that the basaltic crust component of subducted oceanic lithosphere would be 0.1–0.2 g/cm 3 less dense than surrounding mantle pyrolite between the depths of 660–800 km, thereby confirming an earlier hypothesis of Anderson. Moreover, the underlying layer of harzburgite would be ∼ 0.05 g/cm 3 less dense than pyrolite throughout most of this depth interval. These buoyancy relationships contribute to a barrier which impedes and may sometimes prevent the entry of slabs into the lower mantle.

An evaluation of the equation of state of liquid carbon at very high pressure

By comparison of calculated Hugoniot temperature of strongly shocked graphites with the currently most reliable, theoretical phase diagram of carbon, part of the principal Hugoniot of graphite determined by Gust [ Phys. Rev. B22, 4744–4756 (1980)] and Ragan et al. [In Shock Waves in Condensed Matter 1983 (Edited by J. R. Asay, R. A. Graham and J. K. Staub), pp. 77–80, Elsevier, Amsterdam (1984)] involves the liquid state of carbon although it appears to be substantially indistinguishable from that of diamond with respect to the shock velocity ( U s ) particle velocity ( u p ) relation. The equation of state parameters of liquid carbon, derived from strongly shocked graphite data, are obtained by assuming that the pressure derivative of the bulk modulus at zero pressure is close to 4. The best fit is given by the U s − u P relation U s = 2.45 + 1.25 u p ,( km/ s) as the principal Hugoniot of liquid carbon, with the zero-pressure density of 1.70 ± 0.05 g/ cm 3. The estimated zero-pressure density and bulk modulus for the liquid produced at very high pressures (~ 1 TPa) differ little from that of the low-pressure liquid (~ 1 GPa). This may suggest that the structure of liquid carbon produced by strong shocks does not change greatly with increasing pressure to about a few TPa probably because of the extreme temperature of the shock-produced liquid.

Modified potential-induced-breathing model of potentials between close-shell ions.

We have developed a simple ab initio model for the calculation of the thermoelastic properties of ionic compounds. The model is based on the Gordon-Kim-type electron-gas theory with spherically symmetric relaxation of ionic charge densities. The relaxation is controlled by a spherically averaged potential due to the total crystal charge density. The potential is self-consistent with the charge distribution, and contains Coulomb, exchange, and correlation contributions. We find that this potential yields anions that are slightly smaller than those stabilized by a point-ion Coulomb potential only. In the case of MgO, this results in a zero-pressure density that differs from experiment by less than 1%, a significant improvement over models that include only point-ion stabilization potentials. Further, the calculated equations of state and B1-B2 phase-transition pressures of NaCl, KCl, MgO, CaO, and SrO are in equally good agreement with data. The calculated equation of state and structure of the more covalent and less symmetric ${\mathrm{SiO}}_{2}$ stishovite is only slightly less accurate.

Equation of state in a strong magnetic field - Finite temperature and gradient corrections

The equation of state for condensed matter in a strong magnetic field is constructed. The regime for which statistical models and spherical Wigner-Seitz lattice cells are valid approximations is treated. The equation of state for a free nonrelativistic homogeneous electron gas in a uniform magnetic field is examined as a function of temperature, after which this treatment is refined by incorporating Coulomb interactions in a magnetic Thomas-Fermi model which allows for finite temperature. Gradient corrections to the zero-temperature equation of state are then evaluated by constructing a magnetic Thomas-Fermi-Dirac-Weizsaecker model, these corrections having a considerable effect on the zero-pressure density for matter in strong magnetic fields. Finally, the hydrostatic equilibrium equation for the surface structure of a neutron star is integrated using the presently computed equations of state. 52 refs.

A new high-pressure form of MgAl2O4

MAGNESIUM aluminium spinel (MgAl2O4) is a common constituent of low-pressure peridotite xenoliths, and is an important host mineral for aluminium and other trivalent cations in the shallow upper mantle. Shock-wave compression data for MgAl2O4 demonstrated1 that spinel would transform to denser phases at pressures greater than 40 GPa, although there was much uncertainty in the pressure estimation. Later, spinel was found to transform under static compression to the denser oxide mixture (MgO periclase + A12O3 corundum2,3) at pressures above 15 GPa (ref. 4). Detailed analyses of the shock-compression data, however, suggested the presence of a still denser phase of MgAl2O4 spinel at much higher pressures5,6. Here we report the transformation of MgAl2O4 spinel to a new high-pressure form at pressures above 25 GPa in a multi-anvil high-pressure apparatus. The new MgAl2O4 phase has a structure similar to that of CaFe2O4(calcium ferrite) and its zero-pressure density is 3.937(3) g cm-3, which is ∼2% denser than the lower-pressure assemblage of periclase + corundum. We suggest that this high-pressure form of MgAl2O4 may be an important host of aluminium in the Earth's lower mantle.

High-pressure transformation of eclogite to garnetite in subducted oceanic crust

The mineral composition of oceanic crust is a function of pressure and temperature and thus changes as a slab of crust descends a subduction zone. A knowledge of the mineralogy of subducted material would provide important constraints on its geophysical characteristics. We have sought, by means of high pressure laboratory experiments (in the pressure range 4.6–18 GPa) on a synthetic mix with the composition of mid-ocean ridge basalt (MORB), to determine the sequence of mineralogical changes. We find that at 1,200°C, solid solution of pyroxene in garnet begins around 10 GPa, and increases substantially between 12 and 15 GPa. Complete transformation of eclogite to garnetite is achieved at 15 GPa. The garnetite has a zero-pressure density of 3.76 g cm−3 and accordingly would be denser than the surrounding mantle throughout its stability field, which extends to depths of ˜600 km. If subducted to greater depths, garnetite may transform to perovskitite.