Bulk Modulus KT Research Articles

Structure and compressibility of Fe-bearing Al-phase D

Abstract Due to its large thermal stability, Al-phase D, the (Al,Fe3+)2SiO6H2 member of the dense hydrous magnesium silicate (DHMS) phase D, may survive along hot subduction geotherms or even at ambient mantle temperatures in the Earth’s transition zone and lower mantle, therefore potentially playing a major role as a water reservoir and carrier in the Earth’s interior. We have investigated the crystal structure and high-pressure behavior of Fe-bearing Al-phase D with a composition of Al1.53(2)Fe0.22(1) Si0.86(1)O6H3.33(9) by means of single-crystal X-ray diffraction. While the structure of pure Al-phase D (Al2SiO6H2) has space group P63/mcm and consists of equally populated and half-occupied (Al,Si)O6 octahedra, Fe-incorporation in Al-phase D seems to induce partial ordering of the cations over the octahedral sites, resulting in a change of the space group from P63/mcm to P6322 and in well-resolved diffuse scattering streaks observed in X-ray images. The evolution of the unit-cell volume of Fe-bearing Al-phase D between room pressure and 38 GPa, determined by means of synchrotron X-ray diffraction in a diamond anvil cell, is well described by a third-order Birch-Murnaghan equation of state having an isothermal bulk modulus KT0 = 166.3(15) GPa and first pressure derivative KT0′ = 4.46(12). Above 38 GPa, a change in the compression behavior is observed, likely related to the high-to-low spin crossover of octahedrally coordinated Fe3+. The evolution of the unit-cell volume across the spin crossover was modeled using a recently proposed formalism based on crystal-field theory, which shows that the spin crossover region extends from approximately 30 to 65 GPa. Given the absence of abrupt changes in the compression mechanism of Fe-bearing Al-phase D before the spin crossover, we show that the strength of H-bonds and likely their symmetrization do not greatly affect the elastic properties of phase D solid solutions, independently of their compositions.

Thermal equation of state of ice-VII revisited by single-crystal X-ray diffraction

Abstract Ice-VII is a high-pressure polymorph of H2O ice and an important mineral widely present in many planetary environments, such as in the interiors of large icy planetary bodies, within some cold subducted slabs, and in diamonds of deep origin as mineral inclusions. However, its stability at high pressures and high temperatures and thermoelastic properties are still under debate. In this study, we synthesized ice-VII single crystals in externally heated diamond-anvil cells and conducted single-crystal X-ray diffraction experiments up to 78 GPa and 1000 K to revisit the high-pressure and high-temperature phase stability and thermoelastic properties of ice-VII. No obvious unit-cell volume discontinuity or strain anomaly of the high-pressure ice was observed up to the highest achieved pressures and temperatures. The volume-pressure-temperature data were fitted to a high-temperature Birch-Murnaghan equation of state formalism, yielding bulk modulus KT0 = 21.0(4) GPa, its first pressure derivative KT0′ = 4.45(6), dK/dT = –0.009(4) GPa/K, and thermal expansion relation αT = 15(5) × 10–5 + 15(8) × 10–8 × (T – 300) K–1. The determined phase stability and thermoelastic properties of ice-VII can be used to model the inner structure of icy cosmic bodies. Combined with the thermoelastic properties of diamonds, we can reconstruct the isomeke P-T paths of ice-VII inclusions in diamond from depth, offering clues on the water-rich regions in Earth’s deep mantle and the formation environments of those diamonds.

P-V-T equation of state of α-ScOOH.

ABSTRACT In this study, an in situ X-ray diffraction study of α-ScOOH, scandium oxyhydroxide with a diaspore-type structure, was conducted at a pressure and temperature of up to 4.12 GPa and 700 K, respectively, to determine the pressure-volume-temperature (P-V-T) equation of state (EoS). Using a least-squares fit of the second-order Birch–Murnaghan EoS to the P-V-T data, the EoS parameters of α-ScOOH were determined as bulk modulus KT 0 = 101(1) GPa, (∂KT /∂T) P = −0.009(5) GPa K−1, and thermal expansion coefficient at zero pressure α = 3.12(6) 10−5 K−1. α-ScOOH exhibits anisotropic compression and thermal expansion behaviors, which are consistent with those of previous studies on diaspore-type oxyhydroxides. α-ScOOH is more compressible than other diaspore-type oxyhydroxides, and the product of the bulk modulus and volume is approximately constant among diaspore-type M3 + OOH (M = Al, Sc, and Fe).

Elastic and magnetic properties of Fe3P up to core pressures: Phosphorus in the Earth's core

Phosphorus (P) is considered a possible light element alloying with iron (Fe) in the Earth's core due to its siderophile nature and the ubiquity of P-bearing iron alloys in iron meteorites. The sequestration of P by liquid metals during the core formation possibly results in the relatively low concentration of P in the bulk silicate Earth. In this study, we performed single-crystal and powder X-ray diffraction, synchrotron Mössbauer spectroscopy and nuclear resonant inelastic X-ray scattering measurements in diamond anvil cells to investigate the elastic and magnetic properties of Fe3P under high pressures. Our X-ray diffraction results suggest that there is no structural phase transition up to 111 GPa. However, a volume collapse was observed at 21.5 GPa in Fe3P, ascribed to a magnetic transition as evidenced by synchrotron Mössbauer spectroscopy results. Fitting the volume-pressure data by the Birch-Murnaghan equation of state gives bulk modulus KT0=162.4(7) GPa, its first pressure derivative KT0′=4.0 (fixed) and zero-pressure volume V0=370.38(6) Å3 for the magnetic phase and KT0=220(7) GPa, KT0′=4.0 (fixed) and V0=357(1) Å3 for the non-magnetic phase. Sound velocities of Fe3P were determined up to 152 GPa by nuclear resonant inelastic X-ray scattering, demonstrating that Fe3P bears a low shear velocity and high Poisson's ratio at core pressures compared to Fe and Fe3S. When forming a solid solution Fe3(S,P) with Fe3S at core pressures, Fe3P may favorably influence the elastic properties of Fe3(S,P) to match the seismic observations of the inner core.

In-situ X-ray diffraction study on β-CrOOH at high pressure and high-temperature

ABSTRACTHigh pressure hydrous phases with distorted rutile-type structure have attracted much interest as potential water reservoirs in the Earth’s mantle. An in-situ X-ray diffraction study of β-CrOOH was performed at high pressures of up to 6.2 GPa and high-temperatures of up to 700 K in order to clarify the temperature effect on compression behaviors of β-CrOOH. The P-V-T data fitted to a Birch–Murnaghan equation of state yielded the following results: isothermal bulk modulus KT0 = 191(4) GPa, temperature derivative (∂KT/∂T)P = −0.04(2) GPa K−1, and volumetric thermal expansion coefficient α = 3.3(2) × 10−5 K−1. In this study, at 300 K, the a-axis became less compressible at pressures above 1–2 GPa. We found that the pressure where the slopes of a/b and a/c ratios turned positive increased with temperature. This is the first experimental study indicating the temperature dependence of the change in the axial compressibility in distorted rutile-type M3+OOH.

Compressibility and thermal expansion of natural clinopyroxene Di0.66Hd0.13Jd0.12Ts0.05

Abstract A natural clinopyroxene (cpx) has been experimentally studied by in-situ X-ray powder diffraction combined with an externally heated diamond anvil cell (DAC) technique in the temperature range 300–673 K and at pressures up to 15 GPa. The specimen has a composition of Di0.66Hd0.13Jd0.12Ts0.05 on the basis of four end-members, diopside (CaMgSi2O6), hedenbergite (CaFeSi2O6), jadeite (NaAlSi2O6), and Mg-Tschermak (MgAl(AlSi)O6). By combining the current data with literature results, an empirical relationship, V0 (A3) = 392.5(6.2) + 46.7(6.5) × Di + 57.6(6.3) × Hd + 9.9(6.2) × Jd has been obtained to describe the relationship between the unit-cell volume and the composition of Di-Jd-Hd solid solution. The isothermal bulk modulus KT0 = 112(3) GPa and its pressure derivative K′T0 = 5.0(7) are obtained by fitting pressure-volume data with a 3rd-order Birch-Murnaghan equation of state (B-M EoS). The volume thermal expansion coefficients are determined to be α0 = 2.97(8) × 10−5/K and 2.82(2) × 10−5/K at ∼6.9(2) GPa and 8.5(2) GPa, respectively, from which ∂α/∂P = −9.3 × 10−7/K GPa−1 and ∂KT/∂T = −0.012 GPa/K are resulted for the current Di0.66Hd0.13Jd0.12Ts0.05.

Transformation pathways and isothermal compressibility of a MTN-type clathrasil using penetrating and non-penetrating fluids

The high-pressure behavior of the natural MTN-type clathrasil chibaite was investigated with in situ single-crystal X-ray diffraction and Raman spectroscopy under hydrostatic pressures up to 10.3 GPa. The experiments were conducted in diamond-anvil cells using 4:1 methanol-ethanol mixture (ME), helium (He) and neon (Ne) as pressure-transmitting media. The pressure dependent unit-cell volumes of the room-pressure polymorph yield an isothermal bulk modulus KT0 = 25.75 (19) GPa for the compression in the non-penetrating ME fluid. Due to the penetration of the Ne and He atoms into the cages of the framework, the crystal structure is significantly stiffened resulting in KT0 = 42.5 (1.2) GPa (Ne) and KT0 = 58 (2) GPa (He). Under the influence of pressure both the evolution of the Raman spectra and the change in cell metrics indicate a distortion of the lattice without leading to a complete pressure-induced amorphization, as observed for many comparable porous structures. Compressed in the non-penetrating ME, the cubic Fd3¯m framework of chibaite undergoes a first transformation step in the pressure range between 1.7 GPa and 2.2 GPa and a second one between 3.9 GPa and 4.3 GPa. The accompanied formation of crystal domains did not allow a reliable determination of the distorted crystal structures. The unit-cell parameters might suggest a monoclinic metric for pressures >1.7 GPa and a monoclinic or tetragonal metric for pressures >3.9 GPa. However, in some samples even the co-existence of crystal domains of a different degree of lattice distortions has been proved.

Single crystal growth, characterization and high-pressure Raman spectroscopy of impurity-free magnesite (MgCO3)

The understanding of the physical and chemical properties of magnesite (MgCO3) under deep-mantle conditions is highly important to capture the essence of deep-carbon storage in Earth’s interior. To develop standard rating scales, the impurity-free magnesite single crystal, paying particular attention to the case of avoiding adverse impacts of Ca2+, Fe2+, and Mn2+ impurities in natural magnesite, is undoubtedly necessary for all research of magnesite, including crystalline structural phase transitions, anisotropic elasticity and conductivity, and equation of state (EoS). Thus, a high-quality single crystal of impurity-free magnesite was grown successfully for the first time using the self-flux method under high pressure–temperature conditions. The size of the magnesite single crystal, observed in a plane-polarized microscope, exceeds 200 μm, and the crystal exhibits a rhombohedral structure to cleave along the (101) plane. In addition, its composition of Mg0.999 ± 0.001CO3 was quantified through electron probing analysis. The structural property was investigated by means of single crystal X-ray diffraction and the unit cell dimensions obtained in the rhombohedral symmetry of the $$R\bar {3}c$$ space group are a = 4.6255 (3) and c = 14.987 (2), and the final R = 0.0243 for 718 reflections. High-pressure Raman spectroscopy of the magnesite single crystal was performed up to 27 GPa at ambient temperature. All Raman active bands, ν i, without any splitting increased almost linearly with increasing pressure. In combination with the high-pressure Raman results $$\frac{{{\text{d}}{\nu _i}}}{{{\text{d}}P}}$$ and the bulk modulus K T (103 GPa) reported from magnesite EoS studies, the mode Gruneisen parameters (1.49, 1.40, 0.26, and 0.27) of each vibration (T, L, ν 4, and ν 1) were calculated.

Isothermal equation of state and phase stability of Fe5Si3 up to 96 GPa and 3000 K

AbstractThe composition of Earth's core has first‐order implications for understanding the thermal and chemical history of the deep Earth. The present work measures the pressure‐volume equation of state of Fe5Si3 to 96 GPa in a diamond anvil cell using noble gas pressure media and demonstrates that Fe5Si3 is not stable at high temperature and pressure but reappears during thermal quench. The isothermal equation of state at ambient temperature of Fe5Si3 is given by the bulk modulus KT,0 = 167 (8) and KT,0′ = 5.1 (2), with V0 = 56.29 cm 3 mol−1. At high temperatures and pressures we observed the disappearance of hexagonal Fe5Si3 diffraction peaks and the appearance of peaks corresponding to cubic FeSi and Fe3Si structures at 18 GPa and at the lowest measurable temperature (~1300 K), indicating that Fe5Si3 is not stable at high temperature. Upon temperature quench diffraction peaks corresponding to Fe5Si3 reappear, confirming its stability at ambient temperature and high pressure.

Thermodynamic properties of Fe-S alloys from molecular dynamics modeling: Implications for the lunar fluid core

Density and sound velocity of Fe-S liquids for the P-T parameters of the lunar core have not been constrained well. From the analysis of seismic wave travel time, Weber et al. (2011) proposed that the lunar core is composed of iron alloyed with ⩽6wt% of light elements, such as S. A controversial issue in models of planetary core composition concerns whether Fe-S liquids under high pressure – temperature conditions provide sound velocity and density data, which match the seismic model. Here we report the results of molecular dynamics (MD) simulations of iron-sulfur alloys based on Embedded Atom Model (EAM). The results of calculations include caloric, thermal and elastic properties of Fe-S alloys at concentrations of sulfur 0–18at.%, temperatures up to 2500K and pressures up to 14GPa. The effect of sulfur on the elastic properties of Fe-rich melts is most evident in the notably decreased density with added S content. In the MD simulation, the density and bulk modulus KT of liquid Fe-S decrease with increasing sulfur content, while the bulk modulus KS decreases as a whole but has some fluctuations with increasing sulfur content. The sound velocity increases with increasing pressure, but depends weakly on temperature and the concentration of sulfur. For a fluid Fe-S core of the Moon (∼5GPa/2000K) with 6–16at.% S (3.5–10wt%), the sound velocity and density may be estimated at the level of 4000ms−1 and 6.25–7.0gcm−3. Comparison of thermodynamic calculations with the results of interpretation of seismic observations shows good agreement of P-wave velocities in the liquid outer core, while the core density does not match the seismic models. At such concentrations of sulfur and a density by 20–35% higher than the model seismic density, a radius for the fluid outer core should be less than about 330km found by Weber et al. because at the specified mass and moment of inertia values of the Moon an increase of the core density leads to a decrease of the core radius. These results are important for modeling the current state and composition of the lunar core and can be applied to models of large satellites’ core properties.

Spin transition of ferric iron in the NAL phase: Implications for the seismic heterogeneities of subducted slabs in the lower mantle

Al-rich phases (NAL: new hexagonal aluminous phase and CF: calcium–ferrite phase) are believed to constitute 10∼30 wt% of subducted mid-ocean ridge basalt (MORB) in the Earth's lower mantle. In order to understand the effects of iron on compressibility and elastic properties of the NAL phase, we have studied two single-crystal samples (Fe-free Na1.14Mg1.83Al4.74Si1.23O12 and Fe-bearing Na0.71Mg2.05Al4.62Si1.16Fe2+0.09Fe3+0.17O12) using synchrotron nuclear forward scattering (NFS) and X-ray diffraction (XRD) combined with diamond anvil cells up to 86 GPa at room temperature. A pressure-induced high-spin (HS) to low-spin (LS) transition of the octahedral Fe3+ in the Fe-bearing NAL is observed at approximately 30 GPa by NFS. Compared to the Fe-free NAL, the Fe-bearing NAL undergoes a volume reduction of 1.0% (∼1.2 Å3) at 33∼47 GPa as supported by XRD, which is associated with the spin transition of the octahedral Fe3+. The fits of Birch–Murnaghan equation of state (B–M EoS) to P–V data yield unit-cell volume at zero pressure V0=183.1(1) Å3 and isothermal bulk modulus KT0=233(6) GPa with a pressure derivative KT0′=3.7(2) for the Fe-free NAL; V0-HS=184.76(6) Å3 and KT0-HS=238(1) GPa with KT0-HS′=4 (fixed) for the Fe-bearing NAL. The bulk sound velocities (VΦ) of the Fe-free and Fe-bearing NAL phase are approximately 6% larger than those of Al, Fe-bearing bridgmanite and calcium silicate perovskite in the lower mantle, except for the spin transition region where a notable softening of VΦ with a maximum reduction of 9.4% occurs in the Fe-bearing NAL at 41 GPa. Considering the high volume proportion of the NAL phase in subducted MORB, the distinct elastic properties of the Fe-bearing NAL phase across the spin transition reported here may provide an alternative plausible explanation for the observed seismic heterogeneities of subducted slabs in the lower mantle at depths below 1200 km.

Mechanical instability and nucleation in a Lennard–Jones fcc crystal at limiting stretching

The method of molecular dynamics simulation has been used to investigate the mechanism of phase decay of a Lennard–Jones fcc crystal close to the boundary of ‘ideal strength’. The attainability of states where the isothermal bulk modulus KT=ρ(∂p/∂ρ)T=0 and KT<0 has been demonstrated at negative pressures. It has been shown that the decay of the crystal phase proceeds by different activation mechanisms: (i) by the formation of voids at temperatures below that of the endpoint of the melting line and (ii) by liquid-phase critical nuclei formation above this temperature.

Volume Dependence of Thermodynamic Properties for Solids at high Temperatures

Abstract A new computing model on the volume dependence of the product αKT of the thermal expansion coefficient α and the isothermal bulk modulus KT is proposed straightforward in this paper. Based on this revised formula, the volume dependence of Grüneisen parameter, entropy, Anderson-Grüneisen parameter, and first pressure derivative of bulk modulus, respectively, are thus investigated. The calculated results agree well with the previous work for magnesium oxide, sodium chloride, lithium, sodium, and potassium.

Single‐crystal equation of state of phase D to lower mantle pressures and the effect of hydration on the buoyancy of deep subducted slabs

An understanding of the physical properties of the hydrous magnesium silicate phase D is important for the interpretation of the seismic anomalies observed in subducted slabs and to evaluate the effect of hydration on slab dynamics. Here we report the equation of state of phase D (Mg1.1Si1.8H2.5O6) up to 65 GPa obtained from high‐precision single‐crystal X‐ray diffraction. A single‐crystal of phase D was loaded in a diamond anvil cell using helium as pressure transmitting medium to ensure quasi‐hydrostatic conditions during the entire data collection. The volume of phase D decreases smoothly over the entire pressure range, without the anomalies in the compressibility reported at 40 GPa in previous powder diffraction studies. If existing in phase D, a hydrogen bond symmetrization transition as predicted by first‐principles calculation is therefore not associated with anomalies in the volume compression behavior. The isothermal bulk modulus KT and its pressure derivative K′T obtained from the fitting of the unit cell volumes using a third‐order Birch‐Murnaghan equation of state are KT = 151.4 ± 1.2 GPa and K′T = 4.89 ±0.08, respectively. This bulk modulus is in good agreement with a recent single‐crystal Brillouin scattering experiment. The presence of 16 vol. % of phase D in hydrous peridotite lithologies reduces the density by up to 2.6% at upper most lower mantle pressure‐temperature conditions (1273 K and 30 GPa), phase D is thus a potential candidate to influence the buoyancy of hydrated stagnant slabs below the transition zone.

Spin transition of Fe3+ in Al-bearing phase D: An alternative explanation for small-scale seismic scatterers in the mid-lower mantle

Among dense-hydrous magnesium silicates potentially transporting H2O into Earthʼs deep interior, phase D (MgSi2H2O6) exhibits the highest P–T stability range, extending into the lower mantle along cold slab geotherms. We have studied the compressibility and spin state of Fe in Al-bearing phase D up to 90 GPa using synchrotron X-ray diffraction and X-ray emission spectroscopy. Fe–Al-bearing phase D was synthesized at 25 GPa and 1400 °C with approximate composition MgSi1.5Fe0.15Al0.32H2.6O6, where nearly all of the Fe is ferric (Fe3+). Analysis of Fe-Kβ emission spectra reveals a gradual, pressure-induced high-spin (HS) to low-spin (LS) transition of Fe3+ extending from 40 to 65 GPa. The fitted equation of state for high-spin Fe–Al-bearing phase D results in a bulk modulus KT0=147(2) GPa with pressure derivative K′=6.3(3). An equation of state over the entire pressure range was calculated using the observed variation in low-spin fraction with pressure and a low-spin bulk modulus of KT0=253(30) GPa, derived from the data above 65 GPa. Pronounced softening in the bulk modulus occurs during the spin transition, reaching a minimum at 50 GPa (∼1500 km) where the bulk modulus of Fe–Al phase D is about 35% lower than Fe–Al-bearing silicate perovskite. Recovery of the bulk modulus at 50–65 GPa results in a structure that has a similar incompressibility as silicate perovskite above 65 GPa. Similarly, the bulk sound velocity of Fe–Al phase D reaches a minimum at ∼50 GPa, being about 10% slower than silicate perovskite. The potential association of Fe–Al phase D with subducted slabs entering the lower mantle, along with its elastic properties through the Fe3+ spin transition predicted at 1200–1800 km, suggests that phase D may provide an alternative explanation for small-scale mid-lower mantle seismic scatterers and supports the presence of deeply recycled sediments in the lower mantle.

High‐Pressure Behavior and Phase Stability of Al5BO9, a Mullite‐Type Ceramic Material

Phase stability, elastic behavior, and pressure‐induced structural evolution of synthetic boron‐mullite Al5BO9 (a = 5.6780(7), b = 15.035(6), and c =7.698(3) Å, space group Cmc21, Z = 4) were investigated up to 25.6(1) GPa by in situ single‐crystal synchrotron X‐ray diffraction with a diamond anvil cell (DAC) under hydrostatic conditions. No evidence of phase transition was observed up to 21.7(1) GPa. At 25.6(1) GPa, the refined unit‐cell parameters deviated significantly from the compressional trend, and the diffraction peaks appeared broader than at lower pressure. At 26.7(1) GPa, the diffraction pattern was not indexable, suggesting amorphization of the material or a phase transition to a high‐pressure polymorph. Fitting the P–V data up to 21.7(1) GPa with a second‐order Birch–Murnaghan Equation‐of‐State, we obtained a bulk modulus KT0 = 164(1) GPa. The axial compressibilities, here described as linearized bulk moduli, are as follows: KT0(a) = 244(9), KT0(b) = 120(4), and KT0(c) = 166(11) GPa (KT0(a):KT0(b):KT0(c) = 2.03:1:1.38). The structure refinements allowed a description of the main deformation mechanisms in response to the applied pressure. The stiffer crystallographic direction appears to be controlled by the infinite chains of edge‐sharing octahedra running along [100], making the structure less compressible along the a‐axis than along the b‐ and c‐axis.

High-pressure X-ray study of LiCrSi2O6 clinopyroxene and the general compressibility trends for Li-clinopyroxenes

High-pressure single-crystal X-ray diffraction measurements of synthetic LiCrSi2O6 clinopyroxene (with space group P21/c) were performed in a diamond-anvil cell up to 7.970 GPa. No phase transition has been observed within the pressure range investigated, but the elastic behavior at lower pressures (up to ~2.5 GPa) is affected by an anomalous softening due to the proximity of the phase transition to the HT-C2/c phase at 330 K and at ambient pressure. A third-order Birch–Murnaghan equation of state fitted to the compression data above 2.5 GPa yields a bulk modulus K T0 = 93(2) GPa and its first derivative K′ = 8.8(6). The structural data measured up to 7.970 GPa confirm that the space group P21/c is maintained throughout the whole pressure range investigated. The atomic parameters, obtained from the integrated diffraction intensities, suggest that the Li coordination polyhedron changes its coordination number from 5 to 6 at 6–7 GPa by means of the approach of the bridging O atom, related to the increased kinking of the B tetrahedral chain. Furthermore, at higher pressures, the structural evolution of LiCrSi2O6 provides evidence in the variation of kinking angles and bond lengths of a potential phase transition above 8 GPa to the HP-C2/c space group. A comparison of the Li-clinopyroxenes (M1 = Cr, Al, Sc, Ga, Mg + Fe) previously investigated and our sample shows that their elastic behavior and structural mechanisms of compression are analogous.

P‐V‐T equation of state for ε‐iron up to 80 GPa and 1900 K using the Kawai‐type high pressure apparatus equipped with sintered diamond anvils

In order to determine the P‐V‐T equation of state of ε‐iron, in situ X‐ray observations were carried out at pressures up to 80 GPa and temperatures up to 1900 K using the Kawai‐type high pressure apparatus equipped with sintered diamond anvils which was interfaced with synchrotron radiation. The present results indicate the unit cell volume at ambient conditionsV0 = 22.15(5) Å3, the isothermal bulk modulus KT0 = 202(7) GPa and its pressure derivative K′T0 = 4.5(2), the Debye temperature θ0 = 1173(62) K, Grüneisen parameter at ambient pressure γ0 = 3.2(2), and its logarithmic volume dependence q = 0.8(3). Furthermore, thermal expansion coefficient at ambient pressure was determined to be α0(K−1) = 3.7(2) × 10−5 + 7.2(6) × 10−8(T‐300) and Anderson‐Grüneisen parameterδT = 6.2(3). Using these parameters, we have estimated the density of ε‐iron at the inner core conditions to be ∼3% denser than the value inferred from seismological observation. This result indicates that certain amount of light elements should be contained in the inner core as well as in the outer core but in definitely smaller amount.

Thermal equation of state of CaIrO3 post-perovskite

The pressure-volume-temperature (P-V-T) relation of CaIrO3 post-perovskite (ppv) was measured at pressures and temperatures up to 8.6 GPa and 1,273 K, respectively, with energy-dispersive synchrotron X-ray diffraction using a DIA-type, cubic-anvil apparatus (SAM85). Unit-cell dimensions were derived from the Le Bail full profile refinement technique, and the results were fitted using the third-order Birth-Murnaghan equation of state. The derived bulk modulus KT0 at ambient pressure and temperature is 168.3 ± 7.1 GPa with a pressure derivative K 0 T0 = 5.4 ± 0.7. All of the high temperature data, combined with previous experimental data, are fitted using the high-temperature Birch-Murnaghan equation of state, the thermal pressure approach, and the Mie-Grunei- sen-Debye formalism. The refined thermoelastic parameters for CaIrO3 ppv are: temperature derivative of bulk modu- lus ðoKT =oTÞ P =- 0.038 ± 0.011 GPa K -1 , aKT = 0.0039 ± 0.0001 GPa K -1 , oKT =oT ðÞ V =- 0.012 ± 0.002 GPa K -1 , and o 2 P=oT 2 �� V = 1.9 ± 0.3 9 10 -6

Diaspore crystal structure and compressibility at high pressures and high temperature

We have determined the unit-cell parameters of diaspore α-AlO(OH) at high pressures (13.5–27.8 GPa) and at high temperature (1900 K). Experimental data are compared with the theoretically predicted crystal structure variations derived from density functional theory (DFT) calculations. The experimental analysis establishes that the a axial direction is more compressible than the b and c axial directions in the low-pressure range (13.5–18 GPa) and at 1900 K, whereas all three directions show similar behaviors in the high-pressure range (18–27.8 GPa). The diaspore isothermal bulk modulus KT values are 137.6 GPa, 124.8 GPa, and 141.3 GPa, respectively, at 300 K, at 1900 K, and again at 300 K after quenching. By comparison, the diaspore isothermal bulk modulus KT computed at 300 K and at ambient pressure in the framework of the plane-wave pseudopotential approach is equal to 129.3 GPa.