In situ observation of a garnet/perovskite transition in CaGeO<Subscript>3</Subscript>

We used an in situ measurement method to investigate the phase transition of CaGeO₃ polymorphs under high pressures and temperatures. A multi-anvil high-pressure apparatus combined with intense synchrotron X-ray radiation was used. The transition boundary between a garnet and a perovskite phase at T = 900–1,650 K and P = 3–8 GPa was determined as occurring at P (GPa) = 9.0−0.0023 × T (K). The transition pressure determined in our study is in general agreement with that observed in previous high-pressure experiments. The slope, dP/dT, of the transition determined in our study is consistent with that calculated from calorimetry data.     

Stability and P–V–T equation of state of KAlSi3O8-hollandite determined by in situ X-ray observations and implications for dynamics of subducted continental crust material

In situ X-ray diffraction measurements of KAlSi₃O₈-hollandite (K-hollandite) were performed at pressures of 15–27 GPa and temperatures of 300–1,800 K using a Kawai-type apparatus. Unit-cell volumes obtained at various pressure and temperature conditions in a series of measurements were fitted to the high-temperature Birch-Murnaghan equation of state and a complete set of thermoelastic parameters was obtained with an assumed K′_300,0=4. The determined parameters are V _300,0=237.6(2) Å³, K _300,0=183(3) GPa, (?K _T,0/?T) _P =?0.033(2) GPa K^?1, a ₀=3.32(5)×10^?5 K^?1, and b ₀=1.09(1)×10^?8 K^?2, where a ₀ and b ₀ are coefficients describing the zero-pressure thermal expansion: α _T,0 = a ₀ + b ₀ T. We observed broadening and splitting of diffraction peaks of K-hollandite at pressures of 20–23 GPa and temperatures of 300–1,000 K. We attribute this to the phase transitions from hollandite to hollandite II that is an unquenchable high-pressure phase recently found. We determined the phase boundary to be P (GPa)=16.6 + 0.007 T (K). Using the equation of state parameters of K-hollandite determined in the present study, we calculated a density profile of a hypothetical continental crust (HCC), which consists only of K-hollandite, majorite garnet, and stishovite with 1:1:1 ratio in volume. Density of HCC is higher than the surrounding mantle by about 0.2 g cm^?3 in the mantle transition zone while this relation is reversed below 660-km depth and HCC becomes less dense than the surrounding mantle by about 0.15 g cm^?3 in the uppermost lower mantle. Thus the 660-km seismic discontinuity can be a barrier to prevent the transportation of subducted continental crust materials to the lower mantle and the subducted continental crust may reside at the bottom of the mantle transition zone.     

High-pressure polymorphism and structural transitions of norsethite,BaMg(CO3)2

In situ high-pressure investigations on norsethite, BaMg(CO₃)₂, have been performed in sequence of diamond-anvil cell experiments by means of single-crystal X-ray and synchrotron diffraction and Raman spectroscopy. Isothermal hydrostatic compression at room temperature yields a high-pressure phase transition at P _c ≈ 2.32 ± 0.04 GPa, which is weakly first order in character and reveals significant elastic softening of the high-pressure form of norsethite. X-ray structure determination reveals C2/c symmetry (Z = 4; a = 8.6522(14) Å, b = 4.9774(13) Å, c = 11.1542(9) Å, β = 104.928(8)°, V = 464.20(12) Å³ at 3.00 GPa), and the structure refinement (R ₁ = 0.0763) confirms a distorted, but topologically similar crystal structure of the so-called γ-norsethite, with Ba in 12-fold and Mg in octahedral coordination. The CO₃ groups were found to get tilted off the ab-plane direction by ~16.5°. Positional shifts, in particular of the Ba atoms and the three crystallographically independent oxygen sites, give a higher flexibility for atomic displacements, from which both the relatively higher compressibility and the remarkable softening originate. The corresponding bulk moduli are K ₀ = 66.2 ± 2.3 GPa and dK/dP = 2.0 ± 1.8 for α-norsethite and K ₀ = 41.9 ± 0.4 GPa and dK/dP = 6.1 ± 0.3 for γ-norsethite, displaying a pronounced directional anisotropy (α: β _a ^?1  = 444(53) GPa, β _c ^?1  = 76(2) GPa; γ: β _a ^?1  = 5.1(1.3) × 10³ GPa, β _b ^?1  = 193(6) GPa β _c ^?1  = 53.4(0.4) GPa). High-pressure Raman spectra show a significant splitting of several modes, which were used to identify the transformation in high-pressure high-temperature experiments in the range up to 4 GPa and 542 K. Based on the experimental series of data points determined by XRD and Raman measurements, the phase boundary of the α-to-γ-transition was determined with a Clausius–Clapeyron slope of 9.8(7) × 10^?3 GPa K^?1. An in situ measurement of the X-ray intensities was taken at 1.5 GPa and 411 K in order to identify the nature of the structural variation on increased temperatures corresponding to the previously reported transformation from α- to β-norsethite at 343 K and 1 bar. The investigations revealed, in contrast to all X-ray diffraction data recorded at 298 K, the disappearance of the superstructure reflections and the observed reflection conditions confirm the anticipated \(R\bar{3}m\) space-group symmetry. The same superstructure reflections, which disappear as temperature increases, were found to gain in intensity due to the positional shift of the Ba atoms in the γ-phase.     

Expansivity and compressibility of wadeite-type K2Si4O9 determined by in situ high T/P experiments, and their implication

Wadeite-type K₂Si₄O₉ was synthesized with a cubic press at 5.4 GPa and 900 °C for 3 h. Its unit-cell parameters were measured by in situ high-T powder X-ray diffraction up to 600 °C at ambient P. The T–V data were fitted with a polynomial expression for the volumetric thermal expansion coefficient (α_T = a ₀ + a ₁ T), yielding a ₀ = 2.47(21) × 10^?5 K^?1 and a ₁ = 1.45(36) × 10^?8 K^?2. Compression experiments at ambient T were conducted up to 10.40 GPa with a diamond-anvil cell combined with synchrotron X-ray radiation. A second-order Birch–Murnaghan equation of state was used to fit the P–V data, yielding K _T = 97(3) GPa and V ₀ = 360.55(9) Å³. These newly determined thermal expansion data and compression data were used to thermodynamically calculate the P–T curves of the following reactions: 2 sanidine (KAlSi₃O₈) = wadeite (K₂Si₄O₉) + kyanite (Al₂SiO₅) + coesite (SiO₂) and wadeite (K₂Si₄O₉) + kyanite (Al₂SiO₅) + coesite/stishovite (SiO₂) = 2 hollandite (KAlSi₃O₈). The calculated phase boundaries are generally consistent with previous experimental determinations.     

Pressure dependence of Néel transition in (Mg,Fe)O

Pressure dependence of Néel temperature (T _N) in (Mg_0.20Fe_0.80)O, (Mg_0.25Fe_0.75)O, and (Mg_0.30Fe_0.70)O was newly measured up to 1.14 GPa, using superconducting quantum interference device magnetometer and piston–cylinder-type pressure cell under hydrostatic condition. The dT _N/dP values of (Mg_0.20Fe_0.80)O, (Mg_0.25Fe_0.75)O, and (Mg_0.30Fe_0.70)O were determined as 4.0 ± 0.3, 2.7 ± 0.3, and 4.4 ± 0.4 K/GPa, respectively, in linear approximation; however, the T _N deviated from the linearity under nonhydrostatic conditions. The compositional dependence of dT _N/dP in (Mg_1?X Fe _X )O showed a rapid decay with increasing Mg components at X ≥ 0.75 and the trend ended at X = 0.70. The estimated Néel transition pressure at room temperature by extrapolating these linearities are very similar to the rhombohedral distortion determined by previous X-ray diffraction studies for X ≥ 0.75, which suggests that the rhombohedral phase of (Mg_1?X Fe _X )O (X ≥ 0.75) at room temperature is antiferromagnetic under hydrostatic conditions.     

High-temperature compression experiments of CaSiO3 perovskite to lowermost mantle conditions and its thermal equation of state

In order to examine pressure–volume–temperature (P–V–T) relations for CaSiO₃ perovskite (Ca-perovskite), high-temperature compression experiments with in situ X-ray diffraction were performed in a laser-heated diamond anvil cell (DAC) to 127 GPa and 2,300 K. We also employed an external heating system in the DAC in order to obtain P–V data at a moderate temperature of 700 K up to 113 GPa, which is the reference temperature for constructing an equation of state. The P–V data at 700 K were fitted to the second-order Birch–Murnaghan equation of state, yielding K _700,1bar = 207 ± 4 GPa and V _700,1bar = 46.5 ± 0.1 Å³. Thermal pressure terms were evaluated in the framework of the Mie–Grüneisen–Debye model, yielding γ _700,1bar = 2.7 ± 0.3, q _700,1bar = 1.2 ± 0.8, and θ _700,1bar = 1,300 ± 500 K. A thermodynamic thermal pressure model was also employed, yielding α_700,1bar = 5.7 ± 0.5 × 10^?5/K and (?K/?T) _V  = ?0.010 ± 0.004 GPa/K. Computed densities along a lower mantle geotherm demonstrate that Ca-perovskite is denser than the surrounding lower mantle, suggesting that Ca-perovskite-rich rocks do not rise up through the lower mantle. One of such rocks might be a residue of partial melting of subducted mid-oceanic ridge basalt (MORB) at the base of the mantle. Since the partial melt is FeO-rich and therefore denser than the mantle, all the components of subducted MORB may not return to shallow levels.     

The effect of cation ordering and temperature on the high-pressure behaviour of dolomite

Synchrotron single-crystal X-ray diffraction experiments at high-pressure and high-temperature conditions were performed up to 20 GPa and 573.0(2) K on a fully ordered stoichiometric dolomite and a partially disordered stoichiometric dolomite [order parameter, s = 0.26(6)]. The ordered dolomite was found to be stable up to approximately 14 GPa at ambient temperature and up to approximately 17 GPa at T = 573.0(2) K. The P–V data from the ambient temperature experiments were analysed by a second-order Birch–Murnaghan equation-of-state giving K ₀ = 92.7(9) GPa for the ordered dolomite and K ₀ = 92.5(8) GPa for the disordered dolomite. The high-temperature data, collected for the ordered sample, were fitted by a third-order Birch–Murnaghan equation-of-state resulting in K ₀ = 95(6) GPa and K′ = 2.6(7). In order to compare the three experiments results, a third-order Birch–Murnaghan equation-of-state was also calculated for the ambient temperature experiments giving K ₀ = 93(3) GPa, K′ = 3.9(6) for the ordered dolomite and K ₀ = 92(3) GPa, K′ = 4.0(4) for the disordered dolomite. The derived axial moduli show that dolomite compresses very anisotropically, being the c-axis approximately three times more compressible than the a-axis. The axial compressibility increases as T increases, and the a-axis is the most temperature-influenced axis. On the contrary, axial compressibility is not influenced by disordering. Structural refinements at different pressures show that Ca and Mg octahedra are almost equally compressible in the ordered dolomite with K(CaO₆) = 109(4) GPa and K(MgO₆) = 103(3) GPa. On the contrary, CaO₆ compressibility is reduced and MgO₆ compressibility is increased in the disordered crystal structure where K(CaO₆) = 139(4) GPa and K(MgO₆) = 89(4) GPa. Disordering is found to increase CaO₆ and to decrease MgO₆ bond strengths, thus making stiffer the Ca octahedron and softer the Mg octahedron. Cation polyhedra are distorted in both ordered and disordered dolomites and they increase in regularity as P increases. Ordered dolomite approaches regularity at approximately 14 GPa. The increase in regularity of octahedra in the disordered dolomite is strongly affected by the very slow regularization of MgO₆ with respect to CaO₆. The phase transition to the high-pressure polymorph of dolomite (dolomite-II), which is driven by a significant increase in the regularity of both cations polyhedra and mineral crystal structure, occurs in the ordered dolomite at ambient temperature at approximately 14 GPa; whereas no clear evidences of phase transition were observed as regards the disordered crystal structure.     

New insights on pressure,temperature, and chemical stability of CsAlSi<Subscript>5</Subscript>O<Subscript>12</Subscript>, a potential host for nuclear waste

A Cs-bearing polyphase aggregate with composition (in wt%): 76(1)_CsAlSi5O12 + 7(1)_CsAlSi2O6 + 17(1)_amorphous, was obtained from a clinoptilolite-rich epiclastic rock after a beneficiation process of the starting material (aimed to increase the fraction of zeolite to 90 wt%), cation exchange and then thermal treatment. CsAlSi₅O₁₂ is an open-framework compound with CAS topology; CsAlSi₂O₆ is a pollucite-like material with ANA topology. The thermal stability of this polyphase material was investigated by in situ high-T X-ray powder diffraction, the combined P–T effects by a series of runs with a single-stage piston cylinder apparatus, and its chemical stability following the “availability test” (“AVA test”) protocol. A series of additional investigations were performed by WDS–electron microprobe analysis in order to describe the P–T-induced modification of the material texture, and to chemically characterize the starting material and the run products. The “AVA tests” of the polyphase aggregate show an extremely modest release of Cs⁺: 0.05 mg/g. In response to applied temperature and at room P, CsAlSi₅O₁₂ experiences an unquenchable and displacive Ama2-to-Amam phase transition at about 770 K, and the Amam polymorph is stable in its crystalline form up to 1600 K; a crystalline-to-amorphous phase transition occurs between 1600 and 1650 K. In response to the applied P = 0.5 GPa, the crystalline-to-amorphous transition of CsAlSi₅O₁₂ occurs between 1670 and 1770 K. This leads to a positive Clapeyron slope (i.e., dP/dT > 0) of the crystalline-to-amorphous transition. When the polyphase aggregate is subjected at P = 0.5 GPa and T > 1770 K, CsAlSi₅O₁₂ melts and only CsAlSi₂O₆ (pollucite-like; dominant) and Cs-rich glass (subordinate) are observed in the quenched sample. Based on its thermo-elastic behavior, P–T phase stability fields, and Cs⁺ retention capacity, CsAlSi₅O₁₂ is a possible candidate for use in the immobilization of radioactive isotopes of Cs, or as potential solid hosts for ¹³⁷Cs γ-radiation source in sterilization applications. More in general, even the CsAlSi₅O₁₂-rich aggregate obtained by a clinoptilolite-rich epiclastic rock appears to be suitable for this type of utilizations.     

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.     

<Emphasis Type="Italic">P</Emphasis>–<Emphasis Type="Italic">V</Emphasis>–<Emphasis Type="Italic">T</Emphasis> equation of state of CaAl<Subscript>4</Subscript>Si<Subscript>2</Subscript>O<Subscript>11</Subscript> CAS phase

The thermoelastic parameters of the CAS phase (CaAl₄Si₂O₁₁) were examined by in situ high-pressure (up to 23.7 GPa) and high-temperature (up to 2,100 K) synchrotron X-ray diffraction, using a Kawai-type multi-anvil press. P–V data at room temperature fitted to a third-order Birch–Murnaghan equation of state (BM EOS) yielded: V _0,300 = 324.2 ± 0.2 Å³ and K _0,300 = 164 ± 6 GPa for K′ _0,300 = 6.2 ± 0.8. With K′ _0,300 fixed to 4.0, we obtained: V _0,300 = 324.0 ± 0.1 Å³ and K _0,300 = 180 ± 1 GPa. Fitting our P–V–T data with a modified high-temperature BM EOS, we obtained: V _0,300 = 324.2 ± 0.1 Å³, K _0,300 = 171 ± 5 GPa, K′ _0,300 = 5.1 ± 0.6 (?K _0,T /?T) _P  = ?0.023 ± 0.006 GPa K^?1, and α_0,T  = 3.09 ± 0.25 × 10^?5 K^?1. Using the equation of state parameters of the CAS phase determined in the present study, we calculated a density profile of a hypothetical continental crust that would contain ~10 vol% of CaAl₄Si₂O₁₁. Because of the higher density compared with the coexisting minerals, the CAS phase is expected to be a plunging agent for continental crust subducted in the transition zone. On the other hand, because of the lower density compared with lower mantle minerals, the CAS phase is expected to remain buoyant in the lowermost part of the transition zone.     

Thermal equation of state of natural tourmaline at high pressure and temperature

Synchrotron-based in situ angle-dispersive X-ray diffraction experiments were conducted on a natural uvite-dominated tourmaline sample by using an external-heating diamond anvil cell at simultaneously high pressures and temperatures up to 18 GPa and 723 K, respectively. The angle-dispersive X-ray diffraction data reveal no indication of a structural phase transition over the P–T range of the current experiment in this study. The pressure–volume–temperature data were fitted by the high-temperature Birch–Murnaghan equation of state. Isothermal bulk modulus of K ₀ = 96.6 (9) GPa, pressure derivative of the bulk modulus of \(K_{0}^{\prime } = 12.5 \;(4)\), thermal expansion coefficient of α ₀ = 4.39 (27) × 10^?5 K^?1 and temperature derivative of the bulk modulus (?K/?T) _P  = ?0.009 (6) GPa K^?1 were obtained. The axial thermoelastic properties were also obtained with K _a0 = 139 (2) GPa, \(K_{a0}^{\prime }\) = 11.5 (7) and α _a0 = 1.00 (11) × 10^?5 K^?1 for the a-axis, and K _c0 = 59 (1) GPa, \(K_{c0}^{\prime }\) = 11.4 (5) and α _c0 = 2.41 (24) × 10^?5 K^?1 for the c-axis. Both of axial compression and thermal expansion exhibit large anisotropic behavior. Thermoelastic parameters of tourmaline in this study were also compared with that of the other two ring silicates of beryl and cordierite.     

Equation of state, elasticity, and shear strength of pyrite under high pressure

 Physical properties including the equation of state, elasticity, and shear strength of pyrite have been measured by a series of X-ray diffraction in diamond-anvil cells at pressures up to 50 GPa. A Birch–Murnaghan equation of state fit to the quasihydrostatic pressure–volume data obtained from laboratory X-ray source/film techniques yields a quasihydrostatic bulk modulus K _0T =133.5 (±5.2) GPa and bulk modulus first pressure derivative K ^′ _0T =5.73 (±0.58). The apparent equation of state is found to be strongly dependent on the stress conditions in the sample. The stress dependency of the high-pressure properties is examined with anisotropic elasticity theory from subsequent measurements of energy-dispersive radial diffraction experiments in the diamond-anvil cell. The calculated values of K _0T depend largely upon the angle ψ between the diffracting plane normal and the maximum stress axis. The uniaxial stress component in the sample, t=σ₃−σ₁, varies with pressure as t=−3.11+0.43P between 10 and 30 GPa. The pressure derivatives of the elastic moduli dC ₁₁/dP=5.76 (±0.15), dC ₁₂/dP=1.41 (±0.11) and dC ₄₄/dP=1.92 (±0.06) are obtained from the diffraction data assuming previously reported zero-pressure ultrasonic data (C ₁₁=382 GPa, C ₁₂=31 GPa, and C ₄₄=109 GPa). Received: 21 December 2000 / Accepted: 11 July 2001     

Phase boundary between ilmenite and perovskite structures in MnGeO3 determined by in situ X-ray diffraction measurements

In situ X-ray observations of the phase transition from ilmenite to perovskite structure in MnGeO₃ were carried out in a Kawai-type high-pressure apparatus interfaced with synchrotron radiation. The phase boundary between the ilmenite and perovskite structures in the temperature range of 700–1,400°C was determined to be P (GPa) = 16.5(±0.6) − 0.0034(±0.0006)T (°C) based on Anderson’s gold pressure scale. The Clapeyron slope, dP/dT, determined in this study is consistent with that for the transition boundary between the ilmenite and the perovskite structure in MgSiO₃.     

Compressibility of strontium orthophosphate Sr<Subscript>3</Subscript>(PO<Subscript>4</Subscript>)<Subscript>2</Subscript> at high pressure

High pressure in situ synchrotron X-ray diffraction experiment of strontium orthophosphate Sr₃(PO₄)₂ has been carried out to 20.0 GPa at room temperature using multianvil apparatus. Fitting a third-order Birch–Murnaghan equation of state to the P–V data yields a volume of V ₀ = 498.0 ± 0.1 Å³, an isothermal bulk modulus of K _T  = 89.5 ± 1.7 GPa, and first pressure derivative of K _T ′ = 6.57 ± 0.34. If K _T ′ is fixed at 4, K _T is obtained as 104.4 ± 1.2 GPa. Analysis of axial compressible modulus shows that the a-axis (K _a  = 79.6 ± 3.2 GPa) is more compressible than the c-axis (K _c  = 116.4 ± 4.3 GPa). Based on the high pressure Raman spectroscopic results, the mode Grüneisen parameters are determined and the average mode Grüneisen parameter of PO₄ vibrations of Sr₃(PO₄)₂ is calculated to be 0.30(2).     

Stability and equation of state of post-aragonite BaCO3

At ambient conditions, witherite is the stable form of BaCO₃ and has the aragonite structure with space group Pmcn. Above ~10 GPa, BaCO₃ adopts a post-aragonite structure with space group Pmmn. High-pressure and high-temperature synchrotron X-ray diffraction experiments were used to study the stability and equation of state of post-aragonite BaCO₃, which remained stable to the highest experimental P–T conditions of 150 GPa and 2,000 K. We obtained a bulk modulus K ₀ = 88(2) GPa with $K'$  = 4.8(3) and V ₀ = 128.1(5) ų using a third-order Birch-Murnaghan fit to the 300 K experimental data. We also carried out density functional theory (DFT) calculations of enthalpy (H) of two structures of BaCO₃ relative to the enthalpy of the post-aragonite phase. In agreement with previous studies and the current experiments, the calculations show aragonite to post-aragonite phase transitions at ~8 GPa. We also tested a potential high-pressure post–post-aragonite structure (space group C222 ₁ ) featuring four-fold coordination of oxygen around carbon. In agreement with previous DFT studies, ΔH between the C222 ₁ structure and post-aragonite (Pmmn) decreases with pressure, but the Pmmn structure remains energetically favorable to pressures greater than 200 GPa. We conclude that post–post-aragonite phase transformations of carbonates do not follow systematic trends observed for post-aragonite transitions governed solely by the ionic radii of their metal cations.     

Thermal equation of state of synthetic orthoferrosilite at lunar pressures and temperatures

Iron-rich orthopyroxene plays an important role in models of the thermal and magmatic evolution of the Moon, but its density at high pressure and high temperature is not well-constrained. We present in situ measurements of the unit-cell volume of a synthetic polycrystalline end-member orthoferrosilite (FeSiO₃, fs) at simultaneous high pressures (3.4–4.8 GPa) and high temperatures (1,148–1,448 K), to improve constraints on the density of orthopyroxene in the lunar interior. Unit-cell volumes were determined through in situ energy-dispersive synchrotron X-ray diffraction in a multi-anvil press, using MgO as a pressure marker. Our volume data were fitted to a high-temperature Birch–Murnaghan equation of state (EoS). Experimental data are reproduced accurately, with a  $\varDelta P$ Δ P  standard deviation of 0.20 GPa. The resulting thermoelastic parameters of fs are: V ₀ = 875.8 ± 1.4 Å³, K ₀ = 74.4 ± 5.3 GPa, and $\frac{{\text d}K}{{\text d}T} = -0.032 \pm 0.005\,\hbox{GPa K}^{-1}$ d K d T = - 0.032 ± 0.005 GPa K - 1 , assuming ${K}^{\prime}_{0} = 10 $ K 0 ′ = 10 . We also determined the thermal equation of state of a natural Fe-rich orthopyroxene from Hidra (Norway) to assess the effect of magnesium on the EoS of iron-rich orthopyroxene. Comparison between our two data sets and literature studies shows good agreement for room-temperature, room-pressure unit-cell volumes. Preliminary thermodynamic analyses of orthoferrosilite, FeSiO₃, and orthopyroxene solid solutions, (Mg_1?x Fe _x ) SiO₃, using vibrational models show that our volume measurements in pressure–temperature space are consistent with previous heat capacity and one-bar volume–temperature measurements. The isothermal bulk modulus at ambient conditions derived from our measurements is smaller than values presented in the literature. This new simultaneous high-pressure, high-temperature data are specifically useful for calculations of the orthopyroxene density in the Moon.     

Structural change in lead fluorapatite at high pressure

The structure of lead fluorapatite [PbFAP; Pb₁₀(PO₄)₆F₂], crystallized from the melt in a platinum capsule at 1,000°C and 1 atm, has been investigated by single-crystal X-ray diffraction. Crystal data are a = 9.7638 (6), c = 7.2866 (4) Å, space group P6₃/m, R = 0.043, R _w = 0.034. We have also studied the compressional behaviour of the c-axis channel of PbFAP up to 9 GPa at 25°C, using a diamond-anvil cell, synchrotron X-radiation, and Rietveld powder structure refinement. Pressure–volume data for the channel polyhedron of PbFAP fitted to the third-order Birch–Murnaghan equation resulted in K _T  = 33.2 ± 1.2 GPa when K _T ′ is fixed at 4. The c-axis channel of PbFAP is about twice as compressible as the unit-cell volume of PbFAP and the channel of calcium apatites. This is attributed to the anomalous narrowing of the channel of PbFAP with increase in confining pressure. Flexibility of the apatite channel is a key factor in the scavenging of toxic heavy metals by calcium apatites.     

Thermoelastic properties of chromium oxide Cr<Subscript>2</Subscript>O<Subscript>3</Subscript> (eskolaite) at high pressures and temperatures

A new synchrotron X-ray diffraction study of chromium oxide Cr₂O₃ (eskolaite) with the corundum-type structure has been carried out in a Kawai-type multi-anvil apparatus to pressure of 15 GPa and temperatures of 1873 K. Fitting the Birch–Murnaghan equation of state (EoS) with the present data up to 15 GPa yielded: bulk modulus (K _0,T0), 206 ± 4 GPa; its pressure derivative K′_0,T , 4.4 ± 0.8; (?K _0,T /?T) = ?0.037 ± 0.006 GPa K^?1; a = 2.98 ± 0.14 × 10^?5 K^?1 and b = 0.47 ± 0.28 × 10^?8 K^?2, where α _0,T  = a + bT is the volumetric thermal expansion coefficient. The thermal expansion of Cr₂O₃ was additionally measured at the high-temperature powder diffraction experiment at ambient pressure and α _0,T0 was determined to be 2.95 × 10^?5 K^?1. The results indicate that coefficient of the thermal expansion calculated from the EoS appeared to be high-precision because it is consistent with the data obtained at 1 atm. However, our results contradict α ₀ value suggested by Rigby et al. (Brit Ceram Trans J 45:137–148, 1946) widely used in many physical and geological databases. Fitting the Mie–Grüneisen–Debye EoS with the present ambient and high-pressure data yielded the following parameters: K _0,T0 = 205 ± 3 GPa, K′_0,T  = 4.0, Grüneisen parameter (γ ₀) = 1.42 ± 0.80, q = 1.82 ± 0.56. The thermoelastic parameters indicate that Cr₂O₃ undergoes near isotropic compression at room and high temperatures up to 15 GPa. Cr₂O₃ is shown to be stable in this pressure range and adopts the corundum-type structure. Using obtained thermoelastic parameters, we calculated the reaction boundary of knorringite formation from enstatite and eskolaite. The Clapeyron slope (with \({\text{d}}P/{\text{d}}T = - 0.014\) GPa/K) was found to be consistent with experimental data.     

P–V Equations of State and the relative stabilities of serpentine varieties

Serpentines are hydrous phyllosilicates which form by hydration of Mg–Fe minerals. The reasons for the occurrence of the structural varieties lizardite and chrysotile, with respect to the variety antigorite, stable at high pressure, are not yet fully elucidated, and their relative stability fields are not quantitatively defined. In order to increase the database of thermodynamic properties of serpentines, the P–V Equations of State (EoS) of lizardite and chrysotile were determined at ambient temperature up to 10 GPa, by in situ synchrotron X-ray diffraction in a diamond-anvil cell. Neither amorphization nor hysteresis was observed during compression and decompression, and no phase transition was resolved in lizardite. In chrysotile, a reversible change in compression mechanism, possibly due to an unresolved phase transition, occurs above 5 GPa. Both varieties exhibit strong anisotropic compression, with the c axis three times more compressible than the others. Fits to ambient temperature Birch–Murnaghan EoS gave for lizardite V ₀=180.92(3) Å³, K ₀ = 71.0(19) GPa and K′ ₀=3.2(6), and for chrysotile up to 5 GPa, V ₀ = 730.57(31) Å³ and K ₀ = 62.8(24) GPa (K′ ₀ fixed to 4). Compared to the structural variety antigorite is stable at high pressure (HP) (Hilairet et al. 2006), the c axis is more compressible in these varieties, whereas the a and b axes are less compressible. These differences are attributed to the less anisotropic distribution of stiff covalent bonds in the corrugated structure of antigorite. The three varieties have almost identical bulk compressibility curves. Thus the compressibility has negligible influence on the relative stability fields of the serpentine varieties. They are dominated by first-order thermodynamic properties, which stabilizes antigorite at high temperature with respect to lizardite, and by out-of-equilibrium phenomena for metastable chrysotile (Evans 2004).     

Equation of state of MgGeO3 perovskite to 65 GPa: comparison with the post-perovskite phase

The equation of state of MgGeO₃ perovskite was determined between 25 and 66 GPa using synchrotron X-ray diffraction with the laser-heated diamond anvil cell. The data were fit to a third-order Birch–Murnaghan equation of state and yielded a zero-pressure volume (V ₀) of 182.2 ± 0.3 Å³ and bulk modulus (K ₀) of 229 ± 3 GPa, with the pressure derivative (K′₀ = (?K ₀/?P) _T ) fixed at 3.7. Differential stresses were evaluated using lattice strain theory and found to be typically less than about 1.5 GPa. Theoretical calculations were also carried out using density functional theory from 0 to 205 GPa. The equation of state parameters from theory (V ₀ = 180.2 Å³, K ₀ = 221.3 GPa, and K′₀ = 3.90) are in agreement with experiment, although theoretically calculated volumes are systematically lower than experiment. The properties of the perovskite phase were compared to MgGeO₃ post-perovskite phase near the observed phase transition pressure (～65 GPa). Across the transition, the density increased by 2.0(0.7)%. This is in excellent agreement with the theoretically determined density change of 1.9%; however both values are larger than those for the (Mg,Fe)SiO₃ phase transition. The bulk sound velocity change across the transition is small and is likely to be negative [?0.5(1.6)% from experiment and ?1.2% from theory]. These results are similar to previous findings for the (Mg,Fe)SiO₃ system. A linearized Birch–Murnaghan equation of state fit to each axis yielded zero-pressure compressibilities of 0.0022, 0.0009, and 0.0016 GPa^?1 for the a, b, and c axis, respectively. Magnesium germanate appears to be a good analog system for studying the properties of the perovskite and post-perovskite phases in silicates.