<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.     

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-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 Na_1.13Mg_1.51Al_4.47Si_1.62O₁₂ 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) Å, c=2.7695(5) Å, V ₀=182.77(6) Å³ (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 K ₀=176(2) GPa, its pressure derivative K ₀ ^′ =4.9(3), temperature derivative (?K _T /?T) _P =?0.030(3) GPa K^?1 and thermal expansivity α(T)=3.36(6)×10^?5+7.2(1.9)×10^?9 T, while those values of K ₀=181.7(4) GPa, (?K _T /?T) _P =?0.020(2) GPa K^?1 and α(T)=3.28(7)×10^?5+3.0(9)×10^?9 T were obtained when K ₀ ^′ 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.     

Compressibility of Ca3Al2Si3O12 perovskite up to 55 GPa

Compressibility of perovskite-structured Ca₃Al₂Si₃O₁₂ grossular (GrPv) was investigated at high pressure and high temperature by means of angle-dispersive powder X-ray diffraction using a laser-heated diamond anvil cell. We observed the Pbnm orthorhombic distortion for the pure phase above 50 GPa, whereas below this pressure, Al-bearing CaSiO₃ perovskite coexists with an excess of corundum. GrPv has a bulk modulus (K ₀ = 229 ± 5 GPa; \(K_{0}^{{\prime }}\) fixed to 4) almost similar to that reported for pure CaSiO₃ perovskite. Its unit-cell volume extrapolated to ambient conditions (V ₀ = 187.1 ± 0.4 Å³) is found to be ~2.5 % larger than for the Al-free phase. We observe an increasing unit-cell anisotropy with increasing pressure, which could have implications for the shear properties of Ca-bearing perovskite in cold slabs subducted into the Earth’s mantle.     

The compressibility of Fe- and Al-bearing phase D to 30 GPa

High-pressure in situ X-ray diffraction experiment of Fe- and Al-bearing phase D (Mg_0.89Fe_0.14Al_0.25Si_1.56H_2.93O₆) has been carried out to 30.5 GPa at room temperature using multianvil apparatus. Fitting a third-order Birch–Murnaghan equation of state to the P–V data yields values of V ₀ = 86.10 ± 0.05 ų; K ₀ = 136.5 ± 3.3 GPa and K′ = 6.32 ± 0.30. If K′ is fixed at 4.0 K ₀ = 157.0 ± 0.7 GPa, which is 6% smaller than Fe–Al free phase D reported previously. Analysis of axial compressibilities reveals that the c-axis is almost twice as compressible (K _c  = 93.6 ± 1.1 GPa) as the a-axis (K _a  = 173.8 ± 2.2 GPa). Above 25 GPa the c/a ratio becomes pressure independent. No compressibility anomalies related to the structural transitions of H-atoms were observed in the pressure range to 30 GPa. The density reduction of hydrated subducting slab would be significant if the modal amount of phase D exceeds 10%.     

Elastic behavior and pressure-induced structure evolution of topaz up to 45 GPa

The behavior of a natural topaz, Al_2.00Si_1.05O_4.00(OH_0.26F_1.75), has been investigated by means of in situ single-crystal synchrotron X-ray diffraction up to 45 GPa. No phase transition or change in the compressional regime has been observed within the pressure-range investigated. The compressional behavior was described with a third-order Birch–Murnaghan equation of state (III-BM-EoS). The III-BM-EoS parameters, simultaneously refined using the data weighted by the uncertainties in P and V, are as follows: K _V = 158(4) GPa and K _V ′ = 3.3(3). The confidence ellipse at 68.3 % (Δχ² = 2.30, 1σ) was calculated starting from the variance–covariance matrix of K _V and K′ obtained from the III-BM-EoS least-square procedure. The ellipse is elongated with a negative slope, indicating a negative correlation of the parameters K _V and K _V ′, with K _V = 158 ± 6 GPa and K _V ′ = 3.3 ± 4. A linearized III-BM-EoS was used to obtain the axial-EoS parameters (at room-P), yielding: K(a) = 146(5) GPa [β _a = 1/(3K(a)) = 0.00228(6) GPa^?1] and K′(a) = 4.6(3) for the a-axis; K(b) = 220(4) GPa [β _b = 0.00152(4) GPa^?1] and K′(b) = 2.6(3) for the b-axis; K(c) = 132(4) GPa [β _c = 0.00252(7) GPa^?1] and K′(c) = 3.3(3) for the c-axis. The elastic anisotropy of topaz at room-P can be expressed as: K(a):K(b):K(c) = 1.10:1.67:1.00 (β _a:β _b:β _c = 1.50:1.00:1.66). A series of structure refinements have been performed based on the intensity data collected at high pressure, showing that the P-induced structure evolution at the atomic scale is mainly represented by polyhedral compression along with inter-polyhedral tilting. A comparative analysis of the elastic behavior and P/T-stability of topaz polymorphs and “phase egg” (i.e., AlSiO₃OH) is carried out.     

Equation of state of hexagonal aluminous phase in basaltic composition to 63 GPa at 300 K

A laser-heated diamond-anvil cell that is capable of operating up to a pressure of 63 GPa, with X-ray diffraction facilities using a synchrotron radiation source at the SPring-8, has been developed to observe the compressibility of a hexagonal aluminous phase, [K_0.15Na_1.66Ca_0.11Mg_1.29Fe²⁺ _0.86Al_3.13Ti_0.09Si_1.98] _Σ9.27O₁₂. The hexagonal aluminous phase is a potassium host mineral from the subducted oceanic crust in the Earth's lower mantle. A sample was heated using a YAG laser at each pressure increment to relax the deviatoric stress in the sample. X-ray diffraction measurements were carried out at 300 K using an angle-dispersive technique. Pressure was measured using an internal platinum pressure calibrant. The observed unit-cell volumes were used to obtain a third-order Birch–Murnaghan equation of state: unit-cell volume V _o=185.94(±16) ų, density ρ _o=4.145 g/cm³, and bulk modulus K _o=198(±3) GPa when the first pressure is derivative of the bulk modulus K ^′ _o is fixed to 4. The density of hexagonal aluminous phase is lower than that of coexisting Mg-perovskite in the subducted oceanic crust.     

Thermal equation of state of CaIrO<Subscript>3</Subscript> 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 \( K_{T0} \) at ambient pressure and temperature is 168.3 ± 7.1 GPa with a pressure derivative \( K_{T0}^{\prime } \) = 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-Grüneisen-Debye formalism. The refined thermoelastic parameters for CaIrO₃ ppv are: temperature derivative of bulk modulus \( (\partial K_{T} /\partial T)_{P} \) = ?0.038 ± 0.011 GPa K^?1, \( \alpha K_{T} \) = 0.0039 ± 0.0001 GPa K^?1, \( \left( {\partial K_{T} /\partial T} \right)_{V} \) = ?0.012 ± 0.002 GPa K^?1, and \( \left( {\partial^{2} P/\partial T^{2} } \right)_{V} \) = 1.9 ± 0.3 × 10^?6 GPa² K^?2. Using the Mie-Grüneisen-Debye formalism, we obtain Grüneisen parameter \( \gamma_{0} \) = 0.92 ± 0.01 and its volume dependence q = 3.4 ± 0.6. The systematic variation of bulk moduli for several oxide post-perovskites can be described approximately by the relationship K _T0  = 5406.0/V(molar) + 5.9 GPa.     

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.     

P–V–T equation of state of Mn3Al2Si3O12 spessartine garnet

The thermoelastic parameters of synthetic Mn₃Al₂Si₃O₁₂ spessartine garnet were examined in situ at high pressure up to 13 GPa and high temperature up to 1,100 K, by synchrotron radiation energy dispersive X-ray diffraction within a DIA-type multi-anvil press apparatus. The analysis of room temperature data yielded K ₀ = 172 ± 4 GPa and K ₀ ^′  = 5.0 ± 0.9 when V _0,300 is fixed to 1,564.96 Å³. Fitting of P–V–T data by means of the high-temperature third-order Birch–Murnaghan EoS gives the thermoelastic parameters: K ₀ = 171 ± 4 GPa, K ₀ ^′  = 5.3 ± 0.8, (?K _0,T /?T) _P  = ?0.049 ± 0.007 GPa K^?1, a ₀ = 1.59 ± 0.33 × 10^?5 K^?1 and b ₀ = 2.91 ± 0.69 × 10^?8 K^?2 (e.g., α _0,300 = 2.46 ± 0.54 × 10^?5 K^?1). Comparison with thermoelastic properties of other garnet end-members indicated that the compression mechanism of spessartine might be the same as almandine and pyrope but differs from that of grossular. On the other hand, at high temperature, spessartine softens substantially faster than pyrope and grossular. Such softening, which is also reported for almandine, emphasize the importance of the cation in the dodecahedral site on the thermoelastic properties of aluminosilicate garnet.     

Density variations of Cr-rich garnets in the upper mantle inferred from the elasticity of uvarovite garnet

The thermoelastic parameters of Ca₃Cr₂Si₃O₁₂ uvarovite garnet were examined in situ at high pressure up to 13 GPa and high temperature up to 1100 K by synchrotron radiation energy-dispersive X-ray diffraction within a 6-6-type multi-anvil press apparatus. A least-square fitting of room T data to a third-order Birch–Murnaghan (BM3) EoS yielded K₀ = 164.2 ± 0.7 GPa, V₀ = 1735.9 ± 0.3 ų (K’₀ fixed to 4.0). P–V–T data were fitted simultaneously by a modified HT-BM3 EoS, which gave the isothermal bulk modulus K₀ = 163.6 ± 2.6 GPa, K’₀ = 4.1 ± 0.5, its temperature derivative (?K_0,T/?T)_P = –0.014 ± 0.002 GPa K^?1, and the thermal expansion coefficients a₀ = 2.32 ± 0.13 ×10^?5 K^?1 and b₀ = 2.13 ± 2.18 ×10^?9 K^?2 (K’₀ fixed to 4.0). Our results showed that the Cr³⁺ enrichment in natural systems likely increases the density of ugrandite garnets, resulting in a substantial increase of mantle garnet densities in regions where Cr-rich spinel releases chromium through a metasomatic reaction.     

CO<Subscript>2</Subscript> content of andesitic melts at graphite-saturated upper mantle conditions with implications for redox state of oceanic basalt source regions and remobilization of reduced carbon from subducted eclogite

We have performed experiments to determine the effects of pressure, temperature and oxygen fugacity on the CO₂ contents in nominally anhydrous andesitic melts at graphite saturation. The andesite composition was specifically chosen to match a low-degree partial melt composition that is generated from MORB-like eclogite in the convective, oceanic upper mantle. Experiments were performed at 1–3 GPa, 1375–1550?°C, and fO₂ of FMQ ?3.2 to FMQ ?2.3 and the resulting experimental glasses were analyzed for CO₂ and H₂O contents using FTIR and SIMS. Experimental results were used to develop a thermodynamic model to predict CO₂ content of nominally anhydrous andesitic melts at graphite saturation. Fitting of experimental data returned thermodynamic parameters for dissolution of CO₂ as molecular CO₂: ln(K ⁰) = ?21.79?±?0.04, ΔV ⁰?=?32.91?±?0.65 cm³mol^?1, ΔH ⁰?=?107?±?21 kJ mol^?1, and dissolution of CO₂ as CO₃ ^2?: ln(K ⁰ ) = ?21.38?±?0.08, ΔV ⁰?=?30.66?±?1.33 cm³ mol^?1, ΔH ⁰?=?42?±?37 kJ mol^?1, where K ⁰ is the equilibrium constant at some reference pressure and temperature, ΔV ⁰ is the volume change of reaction, and ΔH ⁰ is the enthalpy change of reaction. The thermodynamic model was used along with trace element partition coefficients to calculate the CO₂ contents and CO₂/Nb ratios resulting from the mixing of a depleted MORB and the partial melt of a graphite-saturated eclogite. Comparison with natural MORB and OIB data suggests that the CO₂ contents and CO₂/Nb ratios of CO₂-enriched oceanic basalts cannot be produced by mixing with partial melts of graphite-saturated eclogite. Instead, they must be produced by melting of a source containing carbonate. This result places a lower bound on the oxygen fugacity for the source region of these CO₂-enriched basalts, and suggests that fO₂ measurements made on cratonic xenoliths may not be applicable to the convecting upper mantle. CO₂-depleted basalts, on the other hand, are consistent with mixing between depleted MORB and partial melts of a graphite-saturated eclogite. Furthermore, calculations suggest that eclogite can remain saturated in graphite in the convecting upper mantle, acting as a reservoir for C.     

Stability at high-pressure,elastic behaviour and pressure-induced structural evolution of CsAlSi<Subscript>5</Subscript>O<Subscript>12</Subscript>, a potential host for nuclear waste

The elastic and structural behaviour of the synthetic zeolite CsAlSi₅O₁₂ (a = 16.753(4), b = 13.797(3) and c = 5.0235(17) Å, space group Ama2, Z = 2) were investigated up to 8.5 GPa by in situ single-crystal X-ray diffraction with a diamond anvil cell under hydrostatic conditions. No phase-transition occurs within the P-range investigated. Fitting the volume data with a third-order Birch–Murnaghan equation-of-state gives: V ₀ = 1,155(4) ų, K _T0 = 20(1) GPa and K′ = 6.5(7). The “axial moduli” were calculated with a third-order “linearized” BM-EoS, substituting the cube of the individual lattice parameter (a ³, b ³, c ³) for the volume. The refined axial-EoS parameters are: a ₀ = 16.701(44) Å, K _T0a = 14(2) GPa (β_a = 0.024(3) GPa^?1), K′ _a = 6.2(8) for the a-axis; b ₀ = 13.778(20) Å, K _T0b = 21(3) GPa (β_b = 0.016(2) GPa^?1), K′ _b = 10(2) for the b-axis; c ₀ = 5.018(7) Å, K _T0c = 33(3) GPa (β_c = 0.010(1) GPa^?1), K′ _c = 3.2(8) for the c-axis (K _T0a:K _T0b:K _T0c = 1:1.50:2.36). The HP-crystal structure evolution was studied on the basis of several structural refinements at different pressures: 0.0001 GPa (with crystal in DAC without any pressure medium), 1.58(3), 1.75(4), 1.94(6), 3.25(4), 4.69(5), 7.36(6), 8.45(5) and 0.0001 GPa (after decompression). The main deformation mechanisms at high-pressure are basically driven by tetrahedral tilting, the tetrahedra behaving as rigid-units. A change in the compressional mechanisms was observed at P ≤ 2 GPa. The P-induced structural rearrangement up to 8.5 GPa is completely reversible. The high thermo-elastic stability of CsAlSi₅O_12, the immobility of Cs at HT/HP-conditions, the preservation of crystallinity at least up to 8.5 GPa and 1,000°C in elastic regime and the extremely low leaching rate of Cs from CsAlSi₅O₁₂ allow to consider this open-framework silicate as functional material potentially usable for fixation and deposition of Cs radioisotopes.     

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).     

High-pressure single-crystal X-ray diffraction study of jadeite and kosmochlor

The crystal structures of natural jadeite, NaAlSi₂O₆, and synthetic kosmochlor, NaCrSi₂O₆, were studied at room temperature, under hydrostatic conditions, up to pressures of 30.4 (1) and 40.2 (1) GPa, respectively, using single-crystal synchrotron X-ray diffraction. Pressure–volume data have been fit to a third-order Birch–Murnaghan equation of state yielding V ₀ = 402.5 (4) Å³, K ₀ = 136 (3) GPa, and K ₀ ^′  = 3.3 (2) for jadeite and V ₀ = 420.0 (3) Å³, K ₀ = 123 (2) GPa and K ₀ ^′  = 3.61 (9) for kosmochlor. Both phases exhibit anisotropic compression with unit-strain axial ratios of 1.00:1.95:2.09 for jadeite at 30.4 (1) GPa and 1:00:2.15:2.43 for kosmochlor at 40.2 (1) GPa. Analysis of procrystal electron density distribution shows that the coordination of Na changes from 6 to 8 between 9.28 (Origlieri et al. in Am Mineral 88:1025–1032, 2003) and 18.5 (1) GPa in kosmochlor, which is also marked by a decrease in unit-strain anisotropy. Na in jadeite remains six-coordinated at 21.5 (1) GPa. Structure refinements indicate a change in the compression mechanism of kosmochlor at about 31 GPa in both the kinking of SiO₄ tetrahedral chains and rate of tetrahedral compression. Below 31 GPa, the O3–O3–O3 chain extension angle and Si tetrahedral volume in kosmochlor decrease linearly with pressure, whereas above 31 GPa the kinking ceases and the rate of Si tetrahedral compression increases by greater than a factor of two. No evidence of phase transitions was observed over the studied pressure ranges.     

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).     

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.     

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.     

High-pressure behavior of natural single-crystal epidote and clinozoisite up to 40 GPa

The comparative compressibility and high-pressure stability of a natural epidote (0.79 Fe-total per formula unit, Fe_tot pfu) and clinozoisite (0.40 Fe_tot pfu) were investigated by single-crystal X-ray diffraction and Raman spectroscopy. The lattice parameters of both phases exhibit continuous compression behavior up to 30 GPa without evidence of phase transformation. Pressure–volume data for both phases were fitted to a third-order Birch–Murnaghan equation of state with V ₀ = 461.1(1) ų, K ₀ = 115(2) GPa, and \(K_{0}^{'}\) = 3.7(2) for epidote and V ₀ = 457.8(1) ų, K ₀ = 142(3) GPa, and \(K_{0}^{'}\) = 5.2(4) for clinozoisite. In both epidote and clinozoisite, the b-axis is the stiffest direction, and the ratios of axial compressibility are 1.19:1.00:1.15 for epidote and 1.82:1.00:1.19 for clinozoisite. Whereas the compressibility of the a-axis is nearly the same for both phases, the b- and c-axes of the epidote are about 1.5 times more compressible than in clinozoisite, consistent with epidote having a lower bulk modulus. Raman spectra collected up to 40.4 GPa also show no indication of phase transformation and were used to obtain mode Grüneisen parameters (γ _i) for Si–O vibrations, which were found to be 0.5–0.8, typical for hydrous silicate minerals. The average pressure coefficient of Raman frequency shifts for M–O modes in epidote, 2.61(6) cm^?1/GPa, is larger than found for clinozoisite, 2.40(6) cm^?1/GPa, mainly due to the different compressibility of FeO₆ and AlO₆ octahedra in M3 sites. Epidote and clinozoisite contain about 2 wt% H₂O are thus potentially important carriers of water in subducted slabs.     

Antigorite equation of state and anomalous softening at 6 GPa: an in situ single-crystal X-ray diffraction study

The compressibility of antigorite has been determined up to 8.826(8) GPa, for the first time by single crystal X-ray diffraction in a diamond anvil cell, on a specimen from Cerro del Almirez. Fifteen pressure–volume data, up to 5.910(6) GPa, have been fit by a third-order Birch–Murnaghan equation of state, yielding V ₀ = 2,914.07(23) Å³, K _T0 = 62.9(4) GPa, with K′ = 6.1(2). The compression of antigorite is very anisotropic with axial compressibilities in the ratio 1.11:1.00:3.22 along a, b and c, respectively. The new equation of state leads to an estimation of the upper stability limit of antigorite that is intermediate with respect to existing values, and in better agreement with experiments. At pressures in excess of 6 GPa antigorite displays a significant volume softening that may be relevant for very cold subducting slabs.