Pressure–volume–temperature equation of state of andradite and grossular, by high-pressure and -temperature powder diffraction

 The thermoelastic parameters of natural andradite and grossular have been investigated by high-pressure and -temperature synchrotron X-ray powder diffraction, at ESRF, on the ID30 beamline. The P–V–T data have been fitted by Birch-Murnaghan-like EOSs, using both the approximated and the general form. We have obtained for andradite K ₀=158.0(±1.5) GPa, (dK/dT )₀=−0.020(3) GPa K⁻¹ and α₀=31.6(2) 10⁻⁶ K⁻¹, and for grossular K ₀=168.2(±1.7) GPa, (dK/dT)₀=−0.016(3) GPa K⁻¹ and α₀=27.8(2) 10⁻⁶ K⁻¹. Comparisons between the present issues and thermoelastic properties of garnets earlier determined are carried out. Received: 7 July 2000 / Accepted: 20 October 2000     

Pressure–volume–temperature equations of state: a comparative study based on numerical simulations

 The P–V–T equation of state (EoS) models of Birch–Murnaghan, Vinet and Poirier–Tarantola have been compared with one another and discussed in the light of their ability to reproduce thermoelastic functions and parameters by means of fitting to pressure–volume–temperature data artificially generated for spinel, corundum and forsterite. Numerical simulations relying upon semi-empirical potentials, lattice dynamics and the quasiharmonic approximation have been used to generate P–V–T data. The results obtained indicate that all the P–V–T EoSs tested predict bulk modulus at ambient conditions with errors confined, at worst, within a few percent, and reproduce correctly its dependence on temperature. The derivatives of the bulk modulus versus P and PT are less satisfactorily modelled. The bulk thermal expansion is determined by EoSs within a few percent error, but the deviations increase significantly if the approximation of linear dependence of EoS on temperature is used (linearised thermal pressure model). Received: 30 January 2001 / Accepted: 16 June 2001     

Single-crystal elastic constants of fluorite (CaF2) to 9.3 GPa

 The second-order elastic constants of CaF₂ (fluorite) have been determined by Brillouin scattering to 9.3 GPa at 300 K. Acoustic velocities have been measured in the (111) plane and inverted to simultaneously obtain the elastic constants and the orientation of the crystal. A notable feature of the present inversion is that only the density at ambient condition was used in the inversion. We obtain high-pressure densities directly from Brillouin data by conversion to isothermal conditions and iterative integration of the compression curve. The pressure derivative of the isentropic bulk modulus and of the shear modulus determined in this study are 4.78 ± 0.13 and 1.08 ± 0.07, which differ from previous low-pressure ultrasonic elasticity measurements. The pressure derivative of the isothermal bulk modulus is 4.83 ± 0.13, 8% lower than the value from static compression, and its uncertainty is lower by a factor of 3. The elastic constants of fluorite increase almost linearly with pressure over the whole investigated pressure range. However, at P ≥ 9 GPa, C ₁₁ and C ₁₂ show a subtle structure in their pressure dependence while C ₄₄ does not. The behavior of the elastic constants of fluorite in the 9–9.3 GPa pressure range is probably affected by the onset of a high-pressure structural transition to a lower symmetry phase (α-PbCl₂ type). A single-crystal Raman scattering experiment performed in parallel to the Brillouin measurements shows the appearance of new features at 8.7 GPa. The new features are continuously observed to 49.2 GPa, confirming that the orthorhombic high-pressure phase is stable along the whole investigated pressure range, in agreement with a previous X-ray diffraction study of CaF₂ to 45 GPa. The high-pressure elasticity data in combination with room-pressure values from previous studies allowed us to determine an independent room-temperature compression curve of fluorite. The new compression curve yields a maximum discrepancy of 0.05 GPa at 9.5 GPa with respect to that derived from static compression by Angel (1993). This comparison suggests that the accuracy of the fluorite pressure scale is better than 1% over the 0–9 GPa pressure range. Received: 10 July 2001 / Accepted: 7 March 2002     

Phase relations and chemistry of Ti-rich K-richterite-bearing mantle assemblages: an experimental study to 8.0 GPa in a Ti-KNCMASH system

Experiments have been conducted in a peralkaline Ti-KNCMASH system representative of MARID-type bulk compositions to delimit the stability field of K-richterite in a Ti-rich hydrous mantle assemblage, to assess the compositional variation of amphibole and coexisting phases as a function of P and T, and to characterise the composition of partial melts derived from the hydrous assemblage. K-richterite is stable in experiments from 0.5 to 8.0 GPa coexisting with phlogopite, clinopyroxene and a Ti-phase (titanite, rutile or rutile + perovskite). At 8.0 GPa, garnet appears as an additional phase. The upper T stability limit of K-richterite is 1200–1250 °C at 4.0 GPa and 1300–1400 °C at 8.0 GPa. In the presence of phlogopite, K-richterite shows a systematic increase in K with increasing P to 1.03 pfu (per formula unit) at 8.0 GPa/1100 °C. In the absence of phlogopite, K-richterite attains a maximum of 1.14 K pfu at 8.0 GPa/1200 °C. Titanium in both amphibole and mica decreases continuously towards high P with a nearly constant partitioning while Ti in clinopyroxene remains more or less constant. In all experiments below 6.0 GPa ΣSi + Al in K-richterite is less than 8.0 when normalised to 23 oxygens+stoichiometric OH. Rutiles in the Ti-KNCMASH system are characterised by minor Al and Mg contents that show a systematic variation in concentration with P(T) and the coexisting assemblage. Partial melts produced in the Ti-KNCMASH system are extremely peralkaline [(K₂O+Na₂O)/Al₂O₃ = 1.7–3.7], Si-poor (40–45 wt% SiO₂), and Ti-rich (5.6–9.2 wt% TiO₂) and are very similar to certain Ti-rich lamproite glasses. At 4.0 GPa, the solidus is thought to coincide with the K-richterite-out reaction, the first melt is saturated in a phlogopite-rutile-lherzolite assemblage. Both phlogopite and rutile disappear ca. 150 °C above the solidus. At 8.0 GPa, the solidus must be located at T≤1400 ^°C. At this temperature, a melt is in equilibrium with a garnet- rutile-lherzolite assemblage. As opposed to 4.0 GPa, phlogopite does not buffer the melt composition at 8.0 GPa. The experimental results suggest that partial melting of MARID-type assemblages at pressures ≥4.0 GPa can generate Si-poor and partly ultrapotassic melts similar in composition to that of olivine lamproites. Received: 23 December 1996 / Accepted: 20 March 1997     

Synchrotron powder diffraction study of phengite 3T from the Dora-Maira massif: P -V -T equation of state and petrological consequences

X-ray powder diffraction measurements have been carried out at ESRF (Grenoble, France) on the ID30 beamline to study the equation of state of 3T phengite (Dora-Maira massif, Italian western Alps) by a large volume cell up to P = 50 kbar and T = 1000 K. Several equations of state (EOS) models (the Vinet EOS, the Birch-Murnaghan EOS and its variants, a VT-polynomial expansion) have been used to interpolate the experimental data and discussed in the light of the results achieved. The thermoelastic properties of 3T phengite (bulk modulus, its derivatives versus pressure or temperature, bulk thermal expansion) have been obtained and an isochoric curve with slope P/T = 0.02 kbar/K has been calculated by means of the Vinet EOS. This slope value supports either the occurrence at the peak conditions (about 30 kbar and 1000 K) of an originally Mg/Si-richer and stiffer phengite or a non-isochoric P-T retrograde path. Received: 5 June 1998 / Revised, accepted: 12 December 1998     

Structure and compressibility of synthetic ZnAl2O4 (gahnite) under high-pressure conditions, from synchrotron X-ray powder diffraction

 The structural behavior of synthetic gahnite (ZnAl₂O₄) has been investigated by X-ray powder diffraction at high pressure (0–43 GPa) and room temperature, on the ID9 beamline at ESRF. The equation of state of gahnite has been derived using the models of Birch–Murnaghan, Vinet and Poirier–Tarantola, and the results have been mutually compared (the elastic bulk modulus and its derivatives versus P determined by the third-order Birch–Murnaghan equation of state are K ₀=201.7(±0.9) GPa, K ^′ ₀=7.62(±0.09) and K ^″ ₀=−0.1022 GPa⁻¹ (implied value). The compressibilities of the tetrahedral and octahedral bond lengths [0.00188(8) and 0.00142(5) GPa⁻¹ at P=0, respectively], and the␣polyhedral volume compressibilities of the four-␣and␣sixfold coordination sites [0.0057(2) and 0.0041(2) GPa⁻¹ at P=0, respectively] are discussed. Received: 15 January 2001 / Accepted: 23 April 2001     

Franciscan eclogite revisited: Reevaluation of the P–T evolution of tectonic blocks from Tiburon Peninsula, California, U.S.A.

Summary High-grade blocks in the Franciscan complex at Tiburon, California, record relatively low temperature eclogite-facies metamorphism and blueschist-facies overprinting. The eclogite-facies mineral assemblage contains prograde-zoned garnet + omphacite + epidote ± hornblende (katophoritic and barroisitic Ca–Na amphibole) ± glaucophane + phengite (∼3.5 Si p.f.u.) ± paragonite + rutile + quartz. The blueschist-facies mineral assemblage contains chlorite + titanite + glaucophane + epidote ± albite ± phengite (∼3.3 Si p.f.u.). Albite is not stable in the eclogite stage. New calculations based on garnet-omphacite-phengite thermobarometry and THERMOCALC average-P–T calculations yield peak eclogite-facies P–T conditions of P = 2.2–2.5 GPa and T = 550–620 °C; porphyroclastic omphacite with inclusions of garnet and paragonite yields an average-P–T of 1.8 ± 0.2 GPa at 490 ± 70 °C for the pre-peak stage. The inferred counterclockwise hairpin P–T trajectory suggests prograde eclogitization of a relatively “cold” subducting slab, and subsequent exhumation and blueschist-facies recrystallization by a decreasing geotherm. Although an epidote-garnet amphibolitic assemblage is ubiquitous in some blocks, P–T pseudosection analyses imply that the epidote-garnet amphibolitic assemblage is stable during prograde eclogite-facies metamorphism. Available geochronologic data combined with our new insight for the maximum pressure suggest an average exhumation rate of ∼5 km/Ma, as rapid as those of some ultrahigh pressure metamorphic terranes.     

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     

Tracing the high pressure stage in the polymetamorphic Texel Complex (Austroalpine basement unit, Eastern Alps): P–T–t–d constraints

Summary Integration of new mineral chemical, geochronological and structural data from the Texel Complex yielded information on (re)crystallization and deformation processes in metapelites, eclogites and tonalitic orthogneisses during eclogite facies metamorphism. Maximum P–T conditions reached 1.2 to 1.4 GPa and 540–620 °C in the Upper Cretaceous. In tonalitic orthogneisses and metapelites, substantial garnet growth took place prior to eclogite facies metamorphism and Sm–Nd data indicate the presence of pre-Cretaceous mineral relics. In contrast, complex garnet-growth and -resorption processes are inferred for eclogites, which produced characteristic atoll microstructures and occurred close to the pressure peak of a single, coherent high pressure event. Garnet Sm–Nd data indicate eclogite facies crystallization at 85 ± 5 Ma. While eclogites retained information on the maximum burial stage, matrix phases in metapelites and orthogneisses were intensely recrystallized during the amphibolite facies metamorphic decompression. All the meso- and macro-scale deformation structures formed during the high pressure event and subsequent exhumation. The major mylonitic foliation is represented by the high pressure phases but was refolded during amphibolite facies exhumation. A biotite-whole-rock Rb–Sr age of 70–80 Ma indicates that cooling below about 300 °C occurred in the Upper Cretaceous. Supplementary material to this paper is available in electronic form at Appendix available as electronic supplementary material     

Thermoelastic properties of the high-pressure phase of SnO2 determined by in situ X-ray observations up to 30 GPa and 1400 K

 In situ synchrotron X-ray experiments in the system SnO₂ were made at pressures of 4–29 GPa and temperatures of 300–1400 K using sintered diamond anvils in a 6–8 type high-pressure apparatus. Orthorhombic phase (α-PbO₂ structure) underwent a transition to a cubic phase (Pa3ˉ structure) at 18 GPa. This transition was observed at significantly lower pressures in DAC experiments. We obtained the isothermal bulk modulus of cubic phase K ₀= 252(28) GPa and its pressure derivative K ^′=3.5(2.2). The thermal expansion coefficient of cubic phase at 25 GPa up to 1300 K was determined from interpolation of the P-V-T data obtained, and is 1.7(±0.7) × 10⁻⁵ K⁻¹ at 25 GPa. Received: 7 December 1999 / Accepted: 27 April 2000     

Effect of pressure on the thermal expansion of MgO up to 8.2 GPa

Isobaric volume measurements for MgO were carried out at 2.6, 5.4, and 8.2 GPa in the temperature range 300–1073 K using a DIA-type, large-volume apparatus in conjunction with synchrotron X-ray powder diffraction. Linear fit of the thermal expansion data over the experimental pressure range yields the pressure derivative, (∂α/∂P) _T , of −1.04(8) × 10⁻⁶ GPa⁻¹ K⁻¹ and the mean zero-pressure thermal expansion α_{0, T}  = 4.09(6) × 10⁻⁵ K⁻¹. The α_{0, T} value is in good agreement with results of Suzuki (1975) and Utsumi et al. (1998) over the same temperature range, whereas (∂α/∂P) _T is determined for the first time on MgO by direct measurements. The cross-derivative (∂α²/∂P∂T) cannot be resolved because of large uncertainties associated with the temperature derivative of α at all pressures. The temperature derivative of the bulk modulus, (∂K _T/∂T) _P , of −0.025(3) GPa K⁻¹, obtained from the measured (∂α/∂P) _T value, is in accord with previous findings. Received: 2 April 1999 / Revised, accepted: 22 June 1999     

Constraining the prograde and retrograde P-T-t path of Eocene HP rocks by SHRIMP dating of different zircon domains: inferred rates of heating, burial, cooling and exhumation for central Rhodope, northern Greece

Ion microprobe (SHRIMP) dating was carried out on different zircon domains from metamorphic rocks of the HP-HT terrane of central Rhodope, northern Greece, to constrain the timing of prograde and retrograde stages within a single tectono-metamorphic cycle. A well determined P-T-t(relative) path for the metamorphic rocks of this terrane was used as a petrological basis for the geochronological investigations. Ion microprobe work was assisted by cathodoluminescence (CL) images of the zircon crystals. The geochronological results revealed that Hercynian continental crust was subducted during the Eocene. Several stages of the Eocene tectono-metamorphic cycle – including both the prograde and retrograde parts of the P-T path above ca 300 °C, 0.3 GPa – were dated using zircons from the following rock types: (1) A deformed quartz vein probably formed at ca 300 °C, 0.3 GPa. Zircons in this vein precipitated from a hydrothermal fluid; they yielded an age of 45.3 ± 0.9 Ma which corresponds to the time of a low-T prograde stage of metamorphism. (2) In kyanite eclogites, zircons were entirely reset during eclogite-facies metamorphism. Resetting was very probably enhanced by the presence of fluids derived by H₂O liberating reactions close to the P-peak. They yielded an age of 42.2 ± 0.9 Ma. (3) Orthogneisses surrounding the kyanite eclogites contained zircons with magmatic oscillatory zoned cores, which yielded Hercynian ages of 294 ± 8 Ma (age of granitic protolith formation), whereas CL-bright, metamorphic rims yielded, like the eclogite zircons, ages of 42.0 ± 1.1 Ma. Therefore, both the eclogites and orthogneisses are interpreted to have approached maximum depth at around 42 Ma. (4) In a leucosome of a migmatized orthogneiss, oscillatory zoned zircons yielded an age of 40.0 ± 1.0 Ma. At this time the rocks reached maximum temperatures during early decompression. (5) A late pegmatite crosscutting the schistosity of amphibolites contained oscillatory zoned zircons that yielded a crystallization age of 36.1 ± 1.2 Ma. Thus, the whole tectono-metamorphic cycle above ca 300 °C, 0.3 GPa lasted from 45.3 ± 0.9 Ma to 36.1 ± 1.2 Ma, that is 9.2 Ma with an extreme error value of 2.1 Ma. Based on combined SHRIMP and petrological data, the average rates of heating and burial during subduction (above ca 300 °C, 0.3 GPa) are >94 °C/Ma and >15 mm/a, respectively. Rates of cooling and exhumation (also above 300 °C, 0.3 GPa) are calculated to be >128° C/Ma and >7.7 mm/a. The Eocene age of metamorphism in central Rhodope implies that the terrane of, at least, central Rhodope and the Cyclades very probably was part of the same continental crust. Received: 5 October 1998 / Accepted: 18 January 1999     

The high-pressure and temperature equation of state of a majorite solid solution in the system of Mg4Si4O12-Mg3Al2Si3O12

The high-pressure and temperature equation of state of majorite solid solution, Mj_0.8Py_0.2, was determined up to 23 GPa and 773 K with energy-dispersive synchrotron X-ray diffraction at high pressure and high temperature using the single- and double-stage configurations of the multianvil apparatuses, MAX80 and 90. The X-ray diffraction data of the majorite sample were analyzed using the WPPD (whole-powder-pattern decomposition) method to obtain the lattice parameters. A least-squares fitting using the third-order Birch-Murnaghan equation of state yields the isothermal bulk modulus, K _T0  = 156 GPa, its pressure derivative, K′ = 4.4(±0.3), and temperature derivative (∂K _T /∂T) _P = −1.9(±0.3)× 10⁻² GPa/K, assuming that the thermal expansion coefficient is similar to that of pyrope-almandine solid solution. Received: 5 October 1998 / Revised, accepted: 24 June 1999     

P–V–T equation of state of Ca3Al2Si3O12 grossular garnet

The thermoelastic parameters of synthetic Ca₃Al₂Si₃O₁₂ grossular garnet were examined in situ at high-pressure and high-temperature by energy dispersive X-ray diffraction, using a Kawai-type multi-anvil press apparatus coupled with synchrotron radiation. Measurements have been conducted at pressures up to 20 GPa and temperatures up to 1,650 K: this P, T range covered the entire high-P, T stability field of grossular garnet. The analysis of room temperature data yielded V _0,300 = 1,664 ± 2 ?³ and K ₀ = 166 ± 3 GPa for K^￠₀ K^{\prime}_{0} fixed to 4.0. Fitting of our P–V–T data by means of the high-temperature third order Birch–Murnaghan or the Mie–Grüneisen–Debye thermal equations of state, gives the thermoelastic parameters: (∂K _0,T /∂T) _P  = −0.019 ± 0.001 GPa K⁻¹ and α _0,T  = 2.62 ± 0.23 × 10⁻⁵ K⁻¹, or γ ₀ = 1.21 for fixed values q ₀ = 1.0 and θ ₀ = 823 (Isaak et al. Phys Chem Min19:106–120, 1992). From the comparison of fits from two different approaches, we propose to constrain the bulk modulus of grossular garnet and its pressure derivative to K _T0 = 166 GPa and K^￠_T0 K^{\prime}_{T0}  = 4.03–4.35. Present results are compared with previously determined thermoelastic properties of grossular-rich garnets.     

High-pressure phase transition and behavior of protons in brucite Mg(OH)2: a high-pressure–temperature study using IR synchrotron radiation

 Infrared absorption spectra of brucite Mg (OH)₂ were measured under high pressure and high temperature from 0.1 MPa 25 °C to 16 GPa 360 °C using infrared synchrotron radiation at BL43IR of Spring-8 and a high-temperature diamond-anvil cell. Brucite originally has an absorption peak at 3700 cm⁻¹, which is due to the OH dipole at ambient pressure. Over 3 GPa, brucite shows a pressure-induced absorption peak at 3650 cm⁻¹. The pressure-induced peak can be assigned to a new OH dipole under pressure. The new peak indicates that brucite has a new proton site under pressure and undergoes a high-pressure phase transition. From observations of the pressure-induced peak under various P–T condition, a stable region of the high-pressure phase was determined. The original peak shifts to lower wavenumber at −0.25 cm⁻¹ GPa⁻¹, while the pressure-induced peak shifts at −5.1 cm⁻¹ GPa⁻¹. These negative dependences of original and pressure-induced peak shifts against pressure result from enhanced hydrogen bond by shortened O–H···O distance, and the two dependences must result from the differences of hydrogen bond types of the original and pressure-induced peaks, most likely from trifurcated and bent types, respectively. Under high pressure and high temperature, the pressure-induced peak disappears, but a broad absorption band between 3300 and 3500 cm⁻¹ was observed. The broad absorption band may suggest free proton, and the possibility of proton conduction in brucite under high pressure and temperature. Received: 16 July 2001 / Accepted: 25 December 2001     

An infrared and Raman spectroscopic study of gypsum at high pressures

 We present Raman and infrared spectra of gypsum to 21 GPa at 300 K. Our measurements encompass the internal modes of the (SO₄)⁻⁴ group that lie between 400 and 1150 cm⁻¹, hydroxyl-stretching vibrations between 3200 and 3600 cm⁻¹, and a libration and bending vibrations of the molecular H₂O group. All vibrations of the sulfate group have positive pressure shifts, while the hydroxyl-stretching and -bending vibrations have a mixture of positive and negative pressure shifts: the effect of pressure on the hydrogen bonding of the water molecule thus appears to be complex. Near 5 GPa, the two infrared-active bending vibrations of the water molecule coalesce, and the morphology of the hydroxyl-stretching region of the spectrum shifts dramatically. This behavior is consistent with a pressure-induced phase transition in gypsum in the vicinity of 5–6 GPa, which is observed to be reversible on decompression to zero pressure. The spectral observations are consistent with the onset of increased disorder in the position of the water molecule in gypsum: the sulfate vibrations are largely unaffected by this transition. The Raman-active symmetric stretch of the sulfate group undergoes an apparent splitting near 4 GPa, which is interpreted to be produced by Fermi resonance with an overtone of the symmetric bending vibration. The average mode Grüneisen parameter of the 20 vibrational modes we sample is less than 0.05, in contrast to the bulk thermal Grüneisen parameter of 1.20. Accordingly, the vibrations of both water and sulfate units within gypsum are highly insensitive to volumetric compaction. Therefore, in spite of the changes in the bonding of the water unit near 5 GPa, metastably compressed gypsum maintains strongly bound molecular-like units to over 20 GPa at 300 K. Received: 31 July 2000 / Accepted: 5 April 2001     

High-pressure and high-temperature in situ X-ray diffraction study of iron and corundum to 68 GPa using an internally heated diamond anvil cell

Using powder X-ray diffraction of heated solids to pressures reaching 68 GPa, the pressure-volume-temperature (PVT) data on corundum Al₂O₃ and ɛ-Fe were determined with the following results: *Corundum,*Iron, *Al₂O₃*ɛ-Fe Isothermal bulk*258 (2)*164 (3)  modulus K'_{300, 1} (GPa) Pressure derivative K_{300, 1}*4.88 (4)*5.36 (16) Temperature derivative*–0.020 (2)*–0.043 (3)  (∂K _T,1 /∂T) _P (GPa/K) Molar volume V_300,1*25.59 (2)*6.76 (2)  (cm³/mol) Isobaric thermal expansion at 1 atm (0.101 MPa) is given by (K^–1): α _T =2.6 (2) 10^–5+1.81 (9) 10^–9 T–0.67 (6)/T ² for corundum, and α _T =5.7 (4) 10^–5+4.2 (4) 10^–9 T–0.17 (7)/T ² for iron ɛ-Fe. Received: 1 March 1997 / Revised, accepted: 21 August 1997     

Thermodynamic data of the high-pressure phase Mg5Al5Si6O21(OH)7 (Mg-sursassite)

 Calorimetric and P–V–T data for the high-pressure phase Mg₅Al₅Si₆O₂₁(OH)₇ (Mg-sursassite) have been obtained. The enthalpy of drop solution of three different samples was measured by high-temperature oxide melt calorimetry in two laboratories (UC Davis, California, and Ruhr University Bochum, Germany) using lead borate (2PbO·B₂O₃) at T=700 ^∘C as solvent. The resulting values were used to calculate the enthalpy of formation from different thermodynamic datasets; they range from −221.1 to −259.4 kJ mol⁻¹ (formation from the oxides) respectively −13892.2 to −13927.9 kJ mol⁻¹ (formation from the elements). The heat capacity of Mg₅Al₅Si₆O₂₁(OH)₇ has been measured from T=50 ^∘C to T=500 ^∘C by differential scanning calorimetry in step-scanning mode. A Berman and Brown (1985)-type four-term equation represents the heat capacity over the entire temperature range to within the experimental uncertainty: C _P (Mg-sursassite) =(1571.104 −10560.89×T ^−0.5−26217890.0 ×T ⁻²+1798861000.0×T ⁻³) J K⁻¹ mol⁻¹ (T in K). The P V T behaviour of Mg-sursassite has been determined under high pressures and high temperatures up to 8 GPa and 800 ^∘C using a MAX 80 cubic anvil high-pressure apparatus. The samples were mixed with Vaseline to ensure hydrostatic pressure-transmitting conditions, NaCl served as an internal standard for pressure calibration. By fitting a Birch-Murnaghan EOS to the data, the bulk modulus was determined as 116.0±1.3 GPa, (K ^′=4), V _T,0 =446.49 ³ exp[∫(0.33±0.05) × 10⁻⁴ + (0.65±0.85)×10⁻⁸ T dT], (K _T/T) _P  = −0.011± 0.004 GPa K⁻¹. The thermodynamic data obtained for Mg-sursassite are consistent with phase equilibrium data reported recently (Fockenberg 1998); the best agreement was obtained with Δ_f H ⁰ ₂₉₈ (Mg-sursassite) = −13901.33 kJ mol⁻¹, and S ⁰ ₂₉₈ (Mg-sursassite) = 614.61 J K⁻¹ mol⁻¹. Received: 21 September 2000 / Accepted: 26 February 2001     

Contrasting P-T conditions recorded in ultramafic high-pressure rocks from the Variscan Schwarzwald (F.R.G.)

 This paper presents mineralogical and textural data as well as thermobarometric calculations on ultramafic high-pressure rocks from the Variscan basement of the Schwarzwald (F.R.G.). The rocks form small isolated bodies within low-pressure / high-temperature gneisses and migmatites. The results of this study constrain contrasting P-T evolutions for four garnet-bearing ultramafic high-pressure rocks. Two magnesian garnet-spinal peridotites sampled near the southern margin of the Central Schwarzwald Gneiss Complex (CSGC) were equilibrated at 670–740^° C and 1.4–1.8 GPa. These P-T conditions are similar to those recorded by eclogites intercalated in the same basement unit. Two garnet websterites sampled from the northern part of the CSGC have comparatively low Mg/(Mg+Fe) and low Cr and Ni abundances and are interpreted as former cumulates. These rocks most probably experienced an initial high-temperature stage within the spinel peridotite stability field, followed by re-equilibration at 740–850^° C / 3.2–4.3 GPa and subsequent recrystallization at lower pressures. Further petrologic studies have to reveal whether ultramafic high-pressure rocks of the Schwarzwald can generally be assigned to these two groups which are mainly defined by contrasting peak pressures. Received: 22 August 1994 / Accepted: 19 January 1995     

The Gibbs energy formulation of the α, β, and γ forms of Mg2SiO4 using Grover, Getting and Kennedy's empirical relation between volume and bulk modulus

 The empirical linear relation between volume and logarithm of bulk modulus of a material, discovered by Grover, Getting and Kennedy is taken as the basis for our equation of state. Using the latest experimental information on the adiabatic bulk modulus, the equation of state is applied to the three polymorphs of Mg₂SiO₄ to develop a consistent dataset of their thermodynamic properties in the temperature range of 200–2273 K and a pressure range of 0.1 MPa–30 GPa. The results imply that the bulk sound velocity contrast (v ^β−v ^α)/v ^α increases with temperature along the α–β phase boundary and reaches the value 8.9% at 13.5 GPa, a pressure equivalent to 410 km depth in the Earth. The bulk sound velocity contrast (v ^γ−v ^β)/v ^β decreases with temperature along the β–γ phase boundary and becomes less than 0.7% at temperatures and pressures equivalent to those associated with the 520-km seismic discontinuity in the Earth. Received: 1 August 2000 / Accepted: 1 March 2001