Pressure and temperature dependence of the elastic properties of synthetic MnO

The adiabatic elastic stiffness constants of synthetic single-crystal MnO were measured in this study using pulse superposition interferometry. Data were obtained up to 1.0 GPa in pressure and over the temperature range 273 to 473 K. As a result, we were able to determine the complete set of second-order stiffness moduli (C _ij ^s ) and their pressure and temperature derivatives, as well as higher-order properties for selected modes. Relevant results for the adiabatic bulk modulus are: K ^s=155.1±0.8 GPa; (K^s/P)_T=4.70±0.13; and, (K ^s/T)_P= -0.0203±0.0009 GPa/K. Our results for the second-order moduli are generally consistent with the data from previous studies. However, relative to the estimated uncertainties, small and systematic discrepancies appear to characterize the data set. The available evidence indicates that the differences result from microstructural variations (in particular, microcracks and Mn₃O₄ inclusions) between the synthetic MnO specimens used in different investigations. The pure shear mode C ₄₄ exhibits anomalous soft-mode behavior with both temperature (the ambient derivative is positive) and pressure (the ambient derivative is negative). In both cases the C ₄₄ data trends appear to primarily reflect the influence of Mn-Mn magnetoelastic interactions associated with the onset of a paramagnetic-antiferromagnetic (PM AFM) phase transition.     

Elastic constants of chrome-diopside: application of resonant ultrasound spectroscopy to monoclinic single-crystals

The right-rectangular parallelepiped resonance (RPR) form of resonant ultrasound spectroscopy (RUS) is applied to monoclinic crystal symmetry to determine the 13 adiabatic elastic constants, C_ij, of single-crystal chrome-diopside Di_0.93Hd_0.03Ur_0.02X_0.02 (Di, diopside; Hd, hedenbergite; Ur, ureyite; X, other or unknown). These data represent the first published values of the elastic tensor for a monoclinic single-crystal determined by the RPR method, thus demonstrating the feasibility of this method for studying elasticity of low-symmetry crystals. The lowest 62 modal frequencies of a gem-quality specimen were measured and identified at ambient temperature and pressure. Inverting the modal frequencies results in, respectively C₁₁, C₂₂, C₃₃, C₄₄, C₅₅, C₆₆, C₁₂, C₁₃, C₂₃, C₁₅, C₂₅, C₃₅, C₄₆ values (GPa) of 228.1(1.0), 181.1(0.6), 245.4(1.3), 78.9(0.3), 68.2(0.2), 78.1(0.2), 78.8(0.5), 70.2(0.7), 61.1(0.7), 7.9(0.5), 5.9(0.5), 39.7(0.4), and 6.4(0.2), where numbers in parentheses indicate experimental uncertainty. The corresponding isotropic bulk, K_S, and shear, G, moduli are 116.5 (0.9) and 72.8(0.4) GPa, respectively. When comparing these results with other pyroxene data, we find systematic correlations between M2 site composition and C_ij values for most, but not all, moduli. Unusual compositional dependence near end-member diopside is seen for a few moduli, and is propagated to the K_S and G moduli, which should prompt a reexamination of some C_ij values of end-member diopside.     

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     

Interatomic potentials for CaCO3 polymorphs (calcite and aragonite), fitted to elastic and vibrational data

Calcite and aragonite have been modeled using rigid-ion, two-body Born-type potentials, supplemented by O-C-O angular terms inside the CO₃ groups. A shell model has also been developed for calcite. Atomic charges, repulsive parameters and force constants have been optimized to reproduce the equilibrium crystal structures, the elastic constants and the Raman and infrared vibrational frequencies. The rigid-ion potential RIM (atomic charges:z _O= -0.995e,z _C = 0.985e,z _Ca = 2.0e) fitted to calcite properties is able to account for those of aragonite as well. Experimental unit-cell edges, elastic constants, internal and lattice frequencies are reproduced with average relative errors of 2.1, 5.5, 2.4, 15.1% for calcite and of 0.2, 19.4, 2.5, 11.8% for aragonite, respectively. The RIM potential is suitable for thermodynamic and phase diagram simulations in the CaCO₃ system, and is discussed and compared to other potentials.     

Elasticity of an upper mantle clinopyroxene

The ambient pressure elastic properties of a natural clinopyroxene (C2/c symmetry) from Kilbourne Hole, NM have been determined. In terms of end-members, diopside (CaMgSi₂O₆), hedenbergite (CaFeSi₂O₆), jadeite (NaAlSi₂O₆), cosmochlor (NaCrSi₂O₆), and Mg-Tschermak (MgAl(AlSi)O₆), its composition is Di₇₂He₉Jd₃Cr₃Ts₁₂. The analytic density, based on chemistry and cell parameters is 3.327 (0.003) g/cm³. The elastic constants [c₁₁, c₁₂, c₁₃, c₁₅, c₂₂, c₂₃, c₂₅, c₃₃, c₃₅, c₄₄, c₄₆, c₅₅, c₆₆] are [273.8 (0.9), 83.5 (1.3), 80.0 (1.1), 9.0 (0.6), 183.6 (0.9), 59.9 (1.6), 9.5 (1.0), 229.5 (0.9), 48.1 (0.6), 76.5 (0.9), 8.4 (0.8), 73.0 (0.4), 81.6 (1.0)] GPa where uncertainties are reported at the 95% confidence level. The aggregate (mean of Hashin-Strikman bounds) adiabatic bulk modulus is 117.2 (0.7) GPa, and the shear modulus is 72.2 (0.2) GPa. Although measured moduli are broadly consistent with trends in elasticity versus atomic volume, deviations from the systematics would produce significant (percent level) changes in calculated velocities for candidate mantle mineral assemblages. The compositional dependence of elasticity for several clinopyroxenes is explored on the basis of just the Di+He and Jd+Ts mole fractions. The bulk modulus lies within experimental uncertainties of the linear mixture of end-member properties while the shear modulus deviates by 3%. Received: 29 September 1997 / Revised, accepted: 4 March 1998     

Triclinic elastic constants for low albite

The full set of elastic constants for plagioclase end-member phase albite (NaAlSi₃O₈) is reported for the first time. Velocities of surface acoustic waves (both Rayleigh and pseudo-surface waves) were measured using impulsively stimulated light scattering on polished surfaces having six different orientations (three normal to the Cartesian axes and three lying on diagonals). Data were inverted and results tested using several non-linear optimization techniques. Compliance moduli determined under hydrostatic compression provided additional constraints and reduced covariance in the reported constants. The Cartesian coordinate system associated with the constants (using the unit cell) has the y-axis parallel to the crystal b axis, the x-axis parallel to a* (perpendicular to b and c) and the z-axis consistent with a right-handed coordinate system. The values of the moduli C₁₁, C₁₂, C₁₃, C₁₄, C₁₅, C₁₆, C₂₂, C₂₃, C₂₄, C₂₅, C₂₆, C₃₃, C₃₄, C₃₅, C₃₆, C₄₄, C₄₅, C₄₆, C₅₅, C₅₆, C₆₆ and their 2σ uncertainties (in parentheses) are, respectively, 69.1(0.6), 34.0(0.7), 30.8(0.5), 5.1(0.1), −2.4(0.1), −0.9(0.1), 183.5(2.7), 5.5(2.2), −3.9(0.5), −7.7(0.7), −5.8(0.7), 179.5(2.3), −8.7(0.4), 7.1(0.6), −9.8(0.6), 24.9(0.1), −2.4(0.1), −7.2(0.1), 26.8 (0.2), 0.5(0.1), 33.5(0.2). These constants differ significantly from the previously reported pseudo-monoclinic constants that were based on velocity measurements on polysynthetic twinned crystal aggregates. Differences are consistent with systematic errors in the earlier study associated with sparse data and the presence of cracks and other imperfections.     

The nonlinear elasticity and related properties of anhydrous and hydrous γ-Mg2SiO4: a theoretical study

The second-order elastic constants up to 30 GPa, which encompass the stability field of the spinel forms, their pressure derivatives and the third-order elastic constants of both hydrous and anhydrous -Mg₂SiO₄ have been obtained theoretically. A combination of deformation theory and finite strain elasticity theory has been employed to arrive at the expressions for second-order and third-order elastic constants from the strain energy of the lattice. The strain energy is calculated by taking into account the interactions up to second nearest neighbours in the -Mg₂SiO₄ lattice. This is then compared with the strain-dependent lattice energy from continuum model approximation to obtain the expression of elastic constants. The second-order elastic constants C_ij compare favourably with the measurements in the case of anhydrous as well as hydrous -Mg₂SiO₄ and with other calculations on the anhydrous phase. All the third-order elastic constants of both the compounds are negative. The third-order elastic constant C₁₄₄(–52.41 and –45.07 GPa for anhydrous and hydrous -Mg₂SiO₄, respectively) representing the anisotropy of shear mode has a smaller value than C₁₁₁ (–2443.94 and –2101.25 GPa for anhydrous and hydrous phases, respectively), which corresponds to the longitudinal mode. The pressure-induced variations in the longitudinal elastic constants (i.e.,dC₁₁/dp) are relatively large (4.08 and 4.09 for dry and hydrous ringwoodite, respectively) compared with those for the shear (0.22 and 0.32 for dry and hydrous ringwoodite, respectively) and off-diagonal constants (1.40 and 1.41 for dry and hydrous ringwoodite, respectively). The variation of the shear moduli C_s and anisotropy factor A with pressure have also been studied. The average value of elastic anisotropy is 0.835 in the case of anhydrous -Mg₂SiO₄ and 0.830 in the hydrous phase. The reversal of sign of the Cauchy pressure C₁₂ – C₄₄, which describes the angular character of atomic bonding in metals and other compounds, at around 21 GPa for both the compounds may be a precursor to the phase transition from ringwoodite to periclase and perovskite at an elevated temperature. The aggregate elastic properties like the adiabatic bulk modulus K (175.4 and 150.2 GPa for anhydrous and hydrous phases, respectively), and the isotropic compressional (P) and shear (S) wave velocities were calculated and the mode Grüneisen Parameters (GPs) of the acoustic waves were determined based on the quasi-harmonic approximation. The low temperature limit of both hydrous and anhydrous phases of -Mg₂SiO₄ are positive (1.69 and 1.78, respectively, for hydrous and anhydrous phases) and hence we expect the thermal expansion to be positive down to absolute zero. The Anderson–Grüneisen parameter obtained for hydrous as well as anhydrous phases of -Mg₂SiO₄ from the second-order and third-order elastic constants are 2.30 and 2.29, respectively.     

Elastic properties and stability of coexisting 3T and 2M 1 phengite polytypes

The elastic properties of coexisting natural 3T and 2M ₁ phengite samples (Cima Pal, Sesia Zone; Val Savenca; Western Alps, Italy) with similar chemical compositions have been studied by room temperature–high pressure powder diffraction, using synchrotron radiation on the ID9A beam-line at ESRF (Grenoble, France). The P–V curves have been modelled by the Birch–Murnaghan model; a third-order expansion fitted to the experimental data yields for 3T and 2M ₁ K ₀=60.4(±0.7) GPa, K′=5.79(±0.11) at V ₀=703.8851 ų, and K ₀=57.3(±1.0) GPa, K′=6.97(±0.24) at V ₀=938.8815 ų, respectively. The relative stability of 3T vs. 2M ₁ has been explored as a function of pressure and temperature in terms of configuration and deformation contributions to the Gibbs energy, using the elastic properties determined here and other thermodynamic parameters from earlier investigations. The results presented agree with the hypothesis of stability of the 3T polytype in the high pressure regime.     

Diagenetic effects on the distribution of uranium in live and Holocene corals from the Gulf of Aqaba

We investigated the effects of diagenetic alteration (dissolution, secondary aragonite precipitation and pore filling) on the distribution of U in live and Holocene coral skeletons. For this, we drilled into large Porites lutea coral-heads growing in the Nature Reserve Reef (NRR), northern Gulf of Aqaba, a site close to the Marine Biology Laboratory, Elat, Israel, and sampled the core material and porewater from the drill-hole. In addition, we sampled Holocene corals and beachrock aragonite cements from a pit opened in a reef buried under the laboratory grounds. We measured the concentration and isotopic composition of U in the coral skeletal aragonite, aragonite cements, coral porewater and open NRR and Gulf of Aqaba waters.Uranium concentration in secondary aragonite filling the skeletal pores is significantly higher than in primary biogenic aragonite (17.3 ± 0.6 compared to 11.9 ± 0.3 nmol · g⁻¹, respectively). This concentration difference reflects the closed system incorporation of uranyl tri-carbonate into biogenic aragonite with a U/Ca bulk distribution coefficient (K_D) of unity, versus the open system incorporation into secondary aragonite with K_D of 2.4. The implication of this result is that continuous precipitation of secondary aragonite over ∼1000 yr of reef submergence would reduce the coral porosity by 5% and can produce an apparent lowering of the calculated U/Ca - SST by ∼1°C and apparent age rejuvenation effect of 7%, with no measurable effect on the calculated initial U isotopic composition.All modern and some Holocene corals (with and without aragonite cement) from Elat yielded uniform δ²³⁴U = 144 ± 5, similar to the Gulf of Aqaba and modern ocean values. Elevated δ²³⁴U values of ∼180 were measured only in mid-Holocene corals (∼5000 yr) from the buried reef. The values can reflect the interaction of the coral skeleton with ²³⁴U-enriched ground-seawater that washes the adjacent granitic basement rocks.We conclude that pore filling by secondary aragonite during reef submergence can produce small but measurable effects on the U/Ca thermometry and the U-Th ages. This emphasizes the critical importance of using pristine corals where the original mineralogy and porosity are preserved in paleooceanographic tracing and dating.     

Synchrotron X-ray powder diffraction study of natural P2 /n-omphacites at high-pressure conditions

 Synchrotron X-ray powder diffraction experiments at high pressure conditions (0.0001–13 GPa) were performed at ESRF (Grenoble-F), on the beamline ID9, to investigate the bulk elastic properties of natural P2/n-omphacites, with quasi-ideal composition. The monoclinic cell parameters a, b, c and β were determined as a function of pressure, and their compressibility coefficients are 0.00277(7), 0.00313(8), 0.00292(5) and 0.00116(4) GPa⁻¹, respectively. The third-order Birch-Murnaghan equation of state was used to interpolate the experimental P−V data, obtaining K ₀=116.6(±2.5) GPa and K′₀=6.03(±0.60). K ₀ was also determined by means of the axial and angular compressibilities [122.5(±1.7) GPa], and of the finite Lagrangian strain theory [121.5(±1.0) GPa]. The discrepancies on K ₀ are discussed in the light of a comparison between techniques to determine the bulk modulus of crystalline materials from static compression diffraction data. Received: 22 February 2000 / Accepted: 10 July 2000     

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     

High pressure elasticity and phase transformation in brucite, Mg(OH)2

The first pressure derivatives of the second-order elastic constants have been calculated for brucite, Mg(OH)₂ from the second- and third-order elastic constants. The deformation theory and finite strain elasticity theory have been used to obtain the second- and third-order elastic constants of Mg(OH)₂ from the strain energy of the lattice. The strain energy ϕ is calculated by taking into account the interactions up to third nearest neighbors in the Mg(OH)₂ lattice. ϕ is then compared with the strain dependent lattice energy from continuum model approximation to obtain the expressions of elastic constants. The complete set of six second-order elastic constants C _IJ of brucite exhibits large anisotropy. Since C ₃₃ (= 21.6 GPa), which corresponds to the strength of the material along the c-axis direction, is less than the longitudinal mode C ₁₁ (= 156.7 GPa), the interlayer binding forces are weaker than the binding forces along the basal plane of Mg(OH)₂. The 14 nonvanishing components of the third-order elastic constants, C _IJK , of brucite have been obtained. All the C _IJK of brucite are negative except the values of C ₁₁₄ (= 230.36 GPa), C ₁₂₄ (= 75.45 GPa) and C ₁₃₄ (= 36.98 GPa). The absolute values of the C _IJK are, in general, one order of magnitude greater than the C _IJ ’s in the Mg(OH)₂ system as usually expected for a crystalline material. To our knowledge, no previous data are available to compare the pressure derivatives of brucite. The pressure derivatives of the two components viz., C ₁₄ and C ₃₃ become negative indicating an elastic instability in brucite while under pressure. This may be related to the phase transition of brucite largely involving rearrangements of H atoms revealed in the Raman spectroscopic, powder neutron diffraction and synchrotron X-ray diffraction studies.     

The elastic constants of monoclinic single-crystal chrome-diopside to 1,300 K

Values of the complete adiabatic elastic tensor for single-crystal chrome-diopside (a monoclinic pyroxene mineral) are presented from 298 to 1,300 K. The data were obtained using resonant ultrasound spectroscopy (RUS). They are the first published results for the temperature T dependences of the 13 individual elastic constants C _ij of any clinopyroxene mineral. Each C _ij is appropriately described by a linear function in T throughout the range of T. Values for each (∂C _ij /∂T) _P in GPa K⁻¹ are as follows: C ₁₁, −0.0291; C ₂₂, −0.0248; C ₃₃, −0.0179; C ₄₄, −0.0103; C ₅₅, −0.0077; C ₆₆, −0.0152; C ₁₂, −0.0119; C ₁₃, −0.0064; C ₂₃, 0.0000; C ₁₅, 0.0025; C ₂₅, 0.0022; C ₃₅, −0.0046; and C ₄₆, 0.0026. Values of (∂M/∂T) _P in GPa K⁻¹, where M represents an isotropic bulk property calculated from the C _ij data, are as follows: adiabatic bulk modulus K _S , −0.0123; isothermal bulk modulus K _T , −0.0178; and shear modulus G, −0.00998. Some diopside derivatives, notably (∂K _S /∂T) _P , (∂K _T /∂T) _P , and (∂V _P /∂T) _P , where V _P is the compressional wave velocity, have smaller magnitudes than all other minerals of importance in Earth’s mantle, thus, confirming predictions from systematics studies. We find several dimensionless quantities for this monoclinic mineral have normal values compared to other mantle minerals. Further, αK _T (α is the volume coefficient of thermal expansion) for diopside is approximately independent of both T and volume V at elevated temperature, so its equation of state is accurately expressed in simplified form.     

Stable carbon and oxygen isotope fractionation in bivalve (Placopecten magellanicus) larval aragonite

The relationship between stable isotope composition (δ¹³C and δ¹⁸O) in seawater and in larval shell aragonite of the sea scallop, Placopecten magellanicus, was investigated in a controlled experiment to determine whether isotopes in larval shell aragonite can be used as a reliable proxy for environmental conditions. The linear relationship between δ¹³C_DIC and δ¹³C_aragonite (r² = 0.97, p < 0.0001, RMSE = 0.18) was:

δ¹³C_DIC=1.15(±0.05)∗δ¹³C_aragonite-0.85(±0.04)     

Elasticity of TiO2 rutile to 1800 K

The ambient pressure elastic properties of single-crystal TiO₂ rutile are reported from room temperature (RT) to 1800 K, extending by more than 1200 oK the maximum temperature for which rutile elasticity data are available. The magnitudes of the temperature derivatives decrease with increasing temperature for five of the six adiabatic elastic moduli (C _ij ). At RT, we find (units, GPa): C ₁₁=268(1); C ₃₃=484(2); C ₄₄=123.8(2); C ₆₆=190.2(5); C ₂₃=147(1); and C ₁₂=175(1). The temperature derivatives (units, GPa K⁻¹) at RT are: (∂C ₁₁/∂T) _P =−0.042(5); (∂C ₃₃/∂T) _P =−0.087(6); (∂C ₄₄/∂T) _P =−0.0187(2); (∂C ₆₆/∂T) _P =−0.067(2); (∂C ₂₃/∂T) _P =−0.025; and (∂C ₁₂/∂T) _P −0.048(5). The values for K _S (adiabatic bulk modulus) and μ (isotropic shear modulus) and their temperature derivatives are K _S =212(1) GPa; μ=113(1) GPa; (∂K _S /∂T) _P =−0.040(4) GPa K⁻¹; and (∂μ/∂T) _P =−0.018(1) GPa K⁻¹. We calculate several dimensionless parameters over a large temperature range using our new data. The unusually high values for the Anderson-Gròneisen parameters at room temperature decrease with increasing temperature. At high T, however, these parameters are still well above those for most other oxides. We also find that for TiO₂, anharmonicity, as evidenced by a non-zero value of [∂ln (K _T )/∂lnV] _T , is insignificant at high T, implying that for the TiO₂ analogue of stishovite, thermal pressure is independent of volume (or pressure). Systematic relations indicate that ∂² K _S /∂T∂P is as high as 7×10⁻⁴ K⁻¹ for rutile, whereas ∂²μ/∂T∂P is an order of magnitude less. Received: 19 September 1997 / Revised, accepted: 27 February 1998     

The pressure and temperature dependence of the elastic properties of single-crystal fayalite Fe2SiO4

The nine adiabatic elastic stiffness constants of synthetic single-crystal fayalite, Fe₂SiO₄, were measured as functions of pressure (range, 0 to 1.0 GPa) and temperature (range, 0 to 40° C) using the pulse superposition ultrasonic method. Summary calculated results for a dense fayalite polycrystalline aggregate, based on the HS average of our single-crystal data, are as follows: V_p = 6.67 km/s; V_s = 3.39km/s; K= 127.9 GPa; μ = 50.3 GPa; (?K/?P)_T = 5.2; (?μ/?P)_T=1.5;(?K/?T)_P= ?0.030 GPa/K;and,(?/?T)_P =-0.013 GPa/K (the pressure and temperature data are referred to 25° C and 1 atm, respectively). Accuracy of the single-crystal results was maintained by numerous cross and redundancy checks. Compared to the single-crystal elastic properties of forsterite, Mg₂SiO₄, the fayalite stiffness constants, as well as their pressure derivatives, are lower for each of the on-diagonal (C _ij for which i=j) values, and generally higher for the off-diagonal (C _ij for which i≠j) data. As a result, the bulk moduli (K) and dK/dP for forsterite and fayalite are very similar, but the rigidity modulus (μ) and dμ/dP for polycrystalline fayalite are much lower than their forsterite counterparts. The bulk compression properties derived from this study are very consistent with the static-compression x-ray results of Yagi et al. (1975). The temperature dependence of the bulk modulus of fayalite is somewhat greater (in a negative sense) than that of forsterite. The rigidity dependencies are almost equivalent. Over the temperature range relevant to this study, the elastic property results are generally consistent with the data of Sumino (1978), which were obtained using the RPR technique. However, some of the compressional modes are clearly discrepant. The elastic constants of fayalite appear to be less consistent with a theoretical HCP model (Leibfried 1955) than forsterite, reflecting the more covalent character of the Fe-O bonding in the former.     

Paragonite stability at 700°C in the presence of H<Subscript>2</Subscript>O–NaCl fluids: constraints on H<Subscript>2</Subscript>O activity and implications for high pressure metamorphism

We carried out reversed piston-cylinder experiments on the equilibrium paragonite = jadeite + kyanite + H₂O at 700°C, 1.5–2.5 GPa, in the presence of H₂O-NaCl fluids. Synthetic paragonite and jadeite and natural kyanite were used as starting materials. The experiments were performed on four different nominal starting compositions: X(H₂O)=1.0, 0.90, 0.75 and 0.62. Reaction direction and extent were determined from the weight change in H₂O in the capsule, as well as by optical and scanning electron microscopy (SEM). At X(H₂O)=1.0, the equilibrium lies between 2.25 and 2.30 GPa, in good agreement with the 2.30–2.45 GPa reversal of Holland (Contrib Miner Petrol 68:293–301, 1979). Lowering X(H₂O) decreases the pressure of paragonite breakdown to 2.10–2.20 GPa at X(H₂O)=0.90 and 1.85–1.90 GPa at X(H₂O)=0.75. The experiments at X(H₂O) = 0.62 yielded the assemblage albite + corundum at 1.60 GPa, and jadeite + kyanite at 1.70 GPa. This constrains the position of the isothermal paragonite–jadeite–kyanite–albite–corundum–H₂O invariant point in the system Na₂O–Al₂O₃–SiO₂–H₂O to be at 1.6–1.7 GPa and X(H₂O)~0.65±0.05. The data indicate that H₂O activity, a(H₂O), is 0.75–0.86, 0.55–0.58, and <0.42 at X(H₂O)=0.90, 0.75, and 0.62, respectively. These values approach X(H₂O)², and agree well with the a(H₂O) model of Aranovich and Newton (Contrib Miner Petrol 125:200–212, 1996). Our results demonstrate that the presence or absence of paragonite can be used to place limits on a(H₂O) in high-pressure metamorphic environments. For example, nearly pure jadeite and kyanite from a metapelite from the Sesia Lanzo Zone formed during the Eo-Alpine metamorphic event at 1.7–2.0 GPa, 550–650°C. The absence of paragonite requires a fluid with low a(H₂O) of 0.3–0.6, which could be due to the presence of saline brines.     

Equation of state of iron–silicon alloys to megabar pressure

The stability and pressure–volume equation of state of iron–silicon alloys, Fe-8.7 wt% Si and Fe-17.8 wt% Si, have been investigated using diamond-anvil cell techniques up to 196 and 124 GPa, respectively. Angular–dispersive X-ray diffractions of iron–silicon alloys were measured at room temperature using monochromatic synchrotron radiation and an imaging plate (IP). A bcc–Fe-8.7 wt% Si transformed to hcp structure at around 1636 GPa. The high-pressure phase of Fe-8.7 wt% Si with hexagonal close-packed (hcp) structure was found to be stable up to 196 GPa and no phase transition of bcc–Fe-17.8 wt% Si was observed up to 124 GPa. The pressure–volume data were fitted to a third-order Birch–Murnaghan equation of state (BM EOS) with zero–pressure parameters: V₀=22.2(8) ų, K₀=198(9) GPa, and K₀=4.7(3) for hcp–Fe-8.7 wt% Si and V₀=179.41(45) ų, K₀=207(15) GPa and K₀=5.1(6) for Fe-17.8 wt% Si. The density and bulk sound velocity of hcp–Fe-8.7 wt% Si indicate that the inner core could contain 3–5 wt% Si.     

Delamination and ultra‐deep subduction of continental crust: constraints from elastic wave velocity and density measurement in ultrahigh‐pressure metamorphic rocks

Thirty‐three samples, including 22 eclogites, collected from the Dabie ultrahigh‐pressure (UHP) metamorphic belt in eastern China, have been studied for seismic properties. Compressional (V_p) and shear wave (V_s) velocities in three mutually perpendicular directions under hydrostatic pressures up to 1.0 GPa were measured for each sample. At 1.0 GPa, V_p (7.5–8.4 km s^?1), V_s (4.2–4.8 km s^?1), and densities (3.2–3.6 g cm^?3) in the UHP eclogites are higher than those of UHP orthopyroxenite (7.3–7.5 km s^?1, 4.1–4.3 km s^?1, 3.2–3.3 g cm^?3, respectively) and HP eclogites (7.1–7.9 km s^?1, 4.0–4.5 km s^?1, 3.1–3.5 g cm^?3, respectively). Kyanitites (with 99.5% kyanite) show extremely high velocities and density (9.37 km s^?1, 5.437 km s^?1, 3.581 g cm^?3, respectively). The eclogites show variation of V_p‐ and V_s‐anisotropy up to 9.70% and 9.17%, respectively. Poisson’s ratio (σ) ranges from 0.218 to 0.278 (with a mean of 0.255) for eclogites, 0.281–0.298 for granulites and 0.248 to 0.255 for amphibolites. The σ values for serpentinite (0.341) and marble (0.321) are higher than for other lithologies. The elastic moduli K, G, E of kyanitite were obtained as 163, 102 and 253 GPa, respectively. The V_p and density of representative UHP metamorphic rocks (eclogite & kyanitite) were extrapolated to mantle depth (15 GPa) following a reasonable geotherm, and compared to the one dimension mantle velocity and density model. The comparison shows that V_p and density in eclogite and kyanitite are greater than those of the ambient mantle, with differences of up to ΔV_p > 0.3 km s^?1 and Δρ > 0.3–0.4 g cm^?3, respectively. This result favours the density‐induced delamination model and also provides evidence in support of distinguishing subducted high velocity materials in the upper mantle by means of seismic tomography. Such ultra‐deep subduction and delamination processes have been recognized by seismic tomography and geochemical tracing in the postcollisional magmatism in the Dabie region.     

Single-crystal elastic properties of chondrodite: implications for water in the upper mantle

Chondrodite, a member of the humite group of minerals, forms by hydration of olivine and is stable over a range of temperatures and pressures that includes a portion of the uppermost mantle. We have measured the single crystal elastic properties of a natural chondrodite specimen at ambient conditions using Brillouin spectroscopy. The isotropic aggregate bulk (K) and shear (μ) moduli calculated from the single-crystal elastic moduli, C_ij, are: K_S=118.4(16) GPa and μ=75.6(7) GPa. A comparison of the structures and elasticity of olivine and chondrodite indicate that the replacement of O with (OH,F) in M²⁺O₆ octahedra has a small effect on the elasticity of humite-group minerals. The slightly diminished elastic moduli of humite-group minerals (as compared to olivine) are likely caused by a smaller ratio of strong structural elements (SiO₄ tetrahedra) to weaker octahedra, and perhaps a more flexible geometry of edge-sharing MO₄(O,OH,F)₂ octahedra. In contrast to the humite-olivine group minerals, the incorporation of water into garnets and spineloids leads to a more substantial decrease in the elastic properties of these minerals. This contrasting behavior is due to formation of O₄H₄ tetrahedra and vacant hydroxyl-bearing octahedra in the garnets and spineloids, respectively. Therefore, the mechanism of incorporation of H/OH into mineral phases, not only degree of hydration, should be taken into account when estimating the effect of water on the elastic properties of minerals. The bulk elastic wave velocities of chondrodite and olivine are very similar. If humite-like incorporation of OH is predominant in the upper mantle, then the reaction of OH with olivine will have a minor or possibly no detectable effect on seismic velocities. Thus, it may be difficult to distinguish chondrodite-bearing rocks from “anhydrous” mantle on the basis of seismically determined velocities for the Earth. Received: 25 February 1998 / Revised, accepted: 18 August 1998