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High-pressure single-crystal/powder synchrotron X-ray diffraction was carried out on a hydrous pure magnesium pyrope (Mg 3 Al 2 Si 3 O 12 ) containing 900 ppmw H 2 O, synthesized at 4.0 GPa and 1300 K. The pressure-volume ( P - V ) single-crystal data from room pressure to 9.81 GPa at ambient temperature were fitted by a third-order Birch-Murnaghan equation of state (BM-EoS) yielding a unit-cell volume of V 0 = 1505.14 ± 0.38 A 3 , an isothermal bulk modulus of K 0 = 160 ± 3 GPa and its pressure derivative K ′ 0 = 5.2 ± 0.4. When fixing K' 0 = 4.0, the data yielded V 0 = 1504.58 ± 0.32 A 3 and K 0 = 166 ± 2 GPa. The pressure-volume-temperature ( P - V - T ) EoS of the synthetic hydrous pyrope was also measured at temperatures up to 900 K and pressures up to 16.75 GPa, using a diamond anvil cell in conjunction with in situ synchrotron angle-dispersive powder X-ray diffraction. The P - V data at room temperature and in a pressure range of 0.0001–14.81 GPa were then analyzed by a third-order BM-EoS and yielded V 0 = 1505.35 ± 0.25 A 3 , K 0 = 161 ± 2 GPa, K ′ 0 = 5.0 ± 0.3. With K' 0 fixed to 4.0, we also obtained V 0 = 1505.04 ± 0.29 A 3 and K 0 = 167 ± 1 GPa. Consequently, we fitted the P - V - T data with the high-temperature third-order BM-EoS approach and obtained the thermoelastic parameters of V 0 = 1505.4 ± 0.3 A 3 , K 0 = 162 ± 1 GPa, K ′ 0 = 4.9 ± 0.2, the temperature derivative of the bulk modulus ( ∂K 0 / ∂T ) P = −0.018 ± 0.004 GPa K −1 , and the thermal expansion coefficient at ambient conditions α 0 = (3.2 ± 0.1) × 10 −5 K −1 . These properties were consistent with the thermal pressure EoS analysis. These new results on hydrous pyrope were also compared with previous studies of anhydrous pyrope. The main effect of hydration on pyrope is to decrease K 0 and increase K' 0 by increasing the vacancies or unoccupied volume in the structure. The entire dataset enabled us to examine the thermoelastic properties of important mantle garnets and this data has further applications for modeling the P-T conditions in the upper mantle of the Earth’s interior using deep mineral assemblages.

Density of liquid FeS was measured at 1650 K and pressures up to 5.6 GPa using the X-ray absorption radiograph system of the X17B2 beamline at the National Synchrotron Light Source at the Brookhaven National Laboratory. The experimental data were fitted to the third-order Birch–Murnaghan equation of state to calculate the isothermal bulk modulus (K0) of the liquid, yielding K0 = 11 ± 3 GPa when the pressure derivative of bulk modulus is fixed at 5. Combining this result with those from previous studies on Fe–S liquid system, we suggest an exponential relation between the liquid Fe–S alloy bulk modulus and its sulfur content.

The pressure–volume relations of three synthetic garnet samples along pyrope–almandine (Py–Alm) join were measured at ambient temperature and high pressures up to 7, 21 and 19 GPa for Py83Alm17, Py54Alm46 and Py30Alm70, respectively. The obtained P–V data were fitted to the third order Birch–Murnaghan equation of state (EOS). The ambient cell volumes V0 of the three samples were measured to be 1511(1), 1515(2), and 1526(1) A3 respectively. With fixed pressure derivative of the isothermal bulk modulus K′ at 4.3, isothermal bulk moduli K0 of the three samples were determined to be 172(4), 174(2), and 183(2) GPa respectively. These results confirm that almandine content (iron substitution) increase the bulk modulus of the garnet join following a nearly ideal mixing model. The relation between bulk modulus and almandine mole fraction (n) in this garnet join is derived to be K0 = 170 + 15 n. These data can be used to contribute to construction of compositional model of earth mantle.

To date, most of the experiments performed to quantify the hydrolytic weakening of olivine single crystals have been performed at low confining pressure (and low water fugacities). In order to determine if the degree of hydrolytic weakening changes at higher water fugacities (higher water contents), we have performed a series of high pressure ( P ) and high temperature ( T ) deformation experiments in hydrous condition on San Carlos olivine (Fo92) and forsterite (Fo100) single crystals, in a Deformation-DIA apparatus (D-DIA). Deformation was carried out in axial compression along the [1 1 0] c crystallographic reference frame direction in order to activate [1 0 0](0 1 0) dislocation slip system alone, at P ranging from 4 to 7 GPa and T = 1200 °C. Water was supplied during the experiments through dehydration of a talc sleeve (talc → enstatite + coesite + H 2 O) around the sample, while the differential stress and strain rate of the specimen were calculated from in situ X-ray diffraction and time-resolved imaging, respectively. Run products were investigated using Fourier transform infrared (FTIR) spectroscopy, and optical/electron microscopy (SEM and TEM). Structurally bound hydroxyl content (C OH ) derived from absorbance in FTIR spectra, based on the Paterson (1982) relation, were typically between 290 and 720 ppm H/Si in the run products and the majority of these hydroxyls were observed as distinct peaks in the range of wavenumber from 3620 to 3500 cm −1 . TEM reveals that the [1 0 0](0 1 0) slip system was effectively activated and responsible for crystal deformation, and that dislocation glide was significantly assisted by recovering processes such as dislocation climb and dipole annihilation. Combining the experimental data from this study and Mackwell et al. (1985) , we estimate the activation volume V ∗ [110]c for San Carlos olivine in order to produce a reasonable water-fugacity exponent r in the flow law, and obtain V ∗ [110]c = 12.1 cm 3 /mol for r = 0 and V ∗ [110]c = 17.3 cm 3 /mol for r = 1.2. Comparisons of the strengths of the wet single crystals to the strengths of dry single crystals calculated from the rheological laws ( Bai et al., 1991, Darot and Gueguen, 1981, Raterron et al., 2009 ) indicate that the wet single crystal cylinders were between 1.3 and 1.6 times weaker than their dry counterpart at same conditions, which is consistent with previous studies of [1 0 0](0 1 0) olivine rheology performed at low confining pressure (300 MPa).

We investigated the effect of pressure (P) on olivine [1 0 0](0 0 1) and [0 0 1](1 0 0) dislocation slip systems by carrying out deformation experiments in the Deformation-DIA apparatus (D-DIA) on single crystals of Mg2SiO4 forsterite (Fo100) and San Carlos (SC) olivine (Fo89), at P ranging from 5.7 to 9.7 GPa, temperature T = 1473 and 1673 K, differential stress σ in the range 140–1500 MPa, and in water-poor conditions. Specimens were deformed in axisymmetry compression along the so-called [1 0 1]c crystallographic direction, which promotes the dual slip of [1 0 0] dislocations in (0 0 1) plane and [0 0 1] dislocations in (1 0 0) plane. Constant σ and specimen strain rates ( e ˙ ) were monitored in situ by synchrotron X-ray diffraction and radiography, respectively. Comparison of the obtained high-P rheological data with room-P data, previously reported by Darot and Gueguen (1981) for Fo100 and Bai et al. (1991) for SC olivine, allowed quantifying the activation volume V* in classical creep power laws. We obtain V* = 9.1 ± 1.6 cm3/mol for Fo100. For SC olivine, we obtain V* = 10.7 ± 5.0 cm3/mol taking into account the oxygen-fugacity uncertainty during the high-P runs. These results, combined with previous reports, provide complete sets of parameters for quantifying the activities of olivine dislocation slip systems. Extrapolation of the rheological laws obtained for SC olivine crystals to conditions representative of natural deformations show that [1 0 0](0 1 0) slip largely dominates deformation in the shallow upper mantle. At depths greater than ∼65 km along a 20-Ma oceanic geotherm or ∼155 km along a continental geotherm, the dual activity of [1 0 0](0 0 1) and [0 0 1](1 0 0) slips becomes comparable to that of [1 0 0](0 1 0) slip. At depths greater than ∼240 km, [0 0 1](0 1 0) slip becomes dominant over all other investigated slip systems. Such changes in olivine dislocation-slips relative activity provide a straightforward explanation for the seismic anisotropy contrast and attenuation with depth observed in the Earth’s upper mantle.

We report measurements of the deformation stress for San Carlos olivine at pressures of 3–5 GPa, temperatures of 25–1150 °C, and strain rates of 10 −7 –10 −5 s −1 . We determine a deformation stress of approximately 2.5 GPa that is relatively temperature and strain rate independent in the temperature range of 400–900 °C. The deformation experiments have been carried out on a deformation DIA (D-DIA) apparatus, Sam85, at X17B2, NSLS. Powder samples are used in these experiments. Enstatite (MgSiO 3 ) (3–5% total quality of sample) is used as the buffer to control the activity of silica. Ni foil is used in some experiments to buffer the oxygen fugacity. Water content is confirmed by IR spectra of the recovered samples. Samples are compressed at room temperature and are then annealed at 1200 °C for at least 2 h before deformation. The total (plastic and elastic) strains (macroscopic) are derived from the direct measurements of the images taken by X-ray radiograph technique. The differential stresses are derived from the diffraction determined elastic strains. In the regime of 25–400 °C, there is a small decrease of stress at steady state as temperature increases; in the regime of 400 °C to the ‘transition temperature’, the differential stress at steady state (∼2.5 GPa) is relatively insensitive to the changes of temperature and strain rate; however, it drastically decreases to about 1 GPa and becomes temperature-dependent above the transition temperature and thereafter. The transition temperature is near 900 °C. Above the transition temperature, the flow agrees with power law creep measurements of previous investigations. The anisotropy of differential stress in individual planes indicates that the deformation of olivine at low temperature is dominated by [0 0 1](1 0 0). Accounting to a slower strain rate in the natural system, the transition temperature for the olivine in the slab is most likely in the range of 570–660 °C.

Steady-state deformation experiments were carried out in a deformation-DIA (D-DIA) high-pressure apparatus on oriented diopside single crystals, at pressure (P) ranging from 3.8 to 8.8 GPa, temperature (T) from 1100 to 1400 C, and differential stress ({sigma}) between 0.2 and 1.7 GPa. Three compression directions were chosen in order to test the activity of diopside dislocation slip systems, i.e., 1/2 {l_brace}1 {bar 1} 0{r_brace} systems activated together, both [1 0 0](0 1 0) and [0 1 0](1 0 0) systems together, or [0 0 1] dislocation slip activated in (1 0 0), (0 1 0) and {l_brace}1 1 0{r_brace} planes. Constant applied stress and specimen strain rates ({var_epsilon}) were monitored in situ using time-resolved synchrotron X-ray diffraction and radiography, respectively. Transmission electron microscopy (TEM) investigation of the run products revealed that dislocation creep was responsible for sample deformation. Comparison of the present high-P data with those obtained at room-P by Raterron and Jaoul (1991) - on similar crystals deformed at comparable T-{sigma} conditions - allows quantifying the effect of P on 1/2 {l_brace} 1 {bar 1} 0{r_brace} activity. This translates into the activation volume V* = 17 {+-} 6 cm{sup 3}/mol in the corresponding creep power law. Ourmore » data also show that both 1/2 dislocation slips and [0 0 1] have comparable slip activities at mantle P and T, while [1 0 0](0 1 0) and [0 1 0](1 0 0) slip systems remain marginal. These results show that P has a significant effect on high-T dislocation creep in diopside, the higher the pressure the harder the crystal, and that this effect is stronger on 1/2 slip than on [0 0 1] slip.« less

Deformation experiments were carried out in a deformation-DIA high-pressure apparatus (D-DIA) on oriented San Carlos olivine single crystals, at pressure (P) ranging from 3.5 to 8.5 GPa, temperature (T) from 1373 to 1673 K, and in poor water condition. Oxygen fugacity (fO2) was maintained within the olivine stability field and contact with enstatite powder ensured an orthopyroxene activity aopx = 1. Two compression directions were tested, promoting either [1 0 0] slip alone or [0 0 1] slip alone in (0 1 0) crystallographic plane, here called, respectively, a-slip and c-slip. Constant applied stress (σ) and specimen strain rates ( e ˙ ) were monitored in situ using time-resolved X-ray synchrotron diffraction and radiography, respectively. Transmission electron microscopy (TEM) investigation of run products revealed that dislocation creep was responsible for sample deformation. Comparison of the obtained high-P deformation data with the data obtained at room-P by Bai et al. [Bai, Q., Mackwell, S.L., Kohlstedt D.L., 1991, High-temperature creep of olivine single crystals. 1. Mechanical results for buffered samples, Journal of Geophysical Research, 96, 2441–2463] – on identical materials deformed at comparable T–σ–fO2–aopx conditions – allowed quantifying the P effect on a-slip and c-slip rheological laws. A slip transition with increasing pressure, from dominant a-slip to dominant c-slip, is documented. a-slip appears sensitive to pressure, which translates into the high activation volume V a * = 12 ± 4 c m 3 /mol in the corresponding rheological law, while pressure has little effect on c-slip with V c * = 3 ± 4 c m 3 /mol . These results may explain the discrepancy between olivine low-P and high-P deformation data which has been debated in the literature for more than a decade.

An experimental technique for in situ stress and strain measurements at high pressure and temperature using synchrotron X-rays has been developed at the X17B beamline of the National Synchrotron Light Source. The strain is measured by correlating sample-length marks in recorded X-ray radiographs. The stress is measured by simultaneously collecting energy-dispersive X-ray diffraction patterns of the sample in two perpendicular diffraction planes. Differential stress in the sample is derived from the different lattice strains along the different orientations relative to principal stress direction. Example measurements are conducted to study rheological properties of fayalite. Accuracy of the measurement is about 10–100 MPa for stress and about 10 −4 for strain.

The mechanisms responsible for high-temperature olivine deformation are investigated at a pressure of 8 GPa and temperatures up to 1780 K. San Carlos olivine specimens of different average grain sizes (0.5 and 5 μm) were deformed simultaneously between hard-alumina pistons during relaxation experiments. These experiments are carried out in a multi-anvil high-pressure apparatus coupled with synchrotron X-ray radiation. The different grain-size specimens experienced identical P – T –stress condition at any given time. A new method for measuring strains and strain rates (≥10 −6 s −1 ) of specimens at high pressure is documented. This method uses time-resolved in situ X-ray imaging and an image-analysis computation. The microstructures of run products, recovered after being quenched at different temperatures were characterized by transmission electron microscopy (TEM). We find that high-temperature olivine flow is grain-size insensitive at 8 GPa, which suggests that dislocation creep dominates olivine deformation at high pressure. This result is confirmed by the TEM investigation of our deformed specimens in which we find evidences of the activation of olivine dislocation slip systems. Specimen microstructures are consistent with dynamic recrystallization as an assisting process in olivine deformation during the high-pressure experiments. Extrapolation of our results to the low stress level and large grain size expected in the mantle suggests that dislocation creep assisted by dynamic recrystallization may also dominate natural olivine deformation in the upper mantle.

The plastic properties of ringwoodite, a high-pressure modification of olivine, are experimentally determined at the pressure of 20 GPa and temperatures up to 1350 ◦ C. Stress relaxation experiments have been carried out on fine-grained samples using a two-stage T-cup multiple anvil high-pressure apparatus with synchrotron-generated X-rays. We observe the presence of a significant weakening of the shear strength with a decrease from 2.5 to 0.2 GPa between 600 and 1000 ◦ C. In this region, the activation energy, U, is about 275 kJ/mol and it decreases with increasing stress, reaching a value of about 200 kJ/mol when the shear stress attains 2.5 GPa. We propose that the plasticity is associated with vigorous dislocation glide controlled by short-range lattice resistance forces. At lower temperatures, the shear strength is mildly dependent on temperature reaching 3 GPa at room temperature, while above 1000 ◦ C, the flow may be governed by a power-law relation with n about 3.5. © 2003 Elsevier Science B.V. All rights reserved.

Rheological flow laws can be obtained from studies using multi-anvil high-pressure systems with synchrotron-based piezometers and strain metrics. The high flux X-ray source provides minute-scale time resolution with accurate measurement of diffraction patterns and direct sample images. Measurements of length changes with an accuracy of one part in 10 4 are being developed and will provide a new generation of rheological tools. Flow laws derived from peak broadening agree well with literature data for corundum, spinel, and olivine. Properties of several mantle phases are compared for the temperature and pressure regime appropriate to a subducting slab. Temperature dependence of these properties exhibits a strong, temperature insensitive low temperature region, a thermally softened region and a weak high temperature region. The middle of these could be related to the seismogenic zone of a subduction zone. The progression of the temperature for softening with mineral phase suggests that earthquakes deeper than 400 km correspond to higher temperatures than for olivine in the upper 400 km. Plastic instabilities are suggested by these data as the origin of deep earthquakes. © 2001 Elsevier Science B.V. All rights reserved.