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This article is based on the author’s Keynote Address at the 2019 LLC Institute sponsored by the American Bar Association’s Business Law Section. It traces and critiques the shift in the default rules in LLC law away from partnership law and toward corporate law, using the Uniform LLC Acts of 1996 and 2006 as exemplars of the national trend. It focuses on two key issues: the removal of liquidity rights, both the right to dissolve and the right to be bought out, and the removal of easy access to member remedies. It argues that, on both key issues, the default rules have moved away from enforcing the presumed intent of small groups of entrepreneurs who form businesses without the benefit of counsel. By forming LLCs, entrepreneurs across the country are now unwittingly locking themselves in to perpetual entities that offer them no liquidity and present them with costly procedural obstacles to enforcing both their rights under the operating agreement and their statutory rights.

Partial melting experiments were carried on KLB-1 peridotite, a xenolith sample from the Earth's upper mantle, at 1.5 GPa and temperatures from 1 300 to 1 600 ℃, with heating time varies from 1 to 30 min. We quantify the axial temperature gradient in the deformation-DIA apparatus (D-DIA) and constrain the time scale of partial melting by comparing experimental observations with calculated result from pMELTS program. The compositions of the liquid phase and the coexisting solid phases (clinopyroxene, orthopyroxene, and olivine) agree well with those calculated from pMELTS program, suggesting that local chemical equilibrium achieves during partial melting, although longer heating time is required to homogenize the bulk sample. The Mg# (=Mg/(Mg+Fe) mol.%) of olivines from the 1-minute heating experiment changed continuously along the axial of the graphite capsule. A thermal gradient of 50 ℃/mm was calculated by comparing the Mg# of olivine grains with the output of pMELTS program. Olivine grains at the hot end of the graphite capsule from the three experiments heated at 1 400 ℃ but with different annealing time show consistence on Mg#, indicating that partitioning of Fe2+ between the olivine grains and the silicate melt happened fast, and partial melting occurs in seconds.

We report experimental results on the bulk modulus of partially molten peridotite at mantle conditions, using a multi-anvil high pressure apparatus coupled with synchrotron X-ray radiation. A sinusoidal pressure at an amplitude of 180 MPa with period of 360 s is applied to the sample as a function of temperature. The sample volume derived from the X-ray radiograph also demonstrated sinusoidal variation at the same frequency. The derived bulk modulus from the amplitude of the stress and strain shows that the bulk modulus is drastically reduced at the onset of the melting, as predicated by dynamic melting model.

We report detailed procedures for performing compression experiments on rocks and mineral aggregates within a multi-anvil deformation apparatus (D-DIA) coupled with synchrotron X-radiation. A cube-shaped sample assembly is prepared and compressed, at room temperature, by a set of four X-ray transparent sintered diamond anvils and two tungsten carbide anvils, in the lateral and the vertical planes, respectively. All six anvils are housed within a 250-ton hydraulic press and driven inward simultaneously by two wedged guide blocks. A horizontal energy dispersive X-ray beam is projected through and diffracted by the sample assembly. The beam is commonly in the mode of either white or monochromatic X-ray. In the case of white X-ray, the diffracted X-rays are detected by a solid-state detector array that collects the resulting energy dispersive diffraction pattern. In the case of monochromatic X-ray, the diffracted pattern is recorded using a two-dimensional (2-D) detector, such as an imaging plate or a charge-coupled device (CCD) detector. The 2-D diffraction patterns are analyzed to derive lattice spacings. The elastic strains of the sample are derived from the atomic lattice spacing within grains. The stress is then calculated using the predetermined elastic modulus and the elastic strain. Furthermore, the stress distribution in two-dimensions allow for understanding how stress is distributed in different orientations. In addition, a scintillator in the X-ray path yields a visible light image of the sample environment, which allows for the precise measurement of sample length changes during the experiment, yielding a direct measurement of volume strain on the sample. This type of experiment can quantify the stress distribution within geomaterials, which can ultimately shed light on the mechanism responsible for compaction. Such knowledge has the potential to significantly improve our understanding of key processes in rock mechanics, geotechnical engineering, mineral physics, and material science applications where compactive processes are important.

Partial melting in the Earth’s mantle involves a combination of processes such as ionic diffusion and solid–liquid transition. These processes yield an array of characteristic times for the melting kinetics. Both the magnitude and time constant of melt-induced volume strain affect seismic velocity, attenuation, and buoyancy. In situ monitoring of samples during melting are enabled by multi-anvil high-pressure devices coupled with synchrotron X-ray radiation. In this study, the volume strain induced in a sample from melting is measured as a function of time using X-ray images. We find a doubling of the effective thermal expansion for only 2% melt both from our data and from thermodynamic models of peridotite. The characteristic time of melting is determined to be less than one second. These findings have a direct impact on the effect of melting on seismic velocities.

We report the microstructures of two different groups of recovered samples from natural peridotite KLB-1: one has gone through partial melting at 1.5 GPa, and the other group has gone through a solid phase transition from spinel peridotite to garnet peridotite at 5 GPa. Static melting in the KLB-1 sample is dominated by grain boundary melting for times less than 1 min. The melt evolves to the triple junctions for longer times ( t > 30 min). Analogous microstructures were also observed for the solid–solid phase transition studies in which spherical garnet grains form both in triple junctions and along olivine grain boundaries, while thin films (500 nm width) inter granular residues remain between the faceted olivine grains, which could be the relic of pyroxenes. The evolution of such morphologies has implication for the mechanical properties of the material. In addition, partial melting of KLB-1 peridotite occurs fast on a minute’s time scale. The chemistry for constructing the new phase is mostly available in adjacent grains, thus requiring little diffusion. Furthermore, grain boundary diffusion is probably much faster than bulk diffusion thereby facilitating the phase transitions. Thus the melting rate may be faster than the seismic time scale and may be a dominant factor in defining the seismic velocity and attenuation of partially molten regions.

We use the total mass, possible core radius and the observed mean moment of inertia factor of Mars to constrain mineralogical and compositional structures of Mars. We adopt a liquid Fe–S system for the Martian core and construct density models of the interior of Mars for a series of mantle compositions, core compositions and temperature profiles. The moment of inertia factor of the planet is then calculated and compared to the observation to place constraints on Mars composition. Based on the independent constraints of total mass, possible core radius of 1630–1830 km, and the mean moment of inertia factor ( 0.3645 ± 0.0005 ) of Mars, we find that Fe content in the Martian mantle is between 9.9 and 11.9 mol%, Al content in the Martian mantle smaller than 1.5 mol%, S content in the Martian core between 10.6 and 14.9 wt%. The inferred Fe content in the bulk Mars lies between 27.3 and 32.0 wt%, and the inferred Fe/Si ratio in Mars between 1.55 and 1.95, within a range too broad to make a conclusion whether Mars has the same nonvolatile bulk composition as that of CI chondrite. We also conclude that no perovskite layer exists in the bottom of the Martian mantle. Based on the inferred density models, we estimate the flattening factor and J 2 gravitational potential related to the hydrostatic figure of the rotating Mars to be ( 5.0304 ± 0.0098 ) × 10 - 3 and ( 1.8151 ± 0.0065 ) × 10 - 3 , respectively. We also discuss implications of these compositional models to the understanding of formation and evolution of the planet.

The mechanical effect of materials with a zero shear modulus aggregated with solids with non-zero shear moduli has been the primary motivation for why partially molten rocks should have lowered shear wave velocities. We propose that elastic softening associated with the process of melting must also be considered. In this view, seismic waves, propagating in regions of partial melting, perturb the thermodynamic state and drive solid to liquid and liquid to solid, thereby lowering the effective elastic moduli. We present measurements of Young’s modulus for a mantle peridotite, KLB1, at LVZ pressures and temperatures and seismic frequency that support this model. The model predicts that the softening of elastic modulus is controlled by the pressure dependence of melt fraction, ∂F/∂P, and not the percentage of melt present. In contrast to previous models, the P-wave velocity is decreased by nearly the same percentage as the S-wave velocity.

We report development of micro-focusing optics for high-energy x-rays by combining a sagittally bent Laue crystal monchromator with Kirkpatrick-Baez (K–B) X-ray focusing mirrors. The optical system is able to provide a clean, high-flux X-ray beam suitable for pair distribution function (PDF) measurements at high pressure using a diamond anvil cell (DAC). A focused beam of moderate size (10–15 μm) has been achieved at energies of 66 and 81 keV. PDF data for nanocrystalline platinum (n-Pt) were collected at 12.5 GPa with a single 5 s X-ray exposure, showing that the in-situ compression, decompression and relaxation behavior of samples in the DAC can be investigated with this technique. PDFs of n-Pt and nano Au (n-Au) under quasi-hydrostatic loading to as high as 71 GPa indicate the existence of substantial reduction of grain or domain size for Pt and Au nanoparticles at pressures below 10 GPa. The coupling of sagittally bent Laue crystals with K–B mirrors provides a useful means to focus high-energy synchrotron X-rays from a bending magnet or wiggler source.

Here, we present a new experimental protocol to investigate the relationship between texture, plastic strain, and the mechanisms of plastic deformation at high pressure and temperature. The method utilizes synchrotron X-ray radiation as the probing tool, coupled with a large-volume high pressure deformation device (D-DIA). The intensity of X-ray diffraction peaks within the spectrum of the sample is used for sampling texture development in situ. The unique feature of this study is given by the sinusoidal variation of the intensity when a sinusoidal strain is applied to the sample. For a sample of magnesium oxide at elevated pressure and temperature, we demonstrate observations that are consistent with elasto-plastic models for texture development and for diffraction-peak measurements of apparent stress. The sinusoidal strain magnitude was 3%.

In this paper, we report recent progress in high-energy X-ray focusing by using Kirkpatrick-Baez (K–B) mirrors in combination with a sagittally bent Laue monochromator. This combination of optics provides a high flux X-ray beam, which can significantly reduce the data acquisition time for high-pressure pair distribution function (HP-PDF) measurements using the diamond anvil cell (DAC). Demonstration of the HP-PDF technique for the compression/relaxation of nanocrystalline platinum at high pressures is presented.

In this paper, we report recent development of the high-pressure pair distribution function (HP-PDF) measurement technique using a focused high-energy X-ray beam coupled with a diamond anvil cell (DAC). The focusing optics consist of a sagittally bent Laue monochromator and Kirkpatrick-Baez (K–B) mirrors. This combination provides a clean high-energy X-ray beam suitable for HP-PDF research. Demonstration of the HP-PDF technique for nanocrystalline platinum under quasi-hydrostatic condition above 30 GPa is presented.

In this paper, we report some recent developments of the diffraction-based absolute X-ray energy calibration method. In this calibration method, high spatial resolution of the measured detector offset is essential. To this end, a remotely controlled long-translation motorized stage was employed instead of the less convenient gauge blocks. It is found that the precision of absolute X-ray energy calibration (ΔE/E) is readily achieved down to the level of 10−4 for high-energy monochromatic X-rays (e.g. 80 keV). Examples of applications to pair distribution function (PDF) measurements and energy monitoring for high-energy X-rays are presented.

Mechanical oscillation experiments of polycrystalline NaMgF 3 perovskite were carried out at high pressure and temperatures across the orthorhombic to cubic phase boundary. Stress and strain of the sample were measured during the oscillations using X-ray diffraction. The accompanying attenuation and softening of the Young’s modulus peak near the phase boundary. The applied uniaxial stress induces flips the sample between the twin states of the perovskite. For grains oriented parallel to the unique stress axis, the twin state oscillates between (2 0 0) and (0 2 0) orientation, while the grains oriented parallel to radial stress axis align with the (1 1 2) twin state. The induced plastic strain in the polycrystal due to the ferroelastic effect is about 25% of the spontaneous strain. This implies, for the Earth’s lower mantle, that viscous flow of 1% strain can be accommodated by ferroelastic processes.

We report the values of R = d ln( Vs )/d ln( Vp ) due to water as a function of pressure for Mg 2 SiO 4 olivine, wadsleyite, ringwoodite. The results show that ringwoodite has significantly lower R than olivine and wadsleyite; due to the reason that bulk modulus of ringwoodite is more sensitive to water than shear modulus. R of ringwoodite decreases with pressure while R of olivine and wadsleyite increases with pressure. R reported here was calculated using theoretical method derived equation of states. R due to temperature is also reported as a comparison of R due to water. The local value of R in the upper mantle and transition zone can discriminate between lateral variations of water content and temperature as the origin of lateral seismic variations.

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.

We calculated thermo-elastic properties of pyrope (Mg3Al2Si3O12) at mantle pressures and temperatures using Ab initio molecular dynamic simulation. A third-order Birch-Murnaghan equation at a reference temperature of 2 000 K fits the calculations with bulk modulus, K (0)=159.5 GPa, K (0)'=4.3, V (0)=785.89 (3), Gruneisen parameter, gamma (0)=1.15, q=0.80, Anderson Gruneisen parameter delta (T) =3.76 and thermal expansion, alpha (0)=2.93x10(-5) K-1. Referenced to room temperature, where V (0)=750.80 (3), gamma (0) and alpha (0) become 1.11 and 2.47x10(-5) K-1. The elastic properties of pyrope are found to be nearly isotropic at transition zone conditions.

The National Synchrotron Light Source at Brookhaven National Laboratory has been home to a successful high-pressure program for over 20 years. The first dedicated high-pressure diffraction endstation, X17C, was established at NSLS in 1990. A large number of new techniques have been developed at this beamline, including double-sided laser heating [1], single crystal diffraction above 60 GPa [2], X-ray diffraction measurements in a resistive heated diamond anvil cell (DAC) at 1300 K and 1 megabar [3], the first high-pressure and low-temperature experiment [4], and radial diffraction in a DAC [5].

In regions where a high pressure phase is in equilibrium with a low pressure phase, the bulk modulus defined by the P-V relationship is greatly reduced. Here we evaluate the effect of such transitions on the P wave velocity. A model, where cation diffusion is the rate limiting factor, is used to project laboratory data to the conditions of a seismic wave propagating in the two-phase region. We demonstrate that for the minimum expected effect there is a significant reduction of the seismic velocity, as large as 10% over a narrow depth range.

Even though the garnet phase is the second most abundant phase in the upper-mantle and transition-zone, no previous studies have directly measured the effect of majorite content on the strength of garnet under mantle conditions. Here we report the results of constant strain-rate and stress-relaxation experiments on garnets in the pyrope-majorite solid solution which constrain the strength of majoritic containing garnets relative to pyrope as a function of majorite content and temperature. We find that at temperatures below 650 degrees C both pure pyrope and majoritic garnets have the same strength. Conversely, above 650 degrees C we find that majoritic garnets are initially stronger than pure pyrope but weaken with increasing temperature and majorite content and with significant majorite contents are weaker than pyrope above approximately 800 degrees C. We develop a flow law for the entire pyrope majorite solid solution as a function of temperature and majorite content. (C) 2010 Elsevier B.V. All rights reserved.

Magnesium silicate perovskite, the dominant mineral in the lower mantle, is thought to transform into a post-perovskite phase in the mantle’s lowermost region. Laboratory experiments suggest substantial weakening could occur during the transformation from perovskite to post-perovskite, which could explain the anomalous physical properties of the lowermost mantle.

Seismic data recorded in the upper mantle triplication distance range between 10° and 30° are generated by wave propagation through complex upper mantle structure. They can be used to place constraints on seismic velocity structures in the upper mantle, key seismic features near the major discontinuities, and anisotropic structure varying with depth. In this paper, we review wave propagation of the upper mantle triplicated phases, how different key seismic features can be studied using upper mantle triplicated data, and the importance of those seismic features to the understanding of mantle temperature and composition. We present two examples of using array triplicated phases to constrain upper mantle velocity structures and detailed features of a certain discontinuity, with one for a shallow event and the other for deep events. For the shallow event, we present examples of how the array triplication data can be used to constrain several key properties of the upper mantle: existence of a lithospheric lid, existence of a low velocity zone beneath the lithospheric lid, and P/S velocity ratio as a function of depth. For deep events, we show examples of how array triplication data can be used to constrain the detailed structures of a certain discontinuity: velocity gradients above and below the discontinuity, velocity jumps across the discontinuity and depth extents of different velocity gradients. We discuss challenges of the upper mantle triplication study, its connection to other approaches, and its potential for further studying some other important features of the mantle: the existence of double 660-km discontinuities, existence of low-velocity channels near major discontinuities and anisotropy varying with depth.

The thermo-elastic properties of MgSiO3 akimotoite at mantle pressure and temperature conditions are reported based on ab initio molecular dynamic simulations. A third-order Birch–Murnaghan equation at a reference temperature of 2000 K is defined by K0 = 158 GPa, K ′ 0 = 3.7 , G0 = 85.7 GPa, G ′ 0 = 4.5 , V0(2000 K) = 1100.54 A3, the Grűneisen parameter is determined to be γ(V) = γ0(V/V0(2000 K))q with γ0 = 1.84 and q = 1.84, with V(2000 K) = 1048.22 A3. An implied pressure correction is −7.6 GPa in these parameters due to GGA overestimates the pressure. The thermal expansion is determined to be α / α 0 = ( V / V 0 ( 2000 K ) ) δ T in which α0 = 3.21 × 10−5 K−1 and δT = 4.6. Akimotoite may be stable above the 660 discontinuity in relatively low temperature or low aluminium environments. The high velocity and elastic anisotropy of akimotoite provide diagnostics for its presence above the 660 km discontinuity.

Most large-scale geological processes, such as mantle convection and plate tectonics, involve plastic deformation of rocks. However, quantitative experimental studies of plastic properties under deep-mantle conditions are challenging, and major progress in this area has often been associated with the development of new techniques. Until very recently, reliable studies have been conducted only at pressures less than ∼0.5 GPa (∼15 km depth in Earth). By combining novel techniques of synchrotron-based in situ stress-strain measurements with newly designed high-pressure apparatuses, a new generation of experimental studies of plastic deformation of minerals under deep-mantle conditions is emerging. These studies constrain the pressure dependence of deformation of minerals such as olivine and the slip systems in high-pressure minerals such as wadsleyite and perovskite. These results have important implications for the depth variation of mantle viscosity and the geodynamic interpretation of seismic anisotropy.

We constrain SH and P wave velocity structures in the upper mantle beneath southern Africa, using triplicated phases recorded in the epicentral distance range of 11°–28° for one shallow event. We then explore thermal and compositional models appropriate for explaining the inferred seismic structures in the region. Both SH and P wave data suggest presence of a low velocity zone with velocity reductions of at least − 5% for S waves and − 2% for P waves beneath a 150 km thick high-velocity lithospheric lid. Seismic observations also suggest that the P/S ratio is larger (1.88) in the transition zone than in the lithospheric lid (1.70). The inferred P wave velocity jump across the 660-km discontinuity is small (

Deformation experiments were carried out in a Deformation-DIA high-pressure apparatus (D-DIA) on oriented Mg2SiO4 olivine (Fo100) single crystals, at pressure (P) ranging from 2.1 to 7.5 GPa, in the temperature (T) range 1373-1677 K, and in dry conditions. These experiments were designed to investigate the effect of pressure on olivine dislocation slip-system activities, responsible for the lattice-preferred orientations observed in the upper mantle. Two compression directions were tested, promoting either [100] slip alone or [001] slip alone in (010) crystallographic plane. Constant applied stress ({sigma}) and specimen strain rates (Formula) were monitored in situ using time-resolved X-ray synchrotron diffraction and radiography, respectively. Transmission electron microscopy (TEM) investigation of the run products reveals that dislocation creep assisted by dislocation climb and cross slip was responsible for sample deformation. A slip transition with increasing pressure, from a dominant [100]-slip to a dominant [001]-slip, is documented. Extrapolation of the obtained rheological laws to upper-mantle P, T, and {sigma} conditions, suggests that [001]-slip activity becomes comparable to [100]-slip activity in the deep upper mantle, while [001] slip is mostly dominant in subduction zones. These results provide alternative explanations for the seismic anisotropy attenuation observed in the upper mantle, and for the 'puzzling' seismic-anisotropy anomaliesmore » commonly observed in subduction zones.« less

We investigate the rheological behavior of multi-phase aggregates at high pressure and high temperature. Using synchrotron X-ray radiation as the probing tool, we are able to quantify the stress state of individual phases within the aggregates. This method provides fundamental information in interpreting the behavior of two phase/multi-phase mixtures, which contribute to our understanding of the deformation process at deep earth conditions. We choose MgAl2O4 spinel and MgO periclase as our model materials. Mixtures of various volume proportions were deformed in a multi-anvil high pressure deformation apparatus at pressure of 5 GPa and elevated temperatures. Stress is determined from X-ray diffraction, providing a measure of stress in each individual phase of the mixture in situ during the deformation. Macroscopic strain is determined from X-ray imaging. We compare the steady state strength of various mixtures at 1000 °C and 800 °C and at the strain rate in the range of 1.8 to 8.8 × 10− 5 s− 1. Our data indicate that the weak phase (MgO) is responsible for most of the accumulated strains while the strong phase (spinel) is supporting most of the stress when the volume proportion is 75% spinel and 25% MgO. The intermediate compositions (40/60) are much weaker than either of the end members, while the grain sizes for the intermediate compositions (submicrons) are much smaller than the end members (5–10 μm). We conclude that a change in flow mechanism resulting from these smaller grains is responsible for the low strength of the intermediate composition mixtures. This study demonstrates an approach of using synchrotron X-rays to study the deformation behaviors of multi-phase aggregates at high pressure and high temperature.

The effects of cation disorder and pressure on the structural and elastic properties of MgSiO3 majorite (Mj100) and MgSiO3–Mg3Al2Si3O12 solid solution (Py50Mj50) are modelled using the first principle simulations. Our results are consistent with the tetragonal phase as the stable structure for both compositions up to 25 GPa. Both pressure and disorder decrease the differences between c11 and c33, and between c44 and c66, indicating that the elastic properties move closer to cubic. The calculated bulk modulus and shear modulus are comparable with the reported experimental data. The bulk modulus of Mj100 varies little while the shear modulus decreases slightly with increasing cation disorder. The elastic properties of an ordered Py50Mj50 are nearly cubic in symmetry. Mg–Si disorder has much lower energy impact on Py50Mj50 than Mj100. In the Earth's mantle, variation of the Al content in the garnet will more significantly affect the seismic velocities than will the order/disorder of Si and Mg.

Balance sheets for limited liability companies and for partnerships differ from corporate balance sheets in one important respect. Accounting for these alternative forms traditionally includes a separate equity account, or “capital account,” for each owner. Indeed, the statutory default rule of partnership law in most states requires that individual capital accounts be maintained and given economic significance on liquidation or buyout. LLC law does not. However, the federal income tax rules that apply both to partnerships and to most multi-member LLCs closely examine the maintenance and significance of capital accounts to determine the validity of special allocations of tax benefits. A fundamental understanding of capital accounts analysis is therefore important to understand accounting practice, potential state default rules and federal income tax compliance. Perhaps more importantly, capital accounts analysis is a powerful analytic tool to sharpen the understanding of the economic arrangement of the owners, particularly with respect to how and to what extent they have agreed to share different items of loss.

The themoelastic properties of Mg2SiO4 ringwoodite at mantle pressure and temperature conditions are reported based on ab initio molecular dynamic simulations. A third-order Birch-Murnaghan equation at a reference temperature of 2000 K is defined by K-0 = 138 GPa, K-0' = 5.2, and V-0(2000 K) = 560 angstrom(3). The Gruneisen parameter is determined to be gamma(V) = gamma(0)(V/V-0(298 K))(q) with gamma(0) = 1.22 and q = 1.44(5), with V-0(298 K) = 524.56 angstrom(3). The thermal expansion is determined to be (alpha/alpha(0)) = (V/V-0(298 K))(delta T) in which alpha(0) = 2.74 x 10(-5) K-1 and delta(T) = 5.2(1). The bulk modulus is temperature independent at constant volume, while the shear moduli vary with temperature at constant volume. Elastic anisotropy decreases with both pressure and temperature becoming isotropic by the bottom of the upper mantle. (c) 2006 Elsevier B.V. All rights reserved.

Stress analysis in polycrystalline materials reveals that stress can vary considerably among different subpopulations of grains. Samples of MgO and mixtures of MgO and spinel have been studied. After the onset of plastic flow, stronger grains or orientations will support more stress than the weaker grains. A grain to grain fabric develops that enables this stress partitioning. The stress partitioning and the resulting fabric can invalidate static measurements of elastic moduli. However, high temperature flow mechanisms reveal a more isotropic strength behaviour resulting in a more uniform variation of stress with orientation.

Despite the abundance of garnet in deforming regions of the Earth, such as subduction zones, its rheological properties are not well defined by laboratory measurements. Here we report measurements of steady-state plastic properties of pyrope in its stability field (temperature up to 1573 K, pressure up to 6.8 GPa, strain rate {approx}10-5 s-1) using a Deformation-DIA apparatus (D-DIA) coupled with synchrotron radiation. Synthetic pyrope (Py100) and natural pyrope (Py70Alm16Gr14) are both studied in a dry environment. Transmission electron microscopy (TEM) investigation of the run products indicates that dislocation glide, assisted by climb within grains and dynamic recrystallization for grain-boundary strain accommodation, is the dominant deformation process in pyrope. Both synthetic-and natural-pyropes' stress and strain-rate data, as measured in situ by X-ray diffraction and imaging, are best fitted with the single flow law

Knowledge of the rheological properties of mantle materials is critical in modeling the dynamics of the Earth. The high-temperature flow law of olivine defined at mantle conditions is especially important since the pressure dependence of rheology may affect our estimation of the strength of olivine in the Earth's interior. In this study, steady-state high-temperature (up to 1473 K) deformation experiments of polycrystalline olivine (average grain size ? 10 ?m) at pressure up to 9.6 GPa, were conducted using a Deformation-DIA (D-DIA) high-pressure apparatus and synchrotron X-ray radiation. The oxygen fugacity (fo2) during the runs was in-between the iron-wustite and the Ni/NiO buffers' fo2. The water content of the polycrystalline samples was generally about 150 to 200 wt. ppm but was as low as 35 wt ppm. Typically, 30 % strain was generated during the uniaxial compression. Sample lengths during the deformation process as well as the differential stresses were monitored in situ by X-ray radiography and diffraction, respectively. The strain rate was derived with an accuracy of 10?6 s?1. Differential stress was measured at constant strain rate (?10?5 s?1) using a multi-element solid-state detector combined with a conical slit. Recovered specimens were investigated by optical and transmission electron microscopy (TEM).more » TEM shows that dislocation glide was the dominant deformation mechanism throughout the experiment. Evidence of dislocation climb and cross-slip as active mechanisms are also reported. Deformation data show little or no dependence of the dislocation creep flow with pressure, yielding to an activation volume V* of 0 {+-} 5 cm3/mol. These new data are consistent with the high-temperature rheological laws at lower pressures, as reported previously.« less

The most abundant mineral on Earth has a perovskite crystal structure and a chemistry that is dominated by MgSiO3 with the next most abundant cations probably being aluminum and ferric iron. The dearth of experimental elasticity data for this chemically complex mineral limits our ability to calculate model seismic velocities for the lower mantle. We have calculated the single crystal elastic moduli (c(ij)) for (Mg, Fe3+)(Si, Al)O-3 perovskite using density functional theory in order to investigate the effect of chemical variations and spin state transitions of the Fe3+ ions. Considering the favored coupled substitution of Mg2+-Si4+ by Fe3+-Al3+, we find that the effect of ferric iron on seismic properties is comparable with the same amount of ferrous iron. Ferric iron lowers the elastic moduli relative to the Al charge-coupled substitution. Substitution of Fe3+ for Al3+, giving rise to an Fe/Mg ratio of 6%, causes 1.8% lower longitudinal velocity and 2.5% lower shear velocity at ambient pressure and 1.1% lower longitudinal velocity and 1.8% lower shear velocity at 142 GPa. The spin state of the iron for this composition has a relatively small effect (

The crystal structure of NaMgF{sub 3} perovskite (neighborite) has been studied at 4 GPa and temperatures up to 1000 C using the Rietveld structure-refinement method. In situ synchrotron X-ray powder diffraction data was collected using monochromatic radiation. The orthorhombic (Pbnm) to cubic (Pm{bar 3}m) transition was observed when the temperature increased from 900 to 1000 C. Structure refinements show that the ratio of polyhedral volumes of the A and B sites (V{sub A}/V{sub B}) of the orthorhombic phase increases with temperature, approaching the ideal value (5) for the cubic structure. However, this ratio becomes smaller at 4 GPa compared to the result from previous studies at the same temperature but ambient pressure, indicating that pressure makes it more difficult to transform from the orthorhombic phase to the cubic phase in this kind of perovskite.

3^011& at different critical resolved shear stress ratios for the different slip systems. The prediction of the models is correlated with the results of x-ray diffraction measurements. Uniaxial deformation experiments on polycrystalline and single-crystal MgO samples were conducted in situ using white x-ray diffraction with a multielement detector and multianvil high-pressure apparatus at a pressure up to 6 GPa and a temperature of 500 °C. A deformation DIA was used to generate pressure and control at a constant deformation rate. Elastic strains and plastic strains were monitored using x-ray diffraction spectra and x-ray imaging techniques, respectively. The correlation of the data and models suggests that the plastic models need to be used to describe the stress‐strain observations with the presence of plasticity, while the Reuss and Voigt models are appropriate for the elastic region of deformation, before the onset of plastic deformation. The similarity of elastic strains among different lattice planes suggests that the $111% slip system is the most significant slip system in MgO at high pressure and high temperature. © 2004 American Institute of Physics. @DOI: 10.1063/1.1738532#

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.

A new large-volume, high-pressure facility is being utilized and developed as part of GeoSoilEnviroCARS at a third-generation synchrotron, the Advanced Photon Source. This user facility consists of two large-volume presses (LVP), a 2.5 MN (250 ton) LVP installed at the bending magnet beamline, and a 10 MN (1000 ton) LVP at the insertion device beamline. Here we report some techniques currently being developed with the 10 MN LVP and the latest scientific results obtained using the 2.5 MN LVP.

The transfer function of a piezoelectric transducer, buffer rod and sample assembly is used to measure the sound velocity of solid materials. From the recorded transfer function, pulse echo patterns at frequencies of the passband of the input signal are reproduced after convoluting with monochromatic RF input signals. The time delay is obtained by performing pulse echo overlap and phase comparison measurements on reproduced signals. Results for a single crystal of MgO along the [100] direction from this study are in good agreement with previous measurements but have the advantage of offline data analysis and fast data acquisition.

Although the importance of rheological properties in controlling the dynamics and evolution of the whole mantle of Earth is well-recognized, experimental studies of rheological properties and deformation-induced microstructures have mostly been limited to low-pressure conditions. This is mainly a result of technical limitations in conducting quantitative rheological experiments under high-pressure conditions. A combination of factors is changing this situation. Increased resolution of composition and configuration of Earth’s interior has created a greater demand for well-resolved laboratory measurement of the effects of pressure on the behavior of materials. Higher-strength materials have become readily available for containing high-pressure research devices, and new analytical capabilities—in particular very bright synchrotron X-ray sources—are now readily available to high-pressure researchers. One of the biggest issues in global geodynamics is the style of mantle convection and the nature of chemical differentiation associated with convectional mass transport. Although evidence for deep mantle circulation has recently been found through seismic tomography (e.g., van der Hilst et al. (1997)), complications in convection style have also been noted. They include (1) significant modifications of flow geometry across the mantle transition zone as seen from high resolution tomographic studies (Fukao et al. 1992; Masters et al. 2000; van der Hilst et al. 1991) and (2) complicated patterns of flow in the deep lower mantle (~1500–2500 km), perhaps caused by chemical heterogeneity (Kellogg et al. 1999; van der Hilst and Karason 1999). These studies indicate that while large-scale circulation involving the whole mantle no doubt occurs, significant deviations from simple flow geometry are also present. Two mineral properties have strong influence on convection: (1) density and (2) viscosity (rheology) contrasts. In the past, the effects of density contrast have been emphasized (Honda et al. 1993; Kellogg et al. 1999; Tackley et al. 1993), and the influence of …

A new multi-anvil deformation apparatus, based on the widely used 6-8 split-cylinder, geometry, has been developed which is capable of deformation experiments at pressures in excess of 18 GPa at room temperature. In 6-8 (Kawai-type) devices eight cubic anvils are used to compress the sample assembly. In our new apparatus two of the eight cubes which sit along the split-cylinder axis have been replaced by hexagonal cross section anvils. Combining these anvils hexagonal-anvils with secondary differential actuators incorporated into the load frame, for the first time, enables the 6-8 multi-anvil apparatus to be used for controlled strain-rate deformation experiments to high strains. Testing of the design, both with and without synchrotron-X-rays, has demonstrated the Deformation T-Cup (DT-Cup) is capable of deforming 1-2 mm long samples to over 55% strain at high temperatures and pressures. To date the apparatus has been calibrated to, and deformed at, 18.8 GPa and deformation experiments performed in conjunction with synchrotron X-rays at confining pressures up to 10 GPa at 800 °C .

The compressional (P) and shear wave (S) velocities for Mg2SiO4 wadsleyite have been measured to 7 GPa and 873 K using simultaneous ultrasonic interferometry and in situ X-ray diffraction techniques. From the velocity measurements we obtained the pressure and temperature derivatives for the elastic shear (G) and adiabatic bulk (KS) moduli, (∂G/∂P)T=1.5(1), (∂G/∂T)P=−0.017(1) GPa/K, KS=173(2) GPa, (∂Ks/∂P)T=4.2(1), and (∂Ks/∂T)P=−0.012(1) GPa/K; for the P and S waves, we obtained (∂Vs/∂P)T=0.021(1) (km/s)/GPa, (∂Vs/∂T)P=−0.035(2) (km/s)/K, (∂VP/∂P)T=0.065(2) (km/s)/GPa, and (∂VP/∂T)P = −0.038(2) (km/s)/K (values in parentheses are standard deviations, e.g., 1.5(1)=1.5±1). Independent equation of state analysis of P-V-T data provided an estimation of the temperature dependence for the isothermal bulk modulus of (∂KT/∂T)P=−0.022(12) GPa/K and thermal expansion (α=a+bT) coefficients of a=2×10−5 K−1 and b=2.5×10−8 K−2. Using these data along with elastic properties for other mantle phases, a velocity-depth profile for a pyrolite model to 670 km depth is constructed using a finite strain method along a 1673 K adiabat. In the transition zone the pyrolite model has a smaller gradient between 410 and 660 km than the body wave models from synthetic waveform analyses but converges with the seismic profiles at the bottom of the transition zone just above the 660-km discontinuity. The pyrolite model has velocity jumps of 6.9% and 7.9% for P and S waves, respectively, over a thickness of ∼10 km for the phase transformation from olivine to wadsleyite, which is in good agreement with short-period P wave reflection data and a recent fine structure model (C4) for both the velocity jumps and the thickness of the 410-km seismic discontinuity.

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.

High-pressure X-ray diffraction experiments on cubic ZrMo2O8 have shown that the material undergoes a first-order phase transition involving an 11% volume decrease between 0.7 and 2.0 GPa under quasi-hydrostatic conditions. The transition is reversible upon decompression, but shows considerable hysteresis. Similar behavior was observed for cubic HfMo2O8. Under nonhydrostatic conditions, the cubic materials start to amorphize above 0.3 GPa and can be converted to the monoclinic polymorphs when heated under pressure. This is the first time that monoclinic HfMo2O8 was observed.