Bulk modulus measurement at mHz frequencies and high-pressure using synchrotron x-ray radiation.

We report an experimental protocol for measuring the frequency dependence of the bulk modulus carried out in a synchrotron x-ray facility based multi-anvil high-pressure apparatus. An oscillating pressure perturbation characterized by x-ray diffraction produces a volume strain measured by imaging. Together, these yield the bulk modulus of the sample. Here, we report data at 3 mHz as an example of the possibility of providing these data for the frequency range of 1 mHz-100 mHz.

Full waveform analysis for high pressure ultrasonic measurement.

We report a data analysis protocol for ultrasonic velocity measurements carried out in a synchrotron x-ray facility based multi-anvil high-pressure apparatus. Synthetic ultrasonic signals for the time period between echoes from the two ends of the sample assembly are created with a few simple parameters as the echo waveform is modeled by the first echo from the anvil-assembly boundary. Each echo is modeled as a delta function with an amplitude and arrival time and convolved with this waveform. The final waveform, fit to the data, enables analysis of signals with overlapped echoes as they are common in small cell assemblies and high pressure.

Note: Elastic wave velocity measurement using ultrasonic system with two-reflectors.

We report an experiment protocol for ultrasonic velocity measurements carried out in a synchrotron-based multi-anvil high-pressure apparatus. By adding a second reflector in the cell assembly, ultrasonic signals are significantly stabilized for experiments where samples experience structural changes such as phase transition or partial melting. Features of the elastic wave can be calculated from acoustic impedance allowing us to evaluate the possible interference between the sample reflection and other internal multiple reflections. This new protocol allows various forms of samples including cold-pressed powder samples, for which grain size and porosity can be monitored and controlled in situ during the annealing process.

Observation of cation reordering during the olivine-spinel transition in fayalite by in situ synchrotron X-ray diffraction at high pressure and temperature.

The olivine-spinel phase transition in fayalite at high pressure and temperature has been studied using time-resolved x-ray diffraction. Structure refinements show a delay of cation reordering relative to anions during the phase transformation and an increase in the cell volume while the cations reorder into their sites. A significant stress drop in the sample is observed. This experiment, for the first time, quantitatively demonstrates a pseudomartensitic transformation: a diffusionless anion sublattice transition coupled with short-range diffusional cation reordering.

Strength of diamond.

The yield strength of diamond is measured under a pressure of 10 gigapascals at temperatures up to 1550 degrees C by the analysis of x-ray peak shapes on diamond diffraction lines in a powdered sample as a function of pressure and temperature. At room temperature, the diamond crystals exhibit elastic behavior with increasing pressure. Significant ductile deformation is observed only at temperatures above 1000 degrees C at this pressure. The differential yield strength of diamond decreases with temperature from 16 gigapascals at 1100 degrees C to 4 gigapascals at 1550 degrees C. Transmission electron microscopy observations on the recovered sample indicate that the dominant deformation mechanism under high pressure and temperature is crystal plasticity.

Elasticity of agr-Cristobalite: A Silicon Dioxide with a Negative Poisson's Ratio.

Laser Brillouin spectroscopy was used to determine the adiabatic single-crystal elastic stiffness coefficients of silicon dioxide (SiO(2)) in the alpha-cristobalite structure. This SiO(2) polymorph, unlike other silicas and silicates, exhibits a negative Poisson's ratio; alpha-cristobalite contracts laterally when compressed and expands laterally when stretched. Tensorial analysis of the elastic coefficients shows that Poisson's ratio reaches a maximum value of -0.5 in some directions, whereas averaged values for the single-phased aggregate yield a Poisson's ratio of -0.16.

Phase Transition and Thermal Expansion of MgSiO3 Perovskite.

Results from in situ x-ray diffraction experiments with a DIA-type cubic anvil apparatus (SAM 85) reveal that MgSiO(3) perovskite transforms from the orthorhombic Pbnm symmetry to another perovskite-type structure above 600 kelvin (K) at pressures of 7.3 gigapascals; the apparent volume increase across the transition is 0.7%. Unit-cell volume increased linearly with temperature, both below (1.44 x 10(-5) K(-1)) and above (1.55 x 10(-5) K(-1)) the transition. These results indicate that the physical properties measured on the Pbnm phase should be used with great caution because they may not be applicable to the earth's lower mantle. A density analysis based on the new data yields an iron content of 10.4 weight percent for a pyrolite composition under conditions corresponding to the lower mantle. All current equation-of-state data are compatible with constant chemical composition in the upper and lower mantle; thus, these data imply that a chemically layered mantle is unnecessary, and whole-mantle convection is possible.

Elasticity of MgSiO3 in the Perovskite Structure.

The single-crystal elastic moduli of MgSiO(3) in the perovskite structure, the high-pressure polymorph of MgSiO(3) pyroxene, have been determined. The data indicate that a mantle with either pyrolite or pyroxene stoichiometry is compatible with the seismic models appropriate to the earth's lower mantle, provided that the shear modulus of MgSiO(3) perovskite exhibits a strong negative temperature derivative. Such a temperature derivative falls outside of the range expected for a well-behaved refractory ceramic and could result if the pressure-temperature regime of the earth's lower mantle is near that required for a ferroelastic phase transformation of the perovskite phase.

Single-crystal elastic properties of the modified spinel (Beta) phase of magnesium orthosilicate.

The single-crystal elastic moduli of the modified spinel structure (beta phase) of magnesium orthosilicate (Mg(2)SiO(4)) have been measured by Brillouin spectroscopy under ambient conditions. Single crystals with dimensions up to 500 micrometers were grown at 22 gigapascals and 2000 degrees C over a period of 1 hour. Growth of crystals larger than 100 micrometers was achieved only when the pressure was within 5 percent of the pressure of the phase boundary separating the beta- and gamma-phase stability fields. A comparison of the elastic properties of the modified spinel phase with those of the olivine phase suggests that the 400-kilometer seismic discontinuity in the earth's mantle can be described by a mantle with 40 percent olivine. These results confirm that the 400-kilometer discontinuity can be due to the transition from olivine to modified spinel. The amount of olivine that must be present is less than that in a pyrolite model, although the results do not exclude pyrolite as a possible mantle model.