Experimental Methods in Wave Propagation in Solids and Dynamic Viscometry


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Diamond is an important material for planetary science, high-pressure physics, and inertial confinement fusion. In ice-giant planets such as Uranus and Neptune, decomposition of hydrocarbons at high pressure and temperature may lead to the formation of diamond-containing layers in the interior Benedetti et al. Exoplanets that form around C-rich host stars or by local carbon enrichment of a protoplanetary disk may also have diamond and silicon carbide bearing interior layers Bond et al. Carbon is stable in the diamond structure over a wide range of pressures and temperatures.

A phase transformation to a BC8—type structure near 1 TPa followed by a further transition to a simple cubic structure near 3 TPa have been predicted theoretically Yin and Cohen, ; Correa et al.

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The coordination increases from fourfold to sixfold in the simple cubic structure. Theoretical studies have explored the melting behavior of diamond, predicting a maximum in the melting curve around GPa and 8,—9, K Grumbach and Martin, ; Correa et al. A number of ultra-high pressure shock-compression experiments on diamond have been carried out extending to as high as 4 TPa Bradley et al. In decaying shock experiments, it has been found that diamond melts to a dense metallic fluid with a negative melting slope at —1, GPa Brygoo et al.

Evidence for the existence of a new solid phase, possibly BC8, has also been reported in shock-compression experiments at 90— GPa Knudson et al. Figure 8. Ultra-high pressure phase diagram of carbon. Shock temperatures from decaying-shock experiments in diamond samples are shown as black lines. Blue and orange symbols are from theoretical calculations. See Eggert et al. A comparison of the Hugoniot behavior of single-crystal and nanocrystalline diamond has been reported up to 2.

Diamond has also been explored under ramp compression. The pressure—density relationship and strength of diamond has been characterized up to GPa using the Omega laser Bradley et al. In experiments at the National Ignition Facility, measurement of the stress-density relationship of diamond was extended to 5 TPa, achieving 3. These are the highest pressure equation-of-state data recorded under ramp compression and represent the first experimental data in the high-pressure, modest-temperature regime for constraining condensed-matter theory and planetary evolution models at terapascal conditions.

MgO periclase is an endmember of the Mg,Fe O solid solution which is expected to be a major component of the deep mantles of terrestrial planets and exoplanets Figure 1. Its high-pressure behavior has long attracted widespread attention due to its simple rocksalt B1-type structure, wide stability field, and geophysical importance Duffy et al.

Recent interest in the behavior of MgO at ultra-high pressure and temperature has focused on its phase transformation to the B2 CsCl-type structure, its melting behavior, and possible metallization Boates and Bonev, ; Cebulla and Redmer, ; Taniuchi and Tsuchiya, Experimental studies have been conducted using both steady and decaying shocks but have reached conflicting conclusions about the solid-solid phase transition and melting. In contrast, plate-impact experiments performed using the Z machine Figure 9 coupled with theoretical calculations indicate that the B1—B2 transition occurs at lower pressure GPa and melting initiates near GPa and is completed by GPa Root et al.

More recent results using laser-driven steady Miyanishi et al. Figure 9. Optical reflectivity measurements have also been used to place constraints on the electrical conductivity of shocked liquid MgO.

On modeling two-mode vibration sensors for combined density and viscosity measurements

The initial decaying-shock measurements suggested metallization occurred upon melting McWilliams et al. The transformation of periclase to the B2 phase in shock-compression experiments is inferred only indirectly through temperature or density changes. The first direct identification of the B2 phase was made using laser-driven ramp compression combined with X-ray diffraction Coppari et al.

In these experiments, diffraction peaks were recorded for MgO compressed up to GPa. Measured d -spacings were consistent with the B1 phase up to GPa whereas diffraction from the B2 phase was observed from to GPa Figure Temperature is not measured in these ramp-compression experiments, but is expected to be significantly lower than achieved under shock compression. The observation of a B2 peak at higher pressure in the ramp data compared with inferences from shock measurements is consistent with a negative Clapeyron slope for the transition, consistent with theoretical predications.

However, the experimentally measured pressure of the transition GPa is substantially higher than predicted along an isentrope GPa by theory Cebulla and Redmer, This may reflect over-pressurization of the equilibrium phase boundary under the short timescales of dynamic compression.

Understanding possible kinetics factors associated with phase transformations under ultra-high pressure—temperature conditions is an important goal for future experiments. Figure A Interplanar d -spacing vs.


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  • B Density of MgO in the B1 open and filled red and B2 blue structures determined from ramp X-ray diffraction compared with shock data yellow. See Coppari et al. The transformation to the B2 phase is expected to occur in large rocky exoplanets Wagner et al. Empirical systematics and theoretical studies have suggested that the MgO phase transformation may be accompanied by a strong change in rheological properties with the high-pressure B2 phase exhibiting a reduction in viscosity Karato, ; Ritterbex et al. The viscosity of the constituent minerals strongly influences dynamic flow in the mantle and hence is important for understanding the heat flow and the style of mantle convection Driscoll, The negative Clapeyron slope of the phase transition combined with the viscosity reduction may produce mantle layering in super Earths with strong differences in convective flow above and below the transition which may affect the long-term thermal evolution of these planets Shahnas et al.

    Silica is the most abundant oxide component of terrestrial mantles and serves as an archetype for the dense highly coordinated silicates of planetary interiors.

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    Based on theoretical calculations, it is expected that silicates such as post-perovskite will eventually dissociate at conditions of the deep interior of super-Earths Umemoto et al. Consequently, SiO 2 phases are expected to be potentially important constituents of these exoplanets Figure 1. The Hugoniot behavior of quartz at ultra-high pressure has been extensively studied due to its role as an impedance-matching standard for shock experiments Hicks et al.

    A significant degree of non-linearity was found in the shock velocity-particle velocity relationship and attributed to disorder and dissociation in the SiO 2 fluid. Temperatures, shock velocities, and reflectivities were reported using pyrometry and velocimetry measurements on fused silica and quartz starting materials in decaying-shock experiments up to 1 TPa Hicks et al.

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    The specific heat derived from the temperature measurements was found to be substantially above the classical Dulong-Petit limit and attributed to complex polymerization and bond breaking in a melt that evolves from a regime dominated by chemical bonding of Si-O units bonded liquid to an atomic fluid consisting of separated Si and O atoms.

    Electrical conductivity values derived from measured reflectivities assuming Drude behavior indicate the atomic fluid is highly conductive. More recent decaying-shock measurements on quartz, fused silica, and stishovite starting materials extend constraints on the melting curve of SiO 2 to GPa and 8, K Millot et al. The melting curve of SiO 2 and other silicates was found to be higher than that of iron at these extreme conditions. Comparison of these results to planetary adiabats suggests that silica and MgO are likely to be in a solid state in the cores of giant planets such as Neptune and Jupiter.

    However, the deep mantles of large rocky exoplanets may contain long-lived silicate magma oceans. Electrical conductivities inferred from measured reflectivities and a Drude model suggest the conductivity of liquid silica approaches that of liquid iron at TPa pressure and thus liquid silicates in a deep magma ocean could contribute to dynamo generation of magnetic fields in large exoplanets Millot et al. Hugoniot equation-of-state measurements have also be reported for fused silica samples to 1.

    Additional thermodynamic constraints can be obtained from measurements of bulk sound velocities that have been recorded for fused silica and quartz samples compressed into the liquid state to as high as 1. Traditional studies of these compositions using gas-gun shock compression are summarized in Mosenfelder et al. In recent laser-shock work on MgSiO 3 glasses and crystals, the Hugoniot pressure—density equation of state has been measured to GPa Spaulding et al. Initial reports of a liquid-liquid phase transition above GPa and 10, K Spaulding et al.

    Sound velocities along the principal Hugoniot for MgSiO 3 compared with theoretical calculations and diamond anvil cell measurements. Adapted from Fratanduono et al.

    SOME ASPECTS OF ELASTIC WAVE PROPAGATION IN FLUID‐SATURATED POROUS SOLIDS | GEOPHYSICS

    The behavior of forsterite, Mg 2 SiO 4 , shocked beyond GPa has been the subject of studies using laser-driven shocks and magnetic compression Bolis et al. Two studies using laser-shock techniques reached different conclusions regarding the behavior of this material. From measurements of Hugoniot states and shock temperatures, Sekine et al.

    However, later experiments using similar loading techniques did not observe discontinuities in this range Bolis et al. The shock Hugoniot of forsterite was explored from to GPa using both plate-impact experiments and laser-driven decaying shocks, complemented by theoretical calculations Root et al. The shock velocity — particle velocity data in these experiments show a monotonic increase, and no evidence for any phase transformations was detectable.

    Iron is one of the most cosmochemically abundant elements and the major constituent of planetary cores. At even higher pressures, the nature of the expected iron-rich cores in terrestrial-type exoplanets is important for understanding their interior structure and evolution.

    The size of the iron core can also affect the production of partial melt in the mantle due to the steepness of the internal pressure gradient which in turn influences atmospheric formation and evolution through outgassing of the interior Noack et al. Knowledge of the nature of the core is also essential for understanding possible dynamo-generated magnetic fields.

    Experimental Methods in Wave Propagation in Solids and Dynamic Viscometry
    Experimental Methods in Wave Propagation in Solids and Dynamic Viscometry
    Experimental Methods in Wave Propagation in Solids and Dynamic Viscometry
    Experimental Methods in Wave Propagation in Solids and Dynamic Viscometry
    Experimental Methods in Wave Propagation in Solids and Dynamic Viscometry
    Experimental Methods in Wave Propagation in Solids and Dynamic Viscometry
    Experimental Methods in Wave Propagation in Solids and Dynamic Viscometry

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