Impedance Matching Technique. Experimental Techniques. Thermodynamics of Shock Waves. Pages E1-E4. Back Matter Pages About this book Introduction This book introduces the core concepts of the shock wave physics of condensed matter, taking a continuum mechanics approach to examine liquids and isotropic solids. The first four chapters are specifically designed to quickly familiarize physical scientists and engineers with how shock waves interact with other shock waves or material boundaries, as well as to allow readers to better understand shock wave literature, use basic data analysis techniques, and design simple 1-D shock wave experiments.
This is achieved by first presenting the steady one-dimensional strain conservation laws using shock wave impedance matching, which insures conservation of mass, momentum and energy. Here, the initial emphasis is on the meaning of shock wave and mass velocities in a laboratory coordinate system. An overview of basic experimental techniques for measuring pressure, shock velocity, mass velocity, compression and internal energy of steady 1-D shock waves is then presented.
In the second part of the book, more advanced topics are progressively introduced: thermodynamic surfaces are used to describe equilibrium flow behavior, first-order Maxwell solid models are used to describe time-dependent flow behavior, descriptions of detonation shock waves in ideal and non-ideal explosives are provided, and lastly, a select group of current issues in shock wave physics are discussed in the final chapter.
The reduced heating means that solids can be compressed to very high pressure without melting. Furthermore, there is no upper limit on compression achievable by ramp methods, in contrast to shock compression. The technique enables access to the wide range of pressure—temperature states that lie between the isotherm and the Hugoniot Figure 3. Moreover, ramp loading produces measurements of a continuum of pressure—density states along the load curve, unlike traditional steady shock compression which yields only one data point on the Hugoniot per experiment Figure 5.
However, ramp loading can be challenging to maintain experimentally during propagation through a sample because the increase in sound velocity with pressure tends to cause large-amplitude pressure waves to steepen into shocks. This rapidly heats and ablates the material which expands outward at high velocity as a result. Conservation of momentum results in a corresponding compression wave being driven into the sample as the heated material expands backward.
The following expression can be used to estimate the ablation pressure, P ab Drake, :. Based on this expression, the use of a nm laser focused to a 0. A detailed description of the laser-matter interactions involved in generating ultra-high pressures can be found in the literature Drake, ; Falk, Laser facilities in use for dynamic-compression experiments on geological materials include the Omega Laser Facility at the University of Rochester Boehly et al.
Table 1 lists these and selected other major laser facilities and some basic characteristics. Table 1. Characteristics of representative high-powered laser facilities for dynamic-compression experiments. The Omega facility consists of two neodymium:glass laser systems Omega and Omega-EP operating at nm. Omega has 60 beams, each of which can provide up to J of energy.
Optical components known as phase plates are used to smooth intensity variations in the beam. A key feature of laser facilities is their flexible pulse shaping, which allow users to design and apply a range of pulse shapes to produce controlled loading states Figure 5. Individual pulses at Omega can be up to 3. The independent spatial and temporal targeting capability at multi-beam laser facilities allows for complex experimental designs such as driving a compression wave into the sample with some of the beams while using others to generate an X-ray source to probe the compressed sample after a time delay.
Shock Wave and High Pressure Phenomena
NIF has beams capable of delivering up to 1. These capabilities provide the energy and control necessary to ramp compress matter to several terapascals Smith et al. Ultra-high pressure dynamic experiments can also be conducted using the Z machine at Sandia National Laboratory. Z is a pulsed-power facility that can produce currents as high as 20 MA and magnetic fields to 10 MG Matzen et al. Discharge of a large capacitor bank through a closely positioned anode and cathode pair with currents flowing in opposite directions generates a magnetic force that can rapidly accelerate materials at high strain rates with different possible loading profiles including both shock and ramp compression Figure 4D.
Additionally, Z can be used to accelerate flyer plates and thus drive shock waves through plate-impact techniques.
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Experiments on Z have reached GPa along a ramp compression path Kraus, and nearly 1. There are three major dynamic compression techniques being used to achieve ultra-high pressure: steady shock compression, decaying shock compression, and ramp compression. Figure 5 provides an example of how laser pulse shaping left column can achieve each of these and produce different thermodynamic compression paths within a sample under study.
In Figure 5A , a ns near-flat-top laser pulse shape generates a temporally steady-shock traveling through the sample at a pressure-dependent shock speed, U S P. Measurements of shock velocity and temperature as the decaying shock traverses the sample can be used to make a series of continuous measurements along the Hugoniot Figure 5B Millot et al. If the applied laser pulse has a ramp-like shape Figure 5C , the compression wave that propagates through the sample has a pressure-dependent particle velocity, u p P.
Other types of drivers, gas guns and pulsed power, can also be used to access different types of compression pathways Chhabildas and Barker, ; Knudson, Both laser and pulsed-power facilities can be used to generate steady shock waves in samples Figure 5A. For laser experiments, a typical target package consists of a foil sample sandwiched between a polyimide ablator material and a LiF or quartz window Figure 4B.
Ablation of the polyimide produces a steady shock wave in the target package resulting in sample compression to s of GPa Wang et al. Alternatively, the laser pulse may be used to accelerate a flyer plate across a gap to strike a target Swift et al. A similar approach can be used to generate very high impact velocities at pulsed-power facilities. The current pulse is designed so that the flyer plates are shocklessly accelerated such that the impact side of the flyer plate remains at solid density upon impact. In a decaying shock wave experiment, the laser pulse is designed to produce a strong shock that decays as it propagates through the sample Figure 5B.
That is, each successive layer in the material is compressed from its initial condition to a different final Hugoniot state with pressure and temperature decreasing with shock propagation distance Bradley et al. An advantage of this technique is that it allows for measurements along a continuous series of Hugoniot states in a single experiment rather than obtaining only a single datum as in a traditional plate-impact or laser-shock experiment.
The samples used in these experiments must be initially transparent but become ionized and partially reflecting upon shock loading of sufficiently high amplitude typically a few hundred GPa. The sample reflectivity allows for continuous measurements of the shock velocity and shock-front temperature as the shock decays during its transit across the sample see Diagnostics section below. To convert the measured shock velocity to pressure and density requires either knowledge of the Hugoniot relationship of the sample or use of a calibrated standard. Phase transitions such as melting can be identified in these experiments by observation of temperature anomalies associated with energy changes resulting from the transition Bradley et al.
Relative to more traditional supported shock experiments, the main disadvantage of decaying shocks, in addition to restrictions on sample properties, is that the technique may be less likely to achieve equilibrium or a phase transition to a well-defined shock state. The effort to develop dynamic ramp-loading techniques began in the s Barnes et al.
The advent of high-powered laser and pulsed-power facilities reinvigorated this effort Remington et al. In direct-drive experiments, a laser directly impinges on an ablator in the target assembly Figure 4B. Alternatively, in indirect-drive experiments the laser beams are directed into a small hollow gold cylinder called a hohlraum Figure 4C. The laser heats the hohlraum which emits X-rays that impinge on and ablate the sample Smith et al. Indirect drive produces a more spatially uniform compression wave, although some energy loss occurs during the conversion to X-rays.
In a ramp-compression experiment, the in situ particle velocity is measured at two or more positions within the sample under uniaxial strain. This is accomplished using velocimetry measurements described below on a stepped target containing multiple thicknesses Smith et al. Data analysis is performed using a Lagrangian approach and the method of characteristics and involves solution of the differential form of the Rankine-Hugoniot equations Rothman and Maw, Wave interactions arising at the free surface or material interfaces can strongly perturb the analysis, and corrections for these effects must be applied.
The method is strictly applicable in the case of simple wave propagation, where deformation is not affected by changes in compression rate, and the presence of phase transitions and elastic-plastic behavior may lead to non-uniqueness in the solutions. The target design is a key element of a successful dynamic-compression experiment Prencipe et al.
A schematic illustration of representative designs for different types of dynamic-compression experiments is shown in Figure 4. While in some cases, the sample can be directly irradiated by the incident laser, the use of separate ablator material is generally advantageous for smoothing spatial variations in the load arising from the intensity variations in the laser. Depending on experimental requirements, a wide range of materials may be suitable ablators including plastics, beryllium, and diamond. Diamond is particularly useful in ramp-compression experiments as its low compressibility makes it resistant to forming a shock wave.
Samples may be either single crystals or polycrystalline. The thickness of the sample should be optimized to maintain inertially confined loading conditions over the duration of the experiment. In some cases a thin film of a metal such as gold will be deposited in front of the sample as a shield to prevent pre-heating by the laser drive Figure 4B. A window mounted on the back surface of the sample maintains the pressure and avoids rapid release into the surrounding vacuum.
Commonly used window materials include single-crystal diamond, LiF, quartz, and Al 2 O 3. In most cases, a transparent window is desired although materials may lose transparency under dynamic compression. For example, diamonds becomes opaque above its elastic limit near GPa. The different layers of the target package are bonded using glue layers that must be made as thin as possible, ideally submicron.
Additional metallic or anti-reflection coatings may need to be applied to target layers as well. Strict tolerances on thickness, parallelism, roughness, and optical quality are often required. Advances in ultra-high pressure experiments stem not only from development of facilities and but also from advances in diagnostic capabilities Remington et al.
Laser velocimetry and pyrometry are established techniques that provide fundamental continuum-level constraints on the behavior of dynamically compressed materials. More recently, development of X-ray diffraction and absorption spectroscopy capabilities have allowed for examination of atomic-level structural behavior with the potential to greatly enhance our understanding of material response to extreme loading. Measurement of the time history of the velocity at a sample-window interface or free surface by laser interferometry is a primary diagnostic in dynamic-compression experiments.
In this technique, a moving target is illuminated with laser light causing the reflected beam to return with a Doppler shift in frequency. There are a variety of types of laser-interferometer designs suitable for dynamic compression but for ultra-high pressure experiments the VISAR velocity interferometer system for any reflector is the most generally useful Barker and Hollenbach, ; Celliers et al.
In the VISAR approach, the reflected light from the sample at a given time is combined in an interferometer with light reflected at a slightly earlier time and the phase difference between the two beams produces interference fringes which are proportional to the surface or interface velocity Figure 6. An additional role of laser velocimetry is to provide a measure of optical reflectivity of the sample at the VISAR laser wavelength typically at nm.
This is done by comparing the intensity of the reflected VISAR beam with the intensity of the beam prior to compression. Reflectivity measurements can provide information on ionization and electrical conductivity under compression Hicks et al. Figure 6. Pyrometry involves time-resolved measurements of thermal radiation emitted from a shocked solid and can be used to constrain temperatures during shock compression or release Asimow, Temperature measurements provide a means to determine the isochoric heat capacity Hicks et al.
In addition, phase transformations may be revealed by thermal changes associated with latent heat of transition in either steady or decaying-shock experiments Eggert et al. Pyrometry techniques have long been used in gas-gun experiments on a variety of materials with temperatures usually determined using spectroradiometry Asimow, In ultra-high pressure laser-compression experiments, the total thermal self-emission from the shock front is recorded as a function of time using a streak camera Miller et al.
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Ramp-compression experiments do not lend themselves to temperature measurements by pyrometry but alternative methods for obtaining temperature constraints such as X-ray absorption spectroscopy described below are under development. The development of X-ray diffraction techniques under in situ dynamic loading began as early as with the first demonstration of Bragg diffraction from pulsed X-rays on a shocked crystal Johnson et al. Due to the limitations of available X-ray sources, such studies were primarily restricted to examination of single crystals at relatively low pressure.
The application of brighter X-rays sources including laser-plasma sources i. X-ray diffraction can be carried out with a multi-beam laser source in which lasers are used to generate both the dynamically compressed state and the X-ray pulse that probes it. The development of such a system at the Omega laser Rygg et al. A quasi-monochromatic X-ray source is produced by irradiation of a metallic foil e. This creates an ablation plasma in which the atoms are ionized to a He-like state with two bound electrons and produce K-shell emission.
The experimental set-up is shown in Figure 7. The sample is dynamically compressed with either shock or ramp loading using a subset of the beams from the laser. At the expected time of peak compression the laser-plasma X-rays are generated and impinge on the sample. A metallic foil with a pinhole positioned in the sample assembly is used to collimate the incident X-ray beam. Diffracted X-rays are recorded on image plates behind the sample Figure 7. Diffraction from the edges of the pinhole produces peaks that provide a reference to calibrate the diffraction geometry.
At pressures above a few hundred GPa, the rapid increase of X-ray noise from the drive plasma makes detection of diffracted photons from the sample more challenging. Although laser-plasma sources are very bright, the source is uncollimated and only a small fraction of the generated X-rays pass through the sample. Figure 7. Experimental set-up for laser ramp-compression experiments with X-ray diffraction. The target package is affixed to one side of a box and illuminated by laser-plasma X-rays from a Cu, Fe, or Ge foil.
Measured X-ray emission spectra left demonstrate the quasi-monochromatic nature of the radiation. X-rays scattered by the sample are recorded on image plates that line the box interior, while a VISAR laser is focused onto the rear surface of the target package through an aperture in the back panel. Adapted from Wicks et al.
X-ray absorption fine-structure XAFS spectroscopy probes the local atomic environment around an absorption edge of a specific element. The method includes XANES X-ray absorption near edge structure which examines fine structure near an absorption edge and EXAFS extended X-ray absorption fine structure which examines the structure over a larger energy range above the edge.
Both methods arise from interference effects that occur when a photoelectron ejected from an atom by incoming X-rays is scattered by its neighbors. XAFS methods are sensitive to a variety of atomic-level properties including electronic structure, bond lengths, and coordination The decay of interference-produced modulations is controlled by the Debye-Waller factor from which constraints on temperature can be obtained. XAFS is a widely established tool for materials under static high pressures using synchrotron X-ray sources Shen and Mao, and is being adapted for use in ultra-high pressure dynamic compression.
Experiments are performed using a thin sample foil embedded between two diamond layers that serve to confine the sample. Compression is achieved using a series of 1-ns long square laser pulses stacked in time to drive multiple shocks into the sample. A key requirement for XAFS is a bright and smooth X-ray source of sufficient energy range and resolution to capture the absorption fine structure.
The X-ray source pulses are delayed in time relative to the loading pulses to probe the sample at peak pressure. X-rays transmitted through the target are dispersed by a spectrometer and recorded on image plates. A reference spectrum of the X-ray source is recorded in a separate experiment under identical conditions. XAFS measurements have also been reported on laser-driven samples at pressure extending to the multimegabar range using other X-ray sources including laser-driven backlighter foils Denoeud et al.
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.
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.
IOS Press Ebooks - High Pressure Phenomena
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. 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. 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.
Shock Waves and Extreme States of Matter
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. 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. 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. The relative size of core and mantle may affect the ability of the planet to initiate plate tectonics Noack et al.
Another study using the LULI laser showed that Hugoniot equation-of-state measurements could be made on iron laser-shocked to as high as GPa by measurements of shock and particle velocities on stepped targets Benuzzi-Mounaix et al. The behavior of iron under ramp compression was explored with the Omega laser. Using wave-profile measurements on mutliple-thickness iron foils compressed over serveral nanoseconds, the sound speed and stress-density relationship of iron was measured to GPa Wang et al. Time-dependent effects in these experiments due to the low-pressure iron phase transition were overdriven by an initial shock demonstrating the feasibility of a two-stage compression path involving shock followed by ramp compression.
Initial shocks of different amplitudes would futher allow different thermodynamic compression paths to be explored. Higher pressure experiments were performed at the National Ignition Facility where the combination of higher laser power and longer, more complex pulse shapes allowed ramp compression of iron to be extended to 1. The peak pressure in these experiments approaches that predicted at the center of a terrestrial-type exoplanet of three to four Earth masses, representing the first absolute equation-of-state measurements for iron at such conditions. These results provide an experiment-based mass—radius relationship for a hypothetical pure iron planet that can be used to evaluate plausible compositional space for large, rocky exoplanets.
Weighted average of pressure versus density with experimental uncertainties bold blue curve. Hugoniot data are shown as gray triangles and squares. Double-shock data are shown as red squares. A fit to the Hugoniot data gray dashed—dotted line with uncertainties gray shaded region. Also plotted are previous ramp compression data purple curve and static diamond anvil cell data light blue circles.
The ranges of EOS extrapolations of low-pressure static data orange shaded region and first-principles cold curve calculations light blue shaded region represent the uncertainty in the EOS of Fe at TPa pressures. Central pressures for Earth and a 3. Inset: Raw velocity interferogram with extracted free-surface velocity profiles for each of four sample thicknesses.
Modifided after Smith et al. In experiments conducted using the Omega laser, the density, temperature, and local structure of iron were explored using multiple-shock compression combined with EXAFS measurements Ping et al. The results showed that iron remains in a close-packed structure i. A surprising result was that the temperatures inferred from the Debye-Waller factor were higher than expected and may indicate that the dynamic strength of Fe is larger than predicted based on extrapolation of lower pressure data.
Iron samples were sandwiched between plastic and copper to maintain steady pressure conditions during the experiment. The sample was probed with 80 fs, 7. Through a series of pump-probe experiments in which the sample was compressed and the XANES spectrum recorded after different time delays, the Hugoniot of iron was explored to as high as GPa and during isentropic release dowm to 12 GPa. The signature of molten iron was observed above GPa and 5, K, consistent with observations of shock melting in gas-gun experiments.
Iron has also been used in a proof-of-principle experiment to demonstrate EXAFS capabilities on laser-shocked iron using a synchrotron X-ray source. Synchrotron X-rays were dispersed and focused on the sample using a curved crystal. The transmitted X-rays were recorded by a position sensitive detector enabling simultaneous collection of a spectrum extending up to eV above the iron K-edge 7.
The use of a synchrotron source for dynamic-compression experiments has advantages of high energy resolution, large spectral range, and small X-ray spot size, all of which can lead to better recovery of the detailed behavior of the sample. It is also needed for understanding phase relationships in the core, melting point depression relative to pure iron, and potential reactions between the core and mantle Hirose et al. Cosmochemical considerations and planetary formation models suggest that terrestrial-type exoplanets are also likely to incorporate significant quantities of light elements into their cores.
However, existing models for exoplanet interiors have generally assumed a pure iron composition Valencia et al. Silicon is one of the most promising candidates for a core light element as it is abundant cosmochemically but not highly volatile. Si alloys with iron over a wide range of conditions. The effect of silicon incorporation in a rocky exoplanet core was modeled using the above results for the planet Keplerb as a representative example Wicks et al.
This planet has a radius of 1. A model for the planet was constructed assuming a silicate mantle and an iron-rich core. The mantle was assumed to have a Mg-rich composition and was divided into layers as a result of structural phase transitions. The interior structure was calculated by solving the coupled differential equations for hydrostatic equilibrium, mass within a sphere, and the equation of state of each component with solutions constrained to reproduce the observed mass and radius of the planet Figure This illustrates that the incorporation of light elements into exoplanetary cores should be considered in construction of interior structure models.
Relative to a pure iron core, the addition of Si produces a larger core radius and lower densities and pressures in the core. According to models for early solar-system evolution, the planets grew by successive accumulation of materials from impacting bodies Stevenson, As planetary bodies grow in size, larger and more energetic collisions occur.
At late stages of accretion, it is expected that Earth would be impacted multiple times by Moon- and Mars-sized objects. Such giant impacts may play a major role in determining certain characteristics of planets such as their rotation rates and existence of satellites.
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Knowledge of the shock and unloading properties of geological materials is an important component of modeling the effects of large, late-stage collisions. Accurate predictions of material behavior throughout the shock and release process require knowledge of equations of state over a wide range of conditions from the very high pressures and temperatures of the shocked state to the low densities but high temperatures of shock-released material.
During isentropic release from a shocked state, a material may melt or even vaporize due to the entropy gained during shock loading. For many geological materials, traditional shock-compression experiments using gas guns are unable to reach sufficient shock pressure to produce vaporization upon release. The higher pressure achievable with lasers and pulsed power now allow such experiments to be performed Kraus et al. Kraus et al. SiO 2 samples were laser shocked and then allowed to release as a liquid—vapor mixture across a vacuum gap and stagnate against a window.
This enabled measurements of both the temperature and density in the shocked and released SiO 2. The results were used to constrain the entropy of the shocked state and to make an improved determination of the liquid—vapor boundary for SiO 2. It was found that the energy required for vaporization of silicates is much lower than assumed in standard equation-of-state models.
Shock-induced irradiance from quartz, diopside, and forsterite was recorded in decaying shocks that reached as high as GPa. Measurements performed as the samples released from the shocked state and become vaporized revealed the presence of ionic and atomic emission lines in the gas phase. This was due to shock-induced ionization followed by atomic recombination later in time in the expanding vapor.
The ionization and recombination processes affect temperatures, energy partitioning and vapor production. These phenomena need to be accounted for to understand the thermal and chemical evolution of silicate vapor clouds. This has applications to understanding such processes as the impact origin of the Moon and atmospheric blow-off from the early Earth Kurosawa et al.
Using the Sandia Z machine, the entropy of iron along the Hugoniot was measured using shock-and-release experiments Kraus et al. This means that high-velocity impacts at the latter stages of planetary accretion would be able to vaporize the iron cores of impacting planetesimals. This has implications for the geochemical state of the early Earth as the dispersal of vaporized iron over the surface of the Earth would enhance metal-silicate mixing and chemical equilibration.
This process would be less effective on the Moon due to its smaller size and may help to explain differences in mantle siderophile element abundances between the two bodies. Ultra-high pressure experimental data on crystal structure, equations of state, and other properties of geological materials are essential for constraining models for the internal structure, dynamics, and evolution of planets within and outside our solar system.
Dynamic compression experiments play a central role in this effort as ramp and shock compression techniques can reach to as high as several terapascal pressure, directly achieving conditions of large impacts and the deep interior of rocky and giant planets. Ramp and shock-compression equations of state provide accurate constraints on density at ultra-high pressures and provide sensitive tests of theoretical calculations at extreme conditions.
Determination of melting curves at ultrahigh pressure is important for evaluating the physical state of exoplanetary cores and the possible presence of long-lived magma oceans. Transport properties such as thermal and electrical conductivity are also key parameters, with the measurements of the latter providing evidence for possible contributions of the deep magma oceans to planetary magnetic field generation. Lack of constraints on the lattice-level crystal structure under in situ dynamic loading has long been a major limitation of the technique.
This is especially problematic at very high pressures where structural phase transitions often involve very small volume changes making them difficult to detect with continuum-level measurements. The development of pulsed X-ray diffraction techniques for ramp and shock compression is thus a major advance, allowing for unambiguous structure determination and identification of phase transitions at ultrahigh pressures. This allows for experimentally based models of interior mineralogy of rocky exoplanets.
Shock compression and subsequent unloading behavior are also relevant to understanding the formation and early evolution of planets, especially the role of large-scale impacts and the evolution of magma oceans. Shock and unloading processes have applications to such phenomena as the impact origin of satellites, formation of atmospheres and the initial thermal and chemical state of planets and their satellites.
Despite the many advances outlined in this review, there remain fundamental limitations and unanswered questions. Better constraints on the temperatures achieved are needed from both ramp and shock experiments. The short timescales and high strain rates in dynamic compression may preclude the achievement of thermodynamic equilibrium. Phase transitions may need to be significantly overdriven in pressure or may produce metastable phases.
It is thus important to carefully compare the results of dynamic experiments, static experiments, and theoretical calculations to fully understand the effects of time scale and strain rate on material behavior at extreme conditions. Dynamic compression of geological materials at multi-megabar pressure is still in its infancy, but the work reviewed here highlights the considerable progress that has been made in recent years. The development of new large-scale user facilities promises to greatly expand the opportunities for probing Earth materials over a range of pressure, temperature, and strain-rate conditions.
The ability to constrain lattice-level structures and physical properties of geological materials at extreme pressure and temperature will provide the fundamental data which in combination with new astronomical observations, theoretical calculations, and geodynamical models will enable fundamental advances in our understanding of planetary systems.
Both authors listed have made a substantial, direct and intellectual contribution to the work, and approved it for publication. The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest. Sally June Tracy and Eleanor J.
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