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.http://gohu-takarabune.com/policy/localizar-a/tyta-como-ubicar-a.php
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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.
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. 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.
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. 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.
Coincident with these structural modifications are numerous changes, often dramatic, in physical properties. In four decades of high-pressure research, Bridgman , whose work was honoured by the Nobel Prize for Physics, documented effects of pressure on electric conductivity, thermal conductivity, viscosity, melting, reaction kinetics, and other material properties. Pressure was found to induce both continuous and discontinuous changes in matter.
Bridgman and others observed smoothly varying trends in properties such as electric conductivity or volume versus pressure for most materials.
Some substances, however, displayed sharp, reproducible discontinuities in these properties at specific pressures. Dramatic sudden drops in the electric resistance and volume of bismuth, lead, and other metals were carefully documented and provided Bridgman with a useful internal pressure standard for his experiments. These experiments also demonstrated the effectiveness of pressure for studying continuous changes in properties under uniform compression and discontinuous changes phase transitions.
Under sufficiently high pressure, every material is expected to undergo structural transformations to denser, more closely packed atomic arrangements. At room temperature, for example, all gases solidify at pressures not greater than about 15 GPa. Molecular solids like water ice H 2 O and carbon tetrachloride CCl 4 often undergo a series of structural transitions, characterized by successively denser arrangements of molecular units.
A different transition mode is observed in oxides, silicates, and other types of ionic compounds that comprise most rock-forming minerals. In these materials, metal or semimetal atoms such as magnesium Mg or silicon Si are surrounded by regular tetrahedral or octahedral arrangements of four or six oxygen O atoms, respectively. High-pressure phase transitions of such minerals often involve a structural rearrangement that increases the number of oxygen atoms around each central cation.
The common mineral quartz SiO 2 , for example, contains four-coordinated silicon at low pressure , but it transforms to the dense stishovite form with six-coordinated silicon at about 8 GPa. Similarly, the pyroxene mineral with formula MgSiO 3 at room pressure contains magnesium and silicon in six- and four-coordination, respectively, but the pyroxene transforms to the perovskite structure with eight-coordinated magnesium and six-coordinated silicon above 25 GPa.
Each of these high-pressure phase transitions results in a denser structure with increased packing efficiency of atoms. The large internal energy rise can dramatically reduce melt stress on the principal Hugoniot, as well as lower the shock condition for thermally driven processes such as phase transformations and chemical dissociation.
The impedance of porous materials increases to a far greater extent upon shock loading than in first shock compression of solids. Increase in the sound velocity at pressure,. This effect was discussed previously by Boade for pressed copper powders [ 15 , 16 ], and is relevant to the design of 1-dimensional non-released plate impact experiments.
The concepts discussed above will be used to interpret results obtained for the following materials: solid and porous foamed polyurethane [ 6 , 13 , 47 , 48 , 57 , 58 ], Epon- and Jeffamine-based epoxies [ 59 , 60 ], carbon fiber-filled phenolic CP and cyanate ester CE composites [ 5 , 60 , 61 ], and filled polydimethylsiloxane foam SX [ 62 , 63 ]. These materials have been studied extensively over the last decade at Los Alamos National Laboratory, and represent solid-density unfilled polymers, polymer-filler composites, and two types of polymer foams.
Table 1 provides their common names, chemical compositions by weight, and initial densities, which cover a range in the case of foams [ 5 , 6 , 63 , 64 , 65 ]. Polymers and foams discussed in the Results section. All materials were manufactured by Department of Energy laboratories. Polyurethane foams were prepared by condensation polymerization of the isocyanate moiety in methylene diphenyl diisocyanate PMDI with a hydroxyl group, yielding a molar composition normalized to hydrogen of C 0. Representative X-ray computed tomographs for the intermediate density polyurethane foams are shown in Figure 4 [ 6 ].
Taken from Ref. The resin was cured at room temperature in a flat sheet mold, and the porous network was formed by the evolution of hydrogen during curing and cross-linking. Chemical structures of starting materials, curing agent, and final SX foam. The H 2 g released during cross-linking produces the stochastic pore network of the open cell foam. X-ray computed tomograph of SX foam illustrating the open cell, stochastic pore structure.
Most modern shockwave compression experiments are based on projectile impact driven by light gas guns or direct laser drive not discussed here. An additional advantage of gas gun experiments is that complex loading conditions such as shock-release, double shock, or ramp loading can readily be generated using tailored impactors. The Shock and Detonation Physics group at LANL houses a two-stage light gas gun 50 mm launch tube bore [ 67 ], a high-performance powder-driven two-stage gun 28 mm launch tube bore [ 68 ], and a 72 mm launch tube single-stage light gas gun [ 69 ]. Data discussed in Section 3 were generated using several different types of plate impact experiment.
The state of the material at impact was measured directly, and particle velocity at the impact interface u int was monitored with dual velocity-per-fringe vpf interferometers VISARs [ 70 , 71 ]. More recent velocimetric techniques such as photonic Doppler velocimetry PDV [ 72 ] were also used to measure shock velocities and wave profiles at a windowed interface. These experiments typically were performed with the 50 mm launch tube light gas gun.
A Front surface impact geometry. Samples in this case, a composite were mounted to the front of a Lexan projectile, then launched into an oriented  single-crystal LiF window using a two-stage light gas gun. Probe placements are shown at right, based on a rear-view of the target. In the FSI experiments, measured velocities of the sample-LiF interface were combined with projectile velocities u pr to obtain final P , u states in the sample.
This procedure is known as impedance matching. In most experiments, a symmetric impact condition was created by launching either an oxygen-free, high-conductivity OFHC Copper or Aluminum disk into a drive plate of the same material, which was then was backed by a disk of the sample and a thick 9— Shock transit times through the sample were measured independently using 3 each of PDV and VISAR probes—two on the rear surface of the drive plate and one on the rear-windowed interface of the sample. A modified form of the top-hat configuration was also used to obtain shocked states for up to 4 foam samples in a single experiment [ 6 , 63 ].
This setup permitted collection of multiple data in a single experiment, and all with the same impact condition. Figure 8 shows a diagram of the multi-slug configuration that was applied to polyurethane and SX [ 6 , 63 ]. Multi-slug target configurations used at LANL large-bore two-stage gun to obtain up to 4 Hugoniot states in a single experiment. A Four foam samples with different initial densities were glued to the rear surface of a driveplate made of Al or other EOS standard material.
A final configuration was developed specifically to obtain deep-release pathways following shock compression above the threshold for chemical decomposition [ 74 , 75 ]. A polymer sample was affixed to the front of a projectile and driven into an oriented  single-crystal LiF window, similar to the FSI configuration. The window diameter and thickness were both nominally Figure 9 shows the experimental configuration used for deep-release experiments on epoxy and polyethylene [ 75 ], including the probe positions for PDV and VISAR velocimetry measurements.
Particle velocities measured at the interface with dual VISAR and multiple points of PDV were used to characterize the shock state and release isentrope. The EOS of polymers can be described with a variety of models, differing widely in their quality and level of detail. We will distinguish library entries from the framework by the use of all caps followed by an entry number, such as SESAME below. The total Helmholtz free energy is decomposed as [ 76 ].
The first term represents the energy of a static lattice at zero temperature SESAME was developed with metals in mind , with all ions and electrons in their ground state; it is often referred to as the cold curve. The second term represents the free energy of ionic excitations in the ground electronic state, and the last that of electronic excitations in the ionic ground state.
The actual models employed for each are flexible, although some generalizations can be made. For simplicity and computational speed, F elec typically is the Thomas-Fermi or Thomas-Fermi- Dirac model [ 78 , 79 , 80 ]. This is well beyond the point at which they chemically decompose, calling for an entirely different theoretical treatment described in the following section. A feature distinguishing polymers and molecular solids from most metals and oxides is the need for multiple characteristic temperatures due to presence of both relatively low-frequency phonons and high-frequency vibrons.
Use of variable dimension in the latter case permits treatment of chain-like, sheet-like, and 3-D crystalline vibrations [ 7 ]. Several different cold curves have been used for polymers in compression, the Tait form being particularly popular [ 2 , 84 ]. Cold curves for non-polymers often are calibrated to room temperature compression in a diamond anvil cell [ 30 ], where volume is measured by diffraction and pressure by reference to a standard.
The former requires a high degree of crystallinity, which many polymers lack. Another common source for cold curves in metals is density functional theory calculations [ 85 ] which, again, are non-trivial for polymers due to their complex chemical structure. For these reasons, probably the most common basis historically [ 31 ] for building polymer cold curves has been by fitting to shock data [ 86 ].
Because the final term in 16 is small for modest compressions i. If a characteristic temperature or temperatures is assumed, the cold contribution can be obtained by subtraction of the ionic contribution from the Hugoniot. Depending on the details, this procedure can have significant consequences for use of such an EOS in hydrodynamic simulation see Section 3.
The EOS of shock-driven reaction products discussed below were based on thermochemical modeling [ 87 ], where full thermodynamic equilibrium of chemically distinct atomic, molecular, or solid components is assumed. The first two component types are in the fluid phase all non-solids are well above their critical points at the relevant conditions , and their free energies are decomposed into ideal and non-ideal contributions [ 81 ].
The former are treated exactly, based on standard decomposition of the partition function into a product of vibrational harmonic oscillator , rotational rigid-rotor , translational, and electronic contributions. Each of these, in turn, takes gas phase vibrational frequencies, rotational constants, and electronic excitation levels as input parameters [ 88 ].
High-Pressure Shock Compression of Solids VIII: The Science and Technology - Google книги
Non-ideal contributions to the free energy of fluid components were described by soft-sphere perturbation theory [ 89 ] based on exponential-6 pair potentials [ 90 ]. Such potentials have the form. Please note that 18 lacks angular-dependence, meaning that even a constituent with interactions so directional as those of H 2 O is treated as isotropic. In addition to procedures designed to extract effective spherical potentials from anisotropic ones [ 91 ], the quality of this approximation will improve with temperature. The Gibbs free energies of all N f l fluids and N s solid components were combined into that of the mixture via.
The middle sum represents the free energy of mixing - here assumed to be ideal - meaning that all activity coefficients are unity and therefore that mixing is a purely entropic phenomenon [ 92 ]. While obviously a crude approximation, its virtues are computational simplicity and lack of need for cross-potentials. Equation 19 clearly is not unique, and other prescriptions [ 93 , 94 ] have been proposed. Solids contribute no mixing term, as their constituent atoms are assumed to be distinguishable from those of fluid particles. The Los Alamos Shock Compendium [ 31 ] summarizes Hugoniot data from over experiments, and the subset of polymer data were republished separately in a later report by Carter and Marsh CM [ 36 ].
Representative polymers, their threshold pressure for decomposition on their principal Hugoniot, and the percentage volume change upon decomposition. As taken from Ref. Data for all of the polymers recorded in CM display structure in their principal Hugoniots, although its degree varies widely. The extent of this feature can be at least qualitatively correlated with chemical structure, as illustrated in Figure A single PE chain is almost entirely backbone, and the absence of pendant side chain groups means it can pack quite efficiently.
The most compelling evidence that this structure is caused by chemical decomposition, as opposed to some form of phase transition or additional consolidation, was provided in a set of experiments performed at LANL in the s. Samples of PE [ 18 ] and PTFE [ 19 ] were exposed to single-shock, Mach compression waves in heavily confined and hermetically sealed capsules that enabled product recovery. For PE shocked to 28—40 GPa, no PE was recovered; rather, the products were almost entirely methane and hydrogen gas and carbon soot that was neither graphite nor diamond.
One would expect any accompanying temperature rise to be small and, indeed, preliminary calculations indicate that it actually cools upon decomposition [ 96 ]. The fact that only full decomposition products are recovered above the cusp would at least suggest a fortiori that this be the case for other polymers in which the volume collapse is larger. One of the most difficult quantities to measure in a dynamic experiment is temperature, making theoretical estimates particularly valuable.
Thermochemical results for four different solid-density polymers and four foams all polyurethane are shown in Figure 11 , where several features are worthy of note. The temperature increases upon reaction in all three cases, although we predict they drop in SX not shown and in PE, as already noted. This suggests that at least some polymers decompose exothermically under shock loading. Foam product temperatures are a good bit higher than that for solid density at the same pressure, and their slope increases with initial porosity. All reactant curves are black, product curves are red; only the full-density reactant curve is shown for polyurethane.
An even more difficult quantity to measure is chemical composition, and existing means for doing so are highly indirect [ 97 ]. In addition to it providing a more realistic representation of a reacting material, one of the advantages of thermochemical modeling is that it provides some physical basis for predicting this feature. Variations in epoxy composition with increasing pressure are well described by the simple equation.
Polyurethane compositions show even less variation as a function of pressure, and the primary difference between full-density and foam results is the replacement of methane with hydrogen. This is to be expected, in that higher temperatures see Figure 11 enhance the role of entropy, which is maximized by increasing moles of fluid. In each of the three cases—and we find this to be the case in general—the products as a whole are dominated by solid carbon and water.
However, as described in Section 1. This has the effect of reducing the pressure needed to input a given energy, meaning also that shock heating is much greater at a given shock pressure. Standard reaction rate laws such as Arrhenius are strongly temperature-dependent, so perhaps it is not surprising that the pressures needed to observe shock-driven decomposition on the timescale of dynamic experiments drops dramatically as a function of initial porosity.
By taking the threshold for reaction as the midpoint between the lowest-pressure reacted and highest-pressure unreacted points and setting the uncertainty accordingly , we estimated this threshold as a function of initial porosity, as shown in Figure Threshold pressure for shock-driven decomposition of PMDI polyurethane along its principal Hugoniot, as a function of initial porosity. One of the great advantages of modern velocimetric diagnostics is their ability to measure wave profiles.
Older diagnostics provided mean wave speeds based on times of arrival, whereas profiles capture their full temporal evolution including reshock, release, and wave splitting. The last is particularly helpful for identifying shock-driven chemistry, and dramatic multiwave structures have been observed in conjunction with decomposition of organic liquids [ 99 ]. It was only recently that we reported the first observation of multiwave structure due to chemical reaction in a polymer, although with structure much less dramatic than that shown in Ref.
The profiles were selected from shots with input shock stresses ranging from The rounding in the shock front at Reaction occurred in the 2nd wave, and so its risetime provides the timescale for shock-driven decomposition. At The transmitted shock fronts sharpen into single waves above 40 GPa, and rounding in the front disappears within the temporal resolution of the VISAR measurement at The mixed phase region, in which two waves appeared, extended over a large pressure range from 25 to 40 GPa. The profiles span pressures from Average interface particle velocities for each experiment are indicated in the Figure by the dashed lines.
This structure propagates to all thermodynamic loci e. Hugoniot data for epoxy taken from Refs. Figure 16 compares results obtained for epoxy in the experimental configuration of Figure 9. Agreement between theory and experiment is good for the peak velocities, as one would expect given that all the EOS are in part calibrated to Hugoniot data.
The point at which the release wave arrives at the interface is largely a function of the sound speed at pressure in the shocked material, differences that are highlighted in the insets. The improvement is less for the higher pressure shot shown on the right, but still clearly discernible. A more curious feature is the obvious multiwave structure seen in the simulation performed with The origin of this multiwave structure is provided in Figure 17 , where release paths have been included from shocked states above the threshold for reaction. The isentrope from retains the structure built into the cold curve, as shown in Figure 15 right.
Because the products are treated as an entirely separate material—with a different EOS—no such feature is present in Similar results hold for , where the structure due to reaction was not included as part of the cold curve. The way shock-driven transitions are incorporated into EOS representations can thus have hydrodynamic consequences, depending on how hard the material is shocked and how long it is simulated.
Please note that the structure built into the cold curve of see Figure 15 , right is retained also in the isentrope. The reaction is accompanied by an increase in density, the extent of which varies widely and correlates at least qualitatively with initial chain structure and degree of crystallinity. We believe the products of this reaction to be those of full chemical decomposition i. The transition manifests itself as a cusp in the principal Hugoniot Figure 1 A and as multiwave structure in particle velocity profiles obtained in situ Figure 1 B or at interfaces Figure Introduction of porosity complicates the picture largely through the significantly higher temperatures generated in the process of pore collapse.
Thermal expansion due to shock heating can be so considerable that the Hugoniot becomes anomalous in the sense that final volumes actually increase with increasing input stress Figure 3 C , an effect observed also in metal foams. Detonating high explosives also expand as they react, but with exothermic heat release sufficient to drive a self-sustaining wave [ 54 ]. While preliminary indications are that some solid polymers do decompose exothermically Figure 11 , the degree of heat release is insufficient to compensate for the effects of volume collapse and the criterion for detonation is not satisfied.
There are several outstanding questions regarding shock-driven compression and dissociation of polymers and foams. As in the case of high explosives, in situ measurement of the product composition remains challenging experimentally, and even the best post-mortem studies are now decades old [ 18 , 19 ]. X-ray-based methods are promising in their ability to penetrate the optically dense, high-pressure—temperature product mixture, and we have recently reported the evolution of carbon particle size and morphology in a detonating explosive in situ [ , ].
New in situ measurements of reactive wave profiles in polysulfone [ ] demonstrate strong temperature-dependence of chemical reaction rates and complex two-wave structures such as those observed in CP and CE. These wave profiles are being used to calibrate reactive flow models for polymers, the first of their kind. However, EOS temperatures are unconstrained by experiment and most reaction rate forms depend exponentially on temperature, so a great deal of uncertainty regarding the details remains. Many interesting facets of the chemistry—mechanisms, intermediates, even the number of basic steps—are almost completely unknown.
In the absence of such knowledge, there is little justification for use of anything beyond a single, global Arrhenius reaction rate. Precise measurement of shock response in foams is also hindered by several sources of ill-quantified uncertainty. Sample heterogeneity often of an extreme degree, see Figure 4 and high shock temperatures Figure 11 can reduce the quality of velocimetric and embedded gauge data, as well as that of other diagnostics.
Impedance matching to a high impedance impactor or drive plate can result in errors in particle velocity with measured shock velocities. In addition, it remains the case that only the initial first shock breakout is measured in many experiments, and wave profiles that might otherwise display temporal evolution are incapable of doing so. Advances in in situ and spatially resolved diagnostics, such as direct density measurements using proton or X-ray radiography and multiple point or line imaging velocimetry, offer the potential for reducing these errors.
We also thank Stephen Sheffield, E. Mark Byers and Steve DiMarino fired the high-performance powder gun. Department of Energy Contract No.