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Megabar (1 Mbar = 100 GPa) laser shocks on precompressed samples allow reaching unprecedented high densities and moderately high ∼103-104K temperatures. We describe here a complete analysis framework for the velocimetry (VISAR) and pyrometry (SOP) data produced in these experiments. Since the precompression increases the initial density of both the sample of interest and the quartz reference for pressure-density, reflectivity, and temperature measurements, we describe analytical corrections based on available experimental data on warm dense silica and density-functional-theory based molecular dynamics computer simulations. Using our improved analysis framework, we report a re-analysis of previously published data on warm dense hydrogen and helium, compare the newly inferred pressure, density, and temperature data with most advanced equation of state models and provide updated reflectivity values.

The Flexible Imaging Diffraction Diagnostic for Laser Experiments (FIDDLE) is a new diagnostic at the National Ignition Facility (NIF) designed to observe in situ solid-solid phase changes at high pressures using time resolved x-ray diffraction. FIDDLE currently incorporates five Icarus ultrafast x-ray imager sensors that take 2 ns snapshots and can be tuned to collect X-rays for tens of ns. The platform utilizes the laser power at NIF for both the laser drive and the generation of 10 keV X-rays for ∼10 ns using a Ge backlighter foil. We aim to use FIDDLE to observe diffraction at different times during compression to probe the kinetics of phase changes. Pb undergoes two solid-solid phase transitions during ramp compression: from face centered cubic (FCC) to hexagonal close packed (HCP) and HCP to body centered cubic (BCC). Results will be reported on some of the first shots using the FIDDLE diagnostic at NIF on ramp compressed Pb to a peak pressure of ∼110 GPa and a single undriven CeO2 calibration shot. A discussion of the uncertainties in the observed diffraction is included., (© 2024 Author(s). Published under an exclusive license by AIP Publishing.)

This report details the analyses and related uncertainties in measuring longitudinal-stress-density paths in indirect laser-driven ramp equation-of-state (EOS) experiments [Smith et al., Nat. Astron. 2(6), 452-458 (2018); Smith et al., Nature 511(7509), 330-333 (2014); Fratanduono et al., Science 372(6546), 1063-1068 (2021); and Fratanduono et al., Phys. Rev. Lett. 124(1), 015701 (2020)]. Experiments were conducted at the National Ignition Facility (NIF) located at the Lawrence Livermore National Laboratory. The NIF can deliver up to 2 MJ of laser energy over 30 ns and provide the necessary laser power and control to ramp compress materials to TPa pressures (1 TPa = 10 × 106 atmospheres). These data provide low-temperature solid-state EOS data relevant to the extreme conditions found in the deep interiors of giant planets. In these experiments, multi-stepped samples with thicknesses in the range of 40-120 µm experience an initial shock compression followed by a time-dependent ramp compression to peak pressure. Interface velocity measurements from each thickness combine to place a constraint on the Lagrangian sound speed as a function of particle velocity, which in turn allows for the determination of a continuous stress-density path to high levels of compressibility. In this report, we present a detailed description of the experimental techniques and measurement uncertainties and describe how these uncertainties combine to place a final uncertainty in both stress and density. We address the effects of time-dependent deformation and the sensitivity of ramp EOS techniques to the onset of phase transformations., (© 2023 Author(s). Published under an exclusive license by AIP Publishing.)

Triple bonding in the nitrogen molecule (N_{2}) is among the strongest chemical bonds with a dissociation enthalpy of 9.8  eV/molecule. Nitrogen is therefore an excellent test bed for theoretical and numerical methods aimed at understanding how bonding evolves under the influence of the extreme pressures and temperatures of the warm dense matter regime. Here, we report laser-driven shock experiments on fluid molecular nitrogen up to 800 GPa and 4.0  g/cm^{3}. Line-imaging velocimetry measurements and impedance matching method with a quartz reference yield shock equation of state data of initially precompressed nitrogen. Comparison with numerical simulations using path integral Monte Carlo and density functional theory molecular dynamics reveals clear signatures of chemical dissociation and the onset of L-shell ionization. Combining data along multiple shock Hugoniot curves starting from densities between 0.76 and 1.29  g/cm^{3}, our study documents how pressure and density affect these changes in chemical bonding and provides benchmarks for future theoretical developments in this regime, with applications for planetary interior modeling, high energy density science, and inertial confinement fusion research.

The discovery of more than 4500 extrasolar planets has created a need for modeling their interior structure and dynamics. Given the prominence of iron in planetary interiors, we require accurate and precise physical properties at extreme pressure and temperature. A first-order property of iron is its melting point, which is still debated for the conditions of Earth’s interior. We used high-energy lasers at the National Ignition Facility and in situ x-ray diffraction to determine the melting point of iron up to 1000 gigapascals, three times the pressure of Earth’s inner core. We used this melting curve to determine the length of dynamo action during core solidification to the hexagonal close-packed (hcp) structure. We find that terrestrial exoplanets with four to six times Earth’s mass have the longest dynamos, which provide important shielding against cosmic radiation.

Time-resolved radiography can be used to obtain absolute shock Hugoniot states by simultaneously measuring at least two mechanical parameters of the shock, and this technique is particularly suitable for one-dimensional converging shocks where a single experiment probes a range of pressures as the converging shock strengthens. However, at sufficiently high pressures, the shocked material becomes hot enough that the x-ray opacity falls significantly. If the system includes a Lagrangian marker such that the mass within the marker is known, this additional information can be used to constrain the opacity as well as the Hugoniot state. In the limit that the opacity changes only on shock heating, and not significantly on subsequent isentropic compression, the opacity of the shocked material can be determined uniquely. More generally, it is necessary to assume the form of the variation of opacity with isentropic compression or to introduce multiple marker layers. Alternatively, assuming either the equation of state or the opacity, the presence of a marker layer in such experiments enables the non-assumed property to be deduced more accurately than from the radiographic density reconstruction alone. An example analysis is shown for measurements of a converging shock wave in polystyrene at the National Ignition Facility.

Radiography of low-contrast features in high-density materials evolving on a nanosecond timescale requires a bright photon source in the tens of keV range with high temporal and spatial resolution. One application for sources in this category is the study of dynamic material strength in samples compressed to Mbar pressures at the National Ignition Facility, high-resolution measurements of plastic deformation under conditions relevant to meteor impacts, geophysics, armor development, and inertial confinement fusion. We present radiographic data and the modulation transfer function (MTF) analysis of a multi-component test object probed at ∼100 keV effective backlighter energy using a 5 μm-thin dysprosium foil driven by the NIF Advanced Radiographic Capability (ARC) short-pulse laser (∼2 kJ, 10 ps). The thin edge of the foil acts as a bright line-projection source of hard x rays, which images the test object at 13.2× magnification into a filtered and shielded image plate detector stack. The system demonstrates a superior contrast of shallow (5 μm amplitude) sinusoidal ripples on gold samples up to 90 μm thick as well as enhanced spatial and temporal resolution using only a small fraction of the laser energy compared to an existing long-pulse-driven backlighter used routinely at the NIF for dynamic strength experiments.

Carbon is the fourth-most prevalent element in the Universe and essential for all known life. In the elemental form it is found in multiple allotropes, including graphite, diamond and fullerenes, and it has long been predicted that even more structures can exist at pressures greater than those at Earth's core 1-3 . Several phases have been predicted to exist in the multi-terapascal regime, which is important for accurate modelling of the interiors of carbon-rich exoplanets 4,5 . By compressing solid carbon to 2 terapascals (20 million atmospheres; more than five times the pressure at Earth's core) using ramp-shaped laser pulses and simultaneously measuring nanosecond-duration time-resolved X-ray diffraction, we found that solid carbon retains the diamond structure far beyond its regime of predicted stability. The results confirm predictions that the strength of the tetrahedral molecular orbital bonds in diamond persists under enormous pressure, resulting in large energy barriers that hinder conversion to more-stable high-pressure allotropes 1,2 , just as graphite formation from metastable diamond is kinetically hindered at atmospheric pressure. This work nearly doubles the highest pressure at which X-ray diffraction has been recorded on any material.

We study nonideal mixing effects in the regime of warm dense matter (WDM) by computing the shock Hugoniot curves of BN, MgO, and MgSiO 3 . First, we derive these curves from the equations of state (EOS) of the fully interacting systems, which were obtained using a combination of path integral Monte Carlo calculations at high temperature and density functional molecular dynamics simulations at lower temperatures. We then use the ideal mixing approximation at constant pressure and temperature to rederive these Hugoniot curves from the EOS tables of the individual elements. We find that the linear mixing approximation works remarkably well at temperatures above ∼2 × 10 5 K, where the shock compression ratio exceeds ∼3.2. The shape of the Hugoniot curve of each compound is well reproduced. Regions of increased shock compression, which emerge because of the ionization of L and K shell electrons, are well represented, and the maximum compression ratio of the Hugoniot curves is reproduced with high precision. Some deviations are seen near the onset of the L shell ionization regime, where ionization equilibrium in the fully interacting system cannot be well reproduced by the ideal mixing approximation. This approximation also breaks down at lower temperatures, where chemical bonds play an increasingly important role. However, the results imply that the equilibrium properties of binary and ternary mixtures in the regime of WDM can be derived from the EOS tables of the individual elements. This significantly simplifies the characterization of binary and ternary mixtures in the WDM and plasma phases, which otherwise requires large numbers of more computationally expensive first-principles computer simulations.

White dwarfs represent the final state of evolution for most stars 1-3 . Certain classes of white dwarfs pulsate 4,5 , leading to observable brightness variations, and analysis of these variations with theoretical stellar models probes their internal structure. Modelling of these pulsating stars provides stringent tests of white dwarf models and a detailed picture of the outcome of the late stages of stellar evolution 6 . However, the high-energy-density states that exist in white dwarfs are extremely difficult to reach and to measure in the laboratory, so theoretical predictions are largely untested at these conditions. Here we report measurements of the relationship between pressure and density along the principal shock Hugoniot (equations describing the state of the sample material before and after the passage of the shock derived from conservation laws) of hydrocarbon to within five per cent. The observed maximum compressibility is consistent with theoretical models that include detailed electronic structure. This is relevant for the equation of state of matter at pressures ranging from 100 million to 450 million atmospheres, where the understanding of white dwarf physics is sensitive to the equation of state and where models differ considerably. The measurements test these equation-of-state relations that are used in the modelling of white dwarfs and inertial confinement fusion experiments 7,8 , and we predict an increase in compressibility due to ionization of the inner-core orbitals of carbon. We also find that a detailed treatment of the electronic structure and the electron degeneracy pressure is required to capture the measured shape of the pressure-density evolution for hydrocarbon before peak compression. Our results illuminate the equation of state of the white dwarf envelope (the region surrounding the stellar core that contains partially ionized and partially degenerate non-ideal plasmas), which is a weak link in the constitutive physics informing the structure and evolution of white dwarf stars 9 .

Atom-in-jellium calculations of the Einstein frequency were used to calculate the mean displacement of an ion over a wide range of compression and temperature. Expressed as a fraction of the Wigner-Seitz radius, the displacement is a measure of the asymptotic freedom of the ion at high temperature, and thus of the change in heat capacity from six to three quadratic degrees of freedom per atom. A functional form for free energy was proposed based on the Maxwell-Boltzmann distribution as a correction to the Debye free energy, with a single free parameter representing the effective density of potential modes to be saturated. This parameter was investigated using molecular dynamics simulations, and found to be ∼0.2 per atom. In this way, the ion-thermal contribution can be calculated for a wide-range equation of state (EOS) without requiring a large number of molecular dynamics simulations. Example calculations were performed for carbon, including the sensitivity of key EOS loci to ionic freedom.

We report details of an experimental platform implemented at the National Ignition Facility to obtain in situ powder diffraction data from solids dynamically compressed to extreme pressures. Thin samples are sandwiched between tamper layers and ramp compressed using a gradual increase in the drive-laser irradiance. Pressure history in the sample is determined using high-precision velocimetry measurements. Up to two independently timed pulses of x rays are produced at or near the time of peak pressure by laser illumination of thin metal foils. The quasi-monochromatic x-ray pulses have a mean wavelength selectable between 0.6 Å and 1.9 Å depending on the foil material. The diffracted signal is recorded on image plates with a typical 2θ x-ray scattering angle uncertainty of about 0.2° and resolution of about 1°. Analytic expressions are reported for systematic corrections to 2θ due to finite pinhole size and sample offset. A new variant of a nonlinear background subtraction algorithm is described, which has been used to observe diffraction lines at signal-to-background ratios as low as a few percent. Variations in system response over the detector area are compensated in order to obtain accurate line intensities; this system response calculation includes a new analytic approximation for image-plate sensitivity as a function of photon energy and incident angle. This experimental platform has been used up to 2 TPa (20 Mbar) to determine the crystal structure, measure the density, and evaluate the strain-induced texturing of a variety of compressed samples spanning periods 2-7 on the periodic table.

Ramp compression along a low-temperature adiabat offers a unique avenue to explore the physical properties of materials at the highest densities of their solid form, a region inaccessible by single shock compression. Using the National Ignition Facility and OMEGA laser facilities, copper samples were ramp compressed to peak pressures of 2.30 TPa and densities of nearly 30  g/cc, providing fundamental information regarding the compressibility and phase of copper at pressures more than 5 times greater than previously explored. Through x-ray diffraction measurements, we find that the ambient face-centered-cubic structure is preserved up to 1.15 TPa. The ramp compression equation-of-state measurements shows that there are no discontinuities in sound velocities up to 2.30 TPa, suggesting this phase is likely stable up to the peak pressures measured, as predicted by first-principal calculations. The high precision of these quasiabsolute measurements enables us to provide essential benchmarks for advanced computational studies on the behavior of dense monoatomic materials under extreme conditions that constitute a stringent test for solid-state quantum theory. We find that both density-functional theory and the stabilized jellium model, which assumes that the ionic structure can be replaced by an ionic charge distribution by constant positive-charge background, reproduces our data well. Further, our data could serve to establish new international secondary scales of pressure in the terapascal range that is becoming experimentally accessible with advanced static and dynamic compression techniques.

We study the high-pressure strength of Pb and Pb-4wt%Sb at the National Ignition Facility. We measure Rayleigh-Taylor growth of preformed ripples ramp compressed to ∼400  GPa peak pressure, among the highest-pressure strength measurements ever reported on any platform. We find agreement with 2D simulations using the Improved Steinberg-Guinan strength model for body-centered-cubic Pb; the Pb-4wt%Sb alloy behaves similarly within the error bars. The combination of high-rate, pressure-induced hardening and polymorphism yield an average inferred flow stress of ∼3.8  GPa at high pressure, a ∼250-fold increase, changing Pb from soft to extremely strong.

In the canonical ramp compression experiment, a smoothly increasing load is applied to the surface of the sample, and the particle velocity history is measured at two or more different distances into the sample, at interfaces where the surface of the sample can be probed. The velocity histories are used to deduce a stress-density relation, usually using iterative Lagrangian analysis to account for the perturbing effect of the impedance mismatch at the interface. In that technique, a stress-density relation is assumed in order to correct for the perturbation and is adjusted until it becomes consistent with the deduced stress-density relation. This process is subject to the usual difficulties of nonlinear optimization, such as the existence of local minima (sensitivity to the initial guess), possible failure to converge, and relatively large computational effort. We show that, by considering the interaction of successive characteristics reaching a free surface, the stress-density relation can be deduced directly by recursion rather than iteration. This calculation is orders of magnitude faster than iterative analysis and does not require an initial guess. Direct recursion may be less suitable for very noisy data, but it was robust when applied to trial data. The stress-density relation deduced was identical to the result from iterative Lagrangian analysis.

Recent path-integral Monte Carlo and quantum molecular dynamics simulations have shown that computationally efficient average-atom models can predict thermodynamic states in warm dense matter to within a few percent. One such atom-in-jellium model has typically been used to predict the electron-thermal behavior only, although it was previously developed to predict the entire equation of state (EOS). We report completely atom-in-jellium EOS calculations for Be, Al, Si, Fe, and Mo, as elements representative of a range of atomic number and low-pressure electronic structure. Comparing the more recent method of pseudoatom molecular dynamics, atom-in-jellium results were similar: sometimes less accurate, sometimes more. All these techniques exhibited pronounced effects of electronic shell structure in the shock Hugoniot which are not captured by Thomas-Fermi based EOS. These results demonstrate the value of a hierarchical approach to EOS construction, using average-atom techniques with shell structure to populate a wide-range EOS surface efficiently, complemented by more rigorous three-dimensional multiatom calculations to validate and adjust the EOS.

Since Bridgman's discovery of five solid water (H 2 O) ice phases 1 in 1912, studies on the extraordinary polymorphism of H 2 O have documented more than seventeen crystalline and several amorphous ice structures 2,3 , as well as rich metastability and kinetic effects 4,5 . This unique behaviour is due in part to the geometrical frustration of the weak intermolecular hydrogen bonds and the sizeable quantum motion of the light hydrogen ions (protons). Particularly intriguing is the prediction that H 2 O becomes superionic 6-12 -with liquid-like protons diffusing through the solid lattice of oxygen-when subjected to extreme pressures exceeding 100 gigapascals and high temperatures above 2,000 kelvin. Numerical simulations suggest that the characteristic diffusion of the protons through the empty sites of the oxygen solid lattice (1) gives rise to a surprisingly high ionic conductivity above 100 Siemens per centimetre, that is, almost as high as typical metallic (electronic) conductivity, (2) greatly increases the ice melting temperature 7-13 to several thousand kelvin, and (3) favours new ice structures with a close-packed oxygen lattice 13-15 . Because confining such hot and dense H 2 O in the laboratory is extremely challenging, experimental data are scarce. Recent optical measurements along the Hugoniot curve (locus of shock states) of water ice VII showed evidence of superionic conduction and thermodynamic signatures for melting 16 , but did not confirm the microscopic structure of superionic ice. Here we use laser-driven shockwaves to simultaneously compress and heat liquid water samples to 100-400 gigapascals and 2,000-3,000 kelvin. In situ X-ray diffraction measurements show that under these conditions, water solidifies within a few nanoseconds into nanometre-sized ice grains that exhibit unambiguous evidence for the crystalline oxygen lattice of superionic water ice. The X-ray diffraction data also allow us to document the compressibility of ice at these extreme conditions and a temperature- and pressure-induced phase transformation from a body-centred-cubic ice phase (probably ice X) to a novel face-centred-cubic, superionic ice phase, which we name ice XVIII 2,17 .

We have developed an experimental platform for the National Ignition Facility that uses spherically converging shock waves for absolute equation-of-state (EOS) measurements along the principal Hugoniot. In this Letter, we present one indirect-drive implosion experiment with a polystyrene sample that employs radiographic compression measurements over a range of shock pressures reaching up to 60 Mbar (6 TPa). This significantly exceeds previously published results obtained on the Nova laser [R. Cauble et al., Phys. Rev. Lett. 80, 1248 (1998)PRLTAO0031-900710.1103/PhysRevLett.80.1248] at a strongly improved precision, allowing us to discriminate between different EOS models. We find excellent agreement with Kohn-Sham density-functional-theory-based molecular dynamics simulations.

The canonical high pressure equation of state measurement is to induce a shock wave in the sample material and measure two mechanical properties of the shocked material or shock wave. For accurate measurements, the experiment is normally designed to generate a planar shock which is as steady as possible in space and time, and a single state is measured. A converging shock strengthens as it propagates, so a range of shock pressures is induced in a single experiment. However, equation of state measurements must then account for spatial and temporal gradients. We have used x-ray radiography of spherically converging shocks to determine states along the shock Hugoniot. The radius-time history of the shock, and thus its speed, was measured by radiographing the position of the shock front as a function of time using an x-ray streak camera. The density profile of the shock was then inferred from the x-ray transmission at each instant of time. Simultaneous measurement of the density at the shock front and the shock speed determines an absolute mechanical Hugoniot state. The density profile was reconstructed using the known, unshocked density which strongly constrains the density jump at the shock front. The radiographic configuration and streak camera behavior were treated in detail to reduce systematic errors. Measurements were performed on the Omega and National Ignition Facility lasers, using a hohlraum to induce a spatially uniform drive over the outside of a solid, spherical sample and a laser-heated thermal plasma as an x-ray source for radiography. Absolute shock Hugoniot measurements were demonstrated for carbon-containing samples of different composition and initial density, up to temperatures at which K-shell ionization reduced the opacity behind the shock. Here we present the experimental method using measurements of polystyrene as an example.

This corrects the article DOI: 10.1103/PhysRevLett.119.175702.

Nanosecond in situ x-ray diffraction and simultaneous velocimetry measurements were used to determine the crystal structure and pressure, respectively, of ramp-compressed aluminum at stress states between 111 and 475 GPa. The solid-solid Al phase transformations, fcc-hcp and hcp-bcc, are observed at 216±9 and 321±12  GPa, respectively, with the bcc phase persisting to 475 GPa. The high-pressure crystallographic texture of the hcp and bcc phases suggests close-packed or nearly close-packed lattice planes remain parallel through both transformations.

We have performed spectrally resolved x-ray scattering measurements on highly compressed polystyrene at pressures of several tens of TPa (100 Mbar) created by spherically convergent shocks at the National Ignition Facility. Scattering data of line radiation at 9.0 keV were recorded from the dense plasma shortly after shock coalescence. Accounting for spatial gradients, opacity effects, and source broadening, we demonstrate the sensitivity of the elastic scattering component to carbon K-shell ionization while at the same time constraining the temperature of the dense plasma. For six times compressed polystyrene, we find an average temperature of 86 eV and carbon ionization state of 4.9, indicating that widely used ionization models need revision in order to be suitable for the extreme states of matter tested in our experiment.

The melting of bismuth in response to shock compression has been studied using in situ femtosecond x-ray diffraction at an x-ray free electron laser. Both solid-solid and solid-liquid phase transitions are documented using changes in discrete diffraction peaks and the emergence of broad, liquid scattering upon release from shock pressures up to 14 GPa. The transformation from the solid state to the liquid is found to occur in less than 3 ns, very much faster than previously believed. These results are the first quantitative measurements of a liquid material obtained on shock release using x-ray diffraction, and provide an upper limit for the time scale of melting of bismuth under shock loading.

We report direct in situ measurements of the crystal structure of tin between 0.12 and 1.2 TPa, the highest stress at which a crystal structure has ever been observed. Using angle-dispersive powder x-ray diffraction, we find that dynamically compressed Sn transforms to the body-centered-cubic (bcc) structure previously identified by ambient-temperature quasistatic-compression studies and by zero-kelvin density-functional theory predictions between 0.06 and 0.16 TPa. However, we observe no evidence for the hexagonal close-packed (hcp) phase found by those studies to be stable above 0.16 TPa. Instead, our results are consistent with bcc up to 1.2 TPa. We conjecture that at high temperature bcc is stabilized relative to hcp due to differences in vibrational free energy.

We have measured the time-resolved x-ray continuum emission spectrum of ∼30 times compressed polystyrene created at stagnation of spherically convergent shock waves within the Gbar fundamental science campaign at the National Ignition Facility. From an exponential emission slope between 7.7 keV and 8.1 keV photon energy and using an emission model which accounts for reabsorption, we infer an average electron temperature of 375 ± 21 eV, which is in good agreement with HYDRA-1D simulations.

The ultrafast evolution of microstructure is key to understanding high-pressure and strain-rate phenomena. However, the visualization of lattice dynamics at scales commensurate with those of atomistic simulations has been challenging. Here, we report femtosecond x-ray diffraction measurements unveiling the response of copper to laser shock-compression at peak normal elastic stresses of ~73 gigapascals (GPa) and strain rates of 10(9) per second. We capture the evolution of the lattice from a one-dimensional (1D) elastic to a 3D plastically relaxed state within a few tens of picoseconds, after reaching shear stresses of 18 GPa. Our in situ high-precision measurement of material strength at spatial (<1 micrometer) and temporal (<50 picoseconds) scales provides a direct comparison with multimillion-atom molecular dynamics simulations.

Dynamic compression by multiple shocks is used to compress iron up to 560 GPa (5.6 Mbar), the highest solid-state pressure yet attained for iron in the laboratory. Extended x-ray absorption fine structure (EXAFS) spectroscopy offers simultaneous density, temperature, and local-structure measurements for the compressed iron. The data show that the close-packed structure of iron is stable up to 560 GPa, the temperature at peak compression is significantly higher than expected from pure compressive work, and the dynamic strength of iron is many times greater than the static strength based on lower pressure data. The results provide the first constraint on the melting line of iron above 400 GPa.

We report on a focusing x-ray diffraction geometry capable of high-resolution in situ lattice probing from dynamically loaded polycrystalline and amorphous materials. The Seeman-Bohlin-type camera presented here is ideally suited for time-resolved x-ray diffraction measurements performed on high energy multibeam laser platforms. Diffraction from several lattice planes of ablatively shock-loaded 25 mum thick Cu foils was recorded on a focusing circle of diameter D=100 mm with exceptional angular resolution limited only by the spectral broadening of the x-ray source. Excellent agreement was found between the density measured using x-ray diffraction and that inferred from Doppler velocimetry and the known shock Hugoniot of Cu. In addition, x-ray diffraction signal was captured from an amorphous material under static conditions.

We derive expressions for shock formation based on the local curvature of the flow characteristics during dynamic compression. Given a specific ramp adiabat, calculated for instance from the equation of state for a substance, the ideal nonlinear shape for an applied ramp loading history can be determined. We discuss the region affected by lateral release, which can be presented in compact form for the ideal loading history. Example calculations are given for representative metals and plastic ablators. Continuum dynamics (hydrocode) simulations were in good agreement with the algebraic forms. Example applications are presented for several classes of laser-loading experiment, identifying conditions where shocks are desired but not formed, and where long-duration ramps are desired.

Radiation hydrodynamics simulations were used to study the effect of plastic ablators in laser-driven shock experiments. The sensitivity to composition and equation of state was found to be 5%-10% in ablation pressure. As was found for metals, a laser pulse of constant irradiance gave a pressure history which decreased by several percent per nanosecond. The pressure history could be made more constant by adjusting the irradiance history. The impedance mismatch with the sample gave an increase o(100%) in the pressure transmitted into the sample, for a reduction of several tens of percent in the duration of the peak load applied to the sample, and structured the release history by adding a release step to a pressure close to the ablation pressure. Algebraic relations were found between the laser pulse duration, the ablator thickness, and the duration of the peak pressure applied to the sample, involving quantities calculated from the equations of state of the ablator and sample using shock dynamics.

The Gibbs free energies of bcc and fcc Mo are calculated from first principles in the quasiharmonic approximation in the pressure range from 350 to 850 GPa at room temperatures up to 7500 K. It is found that Mo, stable in the bcc phase at low temperatures, has lower free energy in the fcc structure than in the bcc phase at elevated temperatures. Our density-functional-theory-based molecular dynamics simulations demonstrate that fcc melts at higher than bcc temperatures above 1.5 Mbar. Our calculated melting temperatures and bcc-fcc boundary are consistent with the Mo Hugoniot sound speed measurements. We find that melting occurs at temperatures significantly above the bcc-fcc boundary. This suggests an explanation of the recent diamond anvil cell experiments, which find a phase boundary in the vicinity of our extrapolated bcc-fcc boundary.

X-ray diffraction was demonstrated from shock-compressed polycrystalline metals on nanosecond time scales. Laser ablation was used to induce shock waves in polycrystalline foils of Be, 25-125 microm thick. A second laser pulse was used to generate a plasma x-ray source by irradiation of a Ti foil. The x-ray source was collimated to produce a beam of controllable diameter, which was directed at the Be sample. X-rays were diffracted from the sample, and detected using films and x-ray streak cameras. The diffraction angle was observed to change with shock pressure. The diffraction angles were consistent with the uniaxial (elastic) and isotropic (plastic) compressions expected for the loading conditions used. Polycrystalline diffraction will be used to measure the response of the crystal lattice to high shock pressures and through phase changes.

The hydrodynamic operation of the "Forest Flyer" type of explosive launching system for shock physics projectiles was investigated in detail using one and two dimensional continuum dynamics simulations. The simulations were numerically converged and insensitive to uncertainties in the material properties; they reproduced the speed of the projectile and the shape of its rear surface. The most commonly used variant, with an Al alloy case, was predicted to produce a slightly curved projectile, subjected to some shock heating and likely exhibiting some porosity from tensile damage. The curvature is caused by a shock reflected from the case; tensile damage is caused by the interaction of the Taylor wave pressure profile from the detonation wave with the free surface of the projectile. The simulations gave only an indication of tensile damage in the projectile, as damage is not understood well enough for predictions in this loading regime. The flatness can be improved by using a case of lower shock impedance, such as polymethyl methacrylate. High-impedance cases, including Al alloys but with denser materials improving the launching efficiency, can be used if designed according to the physics of oblique shock reflection, which indicates an appropriate case taper for any combination of explosive and case material. The tensile stress induced in the projectile depends on the relative thickness of the explosive, expansion gap, and projectile. The thinner the projectile with respect to the explosive, the smaller the tensile stress. Thus if the explosive is initiated with a plane wave lens, the tensile stress is lower than that for initiation with multiple detonators over a plane. The previous plane wave lens designs did, however, induce a tensile stress close to the spall strength of the projectile. The tensile stress can be reduced by changes in the component thicknesses. Experiments verifying the operation of explosively launched projectiles should attempt to measure porosity induced in the projectile: arrival time measurements are likely to be insensitive to porous regions caused by damaged or recollected material.

We investigate the microscopic melting process of a superheated argon solid using molecular dynamics simulations. We characterize the melting dynamics by following the temperature and time evolutions of liquid atoms and demonstrate the formation of a critical liquid nucleus via fluctuations and subsequent growth. The critical liquid nucleus size (about 120 atoms) obtained from our direct simulations is in accord with the prediction of the classical nucleation theory. The dynamic nucleation and growth of liquid also agree with the Johnson-Mehl-Avrami law, and the growth exponent n approximately 3 at the early stage followed by a substantial increase in n thereafter.

We report a novel crystalline carbon-cage structure synthesized from laser-driven shock wave loading of a graphite-copper mixture to about 14+/-2 GPa and 1000 +/- 200 K. Quite unexpectedly, it can be structurally related to an extremely compressed three-dimensional C60 polymer with random displacement of C atoms around average positions equivalent to those of distorted C60 cages. Thus, the present carbon-cage structure represents a structural crossing point between graphite interlayer bridging and C60 polymerization as the two ways of forming diamond from two-dimensional and molecular carbon.

The TRIDENT laser was used to induce quasi-isentropic compression waves to approximately 15 GPa in samples of Si, by ablative loading using a laser pulse whose intensity increased smoothly over 2.5 ns. The intensity history of the pulse and the velocity history at the opposite surface of the sample were recorded. Experiments were performed using samples of two different thicknesses simultaneously, in which the evolution of the compression wave was clearly visible. Isentropic stress states deduced were consistent with the previously investigated response of Si to uniaxial loading. The ablative loading was simulated using radiation hydrodynamics, with different equations of state in the plasma and condensed regions and including elasticity in the solid Si. These calculations reproduced the measured velocity histories quite well, demonstrating that quasi-isentropic compression was induced with no preheat from the laser drive. Normal continuum behavior was demonstrated to hold below nanosecond time scales for isentropic compression waves, with no evidence for nonequilibrium effects in the crystal lattice. Details of the velocity history over about 10 GPa were reproduced less well, suggesting a deficiency in the model used for compressed Si, which may be consistent with recent theoretical predictions of uniaxial compression at high strain rates.

We examine the Lindemann melting law at different pressures using the vibrational density of states (DOS), equilibrium melting curve, and Lindemann parameter delta(L) (fractional root-mean-squared displacement, rmsd, at equilibrium melting) calculated independently from molecular dynamics simulations of the Lennard-Jones system. The DOS is obtained using spectra analysis of atomic velocities and accounts for anharmonicity. The increase of delta(L) with pressure is non-negligible: delta(L) is about 0.116 and 0.145 at ambient and extreme pressures, respectively. If the component of rmsd normal to a reflecting plane as in the Debye-Waller-factor-type measurements using x rays is adopted for delta(L), these values are about 0.067 (+/-0.002) and 0.084 (+/-0.003), and are comparable with experimental and calculated values for face-centered-cubic elements. We find that the Lindemann relation holds accurately at ambient and high pressures. The non-negligible pressure dependence of delta(L) suggests that caution should be exerted in applying the Lindemann law to obtaining the high pressure melting curve anchored at ambient pressure.

We investigated the asymmetry between superheating and supercooling in solid-liquid transitions using two Landau-type models for the first-order phase transitions, the Landau-Devonshire and Landau-de Gennes models. The Landau models reproduced the asymmetric behavior described by the classical nucleation theory.

Nonequilibrium melting and crystallization of a model Lennard-Jones system were investigated with molecular dynamics simulations to quantify the maximum superheating/supercooling at fixed pressure, and over-pressurization/over-depressurization at fixed temperature. The temperature and pressure hystereses were found to be equivalent with regard to the Gibbs free energy barrier for nucleation of liquid or solid. These results place upper bounds on hysteretic effects of solidification and melting in high heating- and strain-rate experiments such as shock wave loading and release. The authors also demonstrate that the equilibrium melting temperature at a given pressure can be obtained directly from temperatures at the maximum superheating and supercooling on the temperature hysteresis; this approach, called the hysteresis method, is a conceptually simple and computationally inexpensive alternative to solid-liquid coexistence simulation and thermodynamic integration methods, and should be regarded as a general method. We also found that the extent of maximum superheating/supercooling is weakly pressure dependent, and the solid-liquid interfacial energy increases with pressure. The Lindemann fractional root-mean-squared displacement of solid and liquid at equilibrium and extreme metastable states is quantified, and is predicted to remain constant (0.14) at high pressures for solid at the equilibrium melting temperature., ((c) 2004 American Institute of Physics.)

Different methods were compared for constructing models of the behavior of a prototype intermetallic compound, nickel aluminide, for use in radiation hydrodynamics simulations of shock wave generation by ablation induced by laser energy. The models included the equation of state, ionization, and radiation opacity. The methods of construction were evaluated by comparing the results of simulations of an ablatively generated shock wave in a sample of the alloy. The most accurate simulations were obtained using the "constant number density" mixture model to calculate the equation of state and opacity, and Thomas-Fermi ionization. This model is consistent with that found to be most accurate for simulations of ablatively shocked elements.

The Trident laser was used to induce shock waves in samples of solid elements, with atomic numbers ranging from Be to Au, using pulses of 527 nm light around 1 ns long with irradiances of the order of 0.1 to 10 PW/m(2). States induced by the resulting ablation process were investigated using laser Doppler velocimetry to measure the velocity history of the opposite surface. By varying the energy in the laser pulse, relations were inferred between the irradiance and the induced pressure. For samples in vacuo, an irradiance constant in time does not produce a constant pressure. Radiation hydrodynamics simulations were used to investigate the relationship between the precise pulse shape and the pressure history. In this regime of time and irradiance, it was possible to reproduce the experimental data to within their uncertainty by including conductivity-dependent deposition of laser energy, heat conduction, gray radiation diffusion, and three temperature hydrodynamics in the treatment of the plasma, with ionizations calculated using the Thomas-Fermi equation. States induced in the solid sample were fairly insensitive to the details of modeling in the plasma, so Hugoniot points may be estimated from experiments of this type given a reasonable model of the plasma. More useful applications include the generation of dynamic loading to investigate compressive strength and phase transitions, and for sample recovery.

We have used x-ray diffraction with subnanosecond temporal resolution to measure the lattice parameters of orthogonal planes in shock compressed single crystals of silicon (Si) and copper (Cu). Despite uniaxial compression along the (400) direction of Si reducing the lattice spacing by nearly 11%, no observable changes occur in planes with normals orthogonal to the shock propagation direction. In contrast, shocked Cu shows prompt hydrostaticlike compression. These results are consistent with simple estimates of plastic strain rates based on dislocation velocity data.