James Hawreliak

Material dynamics under extreme conditions of pressure and strain rate

Abstract Solid state experiments at extreme pressures (10–100 GPa) and strain rates (106–108s−1) are being developed on high energy laser facilities, and offer the possibility for exploring new regimes of materials science. These extreme solid state conditions can be accessed with either shock loading or with a quasi-isentropic ramped pressure drive. Velocity interferometer measurements establish the high pressure conditions. Constitutive models for solid state strength under these conditions are tested by comparing 2D continuum simulations with experiments measuring perturbation growth from the Rayleigh–Taylor instability in solid state samples. Lattice compression, phase and temperature are deduced from extended X-ray absorption fine structure (EXAFS) measurements, from which the shock induced α–ω phase transition in Ti and the α–ϵ phase transition in Fe, are inferred to occur on subnanosec time scales. Time resolved lattice response and phase can also be measured with dynamic X-ray diffraction measurements, where the elastic–plastic (1D–3D) lattice relaxation in shocked Cu is shown to occur promptly (<1 ns). Subsequent large scale molecular dynamics (MD) simulations elucidate the microscopic dislocation dynamics that underlies this 1D–3D lattice relaxation. Deformation mechanisms are identified by examining the residual microstructure in recovered samples. The slip-twinning threshold in single crystal Cu shocked along the [001] direction is shown to occur at shock strengths of ∼20 GPa, whereas the corresponding transition for Cu shocked along the [134] direction occurs at higher shock strengths. This slip twinning threshold also depends on the stacking fault energy (SFE), being lower for low SFE materials. Designs have been developed for achieving much higher pressures, P>1000 GPa, in the solid state on the National Ignition Facility (NIF) laser.

Powder diffraction from solids in the terapascal regime

A method of obtaining powder diffraction data on dynamically compressed solids has been implemented at the Jupiter and OMEGA laser facilities. Thin powdered samples are sandwiched between diamond plates and ramp compressed in the solid phase using a gradual increase in the drive-laser intensity. The pressure history in the sample is determined by back-propagation of the measured diamond free-surface velocity. A pulse of x rays is produced at the time of peak pressure by laser illumination of a thin Cu or Fe foil and collimated at the sample plane by a pinhole cut in a Ta substrate. The diffracted signal is recorded on x-ray sensitive material, with a typical d-spacing uncertainty of ~0.01 Å. This diagnostic has been used up to 0.9 TPa (9 Mbar) to verify the solidity, measure the density, constrain the crystal structure, and evaluate the strain-induced texturing of a variety of compressed samples spanning atomic numbers from 6 (carbon) to 82 (lead). Further refinement of the technique will soon enable diffraction measurements in solid samples at pressures exceeding 1 TPa.

Analysis of the x-ray diffraction signal for the {alpha}-{epsilon} transition in shock-compressed iron: Simulation and experiment

Recent published work has shown that the phase change of shock-compressed iron along the [001] direction does transform to the {epsilon} [hexagonal close-packed (hcp)] phase similar to the case for static measurements. This article provides an in-depth analysis of the experiment and nonequilibrium molecular dynamics simulations, using x-ray diffraction in both cases to study the crystal structure upon transition. Both simulation and experiment are consistent with a compression and shuffle mechanism responsible for the phase change from body-centered cubic to hcp. Also both show a polycrystalline structure upon the phase transition, due to the four degenerate directions in which the phase change can occur.

Nanosecond white-light Laue diffraction measurements of dislocation microstructure in shock-compressed single-crystal copper

Under uniaxial high-stress shock compression it is believed that crystalline materials undergo complex, rapid, micro-structural changes to relieve the large applied shear stresses. Diagnosing the underlying mechanisms involved remains a significant challenge in the field of shock physics, and is critical for furthering our understanding of the fundamental lattice-level physics, and for the validation of multi-scale models of shock compression. Here we employ white-light X-ray Laue diffraction on a nanosecond timescale to make the first in situ observations of the stress relaxation mechanism in a laser-shocked crystal. The measurements were made on single-crystal copper, shocked along the [001] axis to peak stresses of order 50 GPa. The results demonstrate the presence of stress-dependent lattice rotations along specific crystallographic directions. The orientation of the rotations suggests that there is double slip on conjugate systems. In this model, the rotation magnitudes are consistent with defect densities of order 10(12) cm(-2).

Nanosecond x-ray Laue diffraction apparatus suitable for laser shock compression experiments

We have used nanosecond bursts of x-rays emitted from a laser-produced plasma, comprised of a mixture of mid-Z elements, to produce a quasiwhite-light spectrum suitable for performing Laue diffraction from single crystals. The laser-produced plasma emits x-rays ranging in energy from 3 to in excess of 10 keV, and is sufficiently bright for single shot nanosecond diffraction patterns to be recorded. The geometry is suitable for the study of laser-shocked crystals, and single-shot diffraction patterns from both unshocked and shocked silicon crystals are presented.

Nanosecond x-ray diffraction from polycrystalline and amorphous materials in a pinhole camera geometry suitable for laser shock compression experiments.

Nanosecond pulses of quasimonochromatic x-rays emitted from the K shell of ions within a laser-produced plasma are of sufficient spectral brightness to allow single-shot recording of powder diffraction patterns from thin foils of order millimeter diameter. Strong diffraction signals have been observed in a cylindrical pinhole camera arrangement from both polycrystalline and amorphous foils, and the experimental arrangement and foil dimensions are such that they allow for laser shocking or quasi-isentropic loading of the foil during the diffraction process.

Simulating picosecond x-ray diffraction from shocked crystals using post-processing molecular dynamics calculations

Calculations of the patterns of x-ray diffraction from shocked crystals derived from the results of non-equilibrium molecular dynamics (NEMD) simulations are presented. The atomic coordinates predicted from the NEMD simulations combined with atomic form factors are used to generate a discrete distribution of electron density. A fast Fourier transform (FFT) of this distribution provides an image of the crystal in reciprocal space, which can be further processed to produce quantitative simulated data for direct comparison with experiments that employ picosecond x-ray diffraction from laser-irradiated crystalline targets.

Single photon energy dispersive x-ray diffraction.

With the pressure range accessible to laser driven compression experiments on solid material rising rapidly, new challenges in the diagnosis of samples in harsh laser environments are emerging. When driving to TPa pressures (conditions highly relevant to planetary interiors), traditional x-ray diffraction techniques are plagued by increased sources of background and noise, as well as a potential reduction in signal. In this paper we present a new diffraction diagnostic designed to record x-ray diffraction in low signal-to-noise environments. By utilising single photon counting techniques we demonstrate the ability to record diffraction patterns on nanosecond timescales, and subsequently separate, photon-by-photon, signal from background. In doing this, we mitigate many of the issues surrounding the use of high intensity lasers to drive samples to extremes of pressure, allowing for structural information to be obtained in a regime which is currently largely unexplored.

Theory and Simulation of 1D to 3D Plastic Relaxation in Tantalum

In plane shock waves the uniaxial strain rate can greatly exceed the rate at which dislocation flow can relax the concomitant shear stress. The result is an overdriven plastic state in which the compression is 1D uniaxial initially and only after a period of time does the lattice relax to a more 3D compressed state due to plastic flow. Here we use an analytic calculation based on a generalization of the Gilman model of flow involving dislocation evolution to predict the phases of plastic relaxation and to derive an analytic estimate of the relaxation time, including a decomposition into incubation and flow times, suitable for comparison with in-situ x-ray diffraction. We use molecular dynamics (MD) to study the threshold for homogeneous nucleation both in shock compression of single crystal Ta (100). We find that shock heating on the Hugoniot substantially lowers the threshold pressure for homogeneous nucleation.

Measuring stacking fault densities in shock-compressed FCC crystals using in situ x-ray diffraction

A method is presented of in situ measurements of stacking fault densities in shocked face-centred-cubic (FCC) crystals using x-ray diffraction. Using results from both the second and fourth diffraction orders, wherein shifts in the Bragg peaks due to faulting are accounted for, we calculated fault densities present in a molecular dynamics (MD) simulation of shocked single crystal of copper. The results are in good quantitative agreement with dislocation density measurements inferred directly from the MD simulation. The x-ray diffraction method thus presents a real possibility for experimental determination in real time of dislocation densities in crystals during shock wave passage.