K. Rosolankova

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.

High-pressure, high-strain-rate lattice response of shocked materials

Laser-based shock experiments have been conducted in thin Si and Cu crystals at pressures above the published Hugoniot Elastic Limit (HEL) for these materials. In situ x-ray diffraction has been used to directly measure the response of the shocked lattice during shock loading. Static film and x-ray streak cameras recorded x rays diffracted from lattice planes both parallel and perpendicular to the shock direction. In addition, experiments were conducted using a wide-angle detector to record x rays diffracted from multiple lattice planes simultaneously. These data showed uniaxial compression of Si (100) along the shock direction and three-dimensional compression of Cu (100). In the case of the Si diffraction, there was a multiple wave structure observed. This is evaluated to determine whether there is a phase transition occurring on the time scale of the experiments, or the HEL is much higher than previously reported. Results of the measurements are presented.

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.

Multiple film plane diagnostic for shocked lattice measurements (invited)

Laser-based shock experiments have been conducted in thin Si and Cu crystals at pressures above the Hugoniot elastic limit. In these experiments, static film and x-ray streak cameras recorded x rays diffracted from lattice planes both parallel and perpendicular to the shock direction. These data showed uniaxial compression of Si(100) along the shock direction and three-dimensional compression of Cu(100). In the case of the Si diffraction, there was a multiple wave structure observed, which may be due to a one-dimensional phase transition or a time variation in the shock pressure. A new film-based detector has been developed for these in situ dynamic diffraction experiments. This large-angle detector consists of three film cassettes that are positioned to record x rays diffracted from a shocked crystal anywhere within a full π steradian. It records x rays that are diffracted from multiple lattice planes both parallel and at oblique angles with respect to the shock direction. It is a time-integrating measur...

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.

Shock Induced α‐ε Phase Change in Iron: Analysis of MD Simulations and Experiment

Multimillion atom non‐equilibrium molecular dynamics simulations for shock compressed iron are analyzed using Fourier methods to determine the long scale ordering of the crystal. By analyzing the location of the maxima in k‐space we can determine the crystal structure and compression due to the shock. This report presents results from a 19.6GPa simulated shock in single crystal iron and compare them to recent experimental results of shock compressed iron where the crystal structure was determined using in‐situ wide angle x‐ray diffraction.

Picosecond X‐Ray Diffraction from Laser‐Shocked Copper and Iron

In situ X‐ray diffraction allows the determination of the structure of transient states of matter. We have used laser‐plasma generated X‐rays to study how single crystals of metals (copper and iron) react to uniaxial shock compression. We find that copper, as a face‐centred‐cubic material, allows rapid generation and motion of dislocations, allowing close to hydrostatic conditions to be achieved on sub‐nanosecond timescales. Detailed molecular dynamics calculations provide novel information about the process, and point towards methods whereby the dislocation density might be measured during the passage of the shock wave itself. We also report on recent experiments where we have obtained diffraction images from shock‐compressed single‐crystal iron. The single crystal sample transforms to the hcp phase above a critical pressure, below which it appears to be uniaxially compressed bcc, with no evidence of plasticity. Above the transition threshold, clear evidence for the hcp phase can be seen in the diffracti...

X‐Ray Diffraction from Shocked Crystals: Experiments and Predictions of Molecular Dynamics Simulations

When a crystal is subjected to shock compression beyond its Hugoniot Elastic Limit (HEL), the deformation it undergoes is composed of elastic and plastic strain components. In situ time‐dependent X‐ray diffraction, which allows direct measurement of lattice spacings, can be used to investigate such phenomena. This paper presents recent experimental results of X‐ray diffraction from shocked fcc crystals. Comparison is made between experimental data and simulated X‐ray diffraction using a post‐processor to Molecular Dynamics (MD) simulations of shocked fcc crystals.

Direct Observation of the α‐ε Transition in Shocked Single Crystal Iron

In‐situ x‐ray diffraction was used to study the response of single crystal iron under shock conditions. Measurements of the response of [001] iron showed a uniaxial compression of the initially bcc lattice along the shock direction by up to 6% at 13 GPa. Above this pressure, the lattice responded with a further collapse of the lattice by 15–18% and a transformation to the hcp structure. The in‐situ measurements are discussed and results summarized.

Picosecond x-ray diffraction studies of shocked single crystals

The past few years have seen a rapid growth in the development and exploitation of X-ray diffraction on ultrafast time-scales. One area of physics which has benefited particularly from these advances is the the field of shock-waves. Whilst it has been known for many years that crystalline matter, subjected to uniaxial shock compression, can undergo plastic deformation and, for certain materials, polymorphic phase transformations, it has hitherto not been possible to observe the rearrangement of the atoms on the pertinent timescales. We have used laser-plasma generated X-rays to study how single crystals of metals (copper and iron) react to uniaxial shock compression, and observed rapid plastic flow (in the case of copper), and directly observed the famous alpha-epsilon transition in Iron. These studies have been complemented by large-scale multi-million atom molecular dynamics simulations, yielding significant information on the underlying physics.