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.
A general formulation was developed to represent material models for applications in dynamic loading. Numerical methods were devised to calculate response to shock and ramp compression, and ramp decompression, generalizing previous solutions for scalar equations of state. The numerical methods were found to be flexible and robust, and matched analytic results to a high accuracy. The basic ramp and shock solution methods were coupled to solve for composite deformation paths, such as shock-induced impacts, and shock interactions with a planar interface between different materials. These calculat…
Ramp compression experiments characterize high-pressure states of matter at temperatures well below those present in shock compression. However, because temperature is typically not directly measured during ramp compression, it is uncertain how much heating occurs under these shock-free conditions. Here, we performed a series of ab initio simulations on carbon in order to match the density-stress measurements of Smith et al. [Smith, et al., Nature 511, 330 (2014)]. We considered isotropically as well as uniaxially compressed solid carbon in the diamond and BC8 phases, with and without defects,…
When a metallic specimen is plastically deformed, its underlying crystal structure must often rotate in order to comply with its macroscopic boundary conditions. There is growing interest within the dynamic compression community in exploiting x-ray diffraction measurements of lattice rotation to infer which combinations of plasticity mechanisms are operative in uniaxially shock- or ramp-compressed crystals, thus informing materials science at the greatest extremes of pressure and strain rate. However, it is not widely appreciated that several of the existing models linking rotation to slip act…
Nanocrystalline structure and strain in magnesium under extreme dynamic compression
M.N. Miheev Institute of Metal Physics, Ural Branch, Russian Academy of Sciences（俄罗斯科学院乌拉尔分校 M.N. 米赫耶夫金属物理研究所）；NANOTECH Centre, Ural Federal University（乌拉尔联邦大学 NANOTECH 中心）
Quantum molecular dynamic simulations are introduced to study the dynamical, electrical, and optical properties of carbon dioxide under dynamic compressions. The principal Hugoniot derived from the calculated equation of states is demonstrated to be well accordant with experimental results. Molecular dissociation and recombination are investigated through pair correlation functions, and decomposition of carbon dioxide is found to be between 40 and 50 GPa along the Hugoniot, where nonmetal-metal transition is observed. In addition, the optical properties of shock compressed carbon dioxide are a…
We report results of molecular dynamics simulation of shock wave propagation in silicon in [100], [110], and [111] directions obtained using a classical environment-dependent interatomic potential (EDIP). Several regimes of materials response are classified as a function of shock wave intensity using the calculated shock Hugoniot. Shock wave structure in [100] and [111] directions exhibit usual evolution as a function of piston velocity. At piston velocities km/s the shock wave consists of a fast elastic precursor followed by a slower plastic front. At larger piston velocities the single overd…
The high-pressure melting curve of tantalum (Ta) has been the center of a long-standing controversy. Sound velocities along the Hugoniot curve are expected to help in understanding this issue. To that end, we employed a direct-reverse impact technique and velocity interferometry to determine sound velocities of Ta under shock compression in the 10-110 GPa pressure range. The measured longitudinal sound velocities show an obvious kink at ~60 GPa as a function of shock pressure, while the bulk sound velocities show no discontinuity. Such observation could result from a structural transformation …
Diamond is used extensively as a component in high energy density experiments, but existing equation of state (EOS) models do not capture its observed response to dynamic loading. In particular, in contrast with first principles theoretical EOS models, no solid-solid phase changes have been detected, and no general-purpose EOS models match the measured ambient isotherm. We have performed density functional theory (DFT) calculations of the diamond phase to ~10TPa, well beyond its predicted range of thermodynamic stability, and used these results as the basis of a Mie-Greuneisen EOS. We also per…
Silicon (Si) is one of the most abundant elements on Earth, and it is the most important and widely used semiconductor, constituting the basis of modern electronic devices. Despite extensive study, some properties of Si remain elusive. For example, the behaviour of Si under high pressure, in particular at the ultra-high strain rates characteristic of dynamic compression, has been a matter of debate for decades. A detailed understanding of how Si deforms is crucial for a variety of fields, ranging from planetary science to materials design. Simulations suggest that in Si the shear stress genera…
Quantum molecular dynamic simulations have been employed to study the equation of state (EOS) of fluid helium under shock compressions. The principal Hugoniot is determined from EOS, where corrections from atomic ionization are added onto the calculated data. Our simulation results indicate that principal Hugoniot shows good agreement with gas gun and laser driven experiments, and maximum compression ratio of 5.16 is reached at 106 GPa.
Using first-principles molecular dynamics, we calculated the equation of state and shock Hugoniot of various boron phases. We find a large mismatch between Hugoniots based on existing knowledge of the equilibrium phase diagram and those measured by shock experiments, which could be reconciled if the $α$-B$_{12}$/$β\rightarrowγ$-B$_{28}$ transition is significantly over-pressurized in boron under shock compression. Our results also indicate that there exists an anomaly and negative Clapeyron slope along the melting curve of boron at 100 GPa and 1500--3000 Kelvin. These results enable in-depth u…
Quantum molecular dynamic (QMD) simulations are introduced to study the thermophysical properties of liquid deuterium under shock compression. The principal Hugoniot is determined from the equation of states, where contributions from molecular dissociation and atomic ionization are also added onto the QMD data. At pressures below 100 GPa, our results show that the local maximum compression ratio of 4.5 can be achieved at 40 GPa, which is in good agreement with magnetically driven flyer and convergent-explosive experiments; At the pressure between 100 and 300 GPa, the compression ratio reaches …
Based on his 50-year career in static high-pressure research, P. W. Bridgman (PWB) is the father of modern high-pressure physics. What is not generally recognized is that Bridgman was also intimately connected with establishing shock compression as a scientific tool and he predicted major events in shock research that occurred up to 40 years after his death. In 1956 the first phase transition under shock compression was reported in Fe at 13 GPa (130 kbar). PWB said a phase transition could not occur in a ~microsec, thus setting off a controversy. The scientific legitimacy of shock compression …
With the aid of nanosecond time-resolved X-ray diffraction techniques, we have explored the complex structural dynamics of bismuth under laser-driven compression. The results demonstrate that shocked bismuth undergoes a series of structural transformations involving four solid structures: the Bi-I, Bi-II, Bi-III and Bi-V phases. The transformation from the Bi-I phase to the Bi-V phase occurs within 4 ns under shock compression at ~11 GPa, showing no transient phases with the available experimental conditions. Successive phase transitions (Bi-V->Bi-III->Bi-II->Bi-I) during the shock release wit…
Due to its far-reaching applications in geophysics and materials science, quartz has been one of the most extensively examined materials under dynamic compression. Despite 50 years of active research, questions remain concerning the structure and transformation of SiO2 under shock compression. Continuum gas-gun studies have established that under shock loading quartz transforms through an assumed mixed-phase region to a dense high-pressure phase. While it has been often assumed that this high-pressure phase corresponds to the stishovite structure observed in static experiments, there has been …
The principal Hugoniot for liquid hydrogen was obtained up to 55 GPa under laser-driven shock loading. Pressure and density of compressed hydrogen were determined by impedance-matching to a quartz standard. The shock temperature was independently measured from the brightness of the shock front. Hugoniot data of hydrogen provide a good benchmark to modern theories of condensed matter. The initial number density of liquid hydrogen is lower than that for liquid deuterium, and this results in shock compressed hydrogen having a higher compression and higher temperature than deuterium at the same sh…
Wehrenberg et. al. [Nature 550 496 (2017)] used ultrafast in situ x-ray diffraction at the LCLS x-ray free-electron laser facility to measure large lattice rotations resulting from slip and deformation twinning in shock-compressed laser-driven [110] fibre textured tantalum polycrystal. We employ a crystal plasticity finite element method model, with slip kinetics based closely on the isotropic dislocation-based Livermore Multiscale Model [Barton et. al., J. Appl. Phys. 109 (2011)], to analyse this experiment. We elucidate the link between the degree of lattice rotation and the kinetics of plas…
When compressed, a metallic specimen will generally experience changes to its crystallographic texture due to plasticity-induced rotation. Ultrafast x-ray diffraction techniques make it possible to measure rotation of this kind in targets dynamically compressed over nanosecond timescales to the kind of pressures ordinarily encountered in planetary interiors. The axis and the extent of the local rotation can provide hints as to the combination of plasticity mechanisms activated by the rapid uniaxial compression, thus providing valuable information about the underlying dislocation kinetics opera…
We employ quantum molecular dynamic simulations to investigate the behavior of benzene under shock conditions. The principal Hugoniot derived from the equation of state is determined. We compare our firs-principles results with available experimental data and provide predictions of chemical reactions for shocked benzene. The decomposition of benzene is found under the pressure of 11 GPa. The nonmetal-metal transition, which is associated with the rapid C-H bond breaking and the formation of atomic and molecular hydrogen, occurs under the pressure around 50 GPa. Additionally, optical properties…
The properties of hot dense helium at megabar pressures were studied with two first-principles computer simulation techniques, path integral Monte Carlo and density functional molecular dynamics. The simulations predicted that the compressibility of helium is substantially increased by electronic excitations that are present in the hot fluid at thermodynamic equilibrium. A maximum compression ratio of 5.24(4)-fold the initial density was predicted for 360 GPa and 150000 K. This result distinguishes helium from deuterium, for which simulations predicted a maximum compression ratio of 4.3(1). Hu…
Shock compression plate impact experiments conventionally rely on point-wise velocimetry measurements based on laser-based interferometric techniques. This study presents an experimental methodology to measure the free surface full-field particle velocity in shock compression experiments using high-speed imaging and three-dimensional (3D) digital image correlation (DIC). The experimental setup has a temporal resolution of 100 ns with a spatial resolution varying from 90 to 200 $μ$m/pixel. Experiments were conducted under three different plate impact configurations to measure spatially resolved…
Institut de Minéralogie, de Physique des Matériaux et de Cosmochimie, Sorbonne Université, Muséum National d’Histoire Naturelle（矿物学、材料物理与宇宙化学研究所，索邦大学，国家自然历史博物馆）；ISTerre, Université Grenoble Alpes（ISTerre实验室，格勒诺布尔阿尔卑斯大学）；Laboratoire pour l’Utilisation des Lasers Intenses (LULI), Ecole Polytechnique（高强度激光利用实验室（LULI），巴黎综合理工学院）；Earth and Planetary Sciences, Stanford University（地球与行星科学系，斯坦福大学）；School of Earth and Space Exploration, Arizona State University（地球与空间探索学院，亚利桑那州立大学）；European Synchrotron Radiation Facility（欧洲同步辐射装置）
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 c…
We use dedicated microfluidic devices to expose soft hydrogel particles to a rapid change in the externally applied osmotic pressure and observe a non-monotonic response: After an initial rapid compression the particle slowly reswells to approximately its original size. Using a simple phenomenological and a more elaborate poroelastic model, we extract important material properties from a single microfluidic experiment, including the compressive modulus, the gel permeability and the diffusivity of the osmolyte inside the gel. We expect our approach to be relevant to applications such as control…
Recently, deuterium has been the focus of a high level of experimental and theoretical activity that was sparked by a disagreement on the experimental value of the maximum compression along the Hugoniot. The behavior of deuterium at Mbar pressures is not well understood. It is of great interest to understand how the current uncertainty on the hydrogen/deuterium EOS affects the inferred structures of Jupiter and Saturn. In particular, the mass of a core of heavy elements (other than H and He) and the total mass of those heavy elements in these two planets are quite sensitive to the EOS of hydro…
Solid usually becomes harder and tougher under compression, and turns softer at elevated temperature. Recently, compression-induced softening and heating-induced hardening (CISHIH) dual anomaly was predicted in group VB elements such as vanadium. Here, the evidence for this counterintuitive phenomenon is reported. By using accurate high-temperature high-pressure sound velocities measured at Hugoniot states generated by shock-waves, together with first-principles calculations, we observe not only the prominent compression-induced sound velocity reduction, but also strong heating-induced sound v…
A detailed understanding of the material response to rapid compression is challenging and demanding. For instance, the element gold under dynamic compression exhibits complex phase transformations where there exist some large discrepancies between experimental and theoretical studies. Here, we combined large-scale molecular dynamics simulations with a deep potential to elucidate the dynamic compression processes of gold from an atomic level. The potential is constructed by accurately reproducing the free energy surfaces of density-functional-theory calculations for gold, from ambient condition…
