Shock Hugoniot Data Research Articles

Equation of state for shock compression of distended solids

Shock Hugoniot data for full-density and porous compounds of boron carbide, silicon dioxide, tantalum pentoxide, uranium dioxide and playa alluvium are investigated for the purpose of equation-of-state representation of intense shock compression. Complications of multivalued Hugoniot behavior characteristic of highly distended solids are addressed through the application of enthalpy-based equations of state of the form originally proposed by Rice and Walsh in the late 1950's. Additive measures of cold and thermal pressure intrinsic to the Mie-Gruneisen EOS framework is replaced by isobaric additive functions of the cold and thermal specific volume components in the enthalpy-based formulation. Additionally, experimental evidence reveals enhancement of shock-induced phase transformation on the Hugoniot with increasing levels of initial distension for silicon dioxide, uranium dioxide and possibly boron carbide. Methods for addressing this experimentally observed feature of the shock compression are incorporated into the EOS model.

Shock Hugoniot measurements in foam

The present study outlines a new approach to collecting shock Hugoniot data in foams using photonic Doppler velocimetry to perform mid-plane measurements of the foam deformation. Plate impact experiments were carried out to investigate wave propagation in a closed-cell polymeric foam and an open-cell aluminum foam. Dual-wave structures were observed in both materials with the leading precursor wave determined to be an elastic wave. The discussion of the results focuses on the nature of foam compression under high-rate loading, particularly the difference between the strain history in a foam undergoing uniform stress compaction and uniaxial strain compression. These results are discussed in reference to the current interpretations of Taylor-Hopkinson bar experiments on similar metallic foams. The importance of gas-filtration driven flows in the wave dynamics of open-cell foams is discussed in relation to the nature of the precursor waves.

Shock Hugoniot equations of state for binary water-alcohol liquid mixtures

Shock Hugoniot data were obtained using laser generated shock and ultrafast dynamic ellipsometry (UDE) methods for several non-ideal water-alcohol liquid mixtures, with the alcohols being methanol, ethanol, 1-propanol, 2-propanol, 1-butanol, and t-butanol (a.k.a., 2-methyl-2-propanol or tert-butanol). The sound speeds of the mixtures were obtained using Brillouin scattering when not available in the literature. The shock and particle velocities obtained from the UDE data were compared to expectations of the universal liquid Hugoniot (ULH) and to literature shock (plate impact) data where available. The ethanol/water data were presented in a previous publication [Schulze et al., J. Phys. Chem. A 117, 6158–6163 (2013)]. The shock Hugoniot trends for all these mixtures, here represented as deviations from predictions of the ULH, versus fraction of alcohol are quite similar to each other and suggest that complex hydrogen bonding networks in alcohol-water mixtures alter the compressibility of the mixtures.

A multiphase EOS for metals using mGLJ model

A multiphase equation of state (EOS) model for metals is presented using an improved form of the modified generalized Lennard Jones (mGLJ) cold curve which can account for the solid, liquid, and vapor phase including the two phase melting and evaporation region. The mglj cold curve has been used in the past to predict some thermodynamic properties of metals in the compressive phase. According to the authors, if the EOS model satisfies certain spinodal conditions in the liquid–vapor transition region, the EOS should be applicable in the compressive as well as expansion regions. Although the EOS satisfied the spinodal conditions but its validity in the expansion region was not verified. We found that the proposed model could not predict the cohesive energy of the solid properly and hence did not match with electronic structure calculations in the expansion region. So, we propose that instead of relating the parameter ‘n’ appearing in the mglj EOS to the pressure derivative of bulk modulus, one should choose it so as to get good agreement with the experimental value of cohesive energy. In doing so, the cold curve generated matches with electronic structure based calculations in the expansion region. The proposed model has been validated against data available in literature including shock hugoniot and release isentrope data for Aluminum. The melting curve, isobaric expansion curve, liquid–vapor phase diagram and the critical parameters of Aluminum have also been predicted in this work.

Shock Hugoniot Equations of State for Binary Ideal (Toluene/Fluorobenzene) and Nonideal (Ethanol/Water) Liquid Mixtures

Laser shock Hugoniot data were obtained using ultrafast dynamic ellipsometry (UDE) for both nonideal (ethanol/water solutions with mole percent χ(ethanol) = 0%, 3.4%, 5.4%, 7.5%, 9.7%, 11%, 18%, 33%, 56%, 100%) and ideal liquid mixtures (toluene/fluorobenzene solutions with mole percent χ(toluene) = 0%, 26.0%, 49.1%, 74.9%, 100%). The shock and particle velocities obtained from the UDE data were compared to the universal liquid Hugoniot (ULH) and to literature shock (plate impact) data where available. It was found that the water UDE data fit to a ULH-form equation suggests an intercept of 1.32 km/s, lower than the literature ambient sound speed in water of 1.495 km/s (Mijakovic et al. J. Mol. Liq. 2011, 164, 66-73). Similarly, the ethanol UDE data fit to a ULH-form equation suggests an intercept of 1.45 km/s, which lies above the literature ambient sound speed in ethanol of 1.14 km/s. Both the literature plate impact and UDE Hugoniot data lie below the ULH for water. Likewise, the literature plate impact and UDE Hugoniot data lie above the ULH for ethanol. The UDE Hugoniot data for the mixtures of water and ethanol cross the predictions of the ULH near the same concentration where the sound speed reaches a maximum. In contrast, the UDE data from the ideal liquids and their mixtures are well behaved and agree with ULH predictions across the concentration range. The deviations of the nonideal ethanol/water data from the ULH suggest that complex hydrogen bonding networks in ethanol/water mixtures alter the compressibility of the mixture.

Equation of State and Evidence of Enhanced Phase Transformation for the Shock Compression of Distended Compounds

Shear stress and deformation is inherent to shock-wave compression. Shear deformation is enhanced when the material subject to shock compression is in an initial distended state. Shock Hugoniot data for full-density and porous compounds of boron carbide, silicon dioxide, tantalum oxide, uranium dioxide and playa alluvium are investigated for purposes of equation-of-state representation of intense shock compression. Hugoniot data of distended materials reveal evidence of accelerated solid-solid phase transition as a consequence of shock compaction and accompanying enhance shear deformation. A phenomenological thermo-elastic equation-of-state model is constructed that accounts for both deformation- induced phase transformation and the extreme shock compaction of distended solids, and applied to the compounds studied.

Extended data set for the equation of state of warm dense hydrogen isotopes

Laser-driven shock wave measurements on hydrogen and deuterium precompressed in diamond anvil cells from 0.16 to 1.6 GPa provide new shock Hugoniot data over a significantly broader range of density-temperature phase space than was previously achievable. Observations of shock velocity and thermal emission provide complete equation of state data (pressure, density, internal energy, and temperature) in the dense fluid regime up to 175 GPa. This data set is used to benchmark recent advanced ab initio calculations and is seen to be in good agreement with a maximum $8%$ density difference above 100 GPa. Thermodynamic quantities (specific heat and Gruneisen coefficient) are calculated directly from the data and compared to theory. Optical reflectivity data show a continuous transition from an electrically insulating to conducting fluid state and reveal that this transition is increasingly sensitive to temperature with increasing density. Ab initio calculations are observed to underestimate the temperature onset of metallization.

Equation of state and evidence of enhanced phase transformation for shock compression of distended compounds

Shear stress and deformation is inherent to shock-wave compression. Shear deformation is enhanced when the material subject to shock compression is in an initial distended state. Shock Hugoniot data for full-density and porous compounds of boron carbide, silicon dioxide, tantalum pentoxide, uranium dioxide and playa alluvium are investigated for purposes of equation-of-state representation of intense shock compression. Hugoniot data of distended materials reveal evidence of accelerated solid–solid phase transition as a consequence of shock compaction and accompanying enhanced shear deformation. A phenomenological thermo-elastic equation-of-state model is constructed that accounts for both deformation-induced phase transformation and the extreme shock compaction of distended solids, and applied to the compounds studied.

Experimental Study of Equation of State for Concrete

In order to study dynamic mechanical properties of concrete, the impact compression tests of concrete material under three different velocities are conducted using a light gas gun. Flyer and target are made of the same material, the manganin pressure gauge is used to measure the time-pressure curves of the samples. The measured time-pressure curves show that the stress peak will increase with the increase of flyer speed, and the stress peak at different locations will decrease with the increase of dissemination distance. It illustrate that concrete material has obvious rate sensitivity and energy dissipation characteristics. Then, through further analysis of the experimental data, the shock hugoniot relationship is determined, that is a linear relationship between the shock wave speed and the wave particle velocity. Based on the shock hugoniot data of the concrete, the high-pressure polynomial equation of state is fitted.

Pressure–volume–temperature equations of state of Au and Pt up to 300 GPa and 3000 K: internally consistent pressure scales

By using a Mie–Grüneisen-type analysis method, the pressure–volume–temperature equations of state (P–V–T EOSs) of Au and Pt have been determined up to 300 GPa and 3000 K based on the experimental shock Hugoniot and thermodynamic data. The calculated results of Au and Pt show an excellent agreement with available experimental volume compression data over a wide range of pressures and temperatures. A comparison of our results with previous theoretical investigations has also been done. In addition, we have further examined the consistency of our results and the P–V–T EOS of MgO [K. Jin, X.Z. Li, Q. Wu, H.Y. Geng, L.C. Cai, X.M. Zhou, and F.Q. Jing, The pressure–volume–temperature equation of state of MgO derived from shock Hugoniot data and its application as a pressure scale, J. Appl. Phys. 107 (2010), pp. 113518] using simultaneous volume measurements of Au, Pt, and MgO at various temperatures. The good agreement among the P–V–T EOSs of Au, Pt, and MgO implies that these EOSs can be used as the reliable pressure scales in high pressure–temperature diamond anvil cell experiments.

Shock-induced decomposition of a high density glass (ZF6)

The dynamic high-pressure behavior of a high density glass (ZF6) was investigated in this study. The Hugoniot data, shock temperature (TH) and release sound velocity (C) of ZF6 were measured by a time-resolved multi-channel pyrometer in the shock pressure (PH) range of 50–170 GPa. The Hugoniot data is in accord with the Los Alamos Scientific Laboratory (LASL) shock Hugoniot data and shows a good linearity over 21 GPa. Polymorphic phase transitions were identified by the kinks in the measured TH-PH and C-PH relationships. The onset pressures of the transformations are ∼75 and ∼128 GPa, respectively. A thermodynamic calculation suggests that the phase transition at 75 GPa is its disproportionation to massicot (high pressure phase of PbO) and melted silica while the transition at 128 GPa is from the melting of massicot.

Window corrections of z-cut quartz at 1550 nm under elastic, uniaxial compression up to 10 GPa

Z-cut α-quartz single crystals were shocked up to 10 GPa by symmetric impact to carefully examine their performance as an optical window in new velocity interferometers operating at 1550 nm, such as displacement interferometer system for any reflector (DISAR) [Appl. Phys. Lett. 89, 111101 (2006)]. In situ particle velocity measurements allowed the shock Hugoniot data and velocity corrections to be obtained accurately by a simple probe. The results give the elastic Hugoniot state equation as Ds = 6.270 + 1.651up, and the dependence of velocity correction (Δus) on the true particle velocity (up) at 1550 nm is well described by exponential relation Δus = 0.0948 up1.1876. By combining the velocity correction and shock velocity measurements, the relation of the refractive index (n) versus relative density (ρ/ρ0) for z-cut quartz is also determined to be n = 1.0890 + 0.4393 ρ/ρ0. The wave profile measurements also indicate that the pressure limit where z-cut quartz’s response is simple is 10.04 GPa, and it can be used as an optical window within this limit in shock experiments.

Shock compression response of a Zr-based bulk metallic glass up to 110 GPa

Shock wave compression experiments were conducted on a Zr-based bulk metallic glass (BMG, Zr51Ti5Ni10Cu25Al9 in atomic percent) up to 110 GPa. Time-resolved free-surface velocity profiles were measured in a shock stress range from 18 to 28 GPa with velocity interferometer techniques. The shock Hugoniot data in a shock stress range from 53 to 110 GPa were obtained by using electric pin techniques. The time-resolved wave profiles showed a distinct two-wave structure consisting of an elastic precursor followed by a plastic wave. Based on the obtained wave profiles, the Hugoniot elastic limits were determined to be 6.9 to 9.6 GPa. The shock wave velocity (Ds) vs. particle velocity (up) Hugoniot data in a shock stress range from 18 to 110 GPa were linearly fitted by Ds=(4.241±0.035)+(1.015±0.024)up. No evidence of phase transition was found in the performed shock experiments of the Zr-based BMG.

Simulation of shock waves in flyer plate impact experiments

AbstractIn this paper we present a newly developed one-dimensional hydrodynamic simulation code and use it to determine the shock evolution in flyer plate impact experiments. The code is Lagrangian with artificial viscosity and uses shock Hugoniot data in its equation-of-state calculations instead of SESAME data tables. First shock calculations for transparent targets show a good agreement with theoretical predictions, making the code suitable for designing future flyer impact experiments at the Nevada Terawatt Facility.

The pressure-volume-temperature equation of state of MgO derived from shock Hugoniot data and its application as a pressure scale

The pressure-volume-temperature (P-V-T) equation of state (EOS) of MgO is widely used as a pressure scale in static compression experiments. However, there are remarkable inconsistencies among different previously proposed MgO pressure scales. We calculated the P-V-T EOS of MgO up to 300 GPa and 3000 K based on experimental shock Hugoniot data and a simple thermal pressure model within the Mie-Grüneisen-type analysis framework. All of the parameters used can be measured experimentally with high accuracies. We found that, in overall, the calculated P-V-T EOS of MgO has excellent agreement with the available volume compression data over a wide range of pressure and temperature. A comparison of our results with the previous theoretical investigations has also been performed and confirms that our calculated P-V-T EOS of MgO can be used as a reliable pressure scale for static experiments at high pressures and high temperatures.

Ion Equation of State using scaled binding energy model

Global Equation of State models are used to carry out hydrodynamic calculations of inertial confinement fusion systems. There are some such models like QEOS which are used quite routinely in ICF simulations. The empirical content of QEOS, which otherwise does have a strong theoretical basis, provides scope for further research aiming at making the EOS theoretically more sound by reducing the empirical nature of the EOS. To this end, we have made some progress by developing an equation of state which uses a more accurate form for the zero temperature isotherm and a method to calculate the Grüneisen parameter so as to yield an ion equation of state which is better than the Cowan's model used in QEOS. The parameters of the model are taken from experiments or electronic structure calculations. The EOS is verified against the shock Hugoniot data and the melting data of Pb and U, and the phase diagram and Hugoniot of Hf. The stability analysis of some metals like Cu and Mo had also been carried out. The agreement of the calculated results with available experimental data is reasonably good.

Shock induced polymorphism phase transitions in high density glass

Plate impact experiments are conducted on high density glass (HDG) with an initial density of ～4.817g/cm3 (Brand ZF6) at a two-stage light gas gun facility. A copper flyer plate is used as a standard sample. Experimental shock pressure is between 52.1GPa and 167.8GPa. A multi-wavelength pyrometer and optical analyzer technique are used to determine the Hugoniot curve, sound velocity and shock temperature of HDG. The experiment results reveal that polymorphism phase transitions occur in HDG under compression, and the onset pressures are ～23, ～78 and ～120GPa, respectively. The measured sound velocity first increases and arrives at about 78GPa, then decreases rapidly, and increases again with pressure increasing. Beyond ～120 GPa, the longitudinal sound velocity turns in to bulk sound velocity, indicating the melting of HDG. Measured shock temperatures also show discontinuities at ～78 and ～120GPa, after which its increase rate becomes small and consistent with the calculated Lindemann melting line, confirming the above HDG phase transformation behaviors. Our Hugoniot data are consistent well with LASL shock Hugoniot data of HDG, which shows discontinuity only at about 23GPa, indicating that the phase transitions at 78 and 120GPa are not first-order ones. Our shock data and the gained knowledge of dynamic response behavior of HDG are valuable for improving the accuracies in sound velocity measurements for metals and non-metals at pressures over a megabar range.

TheP-V-Tequation of state of Au and Pt: An alternative pressure scale in highP-Texperiments

The pressure-volume-temperature equations and state (EOS) of Au and Pt have been investigated to the relative volume change of 0.5–0.6 and temperature up to 3000 K based on experimental shock Hugoniot data and a simple thermal pressure model within the Mie-Gruneisen-type analysis framework. The calculated results have excellent agreement with the available volume compression data over a wide range of pressure and temperatrure. The comparison of the calculated results with the previous theoretical investigations also has been performed. The crosscheck on independent data and the excellent agreements with experimental data confirm that the present isothermal EOS for these pressure standard materials can be used as high-pressure scales for static DAC experiments.

Shock Hugoniot and temperature data for polystyrene obtained with quartz standard

Equation-of-state data, not only pressure and density but also temperature, for polystyrene (CH) are obtained up to 510 GPa. The region investigated in this work corresponds to an intermediate region, bridging a large gap between available gas-gun data below 60 GPa and laser shock data above 500 GPa. The Hugoniot parameters and shock temperature were simultaneously determined by using optical velocimeters and pyrometers as the diagnostic tools and the α-quartz as a new standard material. The CH Hugoniot obtained tends to become stiffer than a semiempirical chemical theoretical model predictions at ultrahigh pressures but is consistent with other models and available experimental data.

Simple method for reducing shock-wave equation of state to zero Kelvin isotherm for metals

A thermodynamic formulation is proposed for deducing 0 K isotherm from shock Hugoniot data. In comparison to previous published thermodynamic approaches, the characteristic of this one is not requiring heat capacity as input and the used values of Grüneisen parameter merely confined to around ambient condition. Therefore, it keeps away from the difficulties in determining reliable heat capacity and Grüneisen parameter at high temperatures by experiments and theories. The predicted 0 K isotherms for seven selected metals and their related parameters of initial densities, initial bulk moduli, and their first pressure derivatives are all in well agreement with available experiments and theoretical estimations.