Static Compression Data Research Articles

Shock compression of crystalline TeO2 to the high-pressure fluid regime: Insights from ab initio molecular dynamics simulations

The shock response of fully-dense and porous crystalline tellurium dioxide (TeO2) to the high-pressure and high-temperature fluid regime was investigated within the framework of density functional theory with Mermin’s generalization to finite temperatures. The principal and porous shock Hugoniot curves were predicted from canonical ab initio molecular dynamics (AIMD) simulations, with the phase space sampled along isotherms up to 80 000 K, for densities ranging from ρ=3 to 17 g/cm3. The polymorphs investigated are α-TeO2 paratellurite (P41212), TeO2 cotunnite (Pnma), and TeO2 post-cotunnite (P21/m). Based on the discontinuity found in the calculated Us−up slope of TeO2 post-cotunnite at a shock velocity of Us≃8.35 km/s and a particle velocity of up≃3.64 km/s, the shock melting temperature and pressure are predicted to be ≃6500 K and ≃170 GPa. Results from the AIMD simulations are in line with the static compression data of TeO2 paratellurite and cotunnite, and with the recent shock Hugoniot data for single-crystal α-TeO2 for pressures up to 85 GPa, obtained using the inclined-mirror method and the velocity interferometer system for any reflector combined with powder gun and two-stage light-gas gun.

Thermoelastic Properties of Fe3+‐Rich Jeffbenite and Application to Superdeep Diamond Barometry

AbstractJeffbenite (Mg3Al2Si3O12) is a tetragonal phase found in so far only in superdeep diamonds, and its thermoelastic parameters are a prerequisite for determining entrapment pressures as it is regarded as a potential indicator for superdeep diamonds. In this study, the thermoelastic properties of synthetic Fe3+‐jeffbenite were measured up to 33.7 GPa and 750 K. High‐temperature static compression data were fitted, giving (∂KT0/∂T)P = −0.0107 (4) GPa/K and αT = 3.50 (3) × 10−5 K−1. The thermoelastic properties and phase stability are applied to modeling isomekes, or P‐T paths intersecting possible conditions of entrapment in diamond. We calculate that under ideal exhumation, jeffbenite entrapped at mantle transition zone conditions will exhibit a high remnant pressure at 300 K (Pinc) of ∼5.0 GPa. Elastic geobarometry on future finds of jeffbenite inclusions can use the new equation of state to estimate entrapment pressures for this phase with still highly uncertain stability field in the mantle.

Using maximum likelihood estimation approach to adjust parameters of CARTE thermochemical code.

AbstractUsing thermochemical codes to predict the properties of detonation products and the parameters for detonation modeling of explosives requires the use of very precise theoretical equations of state (EoS). We share the updates to the thermochemical code CARTE, which allows the calculation of thermodynamic properties and chemical compositions of detonation products over a wide range of temperatures and densities. In this paper, we focus on the theoretical EoS of pure fluids, based on the KLRR perturbation method and EXP‐6 potentials. We propose a maximum likelihood approach to fit the EXP‐6 parameters by matching a combination of shock data and static compression data. We present the results obtained on the detonation properties on nitric oxide.

Femtosecond diffraction studies of the sodium chloride phase diagram under laser shock compression

The phase diagram of sodium chloride (NaCl) under laser shock compression has been studied at Linac Coherent Light Source (LCLS) at the x-ray free-electron laser facility. Both solid–solid (B1 → B2) and solid–liquid (B2 → liquid) transitions have been observed along the Hugoniot over nanosecond time scales. By combining structural measurements through in situ x-ray diffraction, pressure determination through velocimetry, and a thermal equation-of-state, the shock-compressed data are used to constrain the phase diagram of NaCl. Transformation into the B2 phase is found to occur at 28(2) GPa, and B2–liquid coexistence is observed between 54(4) and 66(6) GPa, with near full melt at 66(6) GPa. Late-time pressure release from an initial shocked B2-state results in a B2 → B1 back transformation. Our results show agreement with previous static compression data, suggesting that the time scale for melting is very rapid and that equilibrium states in NaCl are being accessed over nanosecond time scales. A multiphase equation-of-state description of NaCl incorporated into a one-dimensional hydrocode is used to interpret pressure and temperature evolution over these rapid time scales.

Investigating the Feasibility of a Cushion Selection Method on Polyethylene Based on a Predictive Model

Cushion materials are very popular and widely used in various applications. Cellular solid has been used for cushioning for many years due to its low weight and high energy absorption capacity. Cushioning selection is the process of selecting a cushioning material to sufficiently cushion an object. There are a few cushion selection methods available in literature. The objective of this report is to investigate the feasibility of a cushion selection method based on predicting the impact absorption capacity from static compressive stress-strain data. This is achieved by comparing the predicted dimensionless deceleration (G) and the measured G. Polyethylene (foam) samples were used to conduct the compression test and drop test. For polyethylene, the predicted G shown higher accuracy at low drop height and became lower accuracy with increasing drop height. A dynamic factor C was introduced to account for the difference. From this report, researchers may explore the feasibility of this cushion selection method on polyethylene or even conduct experiments on other cellular solid specimens in the future.

Does the embedded atom model have predictive power?

Potassium, rubidium, aluminum, iron, nickel, and tin embedded atom models (EAMs) have been used as examples to ascertain how well the properties of a metal are described by EAM potentials calculated from the shape of shock adiabats and/or static compression data (from a function of cold pressure). Verification of the EAM potential implies an evaluation of its predictive power and an analysis of the agreement with experiment both at 0 or 298 K and under shock compression. To obtain consistent results, all contributions of collectivized electrons to energy and pressure need to be taken into consideration, especially in transition metals. Taking account of or ignoring electron contributions has little effect on the calculated melting lines of the models, self-diffusion coefficients, and viscosity. The shape of the melting line is sensitive to the behavior of the repulsive branch of the pair contribution to the EAM potential at small distances.

Equation of State for Shocked Fe‐8.6 wt% Si up to 240 GPa and 4,670 K

AbstractUsing dynamic compression technique, the equation of state for Fe‐8.6 wt% Si was measured up to 240 GPa and 4,670 K. A least squares fit to the experimental data yields the Hugoniot parameters C0 = 4.603±0.101 km/s and λ = 1.505±0.037 with initial density ρ0=7.386±0.021 g/cm3. Based on the Hugoniot data, the calculated isothermal equation of state is consistent with static compression data when the lattice Grüneisen parameter γl =1.65(7.578/ρ) and electronic Grüneisen parameter γe=1.83. The calculated pressure‐density data at 300 K were fitted to a third‐order Birch‐Murnaghan equation of state with zero pressure the parameters K0=192.1±6.3 GPa, =4.71±0.27 with fixed ρ0ε =7.578±0.050 g/cm3. Under the conditions of Earth's core, the densities of Fe‐8.6±2.0 wt% Si and Fe‐3.8±2.9 wt% Si agree with preliminary reference Earth mode (PREM) data of the outer and the inner core, respectively. These are the upper limits for Si in the core assuming Si is the only light element. Simultaneously considering the geophysical and geochemical constraints for a Si‐S‐bearing core, the outer core may contain 3.8±2.9 wt% Si and 5.6±3.0 wt% S.

In situ observation of a phase transition in silicon carbide under shock compression using pulsed x-ray diffraction

The behavior of silicon carbide (SiC) under shock compression is of interest due to its applications as a high-strength ceramic and for general understanding of shock-induced polymorphism. Here we use the Matter in Extreme Conditions beamline of the Linac Coherent Light Source to carry out a series of time-resolved pump-probe x-ray diffraction measurements on SiC laser-shocked to as high as 206 GPa. Experiments on single crystals and polycrystals of different polytypes show a transformation from a low-pressure tetrahedral phase to the high-pressure rocksalt-type (B1) structure. We directly observe coexistence of the low- and high-pressure phases in a mixed-phase region and complete transformation to the B1 phase above 200 GPa. The densities measured by x-ray diffraction are in agreement with both continuum gas-gun studies and a theoretical B1 Hugoniot derived from static-compression data. Time-resolved measurements during shock loading and release reveal a large hysteresis upon unloading, with the B1 phase retained to as low as 5 GPa. The sample eventually reverts to a mixture of polytypes of the low-pressure phase at late times. Our study demonstrates that x-ray diffraction is an effective means to characterize the time-dependent structural response of materials undergoing shock-induced phase transformations at megabar pressures.

Equation of state of iron under core conditions of large rocky exoplanets

The recent discovery of thousands of planets outside our Solar System raises fundamental questions about the variety of planetary types and their corresponding interior structures and dynamics. To better understand these objects, there is a strong need to constrain material properties at the extreme pressures found within planetary interiors1,2. Here we used high-powered lasers at the National Ignition Facility to ramp compress iron over nanosecond timescales to 1.4 TPa (14 million atmospheres)—a pressure four times higher than for previous static compression data. A Lagrangian sound-speed analysis was used to determine pressure, density and sound speed along a continuous isentropic compression path. Our peak pressures are comparable to those predicted at the centre of a terrestrial-type exoplanet of three to four Earth masses 3 , representing the first absolute equation of state measurements for iron at such conditions. These results provide an experiment-based mass–radius relationship for a hypothetical pure iron planet that can be used to evaluate plausible compositional space for large, rocky exoplanets. Iron has been ramp compressed to the pressures it would experience in the core of a 3–4 Earth-mass terrestrial exoplanet, providing experimental constraints on the mass–radius relationship for a hypothetical pure iron planet.

Comment on “Evidence of a first-order phase transition to metallic hydrogen”

A recent paper by Zaghoo et al. presents optical data at high-pressure and high-temperature and interprets the data as evidence for a first-order phase transition to metallic hydrogen during heating. Here we argue that the presented data are contradictory with these claims. Elucidating this issue is important for building a coherent picture that is emerging as the results of theoretical calculations of various levels and experimental investigations employing static and dynamic compression techniques. In this context, the use of adequate probes of the electronic and chemical state is crucial. Optical probes that do not address the energy dependent conductivity while making multiple references to the Drude model are highly speculative. Indeed, the available dynamic and static compression data and theoretical modeling show that study of energy dependent conductivity is important for understanding the nature of hot dense hydrogen. Moreover, the most recent investigations suggest that the critical point, which demarcates the regimes of crossover between insulating and plasma state at low densities to the first order liquid-liquid transition, is above 200 GPa. Below we concentrate on inconsistencies in the interpretation of data in Zaghoo et al, which call for careful examination of their claims and further detailed investigations. We analyze their optical data and use finite element calculations and argue that the high-temperature state studied in Zaghoo et al. is not metallic and that the data cannot discriminate between a first-order phase transition and a continuous phase transition, or even a bandgap drop within one phase

Thermal equation of state of Molybdenum determined from in situ synchrotron X-ray diffraction with laser-heated diamond anvil cells.

Here we report that the equation of state (EOS) of Mo is obtained by an integrated technique of laser-heated DAC and synchrotron X-ray diffraction. The cold compression and thermal expansion of Mo have been measured up to 80 GPa at 300 K, and 92 GPa at 3470 K, respectively. The P-V-T data have been treated with both thermodynamic and Mie–Grüneisen-Debye methods for the thermal EOS inversion. The results are self-consistent and in agreement with the static multi-anvil compression data of Litasov et al. (J. Appl. Phys. 113, 093507 (2013)) and the theoretical data of Zeng et al. (J. Phys. Chem. B 114, 298 (2010)). These high pressure and high temperature (HPHT) data with high precision firstly complement and close the gap between the resistive heating and the shock compression experiment.

Anisomorphic constant fatigue life diagrams of constant probability of failure and prediction of P–S–N curves for unidirectional carbon/epoxy laminates

The effect of stress ratio on statistical distribution of fatigue life of a unidirectional carbon/epoxy composite has been examined. Furthermore, a method for efficiently predicting a family of S–N curves with probability of failure as the parameter for any stress ratio of constant amplitude loading has been developed. For this purpose, fatigue life data are first collected at each of different stress levels for tension–tension (TT), tension–compression (TC) and compression–compression (CC) fatigue loadings, respectively. The experimental results show that the scatter in fatigue life tends to become larger in order of TT, TC and CC loading. Lognormal distribution is used to quantify the statistics of the static tensile and compressive strength data and the fatigue life data for each of different stress levels and stress ratios. It is found that lognormal distribution is applicable approximately not only to the static strength data in tension and compression, but also to the fatigue life data for each of different stress levels and stress ratios. The parameters of the distribution of fatigue life are shown to be dependent on the stress ratio of fatigue loading. The experimental P–S–N curves are established for each of different stress ratios using the distributions fitted to the static strength and fatigue life data. Then, a method for constructing the anisomorphic constant fatigue life (CFL) diagrams of constant probability of failure is developed. The proposed probabilistic anisomorphic CFL diagram approach allows not only accurately predicting the P–S–N curves for different stress ratios, but also adequately describing the stress-ratio dependent scatter in fatigue life of the unidirectional composite.

Probabilistic anisomorphic constant fatigue life diagram approach for prediction of P–S–N curves for woven carbon/epoxy laminates at any stress ratio

A general engineering methodology to construct a family of anisomorphic constant fatigue life (CFL) diagrams with probability of failure as the parameter that allows efficiently predicting P–S–N curves at any stress ratios is developed and validated for a plain weave fabric carbon/epoxy laminate. Constant amplitude fatigue tests are first performed to obtain statistical samples of fatigue life at different stress levels and stress ratios, respectively. Static tensile and compressive strength data are also collected. The Kolmogorov–Smirnov and Anderson–Darling goodness-of-fit tests suggest that both two-parameter lognormal and Weibull distributions are acceptable as the distributions for the static strength and fatigue life data, respectively, at the significance level of 5%. Then, we attempt to develop a methodology for efficient construction of the anisomorphic CFL diagrams for different constant values of probability of failure. It requires the P–S–N curves for any percentile points of the distribution for the critical stress ratio. To come up with this requirement, a probabilistic scaling law is formulated. It takes account of the probability-of-failure dependence of the critical stress ratio and the stress-ratio dependence of the P–S–N curve for the critical stress ratio. Finally, the anisomorphic CFL diagrams for different constant values of probability of failure are predicted using the proposed methodology, and they are shown to be in good agreement with the experimental results. It is also demonstrated that the P–S–N curves can efficiently and accurately be predicted for the woven CFRP laminate at any stress ratios using the proposed probabilistic anisomorphic CFL diagram approach.

Static and dynamic mechanical properties of expanded polystyrene

Abstract Expanded polystyrene (EPS) is commonly used in a variety of applications because of its features of light weight, good thermal insulation, moisture resistance, durability, acoustic absorption and low thermal conductivity. It has been increasingly used in building constructions as core material of structural insulated panels (SIP). Some of those structures during their service life may be subjected to dynamic loads such as accidental or hostile explosion loads and windborne debris impacts. Understanding the dynamic material properties of EPS is essential for reliable predictions of the performances of the structural insulated panels with EPS foam core material. This paper presents static and dynamic compressive and tensile test data of EPS with density 13.5 kg/m3 and 28 kg/m3 at different strain rates. The dynamic strength, Young’s modulus and energy absorption capacities of the two EPS foams at different strain rates are obtained and presented in the paper. Based on the testing data, some empirical relations are derived, which can be used to model EPS properties in numerical simulations of dynamic responses of structural insulated panels with EPS foam core subjected to impact and blast loads.

Equation of state for silicate melts: A comparison between static and shock compression

AbstractThe density data of silicate melts reported by static and shock compression have been compared quantitatively at the pressure condition of the Earth's deep upper mantle. The equation of state based on the static compression data cannot explain the shock compression data, and the systematic differences between them have been revealed. The shock temperatures were estimated with different methods among papers, and the reported values differed considerably from one another. The shock temperatures estimated by assuming phase‐transition‐like structural changes in melts lie between the previous estimates. Many of them are well below the liquidus temperatures of each sample, suggesting that the sample state may have been altered during the shock compression. In addition, some of the shock compression data reanalyzed in the recent paper differ considerably from the original. These results suggest that silicate melts show phase‐transition‐like structural changes at high pressures, which are consistent with the static compression data.

Static compression of (Mg0.83,Fe0.17)O and (Mg0.75,Fe0.25)O ferropericlase up to 58 GPa at 300, 700, and 1100 K

Static compression data of (Mg0.83,Fe0.17)O and (Mg0.75,Fe0.25)O ferropericlases have been measured up to 58 GPa along 300, 700, and 1100 K isotherms, using synchrotron powder X-ray diffraction experiments combined with a Kawai-type, multi-anvil, high-pressure apparatus and sintered diamond anvils. High-temperature and high-pressure equations of state for these two ferropericlases, which have high-spin Fe2+ ions, were developed using measured compression data below 47 GPa, based on the Mie-Grüneisen relation and the Debye thermal model, combined with the 300 K Birch-Murnaghan equation. When the isothermal bulk modulus (K0T) and the Debye temperature (Θ0) are fixed at 160 GPa and 500 K, respectively, the optimized equation-of-state parameters for these two phases are as follows: the pressure derivative of the bulk modulus (K'0T), the Grüneisen constant (γ0), and the q parameter are 4.08 ± 0.02, 1.53 ± 0.04, and 0.7 ± 0.2, respectively, for (Mg0.83,Fe0.17)O; and 4.22 ± 0.03, 1.64 ± 0.04, and 0.7 ± 0.2, respectively, for (Mg0.75,Fe0.25)O. We found that calculated pressures with these equation-of-state parameters accurately reproduce the measured pressures of each ferropericlase below ~50 GPa for the isotherms of 300, 700, and 1100 K. Furthermore, the compression curve indicates that for each ferropericlase at each isothermal compression of 300, 700, and 1100 K, an abrupt volume reduction occurs at ~50 GPa. This volume reduction becomes more pronounced with increasing pressure, as a result of the progressive transition from high-spin to low-spin of the Fe2+ ions in each ferropericlase.

Density contrast between silicate melts and crystals in the deep mantle: An integrated view based on static-compression data

Mineral-physics data of SiO 2, MgSiO 3, and MgO under static compression, together with the physical theories of melting and structural changes in liquid, suggest that the density of silicate melts does not exceed that of crystalline assemblages with the same chemical composition at the pressure range of the deep mantle. Because drastic structural changes accompanied by the increase in the coordination number of silicon are completed in the shallow mantle, SiO 2 component becomes stiff and the compressibility of magnesium silicate melts decreases with SiO 2 content in the deep mantle while it increases with SiO 2 content in the shallow mantle. If the ideal mixing of melts with respect to volume is valid in the deep mantle, as is the case for the shallow mantle, the density contrast is significant in a composition range close to MgSiO 3. Therefore, magmas in a wide composition range would be buoyant in the deep mantle. Chemical compositions of magmas which are neutrally buoyant in the deep mantle have been estimated with a simplified model in (Mg,Fe)O–SiO 2 system.

Shock compression of cubic boron nitride

Hugoniot measurements have been performed on high-purity cubic boron nitride polycrystals in the pressure range up to 296GPa using a two-stage light-gas gun. Hugoniot parameters have been measured by a line reflection method and Fabry–Pérot velocimetry. The Hugoniot elastic limit (HEL) is determined to be 44.3GPa, which is the second highest value after that of diamond. Above the HEL, the Hugoniot compression curve shows a considerable offset from its hydrodynamic compression curve, which is calculated from static-compression data. This result shows that cubic boron nitride preserves its shear strength in the plastic region. Hugoniot data indicate that the cubic phase of boron nitride is stable in the pressure range up to 296GPa.

A molecular dynamics simulation study of the pressure-volume-temperature behavior of polymers under high pressure

Isothermal compression of poly (dimethylsiloxane), 1,4-poly(butadiene), and a model Estane (in both pure form and a nitroplasticized composition similar to PBX-9501 binder) at pressures up to 100 kbars has been studied using atomistic molecular dynamics (MD) simulations. Comparison of predicted compression, bulk modulus, and U(s)-u(p) behavior with experimental static and dynamic compression data available in the literature reveals good agreement between experiment and simulation, indicating that MD simulations utilizing simple quantum-chemistry-based potentials can be used to accurately predict the behavior of polymers at relatively high pressure. Despite their very different zero-pressure bulk moduli, the compression, modulus, and U(s)-u(p) behavior (including low-pressure curvature) for the three polymers could be reasonably described by the Tait equation of state (EOS) utilizing the universal C parameter. The Tait EOS was found to provide an excellent description of simulation PVT data when the C parameter was optimized for each polymer. The Tait EOS parameters, namely, the zero-pressure bulk modulus and the C parameter, were found to correlate well with free volume for these polymers as measured in simulations by a simple probe insertion algorithm. Of the polymers studied, PDMS was found to have the most free volume at low pressure, consistent with its lower ambient pressure bulk modulus and greater increase in modulus with increasing pressure (i.e., crush-up behavior).

Equation of state and high pressure properties of a fluorinated terpolymer: THV 500

We present the results of an investigation of the static compressive and dynamic (shock) responses of a fluorinated terpolymer of tetrafluoroethylene-hexafluoropropylene-vinylidene fluoride (Dyneon THV 500), in an effort to further understand its behavior under static and dynamic high pressures, and elucidate its equation of state properties. Fluorinated polymers, and, in particular, their copolymers, have garnered increasing attention by the static high pressure and shock wave communities, due to their widespread use in engineering applications, and formulation into energetic materials as binders. Shock wave compression experiments performed at two laboratories showed good consistency, and provide the first Hugoniot data for this fluorinated terpolymer. The Hugoniot of THV 500 is in general agreement with that of the related fluoropolymers polytetrafluoroethylene and poly(chlorotrifluoroethylene-co-vinylidene fluoride), reported previously. The static compressive data, combined with measurement of the ambient pressure thermodynamic parameters, have been used to formulate an equation of state based on the Helmholtz free energy, which was shown to adequately represent the dynamic response of the polymer to ∼5 GPa.