Release Adiabat Research Articles

Is It Possible to Determine Normal Burning Parameters from the Detonation Theory?

Within the framework of the classical one-dimensional theory of detonation based on conservation laws, the lower branch of the adiabat of energy release of the combustible mixture as a geometric place of the points of the final state of the system admits a solution for combustion waves whose propagation velocity Dfl ranges from zero to the deflagration velocity: 0 ⩽ Dfl ⩽ Ddef. The normal burning wave propagation velocity Su is located in this interval (0 ⩽ Su ⩽ Ddef), but it is traditionally calculated with the use of the thermal theory of combustion rather than detonation theory. Various approaches to choosing the final state point on the lower branch of the energy release adiabat for normal burning are analyzed in the present paper. Estimates are provided both for the degree of correspondence of the predicted and experimental velocities of flame propagation and for the degree of correspondence of the qualitative behavior of these dependences on the basis parameters of the mixture. For most hydrocarbon fuels considered in the study, the best agreement with the experimental data on Su is provided by the formula defining the flame velocity Dfl as the mean geometric value between the diffusion velocity Sdiff and deflagration velocity Ddef.

Silicate impact-vapor condensate on the Moon: Theoretical estimates versus geochemical data

Abstract We numerically simulated the impacts of asteroids and comets on the Moon in order to calculate the amount of condensate that can be formed after the impacts and compare the results with data for lunar samples. Using available equations of state for quartz and dunite, we have determined pressure and density behind shock waves in these materials for particle velocities from 4 to 20 km/s and obtained release adiabats from various points on the Hugoniot curves to very low pressures. For shock waves with particle velocities behind the front below 8 km/s the release adiabats intersect the liquid branch of the two-phase curve and, during the following expansion, the liquid material vaporizes and does not condense, forming a two-phase mixture of melt and vapor. The condensate can appear during expansion of material compressed by a shock with higher (>8 km/s) velocities. Using our hydrocode SOVA, we have conducted numerical simulations of the impacts of spherical quartz, dunite, and water–ice projectiles into targets of the same materials. Impact velocities were 15–25 km/s for stony projectiles and 20–70 km/s for icy impactors, and impact angles were 45°and 90° to the target surface. Along with the masses of condensates we calculated the masses of vaporized and melted material. Upon the impact of a projectile consisting of dunite into a target of quartz at a speed of 20 km/s at an angle of 45°, vaporized and melted masses of the target are equal to 1.6 and 11 in units of projectile mass, respectively, and the mass of condensate is 0.19. Vaporized and condensed masses of the projectile are 0.16 and 0.02, more than 80% of the projectile mass is melted. The calculated ratio of vaporized to melted mass proved to be on the order of 0.1. However, we calculated that, at impact velocities below 20 km/s, the condensate mass is only a small fraction of the vaporized and melted masses and, consequently, the major part of vapor disperses in vacuum in the form of separate molecules or molecular clusters. At an impact velocity of 15 km/s, the abundance of silicate condensates relative to melt is 0.001–0.0001, in agreement with data from lunar samples. Should the observed condensate abundances be representative, the velocities of major asteroid impacts on the Moon could not substantially exceed 20 km/s. Comet impacts at the same velocities produce much smaller amounts of vapor condensate because the low densities of cometary material induce lower shock pressures in the target.

X-ray absorption spectroscopy of iron at multimegabar pressures in laser shock experiments

Taking advantage of the new opportunities provided by x-ray free electron laser (FEL) sources when coupled to a long laser pulse as available at the Linear Coherent Light Source (LCLS), we have performed x-ray absorption near-edge spectroscopy (XANES) of laser shock compressed iron up to 420 GPa (±50) and 10 800 K (±1390). Visible diagnostics coupled with hydrodynamic simulations were used to infer the thermodynamical conditions along the Hugoniot and the release adiabat. A modification of the pre-edge feature at 7.12 keV in the XANES spectra is observed above pressures of 260 GPa along the Hugoniot. Comparing with ab initio calculations and with previous laser-heated diamond cell data, we propose that such changes in the XANES pre-edge could be a signature of molten iron. This interpretation then suggests that iron is molten at pressures and temperatures higher than 260 GPa (±29) and 5680 K (±700) along the principal Fe Hugoniot.

Hugoniot and impact-induced phase transition of magnesite

Hugoniot equation-of-state and release adiabat results are presented for magnesite to a pressure of ~140 GPa. A sharp change in the shock velocity and particle velocity relation suggests that a phase transition to a high-pressure phase occurs at 107±10 GPa. Decomposition of magnesite was observed by abrupt volume expansion during the pressure release from a pressure over the phase transition and by investigating post-shock magnesites recovered from hypervelocity impacts of mini-flyers performed using a laser-driven acceleration. Post-shock magnesites above 95 GPa contained MgO crystallites and the amount of MgO increased with increasing shock pressure.

Adiabatic release measurements in aluminum from 240-to500-GPa states on the principal Hugoniot

Adiabatic release measurements were performed on aluminum (6061-T6) from ∼240-to500-GPa(∼2.4–5Mbar) states on the principal Hugoniot. Using a magnetically accelerated flyer plate technique, capable of launching macroscopic aluminum flyer plates (approximately 12×25mm in lateral dimension and ∼300μm in thickness) to velocities in excess of 20km∕s, direct impact experiments were performed on a low shock impedance, 200-mg∕cc silica aerogel to determine the aerogel Hugoniot in the pressure range of ∼30–75GPa. Release experiments were then performed in which the aerogel was mounted onto an aluminum base plate, and the initial shock in the base plate was transmitted to the aerogel sample. Given the measured aerogel shock velocities from the release experiments and the measured aerogel Hugoniot from the direct impact experiments, release states on release adiabats of aluminum were ascertained. The results were compared to several equation of state models for aluminum, and a rigorous statistical analysis was performed. The statistical analysis enabled the suitability of these various models in describing the release response of hot, liquid states to be determined. This study enhances our understanding of the release response of aluminum for high-pressure states on the Hugoniot and lends confidence to the use of aluminum as a standard material in impedance-matching experiments.

Dynamic compressibility, release adiabats, and the equation of state of stilbene at high energy densities

The shock adiabat of porous stilbene (1,2-diphenylethylene) up to the pressure P = 41 GPa and the dynamic compressibility of this material in reflected shock waves up to 77 GPa are studied experimentally. The run of the expansion isentropes of stilbene down to 0.1 GPa is determined. The experimental findings are used to construct a semi-empiric equation of state of stilbene for a wide range of high-energy states.

Measurement of a release adiabat from ∼8 Mbar in lead using magnetically driven flyer impact

Using magnetically driven aluminium flyers to generate ∼8 Mbar shocks in lead, which were then transmitted into lower-impedance material samples, points on a lead release adiabat have been measured. The pressure–particle-velocity points were calculated from known sample principal Hugoniots and from shock velocities measured using arrays of fiber-optic active and passive shock breakout diagnostics, and point and line velocity interferometer for a surface of any reflectivity (VISARs). The measured points agree closely with adiabats calculated using models which do not include ionization, or do include it both with, and without, atomic shell effects. Though the data are not sufficient to discriminate between widely different models we may qualitatively identify errors within these models. This is the first attempt to measure a release adiabat from such high pressures.

Shock-wave equation of state of rhyolite

We have obtained new shock-wave equation of state (EOS) and release adiabat data for rhyolite. These data are combined with those of Swegle (1989, 1990) to give an experimental Hugoniot which is described by U_s = 2.53(±0.08) + 3.393(±0.37)u_p for u_p < 0.48 km s^(−1), U_s = 3.85(±0.05) + 0.65(±0.03)up for 0.48 ≤ u_p < 2.29 km s^(−1), U_s = 1.52(±0.08) + 1.67(±0.02)u_p for 2.29 ≤ u_p < 4.37 km s^(−1), and U_s = 3.40(±034) + 1.24(±0.06)u_p for u_p ≥ 4.37 km s^(−1), with ρ_0 = 2.357 ± 0.052 Mg m^(−3). We suggest that the Hugoniot data give evidence of three distinct phases—both low- and high-pressure solid phases and, possibly, a dense molten phase. EOS parameters for these phases are ρ_0 = 2.494 ± 0.002 Mg m^(−3), K_(S0) = 37 ± 2 GPa, K′ = 6.27 ± 0.25, and γ = 1.0(V/V_0) for the low-pressure solid phase; ρ_0 = 3.834 ± 0.080 Mg m^(−3), K_(S0) = 128 ± 20 GPa, K′ = 3.7 ± 1.4, and γ = 1.5 ± 0.5 for the solid high-pressure phase; and ρ_0 = 3.71 ± 0.10 Mg m^(−3), K_(S0) = 127 ± 25 GPa, K′ = 2.1 ± 1.0, and γ = 1.5 ± 1.0 for the dense liquid. Transition regions of the Hugoniot cover the ranges of 9–34 GPa for the low-pressure—high-pressure solid transition and 90–120 GPa for the high-pressure solid—liquid transition. Release paths from high-pressure states, calculated from the EOS parameters, suggest that the material remains in the high-pressure solid phase upon release. Release paths from both the high-pressure solid and liquid fall above the Hugoniot until the Hugoniot enters the low-pressure—high-pressure mixed phase region, when the release paths then cross the Hugoniot and fall below it, ending at significantly higher zero-pressure densities than that of the low-pressure phase. The low-pressure release paths fall very close to the Hugoniot. Estimates of residual heat deposition, based on shock-release path hysteresis, range from 20 to 60 per cent of the shock Hugoniot energy.

Effect of irreversible phase change on shock-wave propagation

New release adiabat data for vitreous GeO_2 are reported up to ∼25 GPa using the VISAR technique. Numerical modeling of isentropic release wave induced dynamic states achieved from one dimensional strain–stress waves is consistent with a phase change that induce an increase in zero-pressure density from 3.7–6.3 Mg/m^3 starting at ∼8 GPa. The first release adiabat data for SiO_2 ( fused quartz) are presented (obtained with immersed foil technique) . Above 10 GPa, the SiO_2 release isentropes, in analogy with GeO_2, are steeper than the Hugoniot in the volume-pressure space, indicating the presence of an irreversible phase transition (to a stishovite-like phase). We simulate propagation of shock-waves in GeO_2, in spherical and planar symmetries, and predict enhanced attenuation for shock pressures ( p) above the phase change initiation pressure (8 GPa) . The pressure from a spherical source decays with propagation radius r, p ∼ r^x, where x is the decay coefficient. Modeling hysteresis of the phase change gives x = −2.71, whereas without the phase change, x = −1.15. An analytical model is also given.

Shock Compressibility, Adiabatic Expansion and Equation of State of Stylbene.

The shock compressibility of stylbene samples with density 1. 13 and 0. 85 g/cc is investigated experimentally up to the pressure about 54 GPa. From three states on principal Hugonion of stylbene at pressures 32, 36 and 44 GPa the reshock and release adiabat paths also are registered using barrier technique. On the base of obtained data semiempirical equation of state for stylbene over a wide range of high-energy-density states is constructed.

Dynamic compression of an Fe–Cr–Ni alloy to 80 GPa

Wave profiles were measured in an Fe–Cr–Ni alloy (stainless steel 304) shock compressed to Hugoniot stresses between 7 and 80 GPa. A single-stage propellant gun was used to generate shock states and time histories were recorded by velocity interferometry. The particle velocity measurements are generally consistent with impedance match calculations to ±2%. Unloading wave velocities were obtained from analysis of the release wave profiles. Using Eulerian finite strain theory and under the assumption of fully elastic initial release, the first and second pressure derivatives of the longitudinal modulus are given by: 7.9(0.5) and −0.16(0.06) GPa-1, where the numbers in parentheses are one standard deviation uncertainties. The first and second pressure derivatives of the adiabatic bulk modulus are: 6.4(1.0) and −0.17(0.08) GPa-1. The unloading wave velocities are generally consistent with extrapolated trends from low-pressure ultrasonic data as well as with higher stress shock measurements on an alloy of similar composition. From 1 bar to 80 GPa, Poisson’s ratio, ν, increases with Hugoniot stress, σ (in GPa), according to the relation: ν=0.29 + 0.0008σ. The Hugoniot elastic limit of 304 steel was found to be 0.35(0.12) GPa, and the initial yield stress is 0.21(0.07) GPa. The elastic precursor velocity was 5.8(0.1) km/s. Numerical simulations of the wave profiles using a constitutive model that incorporates a Bauschinger effect and stress relaxation reproduced the main features observed in the profiles. Release adiabats were also calculated from the measured wave profiles. The shear stress at unloading was determined to vary with stress according to the relation: τ0+τc=0.149+0.018σ, where σ is given in GPa.

Irreversible phase transitions and wave propagation in silicate geologic materials

Shock and unloading experiments on quartz and silicate rocks indicate that the release adiabats lie below the Hugoniot. The hysteresis and energy dissipation inherent in this situation have important wave propagation implications. On loading, there is a pressure-induced transition to the stishovite phase which does not occur under conditions of thermodynamic equilibrium, in that the Hugoniot passes through a metastable mixed-phase region for several tens of GPa. One interpretation of the unloading data is that the transition is not reversible, and the phase mixture remains frozen on unloading. However, material strength may also play a role. A complete thermodynamically consistent equation of state which includes phase transitions and strength effects has been developed and used to examine shock and release data on quartz and silicate rocks in order to quantify the kinetics of the reverse transition and to separate the hysteretic effects due to reverse phase transition kinetics from those due to material strength. The model allows quantitative determination of the effect of reverse transition kinetics on ground shock propagation in silicate materials.

Measuring sound velocities along release adiabats with Manganin stress gauges

We propose a new technique to measure the state of shock-loaded specimens along their release adiabats. The technique is based on symmetric impacts of equal thickness flyer and target disks. A Manganin stress gauge is embedded at the back of the target and backed by a thick Plexiglas disk. The stresses at the specimen–Plexiglas interface are relieved in a stepwise manner which is typical for this type of experiment. From the time duration between consecutive release waves one can determine the sound speed in the released specimen. Drastic changes in sound speed, as in melting, can be detected by these time durations adding more information on the state of the specimen as it unloads from very high shock stresses.

Shock wave properties of anorthosite and gabbro : Boslough, M B; Ahrens, T J J Geophys ResV90, NB9, 10 Aug 1985, P7814–P7820

Shock wave experiments have been conducted on San Gabriel anorthosite and San Marcos gabbro to peak stresses between 5 and 11 GPa using a 40-mm-bore propellant gun. Particle velocity wave profiles were measured directly at several points in each target by means of electromagnetic gauges, and Hugoniot states were calculated by determining shock transit times from the gauge records. The particle velocity profiles yielded sound velocities along the release adiabats which indicate a retention of shear strength upon shock compression for anorthosite, with a loss of strength upon release to nearly zero stress. Sound velocities of anorthosite shocked to peak stresses between 6 and 10 GPa were measured to be between 5.1 and 5.3 km/s upon release to nearly zero stress as compared to ∼6.9 and 5.4 km/s for the expected longitudinal and bulk wave speeds. Stress density release paths in the anorthosite indicate possible transformation of albite to Jadeite + (quartz or coesite), with the amount of albite transformed ranging from as low as 0.05 to as much as 0.19 mass fraction in the 6–10 GPa shock stress range. Electrical interference effects precluded the determination of accurate release paths for San Marcos gabbro. Because of the apparent loss of shear strength during unloading from the shocked state, the fluidlike rheology of anorthosite which is indicated implies that calculations of energy partitioning due to impact onto planetary surfaces based on elastic-plastic models will underestimate the amount of internal energy deposited in the impacted surface material.

Shock wave properties of anorthosite and gabbro

Shock wave experiments have been conducted on San Gabriel anorthosite and San Marcos gabbro to peak stresses between 5 and 11 GPa using a 40‐mm‐bore propellant gun. Particle velocity wave profiles were measured directly at several points in each target by means of electromagnetic gauges, and Hugoniot states were calculated by determining shock transit times from the gauge records. The particle velocity profiles yielded sound velocities along the release adiabats which indicate a retention of shear strength upon shock compression for anorthosite, with a loss of strength upon release to nearly zero stress. Sound velocities of anorthosite shocked to peak stresses between 6 and 10 GPa were measured to be between 5.1 and 5.3 km/s upon release to nearly zero stress as compared to ∼6.9 and 5.4 km/s for the expected longitudinal and bulk wave speeds. Stress density release paths in the anorthosite indicate possible transformation of albite to Jadeite + (quartz or coesite), with the amount of albite transformed ranging from as low as 0.05 to as much as 0.19 mass fraction in the 6–10 GPa shock stress range. Electrical interference effects precluded the determination of accurate release paths for San Marcos gabbro. Because of the apparent loss of shear strength during unloading from the shocked state, the fluidlike rheology of anorthosite which is indicated implies that calculations of energy partitioning due to impact onto planetary surfaces based on elastic‐plastic models will underestimate the amount of internal energy deposited in the impacted surface material.

Shock-induced devolatilization of calcite

The amounts of CO_2 and CO evolved upon shock compression and decompression of calcite to 18 GPa (180 kbar) have been determined using a new gas phase shock recovery technique and gas source mass spectrometry. The data demonstrate that from ∼0.03 to 0.3 mole percent of calcite is devolatilized at shock pressures significantly lower than those predicted (30 GPa) for the onset of volatilization by continuum thermodynamic theory and are in qualitative agreement with release adiabat data for calcite and aragonite. Carbon and oxygen isotope ratios in the shock-released CO_2 are the same as those in the unshocked (hydrothermal) calcite, demonstrating that the CO_2 comes from the calcite rather than other potential sources.

Shock compression of aragonite and implications for the equation of state of carbonates

Hugoniot equation of state and release adiabat results are presented for c cut crystals of aragonite, the high‐pressure polymorph of calcite, shocked to pressures of up to 40 GPa. A Hugoniot elastic limit is observed at 2.5±0.8 GPa and is similar to that of calcite, which, depending on orientation, ranges from 1.5 to 2.5 GPa. A phase transition, possibly displacive, occurs between 5.5 and 7.6 GPa. Above shock pressures of ∼10 GPa, the aragonite and calcite Hugoniots are nearly coincident, suggesting transformation of both polymorphs to the same phase. Model calculations, attempting to characterize the high pressure CaCO3 phase are presented. Aragonite release adiabats centered at pressures between 9 and 14 GPa indicate that states with apparent zero‐pressure densities from 2.9 to 3.2 g/cm3 are achieved upon decompression from progressively greater shock pressures. Observed unloading paths from shock pressures above 17 GPa are significantly and consistently shallower (in a density‐pressure plane) than those from lower pressures, and zero‐pressure densities up to 20% below that of the initial aragonite density are achieved upon unloading; these features suggest that vaporization is occurring upon unloading. According to theoretical shock temperature and entropy calculations, however, the minimum shock pressure for vaporization upon release for aragonite is 55 GPa (and 33 GPa for calcite), significantly higher than the observed value.

Dynamic response of fused quartz in the permanent densification region

A shock wave investigation on fused quartz was performed in the permanent densification region, using a double stage light-gas gun with dc x-ray velocity meter and the electromagnetic particle velocity measurement technique. The elastic limit obtained in this work [(8.81±0.11) GPa] was somewhat lower than the published value. The compression curve obtained was quite different from the published curve and indicated that a rapid volume contraction occured just above the elastic limit. The tetrahedral coordinations seemed to remain at least up to 22 GPa, but above 16 GPa, they would be distorted or in some parts destroyed. The pressure of 16 GPa was considered as the limit of the permanent densification process, and the specific volume at atmospheric pressure interpolated along a hypothetical release adiabat was about 0.32 cm3/g.

Release adiabat measurements on minerals: The effect of viscosity

The current inversion of pressure‐particle velocity data for release from a high‐pressure shock state to a pressure‐density path usually depends critically upon the assumption that the release process is isentropic. It has been shown by Kieffer and Delaney that for geological materials below stresses of ∼150 GPa, the effective viscosity must be ≲103kg m−1 s−1 (104 P) in order that the viscous (irreversible) work carried out on the material in the shock state remains small in comparison to the mechanical work recovered upon adiabatic rarefaction. The available data pertaining to the offset of the Rayleigh line from the Hugoniot curve for minerals, the magnitude of the shear stress in the high‐pressure shock state for minerals, and the direct measurements of the viscosities of several engineering materials shocked to pressures below 150 GPa yield effective viscosities of ∼103kg m−1 s−1 or less. We infer that this indicates that the conditions for isentropic release of minerals from shock states are achieved, at least approximately, and we conclude that the application of the Riemann integral to obtain pressure‐density states along the release adiabats of minerals in shock experiments is valid.

Post-shock temperatures in minerals

An experimental technique was developed for measuring post-shock temperatures in a wide variety of materials, including those of geophysical interest such as silicates. The technique uses an infrared radiation detector to determine the brightness temperature of samples shocked to pressures in the range 5 to approximately 30 GPa; in these experiments measurements were made in two wavelength ranges (4.5 to 5.75 microns and 7 to 14 microns). Reproducible results, with the temperatures in the two wavelength bands generally in excellent agreement, were obtained for aluminum-2024 (10.5 to 33 GPa, 125 to 260 C), stainless steel-304 (11.5 to 50 GPa, 80 to 350 C), crystalline quartz (5.0 to 21.5 GPa, 80 to 250 C), forsterite (7.5 to 28.0 GPa, approximately 30 to 160 C) and Bamble bronzite (6.0 to 26.0 GPa, approximately 30 to 225 C). It is concluded that release adiabat data should be used, wherever available, for calculations of residual temperature, and that adequate descriptions of the shock and release processes in minerals are more complex than generally assumed.