Equation Of State For Aluminum Research Articles

Equation of State for Aluminum at High Pressures

Equation of State for Aluminum at High Pressures

Equation of state remeasurements for aluminum and copper under low-impact loading

In this work, the Hugoniot equation of state for aluminum and copper under low-impact loading was measured by using the plane impact technique and laser Doppler velocimetry. The linear relationship between shock wave velocity and particle velocity was fitted by a least squares method, with D=5.28114+1.306(17)us for an Al pressure range from 2.5 to 13.9 GPa and D=3.9386+1.484(14)us for Cu at 5.7–47.5 GPa. The linear fitting correlation coefficient was greater than 0.99, which was better than the previous experimental data. The results demonstrate that the Doppler pin system has great advantages for measuring the Hugoniot EoS at low shock pressure compared with the electric pin technique The experimental data obtained in this work extend to a lower pressure range. This can provide more accurate Mie–Grüneisen EoS of Al and Cu under low shock pressure.

Shock response and prediction model of equation of state for aluminum powder/rubber matrix composites

The shock response of aluminum powder/rubber matrix composites containing 40, 50, and 60 vol% Al was investigated using the plate impact test and explosive loading technique. The shock stress in the range of 0.61–13.97 GPa was measured and the free surface velocity of the specimen was monitored using the displacement interferometer system for any reflector. The composites' shock Hugoniots were obtained in terms of shock velocity, particle velocity, and shock stress, and a theoretical model for predicting the Hugoniots of the composites was proposed. The results revealed that a steady shock front was generated and propagated in the composites. The shock stress was attenuated with the propagation distance and the attenuation effect became more obvious as the stress increased. The shock velocity had a linear relationship with the particle velocity and the relationships for the composites with 40 and 50 vol% Al were very similar. By comparing the Hugoniots of the three materials and rubber, it was found that the shock behavior of the composites was similar to that of the matrix rubber. Additionally, the rubbery type shock response changed as the aluminum content increased. The shock behavior of the composites was adequately described by the proposed theoretical model.

Investigation on equation of state and ionization equilibrium for aluminum in warm dense matter regime

Warm dense matter is widely found in the high-energy-density-physics researches, such as inertial confinement fusion, X-ray source and wire-array Z-pinch. The equation of state and ionization equilibrium of material in warm dense matter regime play a significant role in explaining experimental results and simulations of physical process. In this paper, the Coulomb interaction between charged particles, and the excluded volume effect due to high density and polarization effect between neutral atoms and charged particles are considered in the equation of state for aluminum in warm dense matter regime. A non-ideal Saha equation is used to account for the ionization equilibrium. The data for pressure and concentration of particles of aluminum plasma are derived by iteration between equation of state and ionization equilibrium model. The pressure and average ionization degree of aluminum plasma are consistent with the calculation results from other models and relevant experimental data. The Coulomb interaction, which dominants the non-ideal effects, is insensitive to temperature and increases with density rising especially near the region of critical density. The excluded volume effect peaks at a density of ～0.5 g/cm<sup>3</sup>. The polarization effect first becomes stronger with density increasing and then decreases at a density of ～0.4 g/cm<sup>3</sup>. The ionization equilibrium results with density ranging from 1.0 × 10<sup>–4</sup> g/cm<sup>3</sup> to 3.0 g/cm<sup>3</sup> and temperature ranging from 1.0 × 10<sup>4</sup> K to 3.0 × 10<sup>4</sup> K reveal that the average ionization degree increases with density sharply increasing near the critical density. The non-ideal effects, which lead the ionization energy to decline and the effective ionization potential of specific ions in aluminum plasma to decrease substantially, are responsible for the sharp increase of average ionization degree near the region of critical density. When the temperature is lower than 12000 K, first and second stage of ionization occur in aluminum plasma, and the system is mainly composed of Al<sup>1+</sup>, Al<sup>2+</sup> and electrons. The average ionization degree can reach 2 at critical density. The third stage of ionization is dominant in the aluminum plasma when plasma temperature is higher than 12000 K. And then, the charged particles in the plasma are composed of Al<sup>3+</sup> and electrons, allowing the average ionization degree to reach 3 at critical density.

Equation of state for aluminum in warm dense matter regime**Project supported by the National Natural Science Foundation of China (Grant No. 51807050), the National Basic Research Program of China (Grant No. 2015CB251002) and the Program for the Top Young and Middle-aged Innovative Talents of Higher Learning Institutions of Hebei, China (Grant No. BJ2017038).

A semi-empirical equation of state model for aluminum in a warm dense matter regime is constructed. The equation of state, which is subdivided into a cold term, thermal contributions of ions and electrons, covers a broad range of phase diagram from solid state to plasma state. The cold term and thermal contribution of ions are from the Bushman–Lomonosov model, in which several undetermined parameters are fitted based on equation of state theories and specific experimental data. The Thomas–Fermi–Kirzhnits model is employed to estimate the thermal contribution of electrons. Some practical modifications are introduced to the Thomas–Fermi–Kirzhnits model to improve the prediction of the equation of state model. Theoretical calculation of thermodynamic parameters, including phase diagram, curves of isothermal compression at ambient temperature, melting, and Hugoniot, are analyzed and compared with relevant experimental data and other theoretical evaluations.

Adiabatic release measurements in aluminum between 400 and 1200 GPa: Characterization of aluminum as a shock standard in the multimegabar regime

Aluminum has been used prolifically as an impedance matching standard in the multimegabar regime (1 Mbar = 100 GPa), particularly in nuclear driven, early laser driven, and early magnetically driven flyer plate experiments. The accuracy of these impedance matching measurements depends upon the knowledge of both the Hugoniot and release or reshock response of aluminum. Here, we present the results of several adiabatic release measurements of aluminum from $\ensuremath{\sim}400\text{--}1200$ GPa states along the principal Hugoniot using full density polymethylpentene (commonly known as TPX), and both $\ensuremath{\sim}190$ and $\ensuremath{\sim}110$ mg/cc silica aerogel standards. These data were analyzed within the framework of a simple, analytical model that was motivated by a first-principles molecular dynamics investigation into the release response of aluminum, as well as by a survey of the release response determined from several tabular equations of state for aluminum. Combined, this theoretical and experimental study provides a method to perform impedance matching calculations without the need to appeal to any tabular equation of state for aluminum. As an analytical model, this method allows for propagation of all uncertainty, including the random measurement uncertainties and the systematic uncertainties of the Hugoniot and release response of aluminum. This work establishes aluminum for use as a high-precision standard for impedance matching in the multimegabar regime.

Two-temperature equation of state for aluminum and gold with electrons excited by an ultrashort laser pulse

A short laser pulse converts metal into a two- temperature state with the electron temperature higher than the ion temperature. To describe the electron contributions to the total internal energy and pressure arising as a result of electron heating, we develop the new analytic approxi- mation formulae for two-temperature thermodynamics of metal. Those approximations are based on quantum cal- culations performed with density functional theory (DFT) packages. DFT calculations provide the internal energies and pressures for densities of the order of solid-state den- sity and for electron temperatures up to 55 kK. The new analytic approximations give a better accuracy in hydrody- namic simulation of laser-matter interaction and should be used instead of the less accurate expressions based on the Fermi model of ideal electron gas, which is widely used for two-temperature states of metal.

Quantum molecular dynamics simulation of shock-wave experiments in aluminum

We present quantum molecular dynamics calculations of principal, porous, and double shock Hugoniots, release isentropes, and sound velocity behind the shock front for aluminum. A comprehensive analysis of available shock-wave data is performed; the agreement and discrepancies of simulation results with measurements are discussed. Special attention is paid to the melting region of aluminum along the principal Hugoniot; the boundaries of the melting zone are estimated using the self-diffusion coefficient. Also, we make a comparison with a high-quality multiphase equation of state for aluminum. Independent semiempirical and first-principle models are very close to each other in caloric variables (pressure, density, particle velocity, etc.) but the equation of state gives higher temperature on the principal Hugoniot and release isentropes than ab initio calculations. Thus, the quantum molecular dynamics method can be used for calibration of semiempirical equations of state in case of lack of experimental data.

Equation of state for aluminum containing helium bubbles

A theoretical model for equation of state (EOS) of aluminum with helium bubbles is presented. Based on this EOS, the influence of helium bubbles on shock loading is examined. The Hugoniot curve (temperature versus pressure as well as shock velocity versus particle velocity) for aluminum containing bubbles is calculated for various bubbles mass, bubbles percentage, and helium EOS models. The bubble mass and concentration seem to affect the measurably Hugoniot curve. The EOS model, implied for the helium in the bubbles, has minor significance, which means our model is not sensitive to the details of the helium EOS. Our findings are consistent with experiments available in the literature.

Semi-empirical equation of state of metals. Equation of state of aluminum

A semi-empirical equation of state for metals is described. Its capabilities are demonstrated by the example of the equation of state for aluminum. New experimental data are presented on the location of the isentrope of aluminum for unloading from the state at p = 229.71 GPa on the shock adiabat to an aerogel (SiO2) of density 0.08 g/cm3.

Multi-phase equation of state for aluminum

AbstractResults of theoretical calculations and experimental measurements of the equation of state (EOS) at extreme conditions are discussed and applied to aluminum. It is pointed out that the available high pressure and temperature information covers a broad range of the phase diagram, but only irregularly and, as a rule, is not thermodynamically complete; its generalization can be done only in the form of a thermodynamically complete EOS. A multi-phase EOS model is presented, accounting for solid, liquid, gas, and plasma states, as well as two-phase regions of melting and evaporation. The thermodynamic properties of aluminum and its phase diagram are calculated with the use of this model. Theoretical calculations of thermodynamic properties of the solid, liquid, and plasma phases, and of the critical point, are compared with results of static and dynamic experiments. The analysis deals with thermodynamic properties of solid aluminum at T = 0 and 298 K from different band-structure theories, static compression experiments in diamond anvil cells, and the information obtained in isentropic-compression and shock-wave experiments. Thermodynamic data in the liquid state, resulting from traditional thermophysical measurements, “exploding wire” experiments, and evaluations of the critical point are presented. Numerous shock-wave experiments for aluminum have been done to measure shock adiabats of crystal and porous samples, release isentropes, and sound speed in shocked metal. These data are analyzed in a self-consistent manner together with all other available data at high pressure.The model's results are shown for the principal shock adiabat, the high-pressure melting and evaporation regions and the critical point of aluminum. New experimental and theoretical data helped to improve the description of the high-pressure, high-temperature aluminum liquid. The present EOS describes with high accuracy and reliability the complete set of available information.

Equation of State for Aluminum

An analytical equation of state is developed for molten aluminum in the temperature range 1600–2400 K. The equation is derived from that by Ihm, Song and Mason (Ihm et al., 1991) in conjunction with the corresponding states correlations of Ghatee and Boushehri (1996). The densities predicted at corresponding temperatures and pressures are fairly consistent with the experiment, at most within ±1%.

Theoretical equation of state for aluminum

Theoretical methods for calculating equations of state are discussed and applied to aluminum. The model includes a treatment of melting, vaporization, and thermal electronic excitation. The thermal electronic terms are shown to cause a plasma phase transition in the hot expanded fluid, affecting the unloading behavior from shocked states. The calculations give good agreement with experimental Hugoniot data, the melting curve, and isobaric expansion measurements.

A new equation of state for aluminum

A new equation of state (EOS) has been produced for aluminum, which accurately reproduces experimental data for both the liquid and solid states. It also has a melting transition that reproduces measurements of the temperature vs pressure along the melt line. The liquid part of the EOS was calculated with the soft-sphere model for liquid metals, and the solid EOS is based upon a Birch-equation cold curve and Grüneisen thermal contributions. The range of the table extends from room temperature to 1.6 eV and from densities of 10−3–103 g/cm3.

Theory of the aluminum shock equation of state to 10 4 Mbar

A composite theoretical shock equation of state for aluminum is compared with experimental data, including new Soviet data to 4000 Mbar. Overall agreement is good, showing that current theoretical models of hot, dense matter are adequate. Significant electron shell structure effects are predicted by ionization equilibrium and self-consistent field models to occur in the 100 Mbar region, but better experimental precision is needed for testing the models here.

Electronic Grüneisen parameter in the shock Hugoniot equation of state of aluminum

The shock Hugoniot equation of state for aluminum has been computed, using the pseudopotential method. The nuclear Gru neisen parameters, used in evaluating the ionic vibration contributions, have been derived from phonon frequencies. The computed electronic Gru neisen-parameter values depart considerably from the value 0.5, used often in analyzing shock-compression experiments. This leads to different Hugoniot temperatures compared with those derived by Al'tshuler et al., although the P-V curve is in good agreement with their experimental results.

An experimental equation of state for aluminum to the debye approximation

An equation of state for aluminum to the Debye approximation has been obtained from the determination of the Debye temperature, Θ, as a function of pressure from 0 to 135 kbar. The variation was determined by use of the Bloch-Grüneisen equation in fitting experimental resistance-temperature data at various pressures. The zero pressure thermodynamic properties of aluminum calculated from the equation of state agree quite well with the corresponding observed quantities. It is found that the Grüneisen ratio, − dln Θ/ dln V, is a linear function of volume at pressures above 40 kbar. An analytical expression which approximates the observed volume dependence of the Debye temperature is given by, Θ = 395 exp( −1.78ΔV V 0 )

An experimental equation of state for aluminum to the debye approximation

An experimental equation of state for aluminum to the debye approximation