Aluminum equation-of-state data in the warm dense matter regime

Real-space formulation of the stress tensor for O(N) density functional theory: Application to high temperature calculations

We present an accurate and efficient real-space formulation of the Hellmann-Feynman stress tensor for O(N) Kohn-Sham density functional theory (DFT). While applicable at any temperature, the formulation is most efficient at high temperature where the Fermi-Dirac distribution becomes smoother and the density matrix becomes correspondingly more localized. We first rewrite the orbital-dependent stress tensor for real-space DFT in terms of the density matrix, thereby making it amenable to O(N) methods. We then describe its evaluation within the O(N) infinite-cell Clenshaw-Curtis Spectral Quadrature (SQ) method, a technique that is applicable to metallic and insulating systems, is highly parallelizable, becomes increasingly efficient with increasing temperature, and provides results corresponding to the infinite crystal without the need of Brillouin zone integration. We demonstrate systematic convergence of the resulting formulation with respect to SQ parameters to exact diagonalization results and show convergence with respect to mesh size to the established plane wave results. We employ the new formulation to compute the viscosity of hydrogen at 10⁶ K from Kohn-Sham quantum molecular dynamics, where we find agreement with previous more approximate orbital-free density functional methods.

Single-Shot Multi-keV X-Ray Absorption Spectroscopy Using an Ultrashort Laser-Wakefield Accelerator Source

Single-shot absorption measurements have been performed using the multi-keV x rays generated by a laser-wakefield accelerator. A 200 TW laser was used to drive a laser-wakefield accelerator in a mode which produced broadband electron beams with a maximum energy above 1 GeV and a broad divergence of ≈15  mrad FWHM. Betatron oscillations of these electrons generated 1.2±0.2×10^{6}  photons/eV in the 5 keV region, with a signal-to-noise ratio of approximately 300∶1. This was sufficient to allow high-resolution x-ray absorption near-edge structure measurements at the K edge of a titanium sample in a single shot. We demonstrate that this source is capable of single-shot, simultaneous measurements of both the electron and ion distributions in matter heated to eV temperatures by comparison with density functional theory simulations. The unique combination of a high-flux, large bandwidth, few femtosecond duration x-ray pulse synchronized to a high-power laser will enable key advances in the study of ultrafast energetic processes such as electron-ion equilibration.

Path integral Monte Carlo simulations of warm dense aluminum

We perform first-principles path integral Monte Carlo (PIMC) and density functional theory molecular dynamics (DFT-MD) calculations to explore warm dense matter states of aluminum. Our equation of state (EOS) simulations cover a wide density-temperature range of 0.1-32.4gcm^{-3} and 10^{4}-10^{8} K. Since PIMC and DFT-MD accurately treat effects of the atomic shell structure, we find two compression maxima along the principal Hugoniot curve attributed to K-shell and L-shell ionization. The results provide a benchmark for widely used EOS tables, such as SESAME, QEOS, and models based on Thomas-Fermi and average-atom techniques. A subsequent multishock analysis provides a quantitative assessment for how much heating occurs relative to an isentrope in multishock experiments. Finally, we compute heat capacity, pair-correlation functions, the electronic density of states, and 〈Z〉 to reveal the evolution of the plasma structure and ionization behavior.

Variational-average-atom-in-quantum-plasmas (VAAQP) code and virial theorem: equation-of-state and shock-Hugoniot calculations for warm dense Al, Fe, Cu, and Pb

The numerical code VAAQP (variational average atom in quantum plasmas), which is based on a fully variational model of equilibrium dense plasmas, is applied to equation-of-state calculations for aluminum, iron, copper, and lead in the warm-dense-matter regime. VAAQP does not impose the neutrality of the Wigner-Seitz ion sphere; it provides the average-atom structure and the mean ionization self-consistently from the solution of the variational equations. The formula used for the electronic pressure is simple and does not require any numerical differentiation. In this paper, the virial theorem is derived in both nonrelativistic and relativistic versions of the model. This theorem allows one to express the electron pressure as a combination of the electron kinetic and interaction energies. It is shown that the model fulfills automatically the virial theorem in the case of local-density approximations to the exchange-correlation free-energy. Applications of the model to the equation-of-state and Hugoniot shock adiabat of aluminum, iron, copper, and lead in the warm-dense-matter regime are presented. Comparisons with other approaches, including the inferno model, and with available experimental data are given. This work allows one to understand the thermodynamic consistency issues in the existing average-atom models. Starting from the case of aluminum, a comparative study of the thermodynamic consistency of the models is proposed. A preliminary study of the validity domain of the inferno model is also included.

An average atom code for warm matter: application to aluminum and uranium

In astrophysics and in other sciences there is sometimes a need for information about the properties of matter, particularly equations of state, in extreme conditions of pressure and temperature. Global equation of state models, which represent solid, fluid and plasma states, typically consist of three parts: the cold curve, the ion-thermal contribution and the electron-thermal contribution. For the calculation of the latest part we present here an average atom embedded in a jellium code. We employ Liberman's relativistic and quantum model of matter which is a significant advance in complexity beyond the commonly used Thomas-Fermi model. We have applied specific algorithms to deal with the highly oscillatory nature of the free wavefunctions at high temperatures and to capture resonances which form in the continuum when bound states are destroyed by pressure ionization. Also we use massive parallel computing to treat the huge number of free wavefunctions at high temperatures (up to 10(9) K). Densities of states of resonant states are shown for uranium. With our code, which we have called Paradisio, we obtain tables of electron-thermal entropies from which free energies and pressures are derived. Our results are compared with those calculated in the Thomas-Fermi approximation and with available experiments. In aluminum, with our quantum code, a shell structure appears on the Hugoniot and a first-order metallic-nonmetallic transition is created at low densities and temperatures.

Equation of state for a partially ionized gas. III

The derivation of equations of state for fluid phases of a partially ionized gas or plasma is addressed from a fundamental point of view. The results of the Thomas-Fermi model always yield pressures which are less than or equal to that of an ideal Fermi gas. On the other hand, the spherical cellular model shows significant "overpressure" relative to the ideal Fermi gas in certain regions of low density and low temperature. This effect is studied in considerable detail. A nonthermodynamic region, more or less overlapping the regions of overpressure, is found. It is characterized by a negative specific heat at constant volume. An independent electron model within a Z -electron cell is employed. The inadequacy of the wave function in the low-density, low-temperature nonthermodynamic region is shown to be the cause of this overpressure. Numerical examples of the theory for several elements (Li, N, Al, K, and Er) are reported. These results reduce in various limits of temperature and density to the expected behavior, except in the aforementioned region.

Experiments and simulations on hot expanded boron

We measured the thermodynamical and transport properties of boron in the warm dense matter regime ( 15000 K<T<25000 K and rho=0.094 g/cm3). Experimental data are compared with quantum molecular dynamics (QMD) simulations. We find a very good agreement between data and calculations, which permits us to transform experimental energies into temperatures, and allows us to compare conductivities with an average atom model coupled with a Kubo-Greenwood calculations. Contact is made between computationally intensive QMD simulation codes and fast average atom models.

Electronic structure and equation of state data of warm dense gold

Equation of state data and electrical resistivity of warm dense gold were measured in the internal energy range 8 - 12 MJ/kg. Experimental results were compared with quantum molecular dynamics simulations. The theoretical results match well the experimental data, allowing a detailed interpretation of the theoretical thermodynamic properties and frequency-dependent conductivities.

Critical Properties of Aluminum

Gibbs ensemble Monte Carlo calculations are performed using a validated embedded-atom potential to obtain the vapor-liquid coexistence curve for elemental aluminum in good agreement with available experimental data up to the boiling point. These calculations are then extended to make a reliable prediction of the critical temperature, pressure, and density of Al, which have previously been known only with very large uncertainties. This demonstrates the ability of modern simulations to predict fundamental physical properties that are extremely difficult to measure directly.

Equation of state for partially ionized carbon at high temperatures

Equation of state for partially ionized carbon at temperatures T approximately > or = 10(5) K is calculated in a wide range of densities, using the method of free energy minimization in the framework of the chemical picture of plasmas. The free energy model includes the internal partition functions of bound species. The latter are calculated by a self-consistent treatment of each ionization stage in the plasma environment taking into account pressure ionization. The long-range Coulomb interactions between ions and screening of the ions by free electrons are included using our previously published analytical model.

Equation of state and transport coefficients for dense plasmas

We hereby present a model to describe the thermodynamic and transport properties of dense plasmas. The electronic and ionic structures are determined self-consistently using finite-temperature density functional theory and Gibbs-Bogolyubov inequality. The main thermodynamic quantities, i.e., internal energy, pressure, entropy, and sound speed, are obtained by numerical differentiation of the plasma total Helmholtz free energy. Electronic electrical and thermal conductivities are calculated from the Ziman approach. Ionic transport coefficients are estimated using those of hard-sphere system and the Rosenfeld semiempirical "universal" correspondence between excess entropy and dimensionless transport coefficients of dense fluids. Numerical results and comparisons with experiments are presented and discussed.