Combined pressure and electrical-resistivity measurements of warm dense aluminum and titanium plasmas

Average-atom Ziman resistivity calculations in expanded metallic plasmas: Effect of mean ionization definition

We present calculations of electrical resistivity for expanded boron, aluminum, titanium, and copper plasmas using the Ziman formulation in the framework of the average-atom model. Our results are compared to experimental data, as well as to other theoretical calculations, relying on the Ziman and Kubo-Greenwood formulations, and based on average-atom models or quantum-molecular-dynamics simulations. The impact of the definition of ionization, paying particular attention to the consistency between the definition and the perfect free electron gas assumption made in the formalism, is discussed. We propose a definition of the mean ionization generalizing to expanded plasmas the idea initially put forward for dense plasmas, consisting in dropping the contribution of quasibound states from the ionization due to continuum ones. It is shown that our recommendation for the calculation of the quasibound density of states provides the best agreement with measurements.

Consistent approach for electrical resistivity within Ziman's theory from solid state to hot dense plasma: Application to aluminum

The approach presented in this work allows a consistent calculation of electrical conductivity of dense matter from the solid state to the hot plasma using the same procedure, consisting in dropping elastic scattering contributions to solid's and liquid's structure factors in the framework of the Ziman theory. The solid's structure factor was computed using a multiphonon expansion. The elastic part is the zero-phonon term and corresponds to Bragg peaks, thermally damped by Debye-Waller attenuation factors. For the liquid, a similar elastic contribution to the structure factor results from a long-range order persisting during the characteristic electron-ion scattering time. All the quantities required for the calculation of the resistivities are obtained from our average-atom model, including the total hypernetted-chain structure factor used from the liquid state to the plasma. No interpolation between two limiting structure factors is required. We derive the correction to apply to the resistivity in order to account for the transient long-range order in the liquid and show that it improves considerably the agreement with quantum-molecular dynamics simulations and experimental aluminum's isochoric and isobaric conductivities. Our results suggest that the long-range order in liquid aluminum could be a slightly compressed fcc one. Two series of ultrafast experiments performed on aluminum were also considered, the first one by Milchberg et al. using short laser pulses and the second one by Sperling et al. involving x-ray heating and carried out on the Linac Coherent Light Source facility. Our attempts to explain the latter assuming an initial liquid state at an ion temperature much smaller than the electron one suggest that the actual initial state before main heating is neither perfectly solid nor a normal liquid.

Importance of finite-temperature exchange correlation for warm dense matter calculations

The effects of an explicit temperature dependence in the exchange correlation (XC) free-energy functional upon calculated properties of matter in the warm dense regime are investigated. The comparison is between the Karasiev-Sjostrom-Dufty-Trickey (KSDT) finite-temperature local-density approximation (TLDA) XC functional [Karasiev et al., Phys. Rev. Lett. 112, 076403 (2014)PRLTAO0031-900710.1103/PhysRevLett.112.076403] parametrized from restricted path-integral Monte Carlo data on the homogeneous electron gas (HEG) and the conventional Monte Carlo parametrization ground-state LDA XC [Perdew-Zunger (PZ)] functional evaluated with T-dependent densities. Both Kohn-Sham (KS) and orbital-free density-functional theories are used, depending upon computational resource demands. Compared to the PZ functional, the KSDT functional generally lowers the dc electrical conductivity of low-density Al, yielding improved agreement with experiment. The greatest lowering is about 15% for T=15 kK. Correspondingly, the KS band structure of low-density fcc Al from the KSDT functional exhibits a clear increase in interband separation above the Fermi level compared to the PZ bands. In some density-temperature regimes, the deuterium equations of state obtained from the two XC functionals exhibit pressure differences as large as 4% and a 6% range of differences. However, the hydrogen principal Hugoniot is insensitive to the explicit XC T dependence because of cancellation between the energy and pressure-volume work difference terms in the Rankine-Hugoniot equation. Finally, the temperature at which the HEG becomes unstable is T≥7200 K for the T-dependent XC, a result that the ground-state XC underestimates by about 1000 K.

Isochoric heating of foamed metal using pulsed power discharge as a making technique of warm dense matter

To generate well-defined warm dense state for evaluating electrical conductivity by using pulsed-power discharge, we have proposed an isochoric heating of foamed metal. Isochoric heating can be achieved by surrounding the foamed metal with a rigid-walled sapphire capillary. We evaluate the temperature and electrical conductivity of the foam∕plasma based on the line-pair method of the foam∕plasma emission and on the voltage-current waveforms. The electrical conductivity observed agrees with previous experiments and predictions. Thus, the proposed technique yields the electrical conductivity of warm dense matter with a well-defined temperature.

Electrical conductivity of dense Al, Ti, Fe, Ni, Cu, Mo, Ta, and W plasmas

We report measurements of electrical conductivity of eight metals in the plasma state at densities ranging from 0.002 to 0.5 times solid density, and with internal energy from 2 to 30 kJ/gm. Data are presented as functions of internal energy and specific volume. Conductivity is observed to fall as the plasma expands for fixed internal energy, and for all but tantalum and titanium shows a minimum at approximately 0.01 times solid density, followed by an increase as the density decreases further.

Pressure and electrical resistivity measurements on hot expanded nickel: comparisons with quantum molecular dynamics simulations and average atom approaches

We present experimental results on pressure and resistivity on expanded nickel at a density of 0.1 g/cm3 and temperature of a few eV. These data, corresponding to the warm dense matter regime, are used to benchmark different theoretical approaches. A comparison is presented between fully three-dimensional quantum molecular dynamics (QMD) methods, based on density functional theory, with average atom methods, that are essentially one dimensional. In this regime the evaluation of the thermodynamic properties as well as electrical properties is difficult due to the concurrence of density and thermal effects which directly drive the metal-nonmetal transition. Experimental pressures and resistivities are given in a tabular form with temperatures deduced from QMD simulations.

Picosecond short-range disordering in isochorically heated aluminum at solid density

Using ultrafast x-ray probing, we experimentally observed a progressive loss of ordering within solid-density aluminum as the temperature raises from 300 K to >10{4} K. The Al sample was isochorically heated by a short ( approximately ps), laser-accelerated proton beam and probed by a short broadband x-ray source around the Al K edge. The loss of short-range ordering is detected through the progressive smoothing of the time-resolved x-ray absorption near-edge spectroscopy (XANES) structure. The results are compared with two different theoretical models of warm dense matter and allow us to put an upper bound on the onset of ion lattice disorder within the heated solid-density medium of approximately 10 ps.

Measurements of terahertz electrical conductivity of intense laser-heated dense aluminum plasmas

We report the electrical conductivity of laser-produced warm dense aluminum plasmas measured using single-shot ultrafast terahertz (THz) frequency spectroscopy. In contrast with experiments performed at optical frequencies, measurements based upon THz probe reflectivity directly determine a quasi-dc electrical conductivity, and therefore the analysis does not require a free-electron Drude model based extrapolation to recover the near zero frequency conductivity. In fact, our experimental results indicate that the Drude model breaks down for warm (>0.6 eV), moderate-dense (<1.6 g/cm(3)) aluminum at THz frequencies. A calculation of THz reflectivity over a non-Fresnel boundary in dense plasmas is also presented.

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.

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.

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

Isochore measurements were performed in the warm dense matter regime. Pressure and internal energy variation of aluminum plasma (density 0.1 g/cm(3) and 0.3 g/cm(3)) are measured using a homogeneous and thermally equilibrated media produced inside an isochoric plasma closed vessel in the internal energy range 20-50 MJ/kg. These data are compared to detailed calculations obtained from ab initio quantum molecular dynamics, average atom model within the framework of the density functional theory, and standard theories. A dispersion between theoretical isochore equation of state is found in the studied experimental thermodynamic regime.

Electrical conductivity of hot expanded aluminum: experimental measurements and ab initio calculations

Experimental measurements and theoretical calculations of the electrical conductivity of aluminum are presented in the strongly coupled partially degenerate regime (rho=0.3 g/cm(3), 5000<T<15 000 K). The experiments were performed in an isochoric plasma closed vessel designed to confine electrical plasma discharges up to 1.5 GPa. Aluminum properties were determined theoretically by ab initio molecular dynamics simulations in the local density approximation, from which the conductivity was computed using the Kubo-Greenwood formula. The theoretical results were validated in the dense coupled regime against previously published experimental results and then applied to our experimental low density regime, showing that the theoretical results overestimate the experimental conductivities.