Issues in the calculations of dc conductivity of warm dense aluminium

Abstract

In the Ziman-Evans formulation, the electrical resistivity involves several quantities like the plasma mean ionization and chemical potential, the electron-ion scattering cross-section, the ion-ion structure factor, and the derivative of the Fermi distribution with respect to electron energy. Therefore, to make significant progress while comparing different models or analysing experimental measurements, it is important to try to get insight into such partial physical quantities.In the present work, we propose to investigate the sensitivity of the resistivity to the different physical quantities required for its computation.

On the Thomas–Fermi model: Gabor J. Kalman's contribution and numerical approximations

“…dp, (7) with V(r 0 ) = z 2 ∕r 0 , V ′ (r 0 ) = −z 2 ∕r 2 0 and V(r) ≈ (Ze)∕r as r → 0. The quantity z = 4𝜋n(r 0 )r 3 0 ∕3 represents the free-electron number, n(r) being the total electron density.…”

“…where (4p4d4f ) 7 means that one has to consider all the possibilities to make (4p) x (4d) y (4d) z with x + y + z = 7 and of course x ≤ 6, y ≤ 10 and z ≤ 14. This results in 35 possibilities, and finally S contains 315 configurations.…”

“…New approaches based on density functional theory are given in Reference [6]. The average‐atom approach—in addition to the Thomas–Fermi calculations discussed here—has been explored more thoroughly (see for instance Reference [7]). The Thomas–Fermi statistical model is relatively simple and has proven to be a powerful method to calculate average properties of the plasma, such as its equation of state and mean ionization.…”

Multi-Configuration Calculation of Ionization Potential Depression

“…where Y m (θ, φ) are the usual spherical harmonics. As the potential is constant outside the ion sphere, the radial wave function of a bound state outside the ion sphere can be written as y n (r) = A n r κ (−ikr) (10) where κ is the modified spherical wave function of the third kind, and the wave vector k is defined as k = √ 2 . The constant A n is determined by the normalization and the boundary conditions at R ws .…”

“…Ionization potential depression (IPD) or continuum lowering in dense plasmas has been the subject of many investigations over the past years [3][4][5][6]. This many-body effect significantly alters the ionization balance and the corresponding charge state distribution, which have a strong influence on thermodynamic [7], transport [8][9][10] and radiative properties of the system [11,12]. Such a topic is of crucial importance for astrophysics (stellar physics, planetary science, ...) [13][14][15][16], solid state physics and inertial confinement fusion [17,18].…”