Thermal and Electrical Conductivities of Aluminum Up to 1000 eV: A First-Principles Prediction

Abstract

Accurate prediction of the thermal and electrical conductivities of materials under extremely high temperatures is essential in high-energy-density physics. These properties govern processes such as stellar core dynamics, planetary magnetic field generation, and laser-driven plasma evolution. However, first-principles methods like Kohn-Sham (KS) density functional theory (DFT) face challenges in predicting these properties due to prohibitively high computational costs. We propose a scheme that integrates the Kubo formalism with a mixed stochastic-deterministic DFT (mDFT) method, which substantially enhances efficiency in computing thermal and electrical conductivities of dense plasmas under extremely high temperatures. As a showcase, this approach enables {\it ab initio} calculations of the thermal and electrical conductivities of Aluminum (Al) up to 1000 eV. Compared to traditional transport models, our first-principles results reveal significant deviations in the thermal and electrical conductivities of Al within the warm dense matter regime, underscoring the importance of accounting for quantum effects when investigating these transport properties of warm dense matter.

Figures (4)

• Figure 1: (Color online) Current response functions $C_{mn}$ of Aluminum, at $T=20~\mathrm{eV}$ (blue) and $T=500~\mathrm{eV}$ (red), including (a) $C_{11}$, (b) $C_{12}$, and (c-d) $C_{22}$. Panel (d) shows the same data as in (c) but with the vertical scale enlarged by 100× for clarity.
• Figure 2: (Color online) (a) Electrical conductivity $\sigma$ and (b) thermal conductivity $\kappa$ of Al from 0.2 to 1000 eV. Shown for comparison are traditional plasma transport models, including the Spitzer model 53PR-Spitzer (green line) and the Lee-More model 84PF-Lee (blue line). Results based on average-atom models are also plotted: Shaffer et al.20E-Shaffer (yellow-gray line) and Wetta et al.20E-Wetta (orange line). First-principles calculations are given by KSDFT (dark red open hexagon) and mDFT (red stars). For $T < 10$ eV, KSDFT results are taken from our previous work 24B-Liu.
• Figure 3: (Color online) Contributions to electrical conductivities of different orbitals at temperatures of (a) 20 eV, (b) 100 eV, and (c) 1000 eV. Blue regions represent the contributions from pure KS orbitals (KS-KS). Red regions denote the additional contributions from mixed stochastic orbitals, which include both transitions between KS and stochastic orbitals (KS-sto) and transitions among stochastic orbitals themselves (sto-sto).
• Figure 4: (Color online) (a) Electronic isochoric heat capacity and (b) effective charge of Aluminum at different temperatures. "FEG" denotes results from the free-electron gas model, with $T \ll T_F$ corresponding to the strongly degenerate limit and $T \gg T_F$ to the weakly degenerate limit. "AA" refers to average-atom model results 23R-Callow. "DFT" results are obtained from KSDFT at $T \leq 10$ eV and from mDFT at higher temperatures.