Potential of mean force for electrical conductivity of dense plasmas

Abstract

The electrical conductivity in dense plasmas can be calculated with the relaxation-time approximation provided that the interaction potential between the scattering electron and the ion is known. To date there has been considerable uncertainty as to the best way to define this interaction potential so that it correctly includes the effects of ionic structure, screening by electrons and partial ionization. Current approximations lead to significantly different results with varying levels of agreement when compared to bench-mark calculations and experiments. We present a new way to define this potential, drawing on ideas from classical fluid theory to define a potential of mean force. This new potential results in significantly improved agreement with experiments and bench mark calculations, and includes all the aforementioned physics self-consistently

Model for the electrical conductivity in dense plasma mixtures

“…Setting N = 1 recovers the single species result, equation (26) of reference [20]. This potential can be rewritten as a sum of Hartree, ion-ion and ion-electron correlation, and electron-electron exchange and correlation terms.…”

Tabular electrical conductivity for aluminium

“…The table ranges from 10 −3 to 1 times solid density, taken here as 2.7 g/cm 3 , and from 10 −2 to 10 3 eV in temperature. We start by calculating the electrical conductivity for the full range of the table using the potential of mean force model by Starrett . This model uses the Bhatnagar, Gross, Krook (BGK) approximation (also known as the relaxation time approximation).…”

“…We start by calculating the electrical conductivity for the full range of the table using the potential of mean force model by Starrett. [15] This model uses the Bhatnagar, Gross, Krook (BGK) [24] approximation (also known as the relaxation time approximation). The electron relaxation time is calculated using the quantum mechanical expression for the momentum transport cross section.…”

“…Simulations around melt are notably difficult to perform with methods such as DFT; also the external constraint applied by the periodic boundary conditions on a small cell can lead to artificial effects, such that representing a disordered (liquid) system under these conditions becomes nontrivial. For F I G U R E 3 (Colour online) Isochore (2.7 g/cm 3 ) comparing the new table DFT-MD (this work), Sesame 29,371, [11] DFT-MD from Witte et al, [40] and the model by Starrett [15] (V MF (r)). DFT-MD, density functional theory-molecular dynamics F I G U R E 4 (Colour online) DFT-MD pair distribution functions along an isochore (2.7 g/cm 3 ).…”

“…We focus on aluminium as it is a widely used conductor, but the approach can be applied to other materials. We employ two methods: the accurate but expensive DFT molecular dynamics (DFT-MD), coupled with the Kubo-Greenwood (KG) approximation, [14] which is practical for degenerate systems, and the more approximate potential of mean force approach, [15,16] which is accurate for moderate to weakly degenerate plasma and is relatively inexpensive.It is also possible to use the KG method with the average atom model, [17][18][19][20][21][22] but we have opted not to use this approach as it remains to be proven that this contains the correct limiting behaviour at high temperature, and is…”