Energy conservation and pressure relaxation in an extended two-temperature model for copper with an electron temperature-dependent interaction potential

Abstract

An implementation of an electron temperature-dependent interaction potential for copper in a two-temperature model-molecular dynamics framework is presented. An algorithm for enforcing energy conservation when using such an interaction is provided that is needed due to the changing interaction strength with the degree of excitation. Furthermore, focus is put on how to treat the pressure differences due to an electron temperature gradient following laser irradiation. The influence of various extensions is investigated in large-scale two-temperature model molecular dynamics simulations and compared to existing approaches.

Figures (13)

• Figure 1: Left: Cohesive free energy of copper depending on the density at various electron temperatures. Right: Single-atom energy depending on the electron temperature. The single-atom energies are fit to a second-order polynomial with the parameters that are given in table \ref{['tab:Fit_parameters']}. RT stands for room temperature, i.e. 0.025851eV. Both figures have previously been shown in Kuemmel_2025_MDT.
• Figure 2: Left: Electron energy of copper depending on the electron temperature obtained from DFT calculations Lin_2008_heat_capacity_coupling and fitted to a second-order polynomial. Right: Electron temperature-dependent electron pressure obtained from DFT calculations Kuemmel_2025_MDT with a second-order polynomial fit. The fit parameters of both are given in table \ref{['tab:Fit_parameters']}.
• Figure 3: Left: Total free energy per atom of various structures depending on the electron temperature. Centre: The same as on the left but shifted so that all free energy curves start at 0.0eV. Right: Total free energy per atom in the unexcited state with a fit to a second-order polynomial. In the left and centre figure, each line corresponds to a different structure with varying degree of disorder. The parameters are given in table \ref{['tab:Fit_parameters']}.
• Figure 4: Density-dependent fit parameters of the lattice energy, which itself depends on the electron temperature. On the left, the fit parameter $p_{k, 0}^{E_{\text{i}}}$, in the centre $p_{k, 1}^{E_{\text{i}}}$ and on the right $p_{k, 2}^{E_{\text{i}}}$ is shown. Each parameter is fitted to a sixth-order polynomial. The parameters of these polynomials are given in table \ref{['tab:fit_parameters_2']}.
• Figure 5: Visualization of the energy distribution in two situations. On the left, the energy of an FD cell changes due to laser light absorption, heat diffusion or advection from $T_{\text{e}}^{0} = 0.5eV$ to $T_{\text{e}}^{1} = 1.0eV$. After the total energy is distributed in such a way that electron energy and total free energy of the lattice correspond to the same electron temperature, a final electron temperature is found. On the right, the electron of the FD cell before the change of energy is above 1.2eV and the FD cell gains energy. Here, the IP is kept constant and the change of energy is completely compensated by the electron energy.