• Lecherbourg, L.
• Recoules, V.
• Jourdain, N.
• Renaudin, P.
• Dorchies, Fabien

Abstract

Using ab initio molecular-dynamics simulations combined with linear-response theory, we studied the x-ray absorption near-edge spectra (XANES) of a two-temperature dense copper plasma. As the temperature increases, XANES spectra exhibit a pre-edge structure balanced by a reduction of the absorption just behind the edge. By performing systematic simulations for various thermodynamic conditions, we establish a formulation to deduce the electronic temperature T e directly from the spectral integral of the pre-edge that can be used for various thermodynamic conditions encountered in a femtosecond heating experiment where thermal nonequilibrium and expanded states have to be considered. Time resolved x-ray absorption near-edge spectroscopy (TR-XANES) was recently extended to the warm dense matter (WDM) regime [1]. This highly transient physics has required specific development to get an appropriate time-resolution (picosecond or less) on XANES measurements. TR-XANES gives a complete picture by probing simultaneously the valence electrons and the atomic local arrangement modifications in WDM situations well beyond the melting. However, the physical interpretation of XANES spectra is not straightforward and a strong connection between theory and experiment is needed to extract information. This issue has been addressed using ab initio molecular dynamics (AIMD) simulations, providing a consistent description of both the electronic and ionic structures, together with x-ray absorption spectra calculation [2,3]. In the past decade, both theoretical and experimental XANES spectroscopy was used to get a deep understanding of the electronic structure modification of metals in the WDM. On aluminum, XANES modification during the solid-liquid-vapor phase transition was observed with picosecond time resolution [4]. With the support of AIMD simulations, this has shown the connection between electronic and ionic modifications. Comparison between measurements and calculations for molybdenum have demonstrated that XANES spectra can be simply interpreted in terms of electron DOS modification when solid molybdenum turns to WDM [5]. Besides the understanding of the phenomena involved, it is possible to have access to the time scales of phase transitions [4,6,7]. XANES spectra were also used to shed light on the DOS modification induced by laser shock compression in metals such as aluminum [8,9] and iron [10,11]. When WDM is transiently produced by femtosecond laser heating, matter faces nonequilibrium situations. It is a great * vanina.recoules@cea.fr scientific challenge to independently resolve the electron and ion dynamics. In principle, TR-XANES can address this physics, but it is necessary to disentangle the corresponding features in XANES spectra, which depend on the considered element. In some light metals such as Be [12] and Al [13], the electronic temperature can be retrieved directly from the slope of the absorption K edge. In most metals with a localized d band, the situation is more complex and this methodology cannot be applied. Recent experiments have been dedicated to femtosecond laser-heated warm dense copper on a synchrotron beamline [3,14]. Using 2-ps time-resolved x-ray spectroscopy, Cho et al. investigated the modification of XANES spectra near the L 2,3 edge. By direct comparison between measured spectra and spectra computed using AIMD, they retrieved the time evolution of the electron temperature and compare it to the behavior obtained using a two-temperature model. The purpose of the present paper is to go further in the calculations and analysis of warm dense copper using AIMD simulations. The interpretation of XANES spectra especially for transition metal is nontrivial and requires a careful analysis. The relation between the electronic temperature T e and pre-edge peak is reproduced. A quasilinear function is extracted to deduce absolute values of T e (up to 3 eV) from the spectral integration of the pre-edge. The impacts of ion temperature T i and density are carefully and independently studied. This shows the validity of this function in the various thermodynamic conditions encountered in a femtosecond heating experiment, including strong thermal nonequilibrium. This provides a practical T e diagnostic to analyze any XANES experiment without the need of additional AIMD calculations. It has been used in a recently published paper that revisits the electron-ion thermal equilibration dynamics on a tabletop setup, emphasizing the critical role of target expansion [15]. Other features are identified above the L edge, in close relation with the crystalline structure.

Topics

• density
• impedance spectroscopy
• molybdenum
• phase
• theory
• experiment
• simulation
• aluminium
• molecular dynamics
• laser emission spectroscopy
• phase transition
• copper
• iron
• X-ray spectroscopy