Atomic and Electronic Structure of Solid-Density Liquid Carbon

The structure of liquid carbon elucidated by in situ X-ray diffraction

Carbon has a central role in biology and organic chemistry, and its solid allotropes provide the basis of much of our modern technology1. However, the liquid form of carbon remains nearly uncharted2, and the structure of liquid carbon and most of its physical properties are essentially unknown3. But liquid carbon is relevant for modelling planetary interiors4,5 and the atmospheres of white dwarfs6, as an intermediate state for the synthesis of advanced carbon materials7,8, inertial confinement fusion implosions9, hypervelocity impact events on carbon materials10 and our general understanding of structured fluids at extreme conditions11. Here we present a precise structure measurement of liquid carbon at pressures of around 1 million atmospheres obtained by in situ X-ray diffraction at an X-ray free-electron laser. Our results show a complex fluid with transient bonding and approximately four nearest neighbours on average, in agreement with quantum molecular dynamics simulations. The obtained data substantiate the understanding of the liquid state of one of the most abundant elements in the universe and can test models of the melting line. The demonstrated experimental abilities open the path to performing similar studies of the structure of liquids composed of light elements at extreme conditions.

Time-Resolved X-ray Emission Spectroscopy and Resonant Inelastic X-ray Scattering Spectroscopy of Laser Irradiated Carbon

The existence of liquid carbon as an intermediate phase preceding the formation of novel carbon materials has been a point of contention for several decades. Experimental observation of such a liquid state requires nonthermal melting of solid carbon materials at various laser fluences and pulse properties. Reflectivity experiments performed in the mid-1980s reached opposing conclusions regarding the metallic or insulating properties of the purported liquid state. Time-resolved X-ray absorption studies showed shortening of C-C bonds and increasing diffraction densities, thought to evidence a liquid or glassy carbon state, respectively. Nevertheless, none of these experiments provided information on the electronic structure of the proposed liquid state. Herein, we report the results of time-resolved resonant inelastic X-ray scattering (RIXS) and time-resolved X-ray emission spectroscopy (XES) studies on amorphous carbon (a-C) and ultrananocrystalline diamond (UNCD) as a function of delay time between the irradiating pulse and X-ray probe. For both a-C and UNCD, we attribute decreases in RIXS or XES signals to transition blocking, relaxation, and finally, ablation. Increased signal at 20 ps following the irradiation of the UNCD is attributed to the probable formation of nanoscale structures in the ablation plume. Differences in the amount of signal observed between a-C and UNCD are explained by the difference in sample thickness and, specifically, incomplete melting of the UNCD film. Comparisons to spectral simulations based on MD trajectories at extreme conditions indicate that the carbon state in our experiments is crystalline. Normal mode analysis confirmed that symmetrical bending or stretching of the C-C bonds in the diamond lattice results in XES spectra with small intensity differences. Overall, we observed no evidence of melting to a liquid state, as determined by the lack of changes in the spectral properties for up to 100 ps delays following the melting pulses.

Saturable Absorption of Free-Electron Laser Radiation by Graphite near the Carbon K-Edge

The interaction of intense light with matter gives rise to competing nonlinear responses that can dynamically change material properties. Prominent examples are saturable absorption (SA) and two-photon absorption (TPA), which dynamically increase and decrease the transmission of a sample depending on pulse intensity, respectively. The availability of intense soft X-ray pulses from free-electron lasers (FELs) has led to observations of SA and TPA in separate experiments, leaving open questions about the possible interplay between and relative strength of the two phenomena. Here, we systematically study both phenomena in one experiment by exposing graphite films to soft X-ray FEL pulses of varying intensity. By applying real-time electronic structure calculations, we find that for lower intensities the nonlinear contribution to the absorption is dominated by SA attributed to ground-state depletion; our model suggests that TPA becomes more dominant for larger intensities (>10¹⁴ W/cm²). Our results demonstrate an approach of general utility for interpreting FEL spectroscopies.

AC/DC: The FERMI FEL Split and Delay Optical Device for Ultrafast X-ray Science

Free-electron lasers (FELs) are the most advanced class of light-sources, by virtue of their unique capability to lase high-brightness pulses characterized by wavelengths spanning the extreme-ultraviolet, the soft and hard X-ray spectral domains, as well as by temporal lengths lying in the femtosecond (fs) timescale. The next step to push the current standards in ultrafast X-ray science is strongly linked to the possibility of engineering and exploiting time-resolved experiments exclusively for FELs pulses, ideally having different colors tunable at specific electronic resonance of the chemical elements. At the seeded FERMI FEL (Trieste, Italy) this goal is committed to the optical device known as AC/DC, which stands for the auto correlator/delay creator. AC/DC is designed to double the incoming FEL pulse splitting the photon beam by inserting a grazing incidence flat mirror, thus preserving the spectral and temporal properties, and further delaying one of these two pulses in time. It can independently tune the FEL pulses fluence on the two optical paths by means of solid-state filters, too. Here, we present a detailed description about this optical device. Strong emphasis is dedicated to the AC/DC opto-mechanical design and to the laser-based feedback systems implemented to compensate for any mismatch affecting the FEL optical trajectory, ascribable to both mechanical imperfections and paraxial errors rising during a temporal delay scan.

Tomography of a seeded free-electron laser focal spot: qualitative and quantitative comparison of two reconstruction methods for spot size characterization

Performing experiments at free-electron lasers (FELs) requires an exhaustive knowledge of the pulse temporal and spectral profile, as well as the focal spot shape and size. Operating FELs in the extreme ultraviolet (EUV) and soft X-ray (SXR) spectral regions calls for designing ad-hoc optical layouts to transport and characterize the EUV/SXR beam, as well as tailoring its spatial dimensions at the focal plane down to sizes in the few micrometers range. At the FERMI FEL (Trieste, Italy) this task is carried out by the Photon Analysis Delivery and Reduction System (PADReS). In particular, to meet the different experimental requests on the focal spot shape and size, a proper tuning of the optical systems is required, and this should be monitored by means of dedicated techniques. Here, we present and compare two reconstruction methods for spot characterization: single-shot imprints captured via ablation on a poly(methyl methacrylate) sample (PMMA) and pulse profiles retrieved by means of a Hartmann wavefront sensor (WFS). By recording complementary datasets at and nearby the focal plane, we exploit the tomography of the pulse profile along the beam propagation axis, as well as a qualitative and quantitative comparison between these two reconstruction methods.