We are accustomed to observing carbon in its elemental form as a solid, ranging from the soft "lead" in pencils to the precious gemstone in diamond rings. While considerable attention has been focused on solid forms of carbon, the properties of liquid carbon are much more difficult to measure accurately. The very strong bonding between carbon atoms that gives diamonds their hardness also makes carbon very difficult to melt, requiring temperatures above 5000 K at pressures above 100 bar. Maintaining such conditions in a laboratory is a challenge that has hampered efforts to fully understand the chemical bonding properties of this biologically, industrially, and environmentally important element. At the ALS, researchers have found a way to rapidly heat a carbon sample and contain the resulting liquid long enough to perform picosecond time-resolved x-ray absorption spectroscopy. The technique provides a way to measure the bonding properties of liquid carbon at near-solid densities that can then be compared with results from molecular dynamics simulations.

Carbon phase diagram. The properties of the liquid phase have remained unclear because of the difficulty in performing experiments at the required temperatures and pressures.

Even the most basic properties of liquid carbon have long been debated because of the challenge of studying the material at the required temperatures and pressures. Liquid carbon is volatile and thus inherently transient in an unconstrained environment. Most experiments involve the rapid melting of a solid sample, followed by observation of the liquid in the short time before it expands and vaporizes. The transient nature of these experiments limits the methods that can be used to probe the liquid properties, with inconsistent results. For example, although the most recent and reliable measurements show that liquid carbon is metallic, reported conductivity values vary by more than an order of magnitude. This may be due to a strong dependence of the liquid properties on temperature and density, but so far no one experiment has demonstrated such a relationship. In addition to experiments, first-principles molecular dynamics simulations have been used to explore the properties of the liquid as a function of temperature and density. The results suggest that the local bonding structure of the liquid varies continuously from twofold to fourfold coordination as the density increases.

K-edge absorption spectra of the unheated solid carbon foils: (a) amorphous carbon prepared by evaporation from an arc source and (b) diamond-like carbon. The red circles are the data. The black curves show the results of fitting the spectrum to various components corresponding to antibonding states. The blue curve is the sum of the fit components.

To investigate this intriguing result, the researchers performed ultrafast x-ray absorption spectroscopy at ALS Beamline 5.3.1. Thin (500-Å) foils of solid carbon were rapidly heated by a femtosecond laser pulse and then probed by a broadband soft x-ray pulse. A grating spectrograph then measured the spectrum of the transmitted x rays in the vicinity of the carbon K edge, providing information about the local bonding environment of the carbon atoms. By varying the relative timing of the x-ray and laser pulses, the (nearly instantaneous) melting process and the subsequent expansion dynamics of the liquid could be probed with 70-ps resolution. To delay the expansion and allow accurate measurements, the foil was "tamped" by a thick (3500-Å) LiF coating on both sides. The large optical band gap of LiF makes it essentially transparent to the laser, and the mechanical stiffness of the tamping layers prevents the foil from expanding on a time scale of about 100 ps, allowing observation of the liquid at densities very near that of the initial solid.

By fitting the resulting absorption spectra and comparing them to a reference spectrum of carbon-60, the researchers were able to establish that low-density liquid carbon contains predominantly twofold-coordinated chain structures (sp hybridization). As the density increased to that of solid forms, bond hybridization increased and threefold-coordinated (graphite-like) and fourfold-coordinated (diamond-like) bonds become more prevalent (indicating sp² and sp³ hybridization, respectively). These observations are consistent with molecular dynamics calculations that rely on a tight-binding model of interatomic bonding. The fits also suggest that the bond length between carbon atoms in the liquid is significantly shorter than those in the solid, an observation also consistent with simulations.

K-edge absorption spectra of liquid carbon at various densities, 100 ps after heating:
(a) untamped, (b) 2.0 g/cm³, and (c) 2.6 g/cm³. The red circles are the data. The black curves show the fit results as in figure above.

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Research conducted by S.L. Johnson (University of California, Berkeley, currently at the Paul Scherrer Institut, Switzerland), P.A. Heimann and O.R. Monteiro (Berkeley Lab), A.G. MacPhee and A.M. Lindenberg (University of California, Berkeley), Z. Chang (Kansas State University), R.W. Lee (Lawrence Livermore National Laboratory), and R.W. Falcone (University of California, Berkeley, and Berkeley Lab).

Research funding: U.S. Department of Energy, Office of Basic Energy Sciences (BES); U.S. Department of Energy High Energy Density Science Grants Program; and Institute for Laser Science and Applications, Lawrence Livermore National Laboratory. Operation of the ALS is supported by BES.

Publication about this research: S.L. Johnson, P.A. Heimann, A.G. MacPhee, A.M. Lindenberg, O.R. Monteiro, Z. Chang, R.W. Lee, and R.W. Falcone, "Bonding in liquid carbon studied by time-resolved x-ray absorption spectroscopy," Phys. Rev. Lett. 94 057407 (2005).