Graphite revisited

Abstract

Laboratory measurements are used to constrain the dielectric tensor for graphite, from microwave to X-ray frequencies. The dielectric tensor is strongly anisotropic even at X-ray energies. The discrete dipole approximation is employed for accurate calculations of absorption and scattering by single-crystal graphite spheres and spheroids. For randomly oriented single-crystal grains, the so-called 1/3--2/3 approximation for calculating absorption and scattering cross sections is exact in the limit a/λ→0 and provides better than ∼10% accuracy in the optical and UV even when a/λ is not small, but becomes increasingly inaccurate at infrared wavelengths, with errors as large as ∼40% at λ=10 μm. For turbostratic graphite grains, the Bruggeman and Maxwell Garnett treatments yield similar cross sections in the optical and ultraviolet, but diverge in the infrared, with predicted cross sections differing by over an order of magnitude in the far-infrared. It is argued that the Maxwell Garnett estimate is likely to be more realistic, and is recommended. The out-of-plane lattice resonance of graphite near 11.5 μm may be observable in absorption with the MIRI spectrograph on James Webb Space Telescope. Aligned graphite grains, if present in the interstellar medium, could produce polarized X-ray absorption and polarized X-ray scattering near the carbon K edge.