Graphite Revisited
  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/lambda -> 0,
provides better than ~10% accuracy in the optical and UV even when a/lambda is
not small, but becomes increasingly inaccurate at infrared wavelengths, with
errors as large as ~40% at lambda = 10 micron. 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 micron may be observable in absorption with the MIRI
spectrograph on JWST. Aligned graphite grains, if present in the ISM, could
produce polarized X-ray absorption and polarized X-ray scattering near the
carbon K edge.
