  We present a high-resolution spectral study of Fe L-shell extinction by the
diffuse interstellar medium (ISM) in the direction of the X-ray binaries Cygnus
X-1 and GX 339-4, using the XMM-Newton reflection grating spectrometer. The
majority of interstellar Fe is suspected to condense into dust grains in the
diffuse ISM, but the compounds formed from this process are unknown. Here, we
use the laboratory cross sections from Kortright & Kim (2000) and Lee et al.
(2009) to model the absorption and scattering profiles of metallic Fe, and the
crystalline compounds fayalite (Fe$_2$SiO$_4$), ferrous sulfate (FeSO$_4$),
hematite ($\alpha$-Fe$_2$O$_3$), and lepidocrocite ($\gamma$-FeOOH), which have
oxidation states ranging from Fe$^{0}$ to Fe$^{3+}$. We find that the observed
Fe L-shell features are systematically offset in energy from the laboratory
measurements. An examination of over two dozen published measurements of Fe
L-shell absorption finds a 1-2 eV scatter in energy positions of the L-shell
features. Motivated by this, we fit for the best energy-scale shift
simultaneously with the fine structure of the Fe L-shell extinction cross
sections. Hematite and lepidocrocite provide the best fits ($\approx +1.1$ eV
shift), followed by fayalite ($\approx +1.8$ eV shift). However, fayalite is
disfavored, based on the implied abundances and knowledge of ISM silicates
gained by infrared astronomical observations and meteoritic studies. We
conclude that iron oxides in the Fe$^{3+}$ oxidation state are good candidates
for Fe-bearing dust. To verify this, new absolute photoabsorption measurements
are needed on an energy scale accurate to better than 0.2 eV.
