  Simulations of defects in paramagnetic materials at high temperature
constitute a formidable challenge to solid state theory due to the interaction
of magnetic disorder, vibrations, and structural relaxations. CrN is a material
where these effects are particularly large due to a strong magneto-lattice
coupling and a tendency for deviations from the nominal 1:1 stoichiometry. In
this work we present a first-principles study of nitrogen vacancies and
nitrogen interstitals in CrN at elevated temperature. We report on formation
energetics, the geometry of interstital nitrogen dimers, and impact on the
electronic structure caused by the defects. We find a vacancy formation energy
of 2.28 eV with a small effect of temperature, a formation energy for N
interstitial in the form of a $\big<111\big>$ oriented split-bond of 3.77 eV
with an increase to 3.97 at 1000 K. Vacancies are found to add three electrons
while split bond interstitial adds one electron to the conduction band. The
band gap of defect-free CrN is smeared out due to vibrations, though it is
difficult to draw conclusion about the exact temperature at which the band gap
closes from our calculations. However, it is clear that at 900 K there is a
non-zero density of electronic states at the Fermi level. At 300 K our results
indicate a boarder case were the band-gap is about to close.
