CrN layers, 0.5 m thick, were grown on MgO͑001͒ at T s ϭ570-775°C by ultrahigh vacuum magnetically unbalanced magnetron sputter deposition in pure N 2 discharges at 20 mTorr. Layers grown at T s р700°C are stoichiometric single crystals exhibiting cube-on-cube epitaxy: (001) CrN ͉͉(001) MgO with ͓100͔ CrN ͉͉͓100͔ MgO. At higher temperatures, N 2 desorption during deposition results in understoichiometric polycrystalline films with N fractions decreasing to 0.35, 0.28, and 0.07 with T s ϭ730, 760, and 775°C, respectively. The surface morphologies of epitaxial CrN͑001͒ layers were found to depend strongly on the incident ion-to-metal flux ratio J N 2 ϩ /J Cr which was varied between 1.7 and 14 with the ion energy maintained constant at 12 eV. The surfaces of layers grown with J N 2 ϩ /J Cr ϭ1.7 consist of self-organized square-shaped mounds, due to kinetic roughening, with edges aligned along orthogonal ͗100͘ directions. The mounds have an average peak-to-valley height ͗h͘ϭ5.1 nm and an in-plane correlation length of ͗d͘ϭ0.21 m. The combination of atomic shadowing by the mounds with low adatom mobility results in the formation of nanopipes extending along the growth direction. Increasing J N 2 ϩ /J Cr to 14 leads, due to increased adatom mobilities, to much smoother surfaces with ͗h͘ϭ2.5 nm and ͗d͘ϭ0.52 m. Correspondingly, the nanopipe density decreases from 870 to 270 m Ϫ2 to Ͻ20 m Ϫ2 as J N 2 ϩ /J Cr is increased from 1.7 to 6 to 10. The hardness of dense CrN͑001͒ is 28.5Ϯ1 GPa, but decreases to 22.5Ϯ1 GPa for layers containing significant nanopipe densities. The CrN͑001͒ elastic modulus, 405Ϯ15 GPa, room-temperature resistivity, 7.7ϫ10 Ϫ2 ⍀ cm, and relaxed lattice constant, 0.4162Ϯ0.0008 nm, are independent of J N 2 ϩ /J Cr .