Electron densities in VN. I. High-precision x-ray-diffraction determination of the valence-electron density distribution and atomic displacement parameters.

Abstract

High-precision, high-resolution x-ray-diffraction measurements were performed on a nearly stoichiometric, spherical single crystal of vanadium nitride [NaCl structure, a=4.137 11(4) A\r{}] using Ag K\ensuremath{\alpha} radiation. Structure factors with an average accuracy of 0.05e were obtained for 90 unique reflections from 12 807 intensity profiles measured at room temperature. Effects due to anisotropic extinction and crystal inhomogeneity were modeled and refined together with a scale factor, metal-atom 4s and 3d and nonmetal-atom 2s and 2p orbital-occupancy factors, \ensuremath{\kappa} expansion-contraction parameters, atomic site occupation, and anharmonic thermal parameters. At convergence, the reliability factors were R=0.0068 (before) and R=0.0031 (after) averaging symmetry-equivalent reflections. The charge distribution around the metal sites showed a positive deformation along [111], corresponding to preferential occupancy of ${t}_{2g}$ orbitals. A comparison with isostructural ${\mathrm{TiC}}_{0.94}$ and ${\mathrm{TiN}}_{0.99}$ showed that the shape of the metal atoms as expressed by the orbital-occupancy ratio p(${t}_{2g}$)/p(${e}_{g}$) changes as a function of valence-electron concentration: p(${t}_{2g}$)/p(${e}_{g}$)=3.3 in ${\mathrm{VN}}_{1.00}$, 1.9 in ${\mathrm{TiN}}_{0.99}$, and 1.0 in ${\mathrm{TiC}}_{0.94}$, in agreement with theoretical predictions.The charge distribution around the nonmetal sites is spherically symmetric. No buildup of charge density occurred between atomic sites. The charge transfer from the metal to the nonmetal site [1.2(1)e] was similar to those in ${\mathrm{TiC}}_{0\mathrm{e}.94}$ [2.1(4)e] and ${\mathrm{TiN}}_{0.99}$ [1.9(4)e]. The occupancy factor of the metal site, ${\mathrm{scrp}}_{\mathrm{V}=0.9986(8)}$, was consistent with chemical analysis (${\mathrm{VN}}_{0.996(3)}$). The mean-square displacements of the metal atoms, 〈${u}^{2}$${〉}_{\mathrm{V}}$=0.006 11(3) A${\mathit{\r{}}}^{2}$, were larger than those of the nonmetal atoms, 〈${u}^{2}$${〉}_{\mathrm{N}}$=0.004 33(7) A${\mathit{\r{}}}^{2}$. No evidence for static atomic displacements and anharmonic thermal vibrations was found.