Valence electron concentration- and N vacancy-induced elasticity in cubic early transition metal nitrides
Soheil Karimi Aghda, Dimitri Bogdanovski, Lukas Löfler, Heng Han Sua, Lena Patterer, Damian M. Holzapfel, Arnaud le Febvrier, Marcus Hans, Daniel Primetzhofer, Jochen M. Schneider
Abstract
Motivated by frequently reported deviations from stoichiometry in cubic transition metal nitride (TMNx) thin films, the effect of N-vacancy concentration on the elastic properties of cubic TiNx, ZrNx, VNx, NbNx, and MoNx (0.72≤x≤1.00) is systematically studied by density functional theory (DFT) calculations. The predictions are validated experimentally for VNx (0.77≤x≤0.97). The DFT results indicate that the elastic behavior of the TMNx depends on both the N-vacancy concentration and the valence electron concentration (VEC) of the transition metal: While TiNx and ZrNx exhibit vacancy-induced reductions in elastic modulus, VNx and NbNx show an increase. These trends can be rationalized by considering vacancy-induced changes in elastic anisotropy and bonding. While introduction of N-vacancies in TiNx results in a significant reduction of elastic modulus along all directions and a lower average bond strength of Ti–N, the vacancy-induced reduction in [001] direction of VNx is overcompensated by the higher stiffness along [011] and [111] directions, resulting in a higher average bond strength of V–N. To validate the predicted vacancy-induced changes in elasticity experimentally, close-to-single-crystal VNx (0.77≤x≤0.97) are grown on MgO(001) substrates. As the N-content is reduced, the relaxed lattice parameter a0, as probed by X-ray diffraction, decreases from 4.128 Å to 4.096 Å. This reduction in lattice parameter is accompanied by an anomalous 11% increase in elastic modulus, as determined by nanoindentation. As the experimental data agree with the predictions, the elasticity enhancement in VNx upon N-vacancy formation can be understood based on the concomitant changes in elastic anisotropy and bonding.