Valence electron concentration- and N vacancy-induced elasticity in cubic early transition metal nitrides

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.