Phase Transition and Behaviors of N-N Bonds in Group-IVB Transition-Metal Pernitrides: First-Principles Calculations under High Pressures

Group-IVB transition-metal pernitrides TMN2 (TM = Ti, Zr, and Hf) remain an open question in terms of their structural diversity under high pressures. Using the evolutionary algorithm method and first-principles calculations in the pressure range of 0-200 GPa, we predict three novel lowest-enthalpy structures, namely, Cmcm, P2(1)/c-alpha, and P21/ c-beta, for ZrN2 and HfN2 systems. To examine the dynamical stabilities of the predicted structures, the phonon dispersions are calculated at 0 GPa and high pressures. The calculations of the mechanical properties show that the novel monoclinic phases of P2(1)/c-alpha-TMN2 and P2(1)/c-beta-TMN2 have Vickers hardness values close to 20 GPa and a bulk modulus higher than 200 GPa, respectively. Through investigating the projected crystal overlap Hamilton populations and Bader charge of the N-N bond, we find that the bulk modulus increases with the increase in the number of filled electrons in the antibonding 1 pi(g)* state of the N-N bond. The N-N bond behavior is studied in the high-pressure range of 0-200 GPa. The results show that the N-N bond lengths of I4/mmm-TMN2, I4/mcm-TMN2, and P2(1)/c-beta-TMN2 gradually decrease except for I4/mmm-ZrN2 in the pressure range of 160-200 GPa, whereas those of Cmcm-TMN2 and P2(1)/c-alpha-TMN2 first increase and then decrease with increasing pressure in the 0-200 GPa range. By analyzing the geometric configuration of the N-N bond and TM atoms, we attribute this abnormal behavior in Cmcm-TMN2 and P2(1)/c-alpha-TMN2 to their quadrangular-like configurations where two N atoms of a nitrogen dumbbell share one TM atom. Furthermore, to study the difference in the structural richness among TiN2, ZrN2, and HfN2, the density of states is investigated.

Automated summary

The study predicts three new lowest-enthalpy structures for ZrN2 and HfN2 systems using the evolutionary algorithm method and first-principles calculations, analyzes their dynamic stability and mechanical properties, and investigates the behavior of the N-N bond under high pressure. Moreover, the differences in structural richness among TiN2, ZrN2, and HfN2 are studied by investigating the density of states.