Energetics of point defects in rocksalt structure transition metal nitrides: Thermodynamic reasons for deviations from stoichiometry

Abstract

First principle calculations of point defect formation energies in group 3–6 transition metal (Me) nitrides MeNx are employed to explain the thermodynamic reasons for the large reported compositional range (typically x = 0.7–1.3) in the rocksalt structure. Both under-stoichiometric (x < 1) and over-stoichiometric (x > 1) compositions are due to relatively low vacancy formation energies that decrease from an average of 2.7 and 4.5 eV for nitrogen and cation vacancies in group 3 nitrides (ScN, YN, LaN) to −1.8 and −0.8 eV in group 6 nitrides (CrN, MoN, WN), indicating that they become thermodynamically stable at zero temperature for group 6 and for group 4–6 nitrides, respectively. Similarly, nitrogen and cation interstitials in tetragonal and 111- or 110-split configurations are unstable for groups 3–5 but become thermodynamically stable for group 6 nitrides, consistent with the mechanical instability of the latter compounds. All antisite defects possess high formation energies and are unlikely to form. The nitrogen chemical potential at finite temperatures and in equilibrium with a N2 gas is strongly affected by the vapor phase entropy, leading to shifts in the defect free energy of, for example, 1.2 eV at 1 Pa N2 at 800 K, causing an increasing likelihood for nitrogen vacancies and cation interstitials at elevated temperatures. In addition, the configurational entropy of point defects causes a correction of e.g. 0.4 eV for a 1% vacancy defect concentration at 800 K. Considering these entropy contributions leads to predicted temperature windows for stoichiometry of e.g. 200–1100 K for TiN, 500–1400 K for ZrN, and 1200–1400 K for HfN, while considerable cation and nitrogen vacancy concentrations are expected for temperatures below and above these ranges, respectively. Schottky pair defects are predicted in VN for T > 200 K and in NbN, TaN, and group 6 nitrides at all temperatures, independent of the N2 partial pressure. The overall results show that thermodynamic arguments (even in the absence of kinetic barriers) can explain many of the reported composition vs temperature and pressure relationships in rocksalt structure nitrides.