Vacancy-induced mechanical stabilization of cubic tungsten nitride

Abstract

First-principles methods are employed to determine the structural, mechanical and thermodynamic reasons for the experimentally reported cubic WN phase. The defect-free rocksalt phase is both mechanically and thermodynamically unstable, with a negative single crystal shear modulus C 44 = -86 GPa and a positive enthalpy of formation per formula unit H f = 0.623 eV with respect to molecular nitrogen and metallic W. In contrast, WN in the NbO phase is stable, with C 44 = 175 GPa and H f = -0.839 eV. A charge distribution analysis reveals that the application of shear strain along [100] in rocksalt WN results in an increased overlap of the t 2g orbitals which causes electron migration from the expanded to the shortened W-W <110> bond axes, yielding a negative shear modulus due to an energy reduction associated with new bonding states 8.1-8.7 eV below the Fermi-level. A corresponding shear strain in WN in the NbO-phase results in an energy increase and a positive shear modulus. The mechanical stability transition from the NaCl to the NbO phase is explored using supercell calculations of the NaCl structure containing C v = 0-25% cation and anion vacancies, while keeping the N-to-W ratio constant at unity. The structure is mechanically unstable for C v < 5%. At this critical vacancy concentration, the isotropic elastic modulus E of cubic WN is zero, but increases steeply to E = 445 GPa for C v = 10%, and then less steeply to E = 561 GPa for C v = 25%. Correspondingly, the hardness estimated using Tian's model increases from 0 to 15 to 26 GPa as C v increases from 5% to 10% to 25%, indicating that a relatively small vacancy concentration stabilizes the cubic WN phase and that the large variations in reported mechanical properties of WN can be attributed to relatively small changes in C v .

High‐Pressure Effect on Elastic Constants and Their Related Properties of MgCa Intermetallic Compound

“…At zero pressure, our result for Pugh's ratio k = G/B is 0.65, which is slightly higher than the value of 0.57 reported by Zhou and Gong . The same value of 0.65 for Pugh's ratio k was reported for cubic tungsten nitride (WN) at zero pressure in the NbO phase . The obtained zero‐pressure Pugh's ratio (0.65) suggests that MgCa in the CsCl‐type structure is brittle since a common criterion for ductility of a material is k < 0.6 and ν > 0.25 .…”

Hot carrier dynamics in plasmonic transition metal nitrides

“…This agreement is well within the sample to sample variation of measured optical properties of TMNs, which are extremely sensitive to stoichiometry, impurities and growth methods [42,43]. These issues are particularly severe for group V and VI TMNs [12,39] and comparison to is normalized such that a uniform carrier distribution is 1. The color scale indicates relative contribution of intraband processes: intraband processes dominate only at low energies, particularly for the Ti-group nitrides in the rock-salt structure, while interband processes dominate hot carrier generation for most of the materials and shown energy range.…”

“…Instead, following Ref. 39 we focus on a symmetric highconcentration limit (25 %) of ion-pair vacancies in the RS structure, which results in the NbO structure shown in Fig. 1(d).…”

Cation and anion vacancies in cubic molybdenum nitride

“…Nevertheless, the introduction of metal vacancies may occur for some transition metal nitrides due to kinetic barriers during growth or even due to thermodynamic driving forces [10], and are expected to strongly affect physical properties. This has recently been shown for the W-N system from both experimental and computational studies [20,21], suggesting considerable vacancy concentrations at both anion and cation sites [21,22]. Consequently, it is interesting to also quantify metal and nitrogen vacancy concentrations in MoN x , which is isoelectric with WN x .…”