Vacancy hardening in single-crystal TiNx(001) layers

We investigate the effect of N vacancies on the mechanical properties of epitaxial δ-TiNx(001) layers with x=0.67–1.0. The relaxed lattice parameter increases linearly with x in good agreement with ab initio density functional calculations, indicating that deviations from stoichiometry are entirely due to anion vacancies. Hardness values increase continuously, while the elastic modulus decreases with increasing N-vacancy concentration. We attribute the observed vacancy hardening to a reduced dislocation mobility arising from an increase in the rate-limiting activation energy for cation migration.