Early transition metals form a variety of compounds with carbon, nitrogen, and oxygen that exhibit favorable structural and functional properties. Many of these compounds adopt the rocksalt crystal structure, consisting of an FCC metal sublattice that accommodates C, N, or O atoms within octahedrally coordinated interstitial sites. Interstitial compounds often tolerate high concentrations of vacancies on the interstitial sublattice, with important consequences for diffusion. To determine the factors that affect diffusion in an interstitial compound, we performed a first-principles statistical mechanics study of nitrogen diffusion in nitrogen deficient ${\mathrm{ZrN}}_y$, a prototypical rocksalt interstitial compound. Nitrogen hops between octahedral sites of the FCC Zr sublattice of ${\mathrm{ZrN}}_y$ are predicted to pass through intermediate tetrahedral sites. This leads to a strong dependence of the migration barrier on the local nitrogen concentration, favoring hops into vacancy clusters. Kinetic Monte Carlo simulations predict that nitrogen hops occur primarily into triple vacancies in ${\mathrm{ZrN}}_y$ and that this mechanism leads to highly correlated diffusion. The reliance on triple vacancy hops as a mechanism of nitrogen diffusion also results in a strong dependence of the diffusion coefficient on the nitrogen concentration of the compound. The qualitative predictions of this work have important implications for diffusion in the large family of transition metal carbides, nitrides, and oxides that adopt the rocksalt crystal structure.

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• Diffusion
• Density functional theory
• Monte Carlo methods