Nitrogen vacancy, self-interstitial diffusion, and Frenkel-pair formation/dissociation inB1TiN studied byab initioand classical molecular dynamics with optimized potentials

Abstract

We use ab initio and classical molecular dynamics (AIMD and CMD) based on the modified embedded-atom method (MEAM) potential to simulate diffusion of N vacancy and N self-interstitial point defects in $B1$ TiN. TiN MEAM parameters are optimized to obtain CMD nitrogen point-defect jump rates in agreement with AIMD predictions, as well as an excellent description of $\mathrm{Ti}{\mathrm{N}}_{x}(\ensuremath{\sim}0.7<x\ensuremath{\le}1)$ elastic, thermal, and structural properties. We determine N dilute-point-defect diffusion pathways, activation energies, attempt frequencies, and diffusion coefficients as a function of temperature. In addition, the MD simulations presented in this paper reveal an unanticipated atomistic process, which controls the spontaneous formation of N self-interstitial/N vacancy $({\mathrm{N}}^{\mathrm{I}}/{\mathrm{N}}^{\mathrm{V}})$ pairs (Frenkel pairs), in defect-free TiN. This entails that the N lattice atom leaves its bulk position and bonds to a neighboring N lattice atom. In most cases, Frenkel-pair ${\mathrm{N}}^{\mathrm{I}}$ and ${\mathrm{N}}^{\mathrm{V}}$ recombine within a fraction of ns; \ensuremath{\sim}50% of these processes result in the exchange of two nitrogen lattice atoms $(\mathrm{N}\ensuremath{-}{\mathrm{N}}^{\mathrm{Exc}})$. Occasionally, however, Frenkel-pair N-interstitial atoms permanently escape from the anion vacancy site, thus producing unpaired ${\mathrm{N}}^{\mathrm{I}}$ and ${\mathrm{N}}^{\mathrm{V}}$ point defects.