Recent calculations based on DFT suggest that it is thermodynamically favourable for N to diffuse across a sharp Ti/TiN interface from TiN to Ti [1]. Only migration of N atom across a sharp Ti/TiN interface is required to create atomically chemical graded interface, as range of Ti-N stoichiometry could be achieved by migration of N without changing Ti site. On TiN side Ti6N5, Ti4N3, Ti3N2 can form that have the same structure as rock salt TiN with ordered N vacancy, similarly on Ti side ~20% N interstitials in Ti are known to be stable. We explore the diffusion path of N migration from TiN to Ti and rate of N diffusion, we calculate the diffusion coefficient of N in:1) TiN, 2) Ti6N5, 3) Ti4N3, 4) Ti, 5) Ti-0.14N 6) Ti-0.2N, and 7) across the sharp Ti/TiN interface. We use DFT to calculate barrier to diffusion of N along various possible paths and frequency at the stable and transition state. Then we calculate the diffusion coefficient, within Arrhenius theory [2]. We show that diffusion coefficient for N diffusion is slowest in TiN, and fastest in Ti, while that across the interface is in between TiN and Ti. Limited diffusion of N from TiN due to low diffusion coefficient leads to the formation of chemically graded interface on annealing alone. We expect to show that diffusivity of N increases as the concentration of N decreases in Ti-N system.
By comparing atomic structure of Ti and Ti2N we found that Ti2N can be obtained by intercalating N at alternate octahedral site in HCP Ti. Using DFT calculation we will study the relative thermodynamic stability of N on the surface of Ti and in Ti2N. We will also calculate diffusion coefficient of N into Ti from the surface and N vacancy in Ti2N to assess kinetics of N diffusion into Ti to form Ti2N.

[1] Gollapalli, Prince & Varalakshmi, J. & Kishor, P.S.V.R.A. & Oza, Prajeet & Yadav, Satyesh. (2022).
Atomically chemically graded Ti/TiN interface. Applied Surface Science. 597. 153637.
10.1016/j.apsusc.2022.153637.
[2] H. H. Wu and D. R. Trinkle, Phys. Rev. Lett. 107, 045504 (2011).