Titanium nitride (TiN) is one of the prototype ceramic materials used as protective hard coatings. Particularly interesting properties exhibits nanostructured TiN, and/or its alloys with different elements, especially $d$-element(s) (e.g. Cr, Zr, Mo, V, Ta, W, Nb etc.), thereby becoming an excellent candidate for the next generation coating industries. Since the working conditions involve high temperatures and the nanostructured coatings are often of a metastable nature, diffusion-driven processes become a crucial building block that cannot be neglected in the coating design. 

We employed {\it ab initio} calculations to quantify the diffusion processes of various $d$-elements in the rock-salt matrix of TiN. It turned out that the diffusion process depends strongly on the diffusing element. Moreover, a hard-sphere model would suggest that a larger atom induces during diffusion larger elastic deformation and hence would lead to a higher diffusion barrier, but this is not the case in the case of $d$-elements diffusion. Nevertheless, these trends are not clearly depicted. According to our initial results, we suggest a strong interaction between the $d$-states of diffusing $d$-elements with the TiN matrix.

We will present atomistic simulation-based results to show the change in diffusion rates of different $d$-elements (3$d$, 4$d$ and 5$d$) in TiN and the effect of $d$-states as quantified using Crystal Orbital Hamilton Population (COHP).