Bulk Diffusion of Impurities in TiN: An ab initio Study

Abstract

TiN-based materials are widely established as protective coatings for cutting tools. Grain interiors (single crystal regions) could serve as reservoirs for functional species, e.g. Al or V, which provide effective lubrication and wear protection at high temperatures by diffusing to the coating surface where they form a protective oxide scale (Al) or a lubricious oxide to reduce friction (V). In this contribution, we will report on our recent work in addressing issues related to the atomistic modeling of mass transport. To do so we employ complementary computational investigations to determine elementary point-defect migration mechanisms in crystalline materials and subsequently their relative rates. The density functional theory (DFT) is used to describe interatomic forces and is the most reliable computational tool to calculate atomic jump rates as a function of temperature. Since TiN is a harmonic crystal it gives us access to temperature based properties derived from the lattice vibration with harmonic and quasi-harmonic approximation. We will present the DFT-based 5-frequency model allowing us to calculate the diffusion coefficient in the crystalline material. Moreover, the influence of the TiN stoichiometry on its diffusion properties is taken into account through the change in the concentrations of the intrinsic point defects as a function of composition. These concentrations are obtained via a thermodynamic formalism based on the dilute solution model. We find that in stoichiometric TiN the vanadium impurity diffusion proceeds via the vacancy mechanism on the Ti sublattice. Furthermore, we also demonstrate that pressure has a notable impact on the diffusivity of V, Al, and Ti in TiN.