Atomically chemically graded Ti/TiN interface

Interface by definition is two-dimensional (2-D) as it separates 2 phases with an abrupt change in structure and chemistry across the interface. The interface between a metal and its nitride is expected to be atomically sharp, as chemical gradation would require the creation of N vacancies in nitrides and N interstitials in metal. Contrary to this belief, using first-principles density functional theory (DFT), we establish that the chemically graded Ti/TiN interface is thermodynamically preferred over the sharp interface. DFT calculated N vacancy formation energy in TiN is 2.4 eV, and N interstitial in Ti is -3.8 eV. Thus, diffusion of N from TiN to Ti by the formation of N vacancy in TiN and N interstitial in Ti would reduce the internal energy of the Ti-TiN heterostructure. Diffusion of N is thermodynamically favorable till ~23% of N has diffused from TiN to Ti, resulting in an atomically chemically graded interface, which we refer to as a 3-D interface. We show gradual variation in lattice parameters and mechanical properties across the Ti/TiN interface. This opens a new way to control properties of metal/ceramic heterostructures, in line with the already established advantage of gradation at interfaces in micrometer length scale.