  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. We show that 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.
Experiments' inability to identify a 3-D interface in Ti/TiN could be
attributed to limitations in identifying chemical composition and structure
with atomic-level resolution at interfaces. We define the sum of N vacancy
formation energy and N interstitial formation energy as driving-force, which
could be used as a convenient way to assess the possibility of forming a 3-D
interface in metal/ceramic heterostructures. We also show gradual variation in
lattice parameters and mechanical properties (like bulk modulus, shear modulus,
Young's modulus, and hardness) across the Ti/TiN interface. 3-D interfaces open
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. For widely explored Ti/TiN multilayer nano-heterostructures, the
possibility of forming 3-D interface could lead to enhanced wear and erosion
resistance.
