Nonequilibrium ab initio molecular dynamics determination of Ti monovacancy migration rates in B1 TiN

Abstract

We use the color diffusion (CD) algorithm in nonequilibrium (accelerated) ab initio molecular dynamics simulations to determine Ti monovacancy jump frequencies in NaCl-structure titanium nitride (TiN), at temperatures ranging from 2200 to 3000 K. Our results show that the CD method extended beyond the linear-fitting rate-versus-force regime [Sangiovanni et al., Phys. Rev. B 93, 094305 (2016)] can efficiently determine metal vacancy migration rates in TiN, despite the low mobilities of lattice defects in this type of ceramic compound. We propose a computational method based on gamma-distribution statistics, which provides unambiguous definition of nonequilibrium and equilibrium (extrapolated) vacancy jump rates with corresponding statistical uncertainties. The acceleration-factor achieved in our implementation of nonequilibrium molecular dynamics increases dramatically for decreasing temperatures from 500 for T close to the melting point T m , up to 33 000 for T ≈ 0.7 T m .

Semi-Empirical Force-Field Model for the Ti1−xAlxN (0 ≤ x ≤ 1) System

“…We found that the migration energies for Ti V and N V in B1-TiN along <110> directions are 4.13 and 4.24 eV, respectively, with saddle-point transition states located halfway between initial and final atomic positions (Figure 7a). The MEAM predictions are in good agreement with DFT-NEB results, which yield energy barriers of ≈3.8 eV for N V [114] and 4.26 eV for Ti V [97]. Experimental values for vacancy migration energies in B1-TiN are scarce in the literature.…”

“…E f V values for N and Ti vacancies (N V and Ti V , respectively), obtained using a N atom in a N 2 molecule and of a Ti atom in hcp-Ti lattice as reference chemical potentials, are E f NV = 3.53 eV and E f TiV = 4.76 eV. The corresponding DFT-based values, found in the literature, lie in the ranges 2.41–2.53 eV (N V ) [95,96] and 2.86–3.11 eV (Ti V ) [96,97]. The discrepancy between MEAM and DFT results becomes less than 10% when using the chemical potential of isolated N and Ti for computing E f V .…”

“…Refractory metal-nitride compounds exhibit relatively low atomic mobilities [139], which may shift the onset of structural transformation to temperatures larger than those predicted in theoretical models. In order to explore possible effects of low point-defect mobilities on the outcome of annealing experiments conducted on Ti-Al-N, we consider the case of the parent compound TiN, for which nitrogen diffusivities D ( T ) are available in the literature [36] (in TiN, Ti migration is even slower than N migration [97]). We consider the model system B1-TiN 1–y with nitrogen vacancy concentrations at the dilute limit (y ≈ 10 –5 ) and diffusivities D (1100 K) ≈ 10 –20±2 cm 2 ·s –1 and D (800 K) ≈ 10 –33±2 cm 2 ·s –1 , as shown in figure 11 of Ref.…”

Effects of surface vibrations on interlayer mass transport: Ab initio molecular dynamics investigation of Ti adatom descent pathways and rates from TiN/TiN(001) islands

“…Molecular dynamics simulations inherently resolve the problems mentioned above by integrating Newton's equations of motion for each atom at any temperature of interest. CMD/AIMD reaction rates for adspecies intra-and interlayer migration [22,59,60,68,111] or desorption [63,112], as well as point defects in bulk [110,113], can be employed in kinetic Monte Carlo simulations [114] to efficiently probe the effects of precursors fluxes and ion-to-metal ratios on film growth modes.…”

“…Lattice anharmonicity is also known to cause deviations from an Arrhenius temperature-dependent behavior for thermodynamic and kinetic properties in bulk systems. For example, it is known that vacancy formation [106,107] and migration (or diffusion, i.e., defect formation + defect migration) energies [108][109][110] may vary considerably from 0 K up to the melting temperature. Molecular dynamics simulations inherently resolve the problems mentioned above by integrating Newton's equations of motion for each atom at any temperature of interest.…”