Mass transport properties of quasiharmonic vs. anharmonic transition-metal nitrides

Abstract

I present a development of the color-diffusion algorithm, used in non-equilibrium (accelerated) ab initio molecular dynamics simulations of point-defect migration in crystals [Sangiovanni et al., Phys. Rev. B 93, 094305 (2016)], to determine the temperature dependence of anion vacancy jump frequencies in rocksalt-structure (B1) TiN and VN characterized by quasiharmonic (TiN) vs. strongly anharmonic (VN) lattice dynamics. Over a temperature range [≈0.6·Tm < T < ≈0.9·Tm] relatively close to the materials melting points Tm, the simulations reveal that anion vacancy migration in TiN and VN exhibits an Arrhenius-like behavior, described by activation energies EaTiN = 4.2 ± 0.3 eV and EaVN = 3.1 ± 0.3 eV, and attempt frequencies νTiN = 8·1015±0.7 s−1 and νVN = 2·1017±0.8 s−1. A comparison of activation energies Ea extracted by Arrhenius linear regression at elevated temperatures with ab initio Ea0K values calculated at 0 Kelvin reveals that, while the nitrogen migration energy EaTiN varies modestly with temperature {∆EaTiN = [Ea(Tm) – Ea(0 K)]/Ea(0 K) ≈ 0.1}, the changes in EaVN vs. T are considerable (∆EaVN ≈ 1). The temperature-induced variations in vacancy migration energies and diffusivities are discussed in relation to the TiN and VN vibrational properties determined via ab initio molecular dynamics at different temperatures. It is argued that static 0-K calculations, which account for thermal expansion effects within the framework of quasiharmonic transition-state theory, accurately reproduce the finite-temperature mass transport properties of TiN. Conversely, the use of molecular dynamics simulations, which explicit treat lattice vibrations at any temperature of interest, is necessary to achieve reliable atomic diffusivities in B1 VN, a crystal phase dynamically stabilized by anharmonic vibrations [Mei et al., Phys. Rev. B 91, 054101 (2015)].