Efficient and accurate determination of lattice-vacancy diffusion coefficients via non equilibriumab initiomolecular dynamics

Abstract

095901 (2012)] in non equilibrium ab initio molecular dynamics (NE-AIMD) and propose a simple efficient approach for the estimation of monovacancy jump rates in crystalline solids at temperatures well below melting. Color-diffusion applied to monovacancy migration entails that one lattice atom (colored atom) is accelerated toward the neighboring defect site by an external constant force F. Considering bcc molybdenum between 1000 and 2800 K as a model system, NE-AIMD results show that the colored-atom jump rate k NE increases exponentially with the force intensity F, up to F values far beyond the linear-fitting regime employed previously. Using a simple model, we derive an analytical expression which reproduces the observed k NE (F ) dependence on F. Equilibrium rates extrapolated by NE-AIMD results are in excellent agreement with those of unconstrained dynamics. The gain in computational efficiency achieved with our approach increases rapidly with decreasing temperatures and reaches a factor of 4 orders of magnitude at the lowest temperature considered in the present study.

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

“…Thus, the system is immersed in a 110 -oriented constant force-field, which is used to accelerate one Ti lattice atom (colored-atom) toward the neighboring vacancy site (see details in Ref. [85]). The force-field acts on the colored-atom with intensity F and on each other atom in the simulation box with opposite forces of intensities F /(N -1) (where N is the total number of atoms in the supercell), thus maintaining the system in mechanical equilibrium (Fig.…”

“…The rapid increase in computational efficiency achieved via CD simulations for decreasing temperatures [85] comes to the cost of much broader uncertainty ranges on extrapolated equilibrium-rate values. Thus, it is necessary to provide an unambiguous and reliable definition of statistical error bars.…”

“…The convenience of using one or the other acceleration method may vary depending on time and length scales involved, as well as on the complexity of the process under investigation [60]. In particular, we have recently proposed a development for the CD algorithm [85], which allows to retrieve monovacancy migration rates in crystalline solids at much lower computational efforts in comparison with the former (yet more general) application [81].…”

“…[85] is instead specifically tailored to determining the kinetics of monoatomic mass-transport pathways occurring over a single energy barrier, where initial and final states are known a priori. Our implementation of CD in nonequilibrium AIMD (NE-AIMD) yields accurate results for vacancy diffusion in bcc Mo and, by exploiting force-field intensities well beyond the linear-response regime [81], provides speed-up factors which increase by several order of magnitudes with decreasing simulation temperatures [85]. The fact that our current method is focused on quantifying the kinetics of a relatively narrow class of diffusion processes does not preclude the possibility of extending its usage to a broader range of problems in practical applications.…”

“…In Ref. [85], we do not include any rigorous treatment of statistical uncertainties on accelerated k NE (F ) rates which, in turn, affect the predictions of lattice-defect jump frequencies k NE→E . Here, we propose a procedure based on gammadistribution statistics which provides unambiguous definition of k NE (F ) and k NE→E average values with corresponding confidence ranges.…”