Effect of atomic scale plasticity on hydrogen diffusion in iron: Quantum mechanically informed and on-the-fly kinetic Monte Carlo simulations

Abstract

We present an off-lattice, on-the-fly kinetic Monte Carlo (KMC) model for simulating stress-assisted diffusion and trapping of hydrogen by crystalline defects in iron. Given an embedded atom (EAM) potential as input, energy barriers for diffusion are ascertained on the fly from the local environments of H atoms. To reduce computational cost, on-the-fly calculations are supplemented with precomputed strain-dependent energy barriers in defect-free parts of the crystal. These precomputed barriers, obtained with high-accuracy density functional theory calculations, are used to ascertain the veracity of the EAM barriers and correct them when necessary. Examples of bulk diffusion in crystals containing a screw dipole and vacancies are presented. Effective diffusivities obtained from KMC simulations are found to be in good agreement with theory. Our model provides an avenue for simulating the interaction of hydrogen with cracks, dislocations, grain boundaries, and other lattice defects, over extended time scales, albeit at atomistic length scales.

Understanding and mitigating hydrogen embrittlement of steels: a review of experimental, modelling and design progress from atomistic to continuum

“…Instead, kMC uses precomputed transition rates along the minimal energy paths between the metastable sites, thereby allowing employment of more precise electronic structure methods. Ramasubramaniam et al [170] have developed an off-lattice, on-the-fly kMC model for simulating stressassisted diffusion and trapping of hydrogen by crystalline defects in BCC iron. The model employs precomputed transition rates obtained with high-accuracy DFT calculations in defect-free parts of the crystal.…”

Fully quantum mechanical calculation of the diffusivity of hydrogen in iron using the tight-binding approximation and path integral theory

“…13,14 An estimate of hydrogen diffusivity can also be provided by employing the kinetic Monte Carlo (kMC) method. 15,16 The fundamental transition rate constants used by kMC can be estimated without knowledge of the dynamics of the system within the framework of the classical transition state theory (TST). 16,17 Unfortunately, when simulations of H diffusion are made at or below room temperature significant deviations from classical behavior are to be expected due to the quantum nature of the proton motion.…”

“…15,16 The fundamental transition rate constants used by kMC can be estimated without knowledge of the dynamics of the system within the framework of the classical transition state theory (TST). 16,17 Unfortunately, when simulations of H diffusion are made at or below room temperature significant deviations from classical behavior are to be expected due to the quantum nature of the proton motion. An explicit treatment of quantum effects is not only desirable for improvement of the accuracy of the simulations, but it can be essential for understanding phenomena and experimental observations depending directly on the quantum nature of the nuclear motion.…”

“…16,17 Modern ab initio modeling provides a good description of the energetics and potential energy surface (PES) in Fe-H systems. However, these calculations of energy barriers can not account for quantum corrections arising from the low mass H atom.…”

“…Although the overall energy barriers are small, as expected for a small atom like H and the geometry of the bcc lattice, they are significantly higher than the experimentally determined activation energies. 16 A quantum treatment of the hydrogen degrees of freedom is mandatory to capture such effects.…”