Abstract
This report presents an accelerated kinetic Monte Carlo (KMC) method to compute the diffusivity of hydrogen in hcp metals and alloys, considering both thermally activated hopping and quantum tunneling. The acceleration is achieved by replacing regular KMC jumps in trapping energy basins formed by neighboring tetrahedral interstitial sites, with analytical solutions for basin exiting time and probability. Parameterized by density functional theory (DFT) calculations, the accelerated KMC method is shown to be capable of efficiently calculating hydrogen diffusivity in α-Zr and Zircaloy, without altering the kinetics of long-range diffusion. Above room temperature, hydrogen diffusion in α-Zr and Zircaloy is dominated by thermal hopping, with negligible contribution from quantum tunneling. The diffusivity predicted by this DFT + KMC approach agrees well with that from previous independent experiments and theories, without using any data fitting. The diffusivity along <c> is found to be slightly higher than that along <a>, with the anisotropy saturated at about 1.20 at high temperatures, resolving contradictory results in previous experiments. Demonstrated using hydrogen diffusion in α-Zr, the same method can be extended for on-lattice diffusion in hcp metals, or systems with similar trapping basins.
Highlights
Regarding the diffusion anisotropy have been reported
An accelerated kinetic Monte Carlo (KMC) method is developed for efficient calculations of H diffusivity in hcp metals, and demonstrated using H diffusion in α-Zr
Using the hopping rates predicted by density functional theory (DFT), the method accurately predicts H diffusivity in α-Zr and Zircaloy, providing reliable data that could be used for upper scale modeling[5,6]
Summary
Regarding the diffusion anisotropy have been reported. Due to the hexagonal symmetry of α-Zr, the diffusivity of H along usually differs from that along (in a plane parallel to and normal to ), with the former suggested to be higher than the latter by Kearns et al.[14]. The hopping rates obtained from DFT calculations need to be incorporated into either analytical theories or other modeling methods such as kinetic Monte Carlo (KMC) to predict diffusivity. The objectives of this paper are threefold: (i) to develop an accelerated KMC method for H diffusion in hcp metals, (ii) to obtain H diffusivity in Zr and Zircaloy in a wide range of temperatures, and (iii) to resolve the controversy in previous experiments on H diffusion anisotropy in α-Zr. A systematic understanding of H diffusion in α-Zr is expected by accomplishing these objectives. In this work the method is demonstrated using Zr and Zircaloy, the same method can be directly applied to other hcp metals and alloys such as Mg and Ti, provided that the required information for hopping rates are available
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