Anisotropic hydrogen diffusion in α-Zr and Zircaloy predicted by accelerated kinetic Monte Carlo simulations

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.The diffusion of hydrogen in hcp metals has attracted extensive research interests for both its scientific merit and technological importance. It is the rate-limiting step for solid hydrogen storage in Mg based alloys 1 and for mechanical property degradation in Ti 2 and Zr alloys 3 . For instance, Zr-based alloys such as Zircaloy2 and Zircaloy4 (denoted as Zircaloy) are widely used as the cladding of fuel rods in nuclear reactors for their excellent corrosion resistance and very low absorption cross-section of thermal neutrons. During their service time, these alloys operate in extremely harsh environments, combining high temperatures and corrosive coolants such as water. In light water reactors, Zircaloy claddings directly contact coolant water, with a local temperature at the interface of about 400 °C. Consequently, Zircaloy react with water, producing an oxide layer at the interface and hydrogen (H), of which a substantial fraction infiltrates into the cladding interior 3 . Due to the low solubility of H in α -Zr, which is the main component of claddings, hydrides precipitate in the cladding matrix 4-6 . Hydride formation can detrimentally affect the cladding integrity primarily in two ways. First, the formation of hydrides reduces the fracture toughness of the cladding matrix 7,8 , increasing the probability of fuel failure when fuel-cladding mechanical interaction (PCMI) occurs during fuel operation. Second, upon cyclic thermal and mechanical loadings, hydrides can dissolve and reorient. During used-fuel storage, fracture may propagate via the so-called delayed-hydride-cracking (DHC) mechanism, which is induced by the dissolving of matrix hydrides and their subsequent re-formation at crack tips 3,9 . To mitigate thes...

Spent nuclear fuel in dry storage conditions – current trends in fuel performance modeling

“…An example of atomic scale calculations is the work of Zhang et al [101] who used Kinetic Monte Carlo (KMC) simulations to predict the hydrogen diffusion measured by Ishioka and Koiwa [102] with a great precision. KMC has also been used by Liyange et al to study the impact of oxygen on hydrogen diffusion [103] .…”

FY17 end of year MARMOT materials model development update

“…As the rate-limiting factor for hydride evolution and delayed hydride cracking, H diffusion in Zr-based alloys can be affected by alloying elements and stress, factors that have been shown to strongly affect H pickup and hydride formation in nuclear fuel claddings. To elucidate these effects, a recently developed accelerated kinetic Monte Carlo method [21] is used to quantify H diffusivities in these alloys under mechanical loading. Accurate predictions of H diffusivities have been obtained from the simulations, with analytical models derived for the usage in engineering scale modeling [22].…”

Tight-binding modeling of interstitial ordering processes in metals: Application to zirconium hydrides

“…Note that even though it has been established, both theoretically and experimentally, that the H atoms should be localized on the tetrahedral sites whatever the crystalline structure, hcp or fcc, the octahedral ones are found quite close in energy in the hcp structure. In this phase, these sites play an important role in hydrogen diffusion [36,37], hydride precipitation [5,38], and embrittlement [39,40]. Nevertheless, since we are concerned here only with equilibrium thermodynamics and not with kinetics, in the fcc structure, we can assume that all hydrogen atoms occupy only the tetrahedral sublattice.…”