H in<i>α</i>-Zr and in zirconium hydrides: solubility, effect on dimensional changes, and the role of defects

Christensen, Mikael; Wolf, W.; Freeman, C. M.; Wimmer, E.; Adamson, Ronald B.; Hallstadius, Lars; Cantonwine, Paul; Mader, E. V.

doi:10.1088/0953-8984/27/2/025402

Cited by 60 publications

(40 citation statements)

References 46 publications

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“…For α-Zr, the lattice constants are calculated as c = 5.18 Å and a = 3.24 Å, agreeing well with previous DFT calculations17182930 and experiments3132. Due to its small size, H stays in hcp metals as an interstitial occupying either the tetrahedral (T) site or the octahedral (O) site, as shown in Fig.…”

Section: Resultssupporting

confidence: 87%

“…. For a more general comparison, most previous DFT calculations1718293033 have predicted that H prefers the tetrahedral site over the octahedral site based on the solution energy as defined in Eq. (21), which was reported to be −0.60 eV in Domain et al 17.…”

Section: Resultsmentioning

confidence: 99%

“…It has been pointed out that while evaluating the relative stability of various H interstitial configurations, the contribution of zero-point-energy (ZPE) in the solution energy should be included due to the small mass of H18. At 0 K, the ZPE of a H atom at interstitial site i is given by .…”

Section: Resultsmentioning

confidence: 99%

“…However, in a more recent experiment, the latter was reported to be over an order higher than the former15. In addition to these experiments, atomic scale studies such as density functional theory (DFT) calculations have also been applied to H diffusion in α-Zr161718. At high temperatures, H diffuses in metals via thermally activated hopping with the hopping rates described by the transition-state-theory (TST).…”

mentioning

confidence: 99%

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

Zhang

Jiang

Bai

2017

Sci Rep

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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 is found to be slightly higher than that along , 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...

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Section: Resultssupporting

confidence: 87%

Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

mentioning

confidence: 99%

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

Zhang

Jiang

Bai

2017

Sci Rep

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“…Tetrahedral sites are preferred by 4.4 kJ/mol to the octahedral sites, disregarding vibrational terms and volume relaxation effects. An in-depth analysis of the site preference including vibrational contributions and non-harmonic effects confirms that the tetrahedral site indeed is the preferred site [57]. The free energy difference with the octahedral site is small, 0.5 kJ/mol at T = 0 K and 8.6 kJ/mol at 600 K.…”

Section: Interstitial Hydrogenmentioning

confidence: 69%

Diffusion of point defects, nucleation of dislocation loops, and effect of hydrogen in hcp-Zr: Ab initio and classical simulations

Christensen¹,

Wolf²,

Freeman³

et al. 2015

Journal of Nuclear Materials

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Dislocation‐Mediated Hydride Precipitation in Zirconium

Liu

Ishii

et al. 2021

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The formation of hydrides challenges the integrity of zirconium (Zr) fuel cladding in nuclear reactors. The dynamics of hydride precipitation are complex. Especially, the formation of the butterfly or bird‐nest configurations of dislocation structures around hydride is rather intriguing. By in‐situ transmission electron microscopy experiments and density functional theory simulations, it is discovered that hydride growth is a hybrid displacive‐diffusive process, which is regulated by intermittent dislocation emissions. A strong tensile stress field around the hydride tip increases the solubility of hydrogen in Zr matrix, which prevents hydride growth. Punching‐out dislocations reduces the tensile stress surrounding the hydride, decreases hydrogen solubility, reboots the hydride precipitation and accelerates the growth of the hydride. The emission of dislocations mediates hydride growth, and finally, the consecutively emitted dislocations evolve into a butterfly or bird‐nest configuration around the hydride.

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H inα-Zr and in zirconium hydrides: solubility, effect on dimensional changes, and the role of defects

Cited by 60 publications

References 46 publications

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

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

Diffusion of point defects, nucleation of dislocation loops, and effect of hydrogen in hcp-Zr: Ab initio and classical simulations

Dislocation‐Mediated Hydride Precipitation in Zirconium

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