First principles density functional theory study of tritium species adsorption on Ni(111) surface and diffusion in nickel-sublayer for tritium storage

Abstract

The nickel-plated zircaloy-4 is used as a tritium (³H) getter in the tritium-producing burnable absorber rods (TPBARs) to capture ³H produced in the ⁶Li-riched annular γ-LiAlO₂ pellet under neutron irradiation. The experimental data and our previous theoretical results showed that the ³H species produced from the γ-LiAlO₂ pellet were mainly ³H₂ and ³H₂O. These ³H species diffuse from the surface of the LiAlO₂ pellet across vacuum to the nickel-plated zircaloy-4 getter and then further diffuse into the getter to chemically form metal hydrides. While a number of studies show that oxygen binds strongly as compared to ³H on the nickel (Ni) layer, the detailed mechanism of ³H species absorption and diffusion across the Ni plate and Ni/Zr interface are still unclear. By employing density functional theory calculations, here we explored the ³H₂ and ³H₂O species adsorption and dissociation on the Ni(111) surface and diffusion into the Ni sublayer. Our results indicated that the ³H₂ and ³H₂O dissociate on the Ni(111) surface. The NiO_x and Ni(O³H)_x could be formed in the Ni layer due to the higher oxygen (O) diffusion energy barrier and formation of Ni vacancy defects. The oxygen was found to be retained in the Ni layer from diffusing across the Ni–Zr interface. This was revealed by comparing the diffusion barriers for ³H with O. ³H was found to have nearly three times smaller diffusion barrier than for O, making ³H comparatively easier to diffuse through the Ni layer. The obtained results provide guidelines for experimental measurements on ³H retention behavior in TPBARs and may open further avenues to explore the impurity effects on ³H diffusion and storage at the Ni/zircaloy interfaces.

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1. Introduction

Zirconium (Zr) and its alloys (zircaloy-4) are widely used in nuclear reactors due to their low neutron absorption cross-section and excellent corrosion resistance.^1–3 In tritium-producing burnable absorber rods (TPBARs), the metal getter tube located between the cladding and the γ-LiAlO₂ pellets is composed of nickel (Ni)-plated zircaloy-4, which is used to capture tritium (³H) species (mainly ³H₂ and ³H₂O) generated from γ-LiAlO₂ pellets during irradiation.⁴ The ³H-related products transfer to the surface of metal Ni upon adsorption and dissociation to form new ³H species and diffuse into the zircaloy-4 getters to form metal hydrides (Zr³H_x). Therefore, exploring ³H species (³H₂, ³H₂O) dissociation on the surface of Ni and diffusion across the interface of Ni-plated zircaloy-4 getters can provide a better understanding of ³H species formation and transport from pellets into the getters.

In recent years, we conducted a series of studies on γ-LiAlO₂ pellets to understand the tritium products and their transport through the pellet materials.^2,5–7 Aside from studying the surface properties of γ-LiAlO₂, we also explored the diffusion of ³H and O³H species on its defective (100) and (101) surfaces, and the ³H₂O formation and desorption from the γ-LiAlO₂(101) and LiAl₅O₈(111) surfaces.^8–13 In our earlier studies, we found that the ³H₂ molecule is the main product initially released from the pellets. With increasing the number of Li vacancies and ³H atoms under irradiation, ³H₂O can be formed and released from the pellets as well. Although we explored ³H diffusion in different zirconium hydrides,^3,14,15 there remained open questions that needed answers: (i) how and which ³H species (³H, O³H, O, or ³H₂, etc.) do diffuse into zircaloy-4 from the surface of γ-LiAlO₂ pellets? (ii) In the case of ³H₂O, can the Ni coating layer retain O by forming NiO_x or Ni(O³H)_x to prevent O diffusion into zircalory-4 getter? Detail answers to these questions provide understanding of NiO_x or Ni(O³H)_x phase formation at various concentration of O and its impact on the ³H and O adsorption and diffusion in Ni layer.

In TPBARs, the ³H₂ and ³H₂O molecules generated from the γ-LiAlO₂ pellets^8–13 are transported to the Ni-plated zircaloy-4 getters. The adsorption and diffusion processes in Ni layer directly impacts the ³H retention rate at the getter. To capture the chemical adsorption kinetics in Ni layer and diffusion process across the Ni and Zrcaloy-4 interface, it is essential to include accurate electronic and magnetic properties of Ni. While the classical diffusion model where diffusion coefficient is extracted from the Brownian motion combined with adsorption/desorption and particle displacement distributions at single molecular levels could provide insight migration and displacement mechanisms for large interfaces, and fluid systems,¹⁶ better understanding of diffusion mechanisms in solid systems with accurate electronic structures could be achieved using density functional theory (DFT) level of calculations. The ³H₂O molecules dissociate on Ni(111) surface according to the reaction mechanism: ³H₂O → O³H + ³H and O³H + ³H → O + ³H + ³H. Previous studies showed that the first dissociation requires an activation energy of 0.68 eV, where ³H₂O is dissociated into an O³H and ³H species.¹⁷ The second process involves the dissociation of O³H into O and ³H and requires a higher activation barrier of 1.25 eV.¹⁷ The ³H₂O species are adsorbed on Ni(111) by occupying a top of a Ni atom, whereas the other three species, O³H, ³H, and O occupy a three-fold hollow site face centred cubic (fcc). As ³H₂ reaches the Ni(111) surface it dissociates into two atomic ³H (³H₂ → ³H + ³H) with a low activation energy. Shirazi et al. obtained activation energies of 0.03 and 0.09 eV for H-coverage of 0.125 and 0.25 monolayer (ML), respectively.¹⁸

To fully address aforementioned open questions, in this study, we explored the ³H₂ and ³H₂O molecules’ dissociation on the surfaces of Ni-plated zircaloy-4 getters to clarify the ³H species that dissolve into the metal getters and calculated the diffusion pathways of these ³H species in the bulk Ni phase to identify species that diffuse across the interface of Ni-plated zircalory-4. While there are comprehensive studies of H₂ and H₂O adsorption on the surfaces of Ni available in the literature,^19,20 here we targeted on the possibility of the nickel oxide/hydroxide (NiO_x, Ni(O³H)_x) phase formation in the Ni-coated layer to prevent O diffusion into the zircaloy-4 getter. We calculated the diffusion pathways of ³H across such oxide/hydroxide layer into the zircaloy-4 getter. By taking Ni(111) surface, we provided detail mechanisms for adsorption and diffusion pathways for ³H. Our hypothesis here is that ³H has a lower diffusion barrier in Ni than O, leading to higher chance of ³H diffusion into the zircalloy getter. Particularly, we determined if O from ³H₂O could be retained in the Ni layer to form the NiO_x/Ni(O³H)_x phase and let only ³H diffuse to the zircaloy-4 getter to form metal hydrides.

This paper is organized as follows. We first present theoretical and computational methodologies implemented in this work. Then we present and discuss the results of our study on NiO species formation and the diffusion mechanisms for ³H in Ni surfaces and subsurface. Finally, we summarize our work and provide further outlook.

2. Theoretical and computational methods

All the calculations were performed based on the DFT with the plane-wave basis set and the pseudopotential as implemented in the Vienna ab initio simulation package (VASP).^21–23 The electron–ion interaction is described with the projector augmented wave method (PAW).^24,25 The exchange and correction energies are described within generalized gradient approximation using the spin-polarized Perdew–Burke–Ernzerhof formulation (GGA-PBE).²⁶ A cutoff energy of 400 eV was used for the plane wave expansion. The convergence criteria for geometry optimizations of total energy and force were 10⁻⁵ eV and 0.01 eV Å⁻¹, respectively. The pseudo-potential of ³H was obtained by modifying the mass in the standard hydrogen (¹H) pseudo-potential. The surface slab was generated from the fully relaxed bulk structure. For the Ni(111) surfaces this study used a five-layered 4 × 4 supercell slab with a vacuum region of 12 Å along the z-axis to avoid interactions between periodically repeated slabs. The bottom two layers were kept fixed in their bulk positions as the rest of the slab including adsorbates were relaxed. The k-point sampling in a reciprocal space was generated using Monkhorst–Pack method and a 3 × 3 × 1 grid size.

Diffusion barriers for reactions were calculated using the climbing nudged elastic band (c-NEB) method.²⁷ For each simulation a minimum of five images were used. The energy difference between the two optimized minima gave the reaction energy. The diffusion barrier was defined as the difference between the transition state and the initial state energies.

3. Results and discussion

3.1. Stability and formation of NiO_x and/or Ni(O³H)_x phase

Based on literature report,^17,18 we determined the mechanisms of dissociation of ³H₂ and ³H₂O molecules on the Ni surfaces to clarify the ³H species that dissolved into the metal getters. With such information, then we focused on the diffusion of these ³H species in the Ni bulk and explored a possibility of forming NiO_x and/or Ni(O³H)_x phases. The stability of Ni metal and its derived compounds, including oxides, hydroxides, and oxyhydroxides can be predicted from DFT combined with thermodynamic analysis. To predict the stability and formation of the NiO_x and/or Ni(O³H)_x phase, we explored the most stable compounds of Ni oxides, hydroxides and oxyhydroxides observed experimentally (Table 1). We computed the equilibrium crystal structures, electronic structures, and thermodynamic energies using DFT with different options of exchange correlation potentials. In addition to the PBE functional, we used the hybrid functional HSE06²⁸ and a PBE+U functional. The HSE06 tends to perform better especially when dealing with oxides. Electronic structures and thermodynamic analysis are combined together to determine the chemical potential domains of Ni(O³H)_x stability and phase formation.

Table 1 Space groups, calculated total and formation energies (eV per f.u.) of Ni–O–H based compounds. Isotopes for H are specifically written as ¹H and ³H

Compound	Space group	Formula unit	Total energy HSE06	Total energy PBE	Total energy PBE+U	ΔH HSE06	ΔH PBE	ΔH PBE corrected	ΔH PBE+U corrected
Ni	Fm3̄m	1	−6.448	−5.459	−1.842
^1H2		1	−7.713	−6.772	−6.772
O2		1	−17.036	−9.862	−9.862
NiO	Fm3̄m	2	−17.970	−11.655	−10.278	−3.004	−1.265	−1.945	−4.184
NiO2	P3̄m1	1	−25.491	−17.350	−14.277	−2.007	−2.029	−3.389	−3.933
Ni2O3	R3̄c	2	−42.851	−29.648	−24.132	−4.402	−3.937	−5.977	−7.694
Ni3O4	Fd3̄m	8	−61.366	−41.783	−34.696	−7.950	−5.681	−8.401	−12.165
Ni(O^3H)2	P3̄m1	1	−37.451	−26.220	−25.071	−6.255	−4.127	−5.487	−7.955
NiOO^3H	R3̄m	2	−31.462	−22.124	−19.789	−4.122	−3.417	−4.777	−6.059

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3.1.1. Calculations of total and formation energies. The formation energy of a Ni_xO_yH_z compound can be defined as follows:

ΔH(Ni_xO_yH_z) = E_DFT(Ni_xO_yH_z) − xμ^solid_Ni − yμ^gas_O − zμ^gas_H (1)

where E_DFT (Ni_xO_yH_z) is the DFT calculated total energy of the compound; μ^solid_Ni, μ^gas_O, and μ^gas_H, are the chemical potentials of Ni, O, and H in their stable elemental solid/gas state; x, y, and z are coefficients of proportionality. Table 1 lists the DFT calculated total and formation energies of the most stable compounds of nickel oxides and hydroxides using different exchange correlation functionals. The formation energy ΔH for the PBE corrected and PBE+U corrected used a corrected value for the O₂ molecule. Our results for the formation energies are in good agreement with literature data.^29,30 The computed total energies and formation energies of these compounds are used to determine the chemical potential domains for the formation of Ni(O³H)_x.

3.1.2. Chemical potential domains for the stability and formation of Ni(O³H)_x. The formation and stability of a system depend on the chemical potential of its constituent elements, which varies with specific equilibrium conditions. In the thermodynamic limits, the chemical potential domains for Ni(O³H)₂ can be determined. The stability of Ni(O³H)₂ against decomposition into its elemental constituents requires a smaller atomic chemical potential than the corresponding elemental solid, i.e.,

μ_i ≤ μ^solid/gas_i, i = Ni, H, O. (2)

Setting Δμ_i = μ_i − μ^solid/gas_i, the above condition becomes

Δμ_i ≤ 0, i = Ni, H, O. (3)

For Δμ_i = 0 we obtain a maximum i-rich condition. Thermodynamic equilibrium of a system requires that a sum of the chemical potentials of its constituent atoms be equal to its formation energy. Therefore, we can write:

Δμ_Ni + 2Δμ_O + 2Δμ_H = ΔH(Ni(OH)₂) (4)

where ΔH(Ni(OH)₂) is the formation energy of bulk Ni(O³H)₂.

To avoid the formation of other oxide compounds (such as NiO, NiO₂, Ni₂O₃, Ni₃O₄, NiOOH), the ranges of chemical potentials for the stability of Ni(O³H)_x are subject to the following additional criteria:

Δμ_Ni + Δμ_O ≤ ΔH(NiO) (5)

Δμ_Ni + 2Δμ_O ≤ ΔH(NiO₂) (6)

2Δμ_Ni + 3Δμ_O ≤ ΔH(Ni₂O₃) (7)

3Δμ_Ni + 4Δμ_O ≤ ΔH(Ni₃O₄) (8)

Δμ_Ni + 2Δμ_O ≤ Δμ_H ≤ ΔH(NiOOH) (9)

Combining eqn (4) and (5)–(9), we computed the chemical potential domains for the formation and stability of Ni(O³H)₂ using the total energies and formation energies calculated above. Fig. 1 shows the stable chemical potential region of the bulk Ni(O³H)₂ in terms of the chemical potentials Δμ_O, Δμ_Ni, and Δμ_H using PBE and HSE06 functionals. The shaded area is the allowed chemical potential range for Ni(O³H)₂ to be a stable phase. In the PBE functional, the limiting stable conditions are defined by five points with coordinates (Δμ_Ni, Δμ_O, and Δμ_H) namely A(−4.13, 0, 0), B(−2.71, 0, −0.71), C(−0.27, −1.22, −0.71), D(0, −1.42, −0.64), and E(0, −2.06, 0) with boundary lines formed by Ni(O³H)₂, NiOO³H, and Ni₃O₄. In contrast, the limiting stable conditions using the HSE06 functional is defined by the following four points with coordinates (Δμ_Ni, Δμ_O, and Δμ_H): A(−6.26, 0, 0), B(−3.00, 0, −1.63), C(0, −3.00, −0.12), and D(0, −3.13, 0) with boundary lines corresponding to Ni(O³H)₂ and NiO.

Fig. 1 The allowed chemical potential domains (shaded regions determined by A, B, C, D, and E) for Ni(O³H)₂ to be stable. (a)–(c) Are results obtained using the PBE functional. (d)–(f) Are results obtained using the HSE06 functional. The secondary phases which are indicated by color-coded lines restrict the stable phase.

To understand the discrepancy between the results from the PBE and HSE06 functionals, we look at the formation energy per atom for nickel oxide compounds. In Fig. 2, we compare the formation energy per atom of the oxide compounds obtained using PBE, HSE06, and PBE+U functionals. The results show that HSE06 correctly predicts NiO as the most stable among all Ni oxides in agreement with the experiments, whereas PBE incorrectly assigns the lowest formation energy to Ni₃O₄.³¹ PBE+U follows the same trend as HSE06. Our results also show that the formation energy per atom of Ni(O³H)₂ is lower than that of NiOO³H in HSE06 (−1.25 eV per at vs. −1.03 eV per at), but it is the reverse in PBE (−0.82 eV per at vs. −0.85 eV per at). Our results agree with that of Huang et al. who studied the role of the exchange interactions on the accuracy of the electrochemical phase diagrams of Ni using first-principles methods.²⁹ They observed that the simulation accuracy tends to increase going from semi-local functionals to non-local hybrid functionals due to the increased electronic exchange attraction. Overall, we found that the HSE06 and PBE+U functionals correctly predict NiO as the most stable oxide. The chemical potential domains are better described using the HSE06 functional.

Fig. 2 Formation energies per atom from PBE, HSE06, and PBE+U functionals for nickel oxide compounds. The blue dashed line connects the formation energies of Ni(O³H)₂ with equal O and ³H content, 0.4. Horizontal dashed lines with solid symbols connect the formation energies of NiOO³H with O content 0.5 and ³H content 0.25.

3.2. Determining the ³H species dissolve from surface into Ni bulk

3.2.1. Tritium (³H) diffusion from Ni(111) surface to bulk. We first calculated the diffusion of a single ³H atom into a pure Ni(111) surface. ³H species diffused on the surface and occupied an interstitial site in the subsurface. There are two possible interstitial sites in the bulk Ni: a tetrahedral (denoted tetra) site and an octahedral (denoted octah) site. Fig. 3 shows the migration of ³H species from the surface into bulk. The calculated migration barrier of ³H from a fcc surface to a subsurface octahedral site is 0.698 eV. The reaction is endothermic by 0.621 eV with activation energy for resurfacing 0.077 eV. This result is in good agreement with previous calculations.^18,32–34 Shirazi et al. found an activation energy of 0.64 eV for a H-coverage of 0.50 monolayer and a resurfacing energy barrier of 0.05 eV.¹⁸ Henkelman et al. calculated energy barriers of 0.6 eV and 0.1 eV for the diffusion of H to the subsurface and the resurfacing of H, respectively.³² An octahedral subsurface H can diffuse into the bulk via a tetrahedral site with an activation energy of 0.454 eV. Greeley and Mavrikakis found an energy barrier of 0.52 eV.³⁵

Fig. 3 (a) Energy barrier and transition pathway for ³H diffusing into a pure Ni(111) surface, (b) initial and final structural configurations.

3.2.2. Migration of ³H species from surface to subsurface after ³H₂O dissociation. Next, we investigated the diffusion of ³H into the surface after a ³H₂O dissociation at partial and complete dissociation. In the partial dissociation, we have an ³H and O³H species lying on the surface. In complete dissociation, we have two ³H species and an O species lying on the surface. Our results in Fig. 4 show a slightly lower diffusion barrier for ³H in the case of a complete dissociation (0.572 eV) compared to that in the partial dissociation (0.618 eV). These two barriers are lower than that of a single ³H atom on the surface diffusing into the subsurface. As ³H₂O dissociates, surface sites are occupied which increases surface coverage leading to a redistribution of electron density. The increase of surface coverage is accompanied by a reduction in activation energy of the diffusion of a surface-bound ³H-atom to the subsurface.

Fig. 4 Energy barrier of ³H species migration from surface to subsurface after ³H₂O dissociation (a). Structures of the initial and final states (b and c).

3.2.3. Migration of O species from surface to subsurface. The migration of O species from a fcc surface site to a subsurface octahedral requires the presence of a defect such as Ni vacancy.³⁶ Our study reveals that in the absence of Ni vacancy O diffusion into the surface is unfavourable. We studied the diffusion of O species in a pure Ni surface with a subsurface V_Ni and the diffusion of O after an ³H₂O dissociation (Fig. 5). Our calculations reveal that presence of ³H helps to reduce the diffusion barrier for O in the Ni(111) surface than in presence of a subsurface V_Ni and without ³H. In the presence of ³H the activation energy and reaction energy are 1.341 eV and 1.226 eV, respectively, as compared to 1.574 eV and 1.510 eV for pure Ni surface with a subsurface V_Ni.

Fig. 5 Migration barrier of O species diffusion into Ni(111) surface. Structures of the initial and final states (b) after ³H₂O dissociation and (c) in bare surface. Orange circle denotes the location of Ni vacancy.

The diffusion barrier for ³H is lower than that for O on the Ni surface and bulk. Therefore, it is favourable for ³H to pass through the Ni coating and reach the Ni–zircalory-4 interface. The calculated diffusion barrier for O is nearly three times that for the diffusion of ³H. Experimentally, Ebisuzki et al.³⁷ and Lu et al.³⁸ obtained the diffusion barriers for H in Ni to be 0.42 and 0.19 eV, respectively. Lu et al.³⁸ also predicted the trapping of H in Ni using electrochemical permeation test and thermal desorption spectroscopy (TDS) and found the reversible trapping energy to be 0.26 eV. Similarly, Zholobov et al.³⁹ and Park et al.⁴⁰ experimentally predicted the diffusion barrier for O in Ni to be 1.89 and 1.70 eV, respectively. These results together with our calculated values indicate that ³H has much higher probability to diffuse through the Ni surface as compared to O.

3.2.4. Diffusion of two ³H species into nickel surface in the presence of O surface species. In this section, we studied the diffusion of two ³H species into Ni(111) surface in the presence of surface O and O³H species. Three different cases were investigated.
3.2.4.1. One O surface species. We studied the diffusion of two ³H atoms into Ni(111) surface after a ³H₂O dissociation. The first ³H is found to migrate into the subsurface with an energy barrier of 0.572 eV while the second ³H is found to have an energy barrier of 0.601 eV (Fig. 6). The presence of a second ³H on the surface contributes to the lowering of the migration barrier for the first ³H.

Fig. 6 (a) Migration barrier and reaction energies of two ³H species on Ni surface after ³H₂O dissociation,⁴¹ and in the presence of two surface O species (green) Structures of the initial and final states (b) for the two ³H species on Ni surface after ³H₂O dissociation and (c) in the presence of two surface O species.

3.2.4.2. Two O surface species. We also studied the diffusion of two ³H species in the presence of two O surface species (Fig. 6). The first ³H migrates into the surface with an even lower barrier and a lower reaction energy compared to the previous cases. The second ³H diffuses with a higher diffusion barrier of 0.643 eV and a reaction energy of 0.481 eV.
3.2.4.3. O and O³H surface species. To understand the effect of O and O³H after disassociation of ³H₂O, we calculated the diffusion of ³H in the presence of O and O³H surface species. The results show that ³H diffuses with a migration barrier of 0.562 eV and a reaction energy of 0.403 eV (Fig. 7). This barrier is much lower than the barrier of a single ³H diffusing on a pure and undefective Ni(111) surface.

Fig. 7 Migration barrier and reaction energy of the diffusion of ³H on the surface in presence of O and O³H species⁴¹ and in the presence of an O in a subsurface octahedral (green) The insets are the initial, transition and final states for the O in a subsurface octahedral.

In all three cases, the diffusion of ³H on the surface is favourable compared to that of O. We also investigated the diffusion of ³H from the surface to the subsurface in the presence of an O at the octahedral site (Fig. 7). Our results reveal that ³H diffuses into a subsurface octahedral site with an energy barrier of 0.595 eV and endothermic reaction energy of 0.452 eV.

3.3. Identifying the energy barrier of ³H species diffusion in the Ni bulk

In this section, we investigate the diffusion of ³H in Ni bulk and the formation of Ni(O³H)_x. We started with the assumption that an O migrates into the subsurface and we studied the diffusion of a ³H species toward O to form Ni(O³H)_x. We studied three different cases with the third case consisting of diffusion of O³H from the surface into the subsurface. However, O³H diffusion into the surface is unfavourable.

3.3.1. Case 1: formation of Ni(O³H)_x through diffusion of a subsurface H species. In this case, a ³H species in a subsurface octahedral site is allowed to diffuse toward O to form a Ni(O³H)_x unit. We obtained an activation barrier of ∼0.55 eV for the diffusion of ³H and formation of Ni(O³H)_x. The reaction is endothermic by 0.125 eV as shown in Fig. 8.

Fig. 8 Diffusion barrier and diffusion pathways for subsurface ³H diffusion and Ni(O³H)_x formation.

3.3.2. Case 2: formation of Ni(O³H)_x through diffusion of a surface ³H species. In this case, a surface ³H species is allowed to diffuse in the surface through a hexagonal closest packed (hcp) site close to the subsurface O species. As shown in Fig. 9, our calculated pathways show that ³H on a fcc site migrate to a hcp surface site with an energy barrier of ∼0.2 eV. Then it diffuses into a subsurface octahedral site away from the subsurface O with an activation energy of 0.87 eV. This barrier is 0.27 eV higher than that of a ³H, migrating from a surface fcc site (Fig. 7). Finally, the diffusing ³H must overcome a barrier of ∼1 eV to form a Ni(O³H)_x complex.

Fig. 9 Diffusion barrier and transition pathways for ³H diffusion into surface and subsurface formation of Ni(O³H)_x.

This study also investigated the diffusion of O species from a subsurface octahedral to a sub-subsurface octahedral. The results show a diffusion barrier of less than 0.4 eV as shown in Fig. 10.

Fig. 10 Diffusion barrier and reaction pathways of O species from a subsurface octahedral to a sub-subsurface octahedral.

David et al. calculated the migration energies of the diffusion along octah–tetrah for O atoms in Ni bulk and found 0.75 eV.⁴² Previous work from Fang et al. revealed that for O to diffuse into nickel bulk requires an activation energy of at least 1.68 eV.⁴³

4. Summary and conclusions

Formation of chemical compounds O³H, ³H₂O, and metal oxide on the Ni surface and subsurface regions can significantly affect adsorption, desorption, diffusion, and hinder ³H and ³H₂ reaching out to the getter material. Experimental evidence shows the presence of above compounds including hydrocarbons forming in Ni and getter materials. In this study, we explored ³H₂ and ³H₂O binding sites and their dissociation on the pure and defective (111) surface of Ni. As it is evident from the earlier studies, the possible dissociation steps of ³H₂O are ³H₂O → O³H + ³H → O + ³H + ³H, and ³H₂ → ³H + ³H. Our calculations also showed that there is a stable chemical potential region where NiO_x or Ni(O³H)_x phases could form. We found that the HSE06 and PBE+U functionals more accurately predict NiO as the most stable oxide as compared other methods employed in this study for the formation energy calculations. The ³H₂ and ³H₂O dissociated on the surface of Ni could diffuse into the subsurface region. We found that the presence of ³H on the surface reduces diffusion barriers for O by more than 15%. The results for the calculation on diffusion barriers showed that O prefers to chemically bsind in the Ni layer to form NiO_x or Ni(O³H)_x. This was evident from the fact that it the calculated diffusion barrier for 3H is 0.48 eV, which is nearly three times smaller than the corresponding value for O in the Ni(111) surface. In addition, we also found that formation of NiO_x or Ni(O³H)_x phase in Ni subsurface layer is limited by diffusion of O and formation of Ni vacancies. We conclude that ³H has higher probability of diffusion through the Ni layer and reaching out to the getter materials as compared to O.

Author contributions

Conceptualization, Y. D. and H. P.; methodology, D. T.; software, Y. D.; validation, D. T.; formal analysis, D. T.; investigation, D. T.; resources, Y. D., D. S., and A. C.; data curation, D. T.; writing – original draft preparation, D. T.; writing – review and editing, H.P., D. S., A. C. and Y. D.; visualization, D. T.; supervision, Y. D.; project administration, Y. D and A. C.; funding acquisition, D. S. and A. C. All authors have read and agreed to the published version of the manuscript.

Data availability

The raw/processed data required to reproduce these findings cannot be shared at this time due to technical or time limitations but may be obtained by contacting corresponding author. The VASP software can be found at https://www.vasp.at. The version of VASP employed for this study is 5.4.4.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

This research was funded by the National Nuclear Security Administration (NNSA) of the U. S. Department of Energy (DOE) through the Tritium Science Research Supporting the Tritium Modernization Program managed by Pacific Northwest National Laboratory (PNNL). This project was also funded by the United States Department of Energy, National Energy Technology Laboratory, in part, through a site support contract. Neither the United States Government nor any agency thereof, nor any of their employees, nor the support contractor, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, or favouring by the United States Government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof.

Notes and references

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