Theoretical study on the hydrogen distribution and diffusion at the PuO2/α-Pu2O3 interface

The interface is a region in the crystal that significantly changes various characteristics. There must be an interface between oxides of different valence states in the surface oxide layer of plutonium. In this work, a first principles approach based on DFT was used to study the hydrogen distribution and diffusion at the PuO2/α-Pu2O3 interface systematically. Our research reveals that at the interface, hydrogen can be captured by the O atoms of PuO2 and by the oxygen vacancies (OVs) of α-Pu2O3, and the capture of OVs is more energetically advantageous. On the PuO2 side, the cost of H atom diffusion towards the interface gradually increases. On the α-Pu2O3 side, the cost of H atoms diffusing inward from the interface gradually increases. OVs that already contain H atoms are more conducive to capturing H atoms. The formation of the interface has little effect on the hydrogen capture ability of O in PuO2, but it will reduce the capture ability of OVs in α-Pu2O3. Overall, the formation of interfaces has no disruptive impact on the behavior of hydrogen in the two plutonium oxides. This is closely related to the fact that α-Pu2O3 originates from PuO2 under anaerobic conditions. The difference in hydrogen behavior comes from the changes in the atomic environment and ion valence state caused by the OVs. This work supports further understanding of the behavior of hydrogen in plutonium oxides and provides a reference for further research on plutonium corrosion prevention.


Introduction
Plutonium is an indispensable material in the nuclear industry.In actinide elements, plutonium's complex 5f electronic state brings it active physical and chemical properties. 1,2][8] Compared to oxidation corrosion, hydrogenation corrosion poses a serious threat to plutonium's safe handling and storage.][11] The induction period mainly involves the interaction between the hydrogen and oxide layer, which is time-consuming and controllable. 12The induction period is key to the entire hydrogenation corrosion process.
Experimental studies have shown that PuO 2 can effectively prevent the entry of hydrogen.The complete PuO 2 layer is the rst barrier for plutonium hydrogenation corrosion.However, the Pu 2 O 3 layer cannot effectively prevent hydrogen erosion and provides the main hydrogen nucleation sites. 13,14Based on the basic understanding of experiments, people have conducted mechanism research on related issues from a microscopic perspective.Sun 15 rst analyzed the collision-induced dissociation of hydrogen molecules on intact and defective PuO 2 layers, nding that hydrogen is more prone to dissociation in defective systems.Only dissociated hydrogen can penetrate the PuO 2 .Yu's 16,17 study about the adsorption mechanism of H 2 and H atoms on the surface of PuO 2 (110) shows that the dissociation barrier of H 2 is 0.48 eV.H atoms tend to exist on the outer surface rather than migrating to the subsurface.
In addition to the surface, the characteristics of hydrogen in the plutonium oxide phase have also received some attention.9][20] This low solubility leads to rapid accumulation of hydrogen in the defect area and rapid diffusion in the PuO 2 layer.Zhang et al. 21,22 conducted a comparative study on the states of hydrogen in PuO 2 and Pu 2 O 3 , concluding that it is very difficult for H to dissolve in intact PuO 2 .In addition, they also found that H is the preferred state of existence in PuO 2 , but H atoms spontaneously recombine in Pu 2 O 3 .It is proposed that the high endothermic adsorption and dissolution properties of hydrogen in PuO 2 are the primary mechanism for hydrogen inhibition rather than hindering the diffusion kinetics of H, which also conrms the relevant conclusions of Ao.Using molecular dynamics methods, Tang 23 analyzed the diffusion behavior of hydrogen in oxygensaturated (OS) and oxygen-unsaturated (OU) plutonium oxides.The results showed that due to the diffusion trap effect

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of OVs, the diffusion coefficient of OU PuO 2 was lower than that of OS PuO 2 .Using a similar method, Tang 24 also analyzed the different roles played by PuO 2 and Pu 2 O 3 in hydrogen inhibition.The hydrogen inhibition effect of PuO 2 is mainly due to the capture of H atoms by lattice oxygen to form hydroxyl groups.For Pu 2 O 3 , when the hydrogen concentration is low, hydrogen erosion can be prevented because OVs act as traps for hydrogen migration.However, when the hydrogen concentration is high enough, it cannot effectively resist hydrogenation corrosion.The above studies indicate that in the oxide layer formed on the surface of plutonium exposed to air, there are signicant differences in the hydrogen-blocking mechanisms between the two typical oxides, PuO 2 and Pu 2 O 3 .In the sandwich structure of PuO 2 /Pu 2 O 3 /Pu, an interface exists between PuO 2 /Pu 2 O 3 , and the behavior of hydrogen at this interface is worth paying attention to.
This work systematically investigated the hydrogen distribution and diffusion behaviors in PuO 2 , a-Pu 2 O 3, and their interface with the rst-principles calculations.Our objective is to elucidate the role of the interface in the interaction process between hydrogen plutonium oxide.The rest of this paper is organized as follows.Our methodological approach and modeling are presented in Section 2, and our results are discussed in Section 3. Section 4 contains our main conclusions.

Methodology
First-principles calculations are conducted using the VASP (Vienna Ab initio Simulation Package) soware package. 25The correlation properties of electronic exchange are described by the GGA-PBE (Perdew-Burke-Ernzerhof of generalized gradient approximation) functional. 26,27A plane-wave kinetic energy cutoff of 520 eV is shown to give an accurate convergence of total energies.The 6s 2 7s 2 6p 6 6d 2 5f 4 electrons of Pu and the 2s 2 2p 4 electrons of O participate in the calculation as valence electrons.
The Hubbard model is used within the DFT + U method in the Dudarev formalism to treat strong on-site Coulomb interaction. 282][33][34][35][36] According to experimental and theoretical calculations (DFT + U), the ground states of Pu 2 O 3 and PuO 2 are set to antiferromagnetic states (AFM). 28,37Correction of van der Waals forces between H, H 2 , and plutonium oxide matrix using DFT-D3 method. 38,39The Brillouin zone selects 6 × 6 × 6 and 6 × 6 × 2 Monkhorst-Pack 40 lattice points for single type oxide model and interface model respectively, with an energy convergence standard of 0.01 eV Å −1 .
The calculation of transition states adopts the CINEB 41,42 method (clipping image nudge elastic band method).The defect formation energy (E a ) of the particle in the plutonium oxide is expressed as where E basement+P shows the total energy of the adsorption system, E basement means the total energy of the basement.E P means the total energy of the free particle.For the simultaneous adsorption of multiple particles of the same type, the average energy (E a-ave ) must be considered.The average energy is expressed as A negative of E a means heat release and spontaneous, and vice versa.n means the number of particles.

Modeling
We rst optimize the structure of PuO 2 single crystal cells, our calculation result for a 0 is 5.432 Å, which differs from the experimental value (5.396 Å) by 0.66%.
Under hypoxic conditions, PuO 2 can be reduced to a-Pu 2 O 3 , which has a similar cubic structure.In the structure of a-Pu 2 O 3 , O atoms occupy the 48e sites, while Pu atoms occupy the 24d and 8a sites.Based on the 2 × 2 × 2 supercell of PuO 2 , 16 O atoms are removed from the 16c (0.25, 0.25, 0.25) sites, and structural relaxation is performed to obtain the a-Pu 2 O 3 single crystal cell.Our calculation result for a 0 is 11.20 Å, which differs from the experimental value (10.98 Å) by 2.2%.
Based on the relationship between the 2 × 2 × 2 supercell of PuO 2 and the single crystal cell of Pu 2 O 3 mentioned above, two approaches can be used to construct the PuO 2 /a-Pu 2 O 3 interface model: (1) Construct a supercell model of PuO 2 by removing O atoms from the corresponding sites in half of the model and constructing it as a-Pu 2 O 3 , followed by relaxation (Fig. 1).
(2) Firstly, a supercell model of PuO 2 is constructed for relaxation, followed by removing O atoms at 16 corresponding sites and relaxation to obtain an a-Pu 2 O 3 model.The relaxed PuO 2 and a-Pu 2 O 3 cell models are concatenated, and then the concatenated model is relaxed (Fig. 2).
Aer calculation, we found that the models obtained by the two approaches have slight differences in size and atomic conguration.In contrast, the rst approach is more in line with PuO 2 being reduced to a-Pu 2 O 3 due to hypoxia.
There is still a question about building a vacuum layer during model construction.If a vacuum layer is constructed, it is necessary to analyze the exposed surface.The surface exposed by the model obtained through the above two approaches is (100) surface (as shown in Fig. 3).The PuO 2 (100) surface is polar and needs to be treated to improve stability. 43If a vacuum layer is not constructed, mutual contamination exists between interfaces in periodic structures.Tang 44 chose to avoid exposing polar surfaces in his research on oxygen atom diffusion.Based on this approach, this work considers increasing the model's thickness to avoid exposing polar surfaces while minimizing mutual contamination between interfaces.
Considering the various aspects of interface model construction mentioned above, we used approach 1 to construct an interface model with sufficient thickness without a vacuum layer, as shown in Fig. 4. The Pu 4+ ions in PuO 2 are difficult to further oxidize to higher valence states.6][47] For PuO 2 , each OV produces the two nearest Pu 3+ ions, similar to the microscopic description of the two electrons le behind when forming OVs in CeO 2 . 48At the interface, there are four OVs on the side of a-Pu 2 O 3 , which can generate eight Pu 3+ ions, of which four belong to the inside of the interface, and four belong to the outside of the interface.The interface contains eight Pu ions, half of which are Pu 4+ and half are Pu 3+ .

Results and discussion
Aer the interface's formation, relaxation will impact the atomic environment at and near the interface.Compared with before and aer structural optimization, the atomic structure near the interface underwent distortion, as shown in Fig. 6.Of particular concern is the distance between each layer of Pu atoms, as shown in Fig. 7.It can be observed that the closer to the interface, the greater the interlayer spacing of Pu atoms on the side of PuO 2 , the smaller the interlayer spacing on the side of a-Pu 2 O 3 .atoms in atomic form. 21For verication, we calculated the defect formation energy of a single H atom incorporated in the rst nearest-neighboring oxygen, octahedral interstitial site, and two oxygen interstitial site, respectively (Fig. 8).The defect formation energies are 0.89 eV, 1.79 eV, and 2.11 eV, respectively, and each oxygen can capture up to four H atoms, which is consistent with the previous research. 21r a-Pu 2 O 3 , there seems to be some controversy over the stable state of hydrogen in it.Zhang thought that H prefers to bind to O-anion according to incorporation energies. 22Tang's molecular dynamics calculation results indicate that no hydroxyl was formed, but a favorable and stable capturing effect from the OV was found. 24To determine the state of hydrogen in a-Pu 2 O 3 within our theoretical system, we calculated the defect formation energy of a single H atom incorporated in an OV and rst nearest-neighboring oxygen.From the perspective of defect formation energy, H atoms are more likely to be captured by OVs.

Hydrogen distribution in the PuO
We are also curious about how many H atoms each OV can accommodate.Table 1 shows the formation energy of defects where different numbers of H atoms are captured in the same OV.Combining two H atoms leads to a signicant decrease in formation energy, indicating that hydrogen molecules embedded in OVs do not interact signicantly with plutonium or oxygen in the surrounding environment.The lower the impact of impurities on the system, the lower the formation energy.The two hydrogen atoms doped with oxygen vacancies in molecular form have a relatively small impact on the system, resulting in a lower formation energy.When the number of H atoms reaches ve, there is a sudden increase in defect formation energy.This indicates that for an OV, four H atoms are the upper limit it can accommodate.Based on this, select the site near the oxygen atom on the side of PuO 2 (hereinaer referred to as site 1-1) and the OV on the side of a-Pu 2 O 3 (hereinaer referred to as site 2-1) as potential existence sites for H atom, as shown in Fig. 9. Aer sufficient relaxation, H atoms still remain near O atom or in OV, indicating that both sites are stable capture points for H atoms.The defect formation energies of H atoms at these two sites are 1.32 eV and 1.17 eV, respectively.The incorporations of H atoms at the interface are endothermic processes.H is more inclined to be absorbed by OV in a-Pu 2 O 3 .
When near the O atom on the side of PuO 2 in the interface, the distance between H and O atoms is about 0.995 Å, and incorporating H atoms increases the system's volume by 7 Å 3 .When in the OV on the side of a-Pu 2 O 3 , incorporating H atoms decreases the system's volume by 2 Å 3 .The lattice volume is closely related to the chemical bonds in the system.Intuitively speaking, adding atoms will increase the system's volume, known as the spatial effect.The chemical bond formed between    Paper RSC Advances the doped atoms and the substrate will reduce the system's volume, called the bonding effect.The volume change of the system aer the impurity's incorporation depends on the mutual cancellation of spatial and bonding effects.When the crystal is at site 1-1, hydrogen acts as a reducing agent, promoting the reduction of low valent Pu with a larger volume in the system.The spatial effect dominates, leading to an increase in the system's volume.When the crystal is at site 2-1, hydrogen acts as an oxidant to promote the high valence Pu with a smaller volume at the oxidation site in the system, and the bonding effect dominates, leading to a decrease in the system's volume.Using hydrogen as a probe can detect the characteristics of Pu atoms at the interface, that is, Pu atoms at the interface can be reduced and oxidized.Through the analysis of interface characteristics above, it is found that the formation of interfaces not only affects the atomic environment at the interface itself, resulting in changes in hydrogen behavior, but also affects the atomic environment near the interface, which also causes changes in hydrogen behavior.The incorporation energies of H atoms at six sites outside the interface, located near the O atoms on the PuO 2 side and at the OVs on the a-Pu 2 O 3 side, were calculated to analyze the area affected by the interface.The incorporation energy of each point is shown in Table 2. On the PuO 2 side, as the distance between the site and the interface increases, the energy required for incorporation also increases.On the side of a-Pu 2 O 3 , the energy required for incorporation decreases as the distance increases.The main reason is that the closer to the interface on the side of PuO 2 , the longer the bond length for Pu-O, and the less oxidation ability of O ions occupied by Pu, which can free up more oxidation ability to interact with adsorbed H atoms.As a comparison, on the side of a-Pu 2 O 3 , the farther the site is from the interface, the stronger the reducing ability of the surrounding Pu, which makes H atoms more easily reduced as oxidants and captured by OVs.For the H atom, diffusing from PuO 2 to a-Pu 2 O 3 has seven processes.The energy barriers in each process are shown in Table 3. Overall, the diffusion energy barrier for H atoms on the PuO 2 side is relatively lower than on the a-Pu 2 O 3 .From the changing trend, the closer the H atoms are to the interface on the side of PuO 2 , the higher the diffusion energy barrier, and the more difficult diffusion.There are two reasons for this situation: rstly, the formation of the interface leads to an increase in the distance between system atoms near the interface (compared to pure PuO 2 ); secondly, the enhanced oxidation ability of O atoms leads to a tighter binding with H. On the side of a-Pu 2 O 3 , the farther the H atoms are away from the interface, the higher the diffusion energy barrier, and the more difficult it is for diffusion to occur.Two factors play a role: rst, the formation of the interface leads to a decrease in the distance between atoms in the system near the interface (compared to pure a-Pu 2 O 3 ); second is that the closer the Pu atom is to the interface, the smaller the radius.During the diffusion of H atoms from one OV to the following OV, they need to "squeeze" through the area formed by the Pu atoms.The smaller the Pu atom radius, the easier this process occurs.
A particular point requires special attention, where H atoms diffuse from Site 1-1 to site 2-1.During this process, the H atom is captured by the O atom and diffuses to be captured by OV.According to the previous analysis, hydrogen exists in an atomic state in PuO 2 and a molecular state (or possibly in an atomic state) in a-Pu 2 O 3 .Multiple H atoms may be diffusing from PuO 2 to a-Pu 2 O 3 and combining in a-Pu 2 O 3 to form H 2 .To this end, a comparative analysis is conducted on two diffusion routes: route 1, a single H atom diffuses from site 1-1 to site 2-1; route 2, a single H atom exists aer site 2-1, while another H atom diffuses from site 1-1 to site 2-1, and the two H atoms merge to form an H 2 .Use the CINEB method to search for several intermediate transition states in two diffusion processes, as shown in Fig. 10.In the two processes, the energy barriers that H atoms need to cross are 0.59 eV and 0.49 eV, that is, route 2 is more likely to cross than route 1. Transition states occur when atoms diffuse to the vicinity of plutonium, where they need to "squeeze" through the region formed by Pu ions with a certain radius.In route 2, Pu atoms are oxidized to higher valence states due to H atoms acting as oxidants.Pu atoms in higher valence states have radii smaller than those in lower valence states.H atoms are more likely to cross energy barriers and complete   Similar to the adsorption of a single H atom on the PuO 2 side of the interface, the maximum number of H atoms accommodated near each oxygen atom is also four.However, the closer to the interface, the lower the energy required for adsorption and the easier for dissolution.On the a-Pu 2 O 3 side, there is a certain change in the situation.At site 2-1 and site 2-2, closer to the interface, the upper limit of H atoms that can be accommodated in OVs is two (recombining into one hydrogen molecule).As the distance between OVs and the interface increases, their ability to accommodate H atoms increases.Site 2-3 and site 2-4 can accommodate four H atoms (recombining into two hydrogen molecules).
A noteworthy situation has emerged in the structural optimization of various models for hydrogen dissolution at the interface of PuO 2 /a-Pu 2 O 3 .To test the capacity of OVs in a-Pu 2 O 3 to accommodate H atoms, different numbers of H atoms were placed in each OV.Perform sufficient relaxation, and if there is a sudden change in energy in the structure aer relaxation, it is considered to have reached the upper limit for accommodating H atoms.When three H atoms were placed in site 2-1, it was found that in the relaxed structure, two H atoms recombined into H 2 , and another H atom was captured by the O atom at site 1-1.This indicates that hydrogen diffusion within the plutonium oxide phase is not unidirectional.When the hydrogen dissolution in a-Pu 2 O 3 locally reaches the upper limit while PuO 2 still has room to accommodate it, there may be a "backow" of hydrogen.

Conclusions
The micromechanisms of the hydrogen behaviors in the PuO 2 / a-Pu 2 O 3 interface are systematically investigated using the rstprinciples calculations method within DFT schemes.
We nd that at the interface, the capture of H atoms by OVs in a-Pu 2 O 3 is more energetically advantageous than that by oxygen in PuO 2 .The energy required for hydrogen diffusion gradually increases from PuO 2 to the interface, as well as from the interface to a-Pu 2 O 3 .OVs that already contain H atoms are more conducive to capturing H atoms.The formation of the interface will reduce the capture ability of OVs in a-Pu 2 O 3 .Overall, the types of hydrogen exhibited at the interface are not fundamentally different from those of the two oxides.a-Pu 2 O 3 is formed by the generation of OVs in PuO 2 under hypoxia conditions.The interface between PuO 2 and a-Pu 2 O 3 acts as a buffer.The behavior differences of hydrogen in different plutonium oxides come from the changes in the atomic environment and ion valence state caused by the OVs.The conclusion of this work supports further understanding of the behavior of hydrogen in plutonium oxides and provides a reference for further research on plutonium corrosion prevention.

3. 1
Properties of PuO 2 /a-Pu 2 O 3 interface The environment around an atom signicantly impacts its exhibited properties, especially for Pu atoms with wandering delocalized and localized 5f electrons.Analyzing the coordination of O atoms around Pu atoms is signicant for understanding the overall interface characteristics.The O atom coordination number around the Pu atom in PuO 2 is eight (4 + 4), with a distance of 2.35 Å, forming a PuO 8 cube, as shown in Fig. 5(a).The O atom coordination number around the Pu atom in a-Pu 2 O 3 is six (3 + 3), forming PuO 6 , and there are two states in coordination conguration, as shown in Fig. 5(b) and (c).The O atom coordination number around the Pu atom at the interface is seven (3 + 4), forming PuO 7 , and there are also two coordination congurations in different states, as shown in Fig. 5(d) and (e).

3. 3
Hydrogen distribution in the PuO 2 /a-Pu 2 O 3 interface H atoms in PuO 2 tend to be captured by O atoms to form hydroxyl groups, and in a-Pu 2 O 3 tend to be trapped by OVs.

Fig. 6
Fig. 6 Structural distortion at the interface.(a) Configuration before structural optimization.(b) Configuration after structural optimization.

Fig. 9
Fig. 9 Incorporation site for H in the PuO 2 /a-Pu 2 O 3 interface.

Fig. 10
Fig. 10 Diffusion behavior for H.The IS means initial state, the TS means transition state and the FS means final state.(a) Route 1.(b) Route 2.

Table 1
Incorporation energy for H in OV.The energy variation represents the change in the total formation energy of all hydrogen atoms caused by adding a doped hydrogen atom −0.33 1.19 −0.11 3.88 © 2024 The Author(s).Published by the Royal Society of Chemistry RSC Adv., 2024, 14, 16600-16606 | 16603

Table 2
Incorporation energy for every site

Table 3
Energy barriers for diffusion Hydrogen dissolution in the PuO 2 /a-Pu 2 O 3 interfaceHydrogen is dissolved in an atomic state in pure PuO 2 (fused with O atoms), and can adsorb four H atoms near each O atom, with the adsorption energy gradually increasing.Hydrogen dissolves in a molecular or atomic state in a-Pu 2 O 3 (captured by OVs), with each OV capable of accommodating four H atoms (which relax and recombine into two H 2 ).From PuO 2 to a-Pu 2 O 3 , the main structure did not undergo signicant changes, and the dissolution mode and characteristics did not change either.The interface model composed of PuO 2 and a-Pu 2 O 3 also inherits these characteristics.
diffusion in this process than in route 1. Hydrogen diffuses from PuO 2 to a-Pu 2 O 3 in atomic form and combines with other H atoms that diffuse to OVs in a-Pu 2 O 3 to form H 2 .3.5