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Differences in the Existence States of Hydrogen in UO and PuO from DFT + U Calculations 2

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Bingyun Ao, Ruizhi Qiu, Haiyan Lu, and Piheng Chen J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.6b05621 • Publication Date (Web): 09 Aug 2016 Downloaded from http://pubs.acs.org on August 15, 2016

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The Journal of Physical Chemistry

Differences in the Existence States of Hydrogen in UO2 and PuO2 from DFT + U Calculations Bingyun Ao,* Ruizhi Qiu, Haiyan Lu and Piheng Chen* Science and Technology on Surface Physics and Chemistry Laboratory, P. O. Box 9071-35, Jiangyou 621907, P.R. China ABSTRACT: First-principles DFT + U methods are performed to calculate the formation energy and to determine the relative stability of hydrogen at the different sites of UO2 and PuO2. Twenty-one incorporation sites for hydrogen, i.e., along the pathway from its first nearest neighboring oxygen to the octahedral interstitial site, are considered. The results indicate that hydrogen in UO2 energetically prefers to exist as a hydride ion ([(UO2)n]+H−) rather than forms a hydroxyl group ([UnO2n−1]+[OH]−). The negative formation energy of hydrogen at the octahedral interstitial site of UO2 shows that hydrogen is soluble and can oxidize uranium ion to the higher valence states. However, hydrogen in PuO2 is relatively stable in the form of [PunO2n−1]+[OH]− with comparison to [(PuO2)n]+H−. The slightly positive formation energy of hydrogen in the form of hydroxyl group in PuO2 reveals that hydrogen is either insoluble or just lies in the edge of solubility. The differences in the existence states of atomic hydrogen in the two dioxides are proposed to be dependent on the nature of 5f electrons of uranium and plutonium; that is, uranium 5f electrons are more delocalized and more favorable to participate in chemical bonding than plutonium 5f electrons.

ACS Paragon Plus Environment

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1. INTRODUCTION Among all the actinide-based compounds, UO2 and PuO2 are the two most concerned because the former is the standard nuclear fuel and the latter is the envisioned nuclear fuel (in the form of U and Pu mixed oxides, or MOX) in the prospective breeder reactors. Moreover, the two dioxides are the most important oxidation products for metallic U and Pu during the process of their storage and application. Up till now, many experimental and theoretical researches have been conducted on their solid-state properties of stoichiometric dioxides and their surface-related properties;1-5 however, systematic results on nonstoichiometric oxides and impurity-related properties of UO2 and PuO2 have been relatively rarely reported.6-10 In fact, impurity atoms may play a decisive role in some properties of solid-state materials.11 An outstanding example is the research and development of semiconductors, in which even a small concentration of impurity atom may strongly influence the electronic properties. It is naturally conceivable that impurity atoms should also influence the properties of UO2 and PuO2, such as electrical and thermal conductivity of interest. Yet, previous reports on the issue were limited on the macroscopically experimental observations and the microscopically theoretical calculations of rare-gas behavior.12-16 Our previous first-principles calculations obtained the fundamental energetics of some nonmetallic impurity atoms (H, He, B, C, N, O, F, Ne, Cl, Ar, Kr and Xe) in PuO2, rare gases in UO2, and Ga in PuO2 and Pu2O3.17-20 Size effect and electron transfer of impurity atoms were proposed to be the two opposite factors in their relative stability. From the point view of physics and chemistry of point defects in materials, further investigations are necessary for the deep understanding of the inherent interactions between impurity atoms and actinide oxides. During the lifetime of the above two dioxides’ fabrication, storage and application, hydrogen is one of the inevitable impurity atoms. Even in the storage process of the dioxides under


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vacuum conditions, the adsorbed water on the oxide surface could be changed into hydrogen by chemical reaction or radiation-induced decomposition.21 Knowledge from the researches on material-hydrogen systems, an old but engaging scientific topic, has demonstrated the extreme complexity of the behavior of hydrogen and its influence on material properties. This is mainly due to the variabilities of site occupation of hydrogen with the smallest atomic radius, and chemical valence states which are very sensitive to chemical surroundings. For an example, hydrogen can exist as a cation, or an anion, or a free atom in solid-state materials. Despite the importance of the potential influence effects arising from hydrogen in UO2 and PuO2, there is still a dearth of relevant comprehensive research in the literature. Some experimental and theoretical studies mainly focused on the surface-related behavior of hydrogen on the surface of the two dioxides.22,23 For the behavior of hydrogen in bulk UO2 and PuO2, very limited studies concentrated on its solubility. Generally, hydrogen solubility is dependent on the stoichiometry and the crystalline nature of UO2 sample. However, the hydrogen species in UO2 have not been completely determined. Sherman et al. suggested that hydrogen in UO2 exist as monatomic species by the measurement of the solubility and release kinetics of hydrogen in single crystal UO2, polycrystalline UO2 and UO2-x.24 More recently, Flitcroft et al. calculated atomic hydrogen solubility in UO2 using first-principles methods, and predicted that hydrogen energetically prefers to occur as a hydride ion rather than a hydroxyl group.25 The results really implied that UO2 was more favorable to be oxidized than to be reduced in the presence of hydrogen. For the hydrogen species in PuO2, however, there is almost no any report available. It is worth pointing out that the investigations on the behavior of hydrogen in metallic Pu show the complicated site preference, hydrogen distribution and hydrogen-vacancy interaction, which even results in the local disorder of hydrogen in Pu hydrides. Moreover, the complicated crystal structure and phase


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transition of Pu hydrides can partially reflect the complicated interaction between Pu and hydrogen.26-29 In order to understand the inherent behavior of hydrogen in UO2 and PuO2, advanced experimental techniques and theoretical methods are required. Yet, the difficulties in handling radioactive actinide oxides and preparing high quality sample hinder such study; at least partially make the direct identification of hydrogen species unreachable. An effective solution to identify hydrogen species in UO2 and PuO2 is the use of first-principles calculations in the framework of density functional theory (DFT). Indeed, many theoretical calculations by means of improved DFT methods for considering strong 5f electrons correlation in actinides have contributed to our understanding of actinide-based materials. Among them, the well established DFT + U (U is Hubbard parameter for quantifying 5f electrons correlation.) methods are the major choice for the systems containing defects. This can be considered as a result of compromise between computational accuracy and efficiency. Meanwhile, other advanced first-principles methods, such as dynamics mean field theory (DMFT), hybrid DFT and GW approximations (G and W denote Green function and the screened Coulomb interaction, respectively.), are mainly limited to the small systems with high symmetry structures. In the present work, following the DFT + U calculations on hydrogen species in UO2 by Flitcroft et al.,25 we have comparatively calculated the formation energy of hydrogen at the different sites along the pathway from the hydroxyl group to the octahedral interstitial site in UO2 and PuO2. The relative stable sites and potential existence states of hydrogen in the two dioxides are predicted. The significant differences of hydrogen behavior in UO2 and PuO2 are clarified in term of their electronic structure. As well known, from the lighter actinide elements to the heavier ones, their 5f electrons take place the interesting delocalization → localization transition, whereas Pu 5f electrons just lie at the critical


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point of the transition. The differences of the existence states of hydrogen in UO2 and PuO2 reasonably reflect the differences in the nature of their 5f electrons, and can be referred to predict the potential existence states of hydrogen in other actinide dioxides.

2. THEORETICAL METHODS Both UO2 and PuO2 crystallize in the face-centered cubic (fcc, space group: 225/Fm3 m) fluorite structures as shown in Figure 1, with the lattice parameters of 5.470 Å and 5.396 Å, respectively. In order to reasonably reflect the experimental hydrogen concentration in the two dioxides, here we use their 2 × 2 × 2 supercells containing 32 metal atoms and 64 O atoms (An32O64; An = U and Pu.) to build the computational configurations. For the sake of marking the pathway of hydrogen, only a conventional cell unit (An4O8) is shown in Figure 1. For their magnetic orders of UO2 and PuO2, we use the widely accepted collinear 1-k antiferromagnetic (AFM) states along (100) lattice direction.4 In fact, our calculations and some similar calculations by other researchers show that the 1-k AFM states are energetically more favorable than nonmagnetic (NM) and ferromagnetic (FM) states. Twenty-one incorporation sites for atomic hydrogen, i.e., along the pathway from its nearest neighboring lattice oxygen to the octahedral interstitial site, are considered, as indicated by the red arrow in Figure 1. The potential existence states of hydrogen in perfect UO2 and PuO2 crystals are supposed to be approximately determined by the formation energy of hydrogen in the above 21 incorporation sites. More complicated incorporation sites, such as various defects which might accommodate hydrogen and require the larger supercells to build the defect configurations, are currently not considered.


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Figure 1. Calculation configurations of An32O64H (An = U, Pu). For the sake of clarity, only a unit cell An4O8H is presented. Twenty-one incorporation sites for hydrogen, i.e., along the pathway from its first nearest neighboring (1nn) oxygen to the octahedral interstitial site as indicated by the red arrow, are considered.

Total energy calculations are performed with VASP code, the projector augmented wave (PAW) method, and relativistic effective core potentials (ECPs).30-32 U 6s27s26p66d25f2, Pu 6s27s26p66d25f4, O 2s22p4 and H 1s1 are treated as valence electrons, respectively. The exchange and correlation interactions are described by the spin-polarized generalized gradient approximation (GGA) in the Perdew-Wang 91 (PW91) functional. Other functionals such as Perdew-Burke-Ernzerhof (PBE) and local density approximation (LDA) have been demonstrated to have a slight influence on the energetics of impurities incorporation into UO2 and PuO2 in our previous calculations. The Hubbard model is used to treat strong on-site Coulomb interaction within the DFT + U method in the Dudarev formalism.33 An effective U (Ueff = U – J; i.e., the difference between the Coulomb U and exchange J parameters, hereafter referred to as U) value


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of 4 eV is selected for both U and Pu 5f electrons. This value has been demonstrated by our previous calculations to be reasonable in reproducing the experimental lattice parameter, bulk modulus, band gap and reaction energy of UO2 and PuO2. Complete relaxation without symmetry constraints is employed for the perfect UO2 and PuO2. This means that the positions of the atoms as well as the lattice parameters of the unit cells are fully relaxed. We find that the total energies of the configurations that are relaxed without symmetry constraints are always smaller than those relaxed with symmetry constraints. With the incorporation of hydrogen, the hydrogen atom and one of its nearest oxygen atoms are fixed for each configuration, and the remaining part of each configuration is still completely relaxed. Convergence is reached when the total energies converge within 1×10−5 eV and the Hellmann-Feynman forces on each ion are less than 0.02 eV/Å. The use of a plane-wave kinetic energy cutoff of 500 eV and 3 × 3 × 3 Monkhorst-Pack k-point sampling are shown to give accurate energy convergence. For the total energy and density of state (DOS) calculations, the tetrahedron method with Blöchl correction is used for the Brillouin-zone integration.34 Pure spin-polarized DFT calculations are performed to determine the total energy of a hydrogen atom in molecular state. We use half the total energy of an H2 molecule as the total energy of a hydrogen atom. Owing to the well-known disadvantages of pure DFT in describing molecule, the scheme selected to calculate the total energy of an H2 molecule is similar to the one proposed by Korzhavyi et al.35 The total energy of an H2 molecule is obtained by the sum of the energy of free hydrogen atom and the well-established dimerization energy (i.e., the reaction energy of 2H = H2).36 The total energy of a free hydrogen atom is calculated by using a periodic cubic cell with a lattice constant of 15 Å and only one k point Γ in the framework of spin-polarized DFT.


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3. RESULTS AND DISSCUSSION From the point view of first-principles calculations, defect formation energy is the most important results for describing the relative stability of impurity in solid-state materials. For the perfect crystal configuration containing only one interstitial impurity atom, the terminology “formation energy”, denoted as Ef, is equal to another two widely-used terminologies “incorporation energy” and “solution energy”, denoted as Ei and Es, respectively. Hereafter, we use Ef for describing the relative stability of hydrogen atom incorporation into perfect AnO2 crystals. It is worth pointing out that above three terminologies are different for the configuration containing multiple defects. The expression of formation energy related to interstitial hydrogen atom in AnO2 is listed as follow: E f (An32O64H) = Etot(An32O64H) − Etot(An32O64) − Etot(H),

(1)

where Etot(An32O64H), Etot(An32O64) and Etot(H) denote the first-principles total energy of An32O64H, An32O64 and H, respectively. The negative formation energy corresponds to energetically favorable and vice versa. It is worth mentioning that our previous calculations regarding the vacancy formation energy of An and O in AnO2, the energetics of non-metallic and metallic impurity atoms in AnO2, and the formation mechanism of hyperstoichiometric oxides (AnO2+x) have demonstrated the reasonability of the calculation methodology.17-20 Based on the previous calculations, the formation energies of hydrogen atom placed along the pathway in Figure 1 are calculated, as shown in Figure 2.


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H Formation Energy (eV)

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10 9 8 7 6 5 4 3 2 1 0 -1 -2

H in UO2 H in PuO2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

2.2

2.4

O-H Distance (Å)

Figure 2. Formation energy of hydrogen in AnO2 as the function of O-H distance. Note that the first minimum energy and the farthest distance correspond to the hydroxyl group and the octahedral interstitial site, respectively.

Figure 2 shows the dependence of hydrogen formation energy on the distance between the hydrogen atom and the first nearest neighboring (1nn) oxygen atom. According to the classification by Flitcroft et al,25 there were three distinct regions for hydrogen in UO2. The first is close to the 1nn oxygen atom, up to 1.13 Å, where the hydrogen is a proton, as part of a hydroxyl group, and there is a nominal U3+ formed. The second region, between 1.13−2.00 Å from the 1nn oxygen atom, is where there is no change in oxidation state of the hydrogen or uranium. In this region the hydrogen is a radical and could be seen as an intermediate state between the hydride and proton species. The final region, when the O-H distance is greater than 2.00 Å, the final hydrogen species is a hydride and this is the most stable hydrogen defect. Generally, our calculation results are in reasonable agreement with the classification proposed by Flitcroft et al except for some differences in the quantity of formation energy and the bonding


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distance of hydroxyl group. When O-H distance is rather shorter than that of hydroxyl group, the hydrogen formation energy is very high, implying that hydrogen is very unstable. This can be well understood by the steric effects of chemical bonds. The hydrogen formation energy significantly decreases with the increase in O-H distance. Interestingly, the hydrogen formation energy attains a minimum negative value (−0.60 eV) when O-H distance is close to 1 Å, a typical distance of hydroxyl group. Nominally, a U3+ ion and an OH− ion form in the chemical configuration, which can be nominally denoted as [UnO2n−1]+[OH]−. After the region, between 1 Å – 1.8 Å of O-H distance, hydrogen is supposed to be an intermediate state. This is primarily because neither hydroxyl group nor hydride could form in the region. Therefore, the hydrogen formation energy is higher than that of hydrogen in the form of hydroxyl group. Bader charge analysis indicates that hydrogen gradually changes from electron-deplete state to electron-rich state. As the O-H distance is longer than 1.8 Å, the hydrogen formation energy is lower than that of hydrogen in the form of hydroxyl group. For the hydrogen atom at the octahedral interstitial site, with the longest O-H distance considered here, the hydrogen formation energy reaches the global minimum negative value (−1.12 eV; −0.52 eV energy difference from the previous minimum value.). The hydride species containing an electron-rich hydrogen (H−) and an electron-deplete U (U5+) are proposed to form in the configuration, which can be nominally denoted as [(UO2)n]+H−. The results demonstrate that hydrogen can oxidize UO2 to higher valence U and the hydride species are the most stable existence states for hydrogen in UO2. For the case of hydrogen in PuO2, as can be found in Figure 2, the energy profile is significantly different from the case of hydrogen in UO2. The most remarkable difference is that all the hydrogen formation energies are positive, suggesting the unstable states of hydrogen in PuO2. There is only one minimum positive energy value (0.35 eV) at the position of hydroxyl


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group. This implies that hydrogen in the form of hydroxyl group is the relatively stable existence state. After that position, the hydrogen formation energy increases with the increase in O-H distance. Particularly, the formation energy of hydrogen at octahedral interstitial site is high to 2.32 eV (1.97 eV energy difference from the minimum energy value.), implying that the formation of hydride specie is energetically unfavorable.37 This agrees well with the conclusion that hyperstoichiometric Pu oxides (Pu valence higher than +4) are very difficult to form under normal chemical conditions.35 In fact, for the Pu-O binary system under normal chemical condition, it is rather difficult for the formation of Pu ion higher than +4 valences, whilst the formation of Pu ion between +3 and +4 valences is relatively favorable.38-40 Hydrogen in PuO2 is relatively stable in the form of [PunO2n−1]+[OH]− with comparison to [(PuO2)n]+H−. The slightly positive formation energy of hydrogen in the form of hydroxyl group in PuO2 reveals that hydrogen is either insoluble or just lies in the edge of solubility, whereas hydrogen solubility in UO2 is higher than in PuO2. Hydrogen in PuO2 mainly remains in proton state and diffuses from one lattice oxygen to the next. On the other hand, there are many concrete experimental evidences of the formation of binary hyperstoichiometric U oxides with the valence states from +4 to +6, some typical oxides such as U4O9, U3O8 and UO3.41-43 Even hydrogen can oxidize U4+ to higher valence states. Yet, hydrogen has the trend to reduce Pu4+ to Pu3+. Hydrogen in UO2 mainly remains in an anion state and diffuses from one octahedral interstitial site to the next. The inherent mechanism of the differences in the hydrogen behavior in UO2 and PuO2 can be attributed to the bonding behavior of 5f electrons. 5f electrons of U are more delocalized (corresponding to bonding) than those of Pu; therefore, U can be more easily oxidized than Pu, which will be addressed later.


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The differences in the existence states of hydrogen in UO2 and PuO2 are referable in understanding the hydriding reactions of metallic U and Pu. In fact, the direct reaction between massive actinide metals and hydrogen is one of the most important issues regarding the surface chemistry of actinide metals, although hydrogen might be introduced via other processes such as the decomposition of H2O. Generally, both U and Pu can quickly react with pure hydrogen; indeed, for the ideal clean surfaces of U and Pu, the reaction energy barriers are evaluated to be close to zero.1 Under the actual conditions, extensive studies have shown that there are many influencing factors in the hydriding kinetic mechanisms.44-46 According to the classification by McGillivray et al., hydriding reactions are generally consisted of four sequential steps: 1) induction, 2) nucleation or acceleration, 3) bulk hydriding, and 4) termination.47 Among them, the first step, i.e., induction period in which no hydrogen consumes and no hydride produces, is the most concerned. This is primarily because the length of induction period is the comprehensive reflection of sample states. The rate of hydrogen sorption depends strongly on the presence and porosity of the impeding nonmetallic layer such as the inevitable oxide layer. Before reaction with the metal, hydrogen has firstly to diffuse through the oxide layer. From the present calculation results, we find that hydrogen can dissolve in UO2 or can react with UO2. For the hydriding reaction, this implies that hydrogen might firstly react with UO2 on the whole oxide layer to form the hydride (UO2)nH before the reaction with metallic U. Consequently, the induction time of the reaction might be relatively long. On the contrary, hydrogen cannot dissolve in PuO2 or cannot react with PuO2. Therefore, for the hydriding reaction, hydrogen might diffuse into the metallic Pu through other pathways. Indeed, many experimental works have demonstrated that the hydriding reaction starts at the so-called active sites off ideal surface structure, such as crack, impurity or defect-containing region, grain boundary, stress-


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concentrated region, corrosion site, and so on. In fact, for the machined Pu samples without any further treatment, the surface structures should be physical discontinuities and those active sites are ubiquitous on the surface region or in the interface region. As a result, hydrogen might preferentially accumulate at those active sites and quickly attack metallic Pu. Correspondingly, the induction time of Pu-H reaction should be shorter than that of U-H reaction, which is in reasonable agreement with experimental observations.48 The differences in the states of hydrogen in the two actinide dioxides can partially account for their roles in the initial hydriding reactions. Other influencing factors in determining overall hydriding reactions are beyond the scope of the present work. The lattice volume is logically related to the behavior of chemical bonding in the configuration. Generally, incorporation of atom makes the configuration expansion, whereas removing atom makes the configuration contraction. However, the bonding nature of the incorporation atom with the host may change the trend. If there is a strong chemical bonding between incorporation atom and the host, the bond length between them tends to decrease. In other words, the lattice volume can be viewed as a result of the two counteracting effects: steric effect and bonding effect. In fact, our previous DFT + U calculations on PuO2 and UO2 incorporated with nonmetallic impurities (H, He, B, C, N, O, F, Ne, Cl, Ar, Kr, Xe and OH) have clearly demonstrated the complicated trends of volume change. As mentioned above, the relaxation scheme is very sensitive to the material containing defect. An important reason for the discrepancy is the choice of relaxation scheme, e.g., “volume only” with symmetry constraint, or “complete” relaxation without symmetry constraint. In fact, complete relaxation is in principle required for the configurations containing defects because of the possibility of anisotropic distortion under the actual conditions. Here, we still adopt the complete relaxation scheme,


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which has been successfully applied in the calculations of PuO2 and UO2 containing nonmetallic impurity atoms. The results indicate that their AFM configurations of both dioxides reduce the cubic symmetry of the fluorite structures to tetragonal structures; that is, lattice parameter c slightly differs from lattice parameters a and b. This is in consistency with other theoretical results using a similar complete relaxation scheme on cubic actinide dioxides.8 Here, we do not intend to discuss the complicated anisotropic distortion or the change of bond length in detail, but only provide the relaxed lattice volumes of the calculation configurations for the purpose of elucidating the general trend resultant from hydrogen at the different sites, as plotted in Figure 3. 1410 1400

H in UO2

1390

H in PuO2

1380 UO2

1370

3

Volume (Å )

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1360 1350 1340 1330 1320 PuO2

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1.0

1.2

1.4

1.6

1.8

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2.2

2.4

O-H Distance (Å)

Figure 3. Lattice volume of the relaxed AnO2 as the function of O-H distance.

Some features can be clearly found from Figure 3. First, the errors of theoretical lattice volumes with comparison to experimental observations are 4.43% and 3.13% for perfect UO2 and PuO2, respectively. Considering the wide range of available theoretical lattice volumes by means of different DFT-based methods, the present DFT + U results are basically reasonable. Second, the lattice volumes of both dioxides decrease with the increasing O-H distance. This


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indicates that steric effect plays the dominated role in controlling the general trend of volume change. With the increasing O-H distance, hydrogen has more free space; thus gives rise to less lattice strain to the host. As hydrogen occupies the octahedral interstitial site, the configuration has the smallest volume. Interestingly, the lattice volume of PuO2 containing hydrogen is always larger than that of perfect PuO2, despite that the octahedral interstitial hydrogen only results in a negligible lattice expansion. On the contrary, when O-H distance is smaller than 1.6 Å, the lattice volume of UO2 containing hydrogen is larger than that of perfect UO2. When O-H distance is larger than 1.6 Å, the lattice volume of UO2 containing hydrogen is smaller than that of perfect UO2. As mentioned above, the volume change can be viewed as the sum of two opposing components: expansive steric effects and contractile bonding effects (or electron-interaction effects). As well known, hydrogen can act as an oxidant or a reductant, depending on the chemical surroundings. For PuO2, it has long been regarded as the highest valence solid-state oxide, and cannot be oxidized under normal conditions to other oxides with Pu valence higher than +4. When hydrogen atom is incorporated into PuO2, hydrogen mainly acts as a reductant, facilitating the formation of a lower valence Pu ion with larger atomic radius; thus the configuration

expands.

For UO2,

it is

relatively more easily oxidized to

some

hyperstoichiometric oxides. Even hydrogen can oxidize UO2 to a higher valence U ion with smaller atomic radius. When O-H distance in UO2 is larger than 1.6 Å, the bonding effect prevails over the steric effect, resulting in the contraction of the configuration. In fact, the trends of lattice volume change are in consistence with the hydrogen formation energy, as shown in Figure 2. The differences of hydrogen atom in UO2 and PuO2 discussed above are also identified by the calculated electronic structures of all the configurations considered here. For the sake of brevity,


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only three typical configurations of each dioxide are discussed: perfect dioxides, dioxides with hydrogen forming hydroxyl group, and dioxides with octahedral interstitial hydrogen. The total and projected density of states (TDOS and PDOS) of UO2 and PuO2 related configurations are presented in Figure 4 and Figure 5, respectively. As expected, UO2 and PuO2 are predicted to exhibit semiconducting ground states with the band gaps of approximately 2.1 eV and 1.6 eV, respectively, which are consistent with experimental observations and other theoretical results from similar GGA + U methods.4 For both dioxides, the actinide 5f and O 2p states show strong hybridizing features, covering a relatively wide energy range below Fermi energy level (EF). As hydrogen is incorporated into the two dioxides, some significant differences occur. For UO2 with hydrogen forming hydroxyl group, although the valence states and conduction states are still well separated, a small amount of unoccupied 5f electron-states which usually represent unstable states occur just below EF, as shown in Figure 4 (b). When hydrogen binds with oxygen to form a hydroxyl group, there are surplus electrons in U atom, facilitating the formation of U3+ and resulting in the occurrence of a relatively unstable configuration. For UO2 with hydride ion, the formation of U5+ results in the disappearance of the unoccupied 5f electron states, as shown in Figure 4 (c). In fact, the slightly changed band gap and DOS profiles with comparison to perfect UO2 can be viewed as the typical features of stability of the configurations with hydrogen. Based on the above standpoint of stability, one might logically deduce the stability of PuO2 containing hydrogen from the electronic structure, as shown in Figure 5. For PuO2 with hydroxyl group, the configuration is relatively more stable than PuO2 with hydride ion. In Figure 5 (b), the surplus 5f electrons of Pu atoms locate below EF and the band gap decreases; however, there is no obvious impurity-induced defect state. In Figure 5 (c), one can find that the band gap almost disappears and impurity-induced defect states occur at the bottom of conduction bands. In addition, with


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comparison to Figure 5 (a), we can find that 5f states of Pu in Figure 5 (c) slightly decrease. This is primarily because more electrons of Pu transfer to oxygen and hydrogen. In fact, the different existence states of hydrogen in UO2 and PuO2 are inherently related to their general properties of electron structures. As well known, U 5f electrons are more delocalized than those of Pu; consequently, the formation of higher valence U ion is more easily than the formation of higher valence Pu ion.49 Hydrogen plays different roles in the two dioxides: oxidation for UO2 whereas reduction for PuO2. The similar phenomenon was also observed for hydrogen in CeO2, a typical analogue of PuO2 because of their similar electron-structure properties of f electrons; that is, hydrogen atom also prefers to form the hydroxyl group in CeO2.50


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(a) UO2

(b) dO-H = 0.947 Å

DOS (arb. unit)

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(c) dO-H = 2.369 Å

Total Uf Op Hs

EF -10

-8

-6

-4

-2

0

2

4

6

8

10

Energy (eV)

Figure 4. Total and projected density of state (TDOS and PDOS) of perfect UO2 and UO2 containing hydrogen. Only two typical configurations are presented: hydrogen forming a hydroxyl group (b) and hydrogen at the octahedral interstitial site (c). The Fermi energy (EF) is scaled to zero and marked by the black dotted line.


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(a) PuO2

(b) dO-H = 0.935 Å

DOS (arb. unit)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(c) dO-H = 2.338 Å

Total Pu f Op Hs

EF -10

-8

-6

-4

-2

0

2

4

6

8

10

Energy (eV)

Figure 5. Total and projected density of state (TDOS and PDOS) of perfect PuO2 and PuO2 containing hydrogen. Only two typical configurations are presented: hydrogen forming a hydroxyl group (b) and hydrogen at the octahedral interstitial site (c). The Fermi energy (EF) is scaled to zero and marked by the black dotted line.

4. CONCLUSION In summary, we have conducted GGA + U calculations to compare the existence states of hydrogen in UO2 and PuO2. Twenty-one incorporation sites for hydrogen, i.e., along the pathway from the hydroxyl group to the octahedral interstitial site, are considered. The formation energy of hydrogen, along with lattice volume and electronic states, are evaluated to determine the


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existence states of hydrogen and to clarify the differences of hydrogen behavior in the two dioxides. The formation energies of hydrogen in UO2 have two minimum values (−0.6 eV and −1.12 eV), corresponding to a hydroxyl group and a hydride, respectively. The latter is proposed to be the globally most stable configuration. However, for hydrogen in PuO2, there is only one minimum formation energy (0.35 eV) at the position of the possible formation of a hydroxyl group, implying that hydrogen is either insoluble or just lies in the edge of solubility. The differences in the existence states of hydrogen in the two dioxides might reveal the differences in the initial induction time of hydriding reactions of U and Pu covered with dioxide layers. The low solubility of hydrogen in PuO2 results in the quick accumulation of hydrogen at the imperfection regions and the quick diffusion through the dioxide layer. Additionally, the changes of lattice volume and electron states have the inherent correlation with the formation energy. U 5f electrons are more delocalized than Pu 5f electrons; as a result, the energetically more favorable configurations of UO2-H give rise to a slight volume contraction and a slight perturbation of electron states.

ASSOCIATED CONTENT AUTHOR INFORMATION Corresponding Authors *Email addresses: [email protected] (BA); [email protected] (PC). Notes The authors declare no competing financial interest.


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ACKNOWLEDGMENTS The research was supported by the National Natural Science Foundation of China (No. 21371160, 11305147, 21401173 and 11404299), the Foundation of President of China Academy of Engineering Physics (No. 2014-1-58), and the Science Challenge Program of China.

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For Table of Contents Only

(a) Hydrogen can dissolve in UO2, whereas hydrogen in PuO2 is either insoluble or just lies in the edge of solubility. (b) Hydrogen acts as an oxidant in UO2 or a reductant in PuO2, forming hydrogen anion or hydroxyl group, respectively.


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