First-Principles Energetics of Some Nonmetallic Impurity Atoms in

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First-Principles Energetics of Some NonMetallic Impurity Atoms in Plutonium Dioxide Bingyun Ao, Haiyan Lu, Ruizhi Qiu, Xiaoqiu Ye, Peng Shi, Piheng Chen, and Xiaolin Wang J. Phys. Chem. C, Just Accepted Manuscript • Publication Date (Web): 08 Jun 2015 Downloaded from http://pubs.acs.org on June 9, 2015

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The Journal of Physical Chemistry

First-Principles Energetics of Some Non-Metallic Impurity Atoms in Plutonium Dioxide Bingyun Ao,* Haiyan Lu, Ruizhi Qiu, Xiaoqiu Ye, Peng Shi, Piheng Chen and Xiaolin Wang Science and Technology on Surface Physics and Chemistry Laboratory, P. O. Box 718-35, Mianyang 621907, Sichuan, China ABSTRACT: The energetics of some typical non-metallic impurity atoms (H, He, B, C, N, O, F, Ne, Cl, Ar, Kr and Xe) in PuO2 are calculated using a projector augmented-wave method under the framework of density functional theory. The Hubbard parameter U and van der Waals corrections are used to describe the strongly correlated electronic behavior of f electrons in Pu and weak interactions of rare gases, respectively. Three incorporation sites of for impurity atoms, i.e., octahedral interstitial, O vacancy, and Pu vacancy sites, are considered. The results indicate that the energetics of impurity atoms depend significantly on the incorporation sites and on atomic properties such as atomic radius and electron affinity. Almost all impurity atoms considered here are energetically unfavorable at the three incorporation sites, with the exception of the F atom at the octahedral interstitial and O vacancy sites. The trends of incorporation energies of rare gas atoms generally reflect a size effect. Furthermore, charge-transfer analysis reveals that the valence electrons can be polarized more easily with increasing atomic number of rare gas elements. Finally, electronic structures of these systems containing impurity atoms also exhibit general trends in their relative stability and chemical bonding character. KEYWORDS: Plutonium dioxide, Crystal defects, Impurity atoms, Density functional theory, Electronic structure

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1. INTRODUCTION Impurity atoms often play a decisive role in the physical properties of solid state materials. An outstanding example is the research, development and application of conventional semiconductors, in which the doping of impurity atoms even at small concentration strongly influences the electronic properties.1 However, the effects of impurity atoms on the properties of nuclear materials are relatively unknown, mainly because of the difficulties in handling these radioactive, toxic and expensive materials.2 Let us take plutonium dioxide (PuO2) as an example: as the envisioned nuclear fuel (in the form of U and Pu mixed oxides, or MOX) in the prospective breeder reactors and the very important storage form of metallic Pu, PuO2 always contains impurity atoms that are introduced during fabrication, purification, and storage.3 More importantly, owing to its radioactivity (mainly in the form of α-decay) and fissionability, many radioactive and fission products such as the widely stuided He, Kr and Xe continuously accumulate in the host and cause gas bubble formation, swelling and microstructure alteration. Pu and other nuclear materials detrimentally affected by rare gases (RG) and radiation damage are susceptible to degradation of material properties, sometimes to the extent that they become unsuitable for use.4-6 Although PuO2 is considered a semiconductor from the point of view of band structure, the effect of impurity atoms here is generally negative—a situation opposite to that of conventional semiconductors, whose material properties often benefit from impurity doping. Despite the importance of the complex effects arising from impurity atoms in PuO2, there is still a dearth of relevant comprehensive studies in the literature. To our knowledge, precise experimental characterization and analysis of the basic properties and behavior of impurity atoms in this system have only rarely been reported; this scarcity can be attributed to the difficulties


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noted above in preparing and handling high-quality PuO2 samples. Available experimental data on impurity atoms in PuO2 and related nuclear fuels mainly concern the release and distribution of RG bubbles.7-10 Some experimental techniques such as X-ray diffraction (XRD) have been used to indirectly probe the influence of impurity atoms effects on structural changes in nuclear fuels.11-13 Generally speaking, there are more reports of macroscopic phenomena than explanations of microscopic mechanisms, and the inherent behavior of impurity atoms and their effect on material properties are still completely understood. Consequently, further studies are needed to elucidate the behavior of impurity atoms in PuO2. A possible solution that complements experiments and serves as a predictive tool in identifying and characterizing impurity defects is the use of first-principles calculations in the framework of density functional theory (DFT). Indeed, first-principles calculations have contributed our understanding of the basic behavior of point defects for the past twenty years.1 In the context of nuclear fuels, many theoretical attempts by means of conventional DFT and improved DFT methods have been applied to the behavior of point defects (including vacancies, self-interstitials, He, Kr, Xe, I, Cs, Sr, etc.) in UO2, which is by far the most commonly used nuclear fuel.14-23 For UO2, the relative stability and the dynamic behavior related to diffusion and migration of point defects and their influence on material properties are now at least partially understood. However, the same cannot be said for PuO2. Limited theoretical reports on the topic have focused only on the defect formation energies of He in PuO2. Freyss et al.24 calculated the incorporation energy and solution energy of He atoms in PuO2, UO2, AmO2 and (Am0.5Pu0.5)O2 by combining an ab initio plane wave pseudopotential method and a point defect model. The results predicted a negative solution energy, indicative of solubility, for He atoms in UO2 (for all stoichiometries) and in hypostoichimetric PuO2. Additionally, the He-atom solution energy in


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AmO2 and (Am0.5Pu0.5)O2, was calculated to be positive for all stoichiometries and incorporation sites. The relatively small formation energy, whether negative or positive, implies that He atoms exist at the edge of solubility and that a competition between bubble precipitation and dissolution can be expected in the four actinide dioxides. Although these pseudopotential methods reasonably reproduce the lattice parameter, bulk modulus and cohesive energy of the four actinide dioxides, other improved DFT methods addressing strongly correlated behavior of f electrons in actinide elements are essential for truly understanding electronic interactions between impurity atoms and actinide dioxides. Gryaznov et al.25 also conducted equivalent calculations for UO2, PuO2 and MOX containing He atoms at the octahedral interstitial sites by introducing the DFT + U approach. Here, U is the Hubbard parameter for describing the strongly correlated behavior of f electrons in actinide elements. In contrast to the results reported by Freyss et al.,24 the incorporation energies of He atoms in the three dioxides were predicted to be slightly positive. Interestingly, the authors found that the relaxation method was particularly useful for calculations of He atom incorporation energy in terms of reproducing experimental band gaps. Inappropriate treatment of symmetry constraints can result in incorrect predictions of the conducting state of actinide dioxides containing octahedral interstitial He atoms. In any case, the influence of octahedral interstitial He atoms on the electronic structure of the actinide dioxide hosts was shown to be insignificant. Recently, Tian et al.26 calculated the incorporation energy of He atoms in the following different PuO2 sites: octahedral interstitial, O vacancy, Pu vacancy, divacancy and Schottky defect. DFT + U results showed that the O vacancy was the most energetically favorable incorporation site for a He atom. However, the electronic structure of PuO2 containing He atoms characterizes a conducting state, which might originate from the inappropriate treatment of symmetry constraints, as discussed by Gryaznov et al.25 Apart from


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the very limited theoretical reports on He-atom behavior in PuO2, it is worth noting that increasingly more theoretical results have emerged on the electronic structure of Pu for the purpose of understanding many peculiar properties of this most complex element, whose 5f electrons lie at the critical point of the itineration → localization transition. Among these properties, the electronic structure of PuO2 has been calculated with various different methods such as standard DFT, DFT + U, hybrid DFT, and dynamical mean field theory (DMFT).27-31 Additionally, some theoretical literature is available on the electronic structure and formation mechanism of hyperstoichiometric Pu oxides, in which an O atom is incorporated into the octahedral interstitial site of PuO2 to form PuO225.32-35 However, the formation mechanism of hyperstoichiometric Pu oxide remains controversial mainly because of the deficiency in understanding basic point-defect behavior in PuO2. In our previous theoretical studies of the formation mechanism of hyperstoichiometric Pu oxide by means of well-established DFT + U methods,36 we calculated and compared the reaction energies of PuO2 and UO2 with a series of molecules (e.g., H2, He, B, C, N2, O2, O3, F2, Cl2, Xe, H2O, H2O2 and their potential radiation-induced radicals and products), and concluded that the experimentally observed hyperstoichiometric Pu oxide might be PuO2(OH)x rather than the widely discussed PuO2.25. In the calculations, only the octahedral interstitial sites accommodating impurity atoms were considered, whereas the intrinsic Pu and O vacancies were not taken into account. In fact, vacancies and vacancy-type defect clusters are more easily formed in radioactive materials than that in non-radioactive materials. This is mainly due to cascade damage resulting from high-energy decay daughters such as U nuclei and α particles (which eventually evolve into He by electron absorption) transmuted from Pu.5,6,37,38 Vacancies and vacancy clusters always play a decisive role in the stability of impurity atoms, especially the


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stability of closed-shell RG atoms, that are considered incompatible with metal atoms. It is worth noting that the electronic interaction between metals and RG atoms has generally been neglected as an area of study; thus we chose two RG atoms (He and Xe) for the purpose of discussing size effects in previous calculations. Interestingly, we found that, in contrast to the behavior of He atom in PuO2, there does exist some amount of charge transfer and chemical bonding between Xe and PuO2, which is in reasonable agreement with recent findings regarding the chemical interactions of RG-metal systems, including RG-actinide materials.39-42 However, apart from O2 and RG, there often exist other impurity atoms, as addressed above, and these impurities could also significantly alter the material properties of PuO2. In this work, we extend our previous studies on the stability and chemical interaction of impurity atoms (H, He, B, C, N, O, F, Ne, Cl, Ar, Kr and Xe) in PuO2 by considering the roles of octahedral interstitial sites, O and Pu vacancies. In fact, Kr is a typical fission product of Pu, and Ar is often used as the glove-box atmosphere when handling radioactive materials. The results identify energetically favorable incorporation sites for impurity atoms in PuO2. The general trends of the relative stability of impurity atoms can be understood in terms of the opposing effects of their atomic radius and electron affinity: a smaller atomic radius and larger electron affinity makes a defect system more stable. Electronic structures of the defect systems also reveal general trends. We expect that these general trends and behavior of the impurity atoms in PuO2 in this work are extendable to other impurity atoms not considered here.

2. THEORETICAL METHODS 2.1. Calculation models


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PuO2 crystallizes in the face-centered cubic (fcc) fluorite (space group: 225/Fm3 m) structure. Here, we use its conventional cell (i.e., Pu4O8 with a lattice parameter of 5.396 Å) to build calculation models containing impurity atoms, as shown in Figure 1. Three incorporation sites of impurity atoms, i.e., octahedral interstitial, O vacancy, and Pu vacancy sites, are considered, corresponding to Pu4O8X (X: impurity atoms), Pu4O7X and Pu3O8X, respectively. These three sites are the ones most widely studied in electronic structure calculations concerning the basic behavior of impurity atoms in oxide-type crystals.1 More complicated defects, such as divacancies or multi-vacancies, Frenkel defects and Schottky defects, which might accommodate impurity atoms and which require a larger supercell to model the defect configurations, are not considered. In any case, our calculation tests regarding model size show that the incorporation energies of octahedral interstitial O in Pu4O8 and Pu32O64 (i.e., the 2 × 2 × 2 Pu4O8 supercell) agree within 8%, which justifies the calculation models used here.

Figure 1. Calculation models of Pu4O8 containing impurity atoms at the following sites: (a) Octahedral interstitial: Pu4O8X; (b) O vacancy: Pu4O7X; (c) Pu vacancy: Pu3O8X. The host structures contain four PuO2 units (i.e., Pu4O8). The grey and red balls designate Pu and O atoms, respectively. The green balls represents incorporated impurity X atoms (X: H, He, B, C, N, O, F, Ne, Cl, Ar, Kr and Xe).


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2.2. DFT methods Total energy calculations are performed with VASP code,43 the projector augmented-wave (PAW) method, and relativistic effective core potentials (ECPs). The exchange and correlation interactions are described by the generalized gradient approximation (GGA) in the PerdewBurke-Ernzerhof (PBE) and Perdew-Wang 91 (PW91) functionals.44,45 The Hubbard model is used to treat strong correlations within the DFT + U method in the Dudarev formalism.46-48 An effective U (Ueff = U – J; i.e., the difference between the Coulomb U and exchange J parameters, hereafter referred to as U) value of 4 eV is selected for the localized 5f electrons of Pu. This value has been shown by our previous calculations to be reasonable in reproducing the experimental lattice parameter, bulk modulus and band gap of PuO2, along with the reaction energies related to PuO2.36 Additionally, we explore U values in the range of 3 ~ 6 eV for calculations related to Pu4O8 and Pu4O9. The U value has a significant influence on the band gap and total energy of the calculated models. However, we find that the variation arising from using different U values for the incorporation energy of O atoms lies in the range of ± 0.1 eV. Thus, the U value does not play a decisive role in the calculations of relative energies. To describe weak interactions in systems containing RG atoms, van der Waals (vdW) dispersion corrections need to be considered. Here, we employ the non-local vdW density functional (vdW-DF) of Dion et al.49,50 (i.e., revPBE-vdW) to evaluate the influence of vdW corrections on the incorporation energy of impurity atoms. Our previous calculations showed that antiferromagnetic (AFM) states are energetically more favorable than nonmagnetic (NM) and ferromagnetic (FM) states and that magnetic orders such as the collinear 1-k and noncollinear 2-k configurations have insignificant influence on the energetics of an incorporated O atom. The more complicated non-collinear 3-k AFM configurations have been applied only for the case of UO2.16-18 For the sake of


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computational efficiency of calculation models, we decide to leave the 3-k structure outside of scope for our present calculations. Therefore, the results of only collinear 1-k AFM configurations related to (100) lattice directions are discussed. In fact, almost all available DFT results on AFM PuO2 are from the 1-k configurations related to the (100) lattice direction.28 Full relaxation without symmetry constraints is adopted. We find that the total energies of the configurations that are relaxed without symmetry constraints are always smaller than those relaxed with symmetry constraints. 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 9 × 9 × 9 Monkhorst-Pack k-point sampling are shown to give accurate convergence of the total energies. For the total energy and density of state (DOS) calculations, the tetrahedron method with Blöchl correction is used for the Brillouin-zone integration.51 Spin-orbit coupling (SOC) interactions have also been proven to be negligible for the calculation of impurity-atom energetics, despite that SOC may play an important role in predicting ground state of actinide materials.27,28 This is mainly due to the fact that the possible calculated energy errors in PuO2 with and without impurity atoms using the same theoretical methods are approximately identical. Pure spin-polarized DFT calculations are performed to determine the total energies of impurity atoms in different molecular states. We use half the total energy of a diatomic molecule (e.g., H2, O2, N2, F2 and Cl2) as the total energy of an impurity atom. Because of the well-known disadvantages of pure DFT in describing molecules, the scheme selected to calculate the total energy of a diatomic molecule is similar to the one proposed by Korzhavyi et al.33 For example, the total energy of H2 is obtained by the sum of the energy of free atom H and the wellestablished dimerization energy (i.e., the reaction energy of 2H = H2).52 The total energy of a


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free atom is calculated by using a periodic cubic cell with a lattice constant of 15 Å and only one k point Γ. The total energies of RG atoms are calculated by this method; note that both pure DFT and vdW DFT are employed in these calculations. Both B and C are in the states of molecular crystals under standard conditions; therefore, we calculate the total energy of their molecular crystals (i.e., α-B and graphite, respectively) to obtain the total energy of single B and C atoms.

2.3. Definition of energetics As can be observed in the literature, discrepancies exist among the relative stability of impurity atoms in nuclear fuels and other materials derived by different authors.1,23,53,54 Apart from the theoretical schemes, different definitions of defect energetics can lead to discrepancy. Generally, the terminology “formation energy of defect”, denoted as Ef, is more widely used than “incorporation energy”, denoted as Ei. Ef is defined as the total energy difference between perfect and defect-containing atomic arrangements. In contrast, Ei is the total energy difference of the configurations before and after formation of the defect of interest. If the configuration contains more than one defect, therefore, Ef is the sum of Ei values of each defect. In the current calculations, Ef = Ei for configurations containing only one octahedral interstitial impurity atom. For configurations containing an impurity atom and a vacancy, Ef does not equal Ei because the former contains the formation energy of vacancy as well. The energy expressions are listed as follows: X EX i (Pu4O8X) = Ef (Pu4O8X) = Etot(Pu4O8X) − Etot(Pu4O8) − Etot(X);

(1)

EX i (Pu4O7X) = Etot(Pu4O7X) − Etot(Pu4O7) − Etot(X);

(2)

XVO

EX f (Pu4O7X) ≡ Ef

(Pu4O7X) = Etot(Pu4O7X) + Etot(O) − Etot(Pu4O8) − Etot(X);

EX i (Pu3O8X) = Etot(Pu3O8X) − Etot(Pu3O8) − Etot(X);


(3) (4)

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XVPu

EX f (Pu3O8X) ≡ Ef

(Pu3O8X) = Etot(Pu3O8X) + Etot(Pu) − Etot(Pu4O8) − Etot(X);

(5)

where VO and VPu denote O and Pu vacancies in Pu4O8, respectively. The total energy Etot(Pu) is calculated for the crystalline phase of fcc δ-Pu using the same GGA + U methods. The Xvacancy complex is the simplest defect cluster in the crystal, and the binding energy Eb is widely used to characterize the binding ability of impurity X atom to vacancy. The binding energy of X to VO or VPu can be expressed as follows: XVO

Eb

X (Pu4O7X) = EX i (Pu4O8X) − Ei (Pu4O7X);

XVPu

Eb

X (Pu3O8X) = EX i (Pu4O8X) − Ei (Pu3O8X).

(6) (7)

For all energy definitions, note that the more positive the incorporation energy and the formation energy, the less stable the defect; this relationship is inverted for the binding energy. In addition, the vacancy formation energy is the basic parameter for the study of defect behavior in solid state materials. The vacancy formation energies of VO and VPu in Pu4O8 are calculated as follows: V

(8)

V

(9)

Ef O = Etot(Pu4O7) + Etot(O) − Etot(Pu4O8); Ef Pu = Etot(Pu3O8) + Etot(Pu) − Etot(Pu4O8).

3. RESULTS AND DISSCUSSION 3.1. Impurity atoms at octahedral interstitial sites We first calculate the incorporation energies of impurity atoms at octahedral interstitial sites of Pu4O8 to verify calculation methods, considering that the available data focus mainly on the configurations of the structure-like actinide dioxides. To our knowledge, the literature contains essentially no reports of DFT calculation that include the vdW functional for describing the weak interactions of RG atoms, though some authors have suggested that vdW contributions might be


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an important reason for why the reported relative stability values differ among research groups.23,25 In Figure 2, we present calculated EX i (Pu4O8X) values using three different DFT methods. PW91 + U and PBE + U are performed on the models containing all the impurity atoms considered here, whereas revPBE + U + vdW are performed only on the models containing RG atoms. We find that the trends and the magnitude of EX i (Pu4O8X) calculated by PW91 + U and PBE + U are very close. Interestingly, the same conclusions can be drawn for EX i (Pu4O8X) of RG atoms when vdW corrections are included. With this inclusion, a very slight fluctuation of incorporation energies for RG atoms can be observed in Figure 2. We therefore conclude that vdW corrections exert negligible influence on the incorporation energies, the benchmark parameter of the current study. This is mainly due to the fact that incorporation energy is a relative value and the calculation errors using the three functional are expected to be in the very close level. Essentially, vdW dispersion is a typical long-range weak-interaction force, which is expected to play a more important role for gases adsorbed on surface than incorporated into bulk. In fact, many DFT studies on RG atoms adsorbed on surfaces have confirmed that the inclusion of vdW corrections can change bond length and adsorption energy, despite the insignificant changes of site preference.55-58 As a result, for the sake of computational efficiency of the many defect models, vdW corrections are excluded from the scope of our calculations. The results calculated by the PW91 + U methods are discussed in the following sections.


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12

PW91 + U PBE + U revPBE + U + vdW

10 8

X

Ei (Pu4O8X) (eV)

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6 4 2 0 -2 H

He

B

C

N

O

F

Ne Cl

Ar

Kr Xe

X

Figure 2. Incorporation energy of impurity X atoms at octahedral interstitial sites of Pu4O8, EX i (Pu4O8X). Previously, we concluded that only F2, the strongest oxidant, can react with Pu4O8 to form higher-valence Pu above +4 (i.e., the only negative incorporation energy in Figure 2) and briefly discussed the influence of impurity atom on incorporation energy.36 Electronic and elastic interactions of impurity atoms with Pu4O8 act in opposition on the magnitude of incorporation energy. To facilitate understanding of these two effects, we choose the electron affinity (EEA) and atomic radius (r) of impurity atoms for describing electronic and elastic interactions, respectively. It is worth mentioning that other properties such as electronegativity have been used to represent the electronic interaction.59 However, electronegativity is not strictly a property of an atom, but rather a property of an atom in a molecule.60 It is usually considered to be a transferable property, varying with chemical environment, or even varying with its definition.61 Particularly, electronegativity is not typically presented for RG atoms, and should be considered meaningless. In principle, He atom has the largest electronegativity of all the elements. This is unreasonable


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for describing its electronic interaction with other materials. In contrast, electron affinity is a well-defined property of an atom that characterizes its ability to absorb electron. Although electron affinities of RG atoms have not been conclusively determined, they are close to zero on quantum mechanical grounds. Considering that the impurity atoms considered here exist within solid-state Pu4O8, we use their empirically measured covalent radii in crystals.62,63 This property arguably more reasonable in the case of the radii of RG atoms because the most widely used radius for RG atoms is the vdW radius, which is incompatible with the covalent radii of non-RG atoms. In Table 1, we give the atomic radius (r) and electron affinity (EEA) for each impurity X atom. Table 1. Atomic Radius (r) and Electron Affinity (EEA) of Impurity X Atoms X

H

He

B

C

N

O

F

Ne

Cl

Ar

Kr

Xe

r (Å)

0.25

0.31

0.85

0.70

0.65

0.60

0.50

0.38

1.0

0.71

0.88

1.08

EEA (KJ/mol)

73

*

27

122

7

141

328

*

349

*

*

*

* Not conclusively determined; usually close to zero and set to zero.

One can find a general trend by comparing Figure 2 with Table 1: EX i (Pu4O8X) is generally proportional to r but inversely proportional to EEA. To describe the relationship more precisely, we plotted the two-dimensional contour map of EX i (Pu4O8X) with respect to both r and EEA by interpolating data within the calculated values, as depicted in Figure 3. Although a mathematical function of EX i (Pu4O8X) with respect to both r and EEA cannot be deduced, clear qualitative trends can be observed in the figure. Generally, atomic radius r plays the dominant role in affecting incorporation energy EX i (Pu4O8X), whereas electron affinity EEA can be viewed to play the secondary role. The parameters r and EEA represent size-dependent and charge-transfer effects, respectively. According to the elastic theory of materials, the energy of a system varies


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1.08 1.0

EXi(Pu4O8X)

0.9

Unit: eV 10.90 10.9 9.65 9.65 8.65 8.65 7.65 7.65 6.65 6.65 5.65 5.65 4.65 4.65 3.65 3.65 2.65 2.65 1.65 1.65 0.650 0.65 -0.350 -0.35 -1.35 -1.35

0.8

r (Å)

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


0.7 0.6 0.5 0.4 0.3 0

50

100

150

200

250

300

349

EEA (KJ/mol)

Figure 3. Contour map of incorporation energies of impurity X atom at an octahedral interstitial site of Pu4O8, EX i (Pu4O8X), as a function of atomic radius r and electron affinity EEA. quadratically for small perturbations in atomic spacing. In the theory of electron transfer, the energy change should be first order in electron affinity, which represents the ability and extent of electron transfer.59,64 As can be qualitatively observed in Figure 3, although the incorporated X atoms with larger r and smaller EEA give rise to larger EX i (Pu4O8X), changes in Ei (Pu4O8X) with

r are more noticeable than with EEA. Certainly, deviation from the relationship is identified in a minority of the impurity atoms considered here, particularly with the B atom. With large r and small EEA, EBi (Pu4O8B) should be much larger than the calculated value of 2.38 eV. The reason is not well understood, and we have removed the data for EBi (Pu4O8B) in the contour map in Figure 3. The choice of reference state on the calculation of Etot(B) and the complicated nature of Pu-B electron interaction are currently speculated to account for the deviation.65 Even so, the


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qualitative trends in the work are expected to be transferable to the incorporation energies of other impurity atoms in Pu4O8 not considered here.

3.2. Energetics of impurity atoms at O and Pu vacancies The formation energy of O and Pu vacancies in Pu4O8 are calculated to be 3.98 eV and 14.10 eV, respectively, which is in reasonable agreement with other theoretical results.24-26 Note that the formation energy of a Pu vacancy in Pu4O8 is much larger than in metallic Pu. The latter is predicted to be less than 1 eV by our atomic-scale simulation methods and other authors’ calculations.37,38,66 The difference arises primarily because metallic Pu is a soft metal with low melting point and low stiffness, facilitating the formation of vacancies, vacancy clusters and voids.5 The energetics related incorporated an impurity X atom into VO and VPu, including incorporation energy, formation energy and binding energy, are given in Figure 4, from which some general conclusions can be drawn. First, the incorporation energies of impurity atoms at VO and VPu sites are generally smaller than those at octahedral interstitial sites. This difference arises because the vacancy in the X-vacancy cluster offsets (to a certain extend) elastic perturbation induced by the impurity atom. Thus, the combined size effect of the impurity atom and vacancy no longer plays a dominant role. However, this does not mean that the incorporation of an impurity atom into a vacancy makes the system energetically more stable. In fact, the formation energy of an X-vacancy cluster characterizes the stability of the defect system containing more than one point defect, as addressed shortly. Second, almost all the formation energies of XVO and XVPu clusters are positive, with the exception that the formation energy of the FVO cluster is slightly negative. This finding indicates that FVO is the only energetically stable cluster among all the XV clusters considered here, similar to the case of impurity atoms at the octahedral sites.


16

Page 17 of 38

Clearly, the formation energies of the XVPu cluster are always much larger than those of the XVO cluster, primarily because the formation energy of VPu is much larger than that of VO. Comparing the energetics of impurity atoms at the three different sites, one finds that the XVO clusters are the most energetically favorable structures, followed by X at octahedral interstitial sites and XVPu structures. Third, almost all the impurity atoms exhibit positive binding energies both at the O vacancy and the Pu vacancy with the exception of the F atom, which has a negative binding energy at the FVPu cluster, which implies the incompatibility between the F atom and Pu vacancy. This is consistent with the previous conclusion that the F atom is the only energetically stable impurity atom at both the octahedral interstitial site and the O vacancy. Before incorporating impurity atoms, both O and Pu vacancies can act as trapping sites for impurity atoms other than for the F atom. X

Ei (Pu3O8X)

24

X

Ei (Pu4O7X)

20

XVPu

Eb (Pu3O8X) XVO

Eb (Pu4O7X)

16

Energy (eV)

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


12

XVPu

Ef

(Pu3O8X)

XVO

Ef (Pu4O7X)

8 4 0 -4 -8 H

He

B

C

N

O

F

Ne Cl Ar

Kr Xe

X

Figure 4. Energetics of impurity X atom in Pu (VPu) and O (OV) vacancies of Pu4O8. X EX i (Pu3O8X): incorporation energy of X at VPu; Ei (Pu4O7X): incorporation energy of X at VO; XVPu

Eb

XVO

(Pu3O8X): binding energy of X to VPu; Eb

(Pu4O7X): binding energy of X to VO;


17


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

XVPu

Ef

XVO

(Pu3O8X): formation energy of XVPu cluster; Ef

Page 18 of 38

(Pu4O7X): formation energy of XVO

cluster. Based on a detailed analysis of the energetics related to vacancies, we find that the energies in Figure 4 change to a smaller extent compared with the incorporation energies in Figure 2. As addressed above, this effect can be attributed in part to the fact that vacancies counteract the elastic strain field caused by impurity atoms. Size effects are no longer the dominant factor in the relative stability of impurity atoms at vacancies. Taking the RG atoms—which exhibit significant size effects at the octahedral sites—as examples, from the He atom to the Kr atom, XVPu

X values of EX i (Pu3O8), Ei (Pu4O7X), Ef

XVO

(Pu3O8X) and Ef

(Pu4O7X) slowly increase with

atomic number. However, the energies slowly decrease from the Kr atom to the Xe atom, despite the fact that the lattice volumes from the He atom to the Xe atom increase with atomic number, as will be addressed later. Therefore, other factors influence the energetics of impurity atoms incorporated into vacancies; one such candidate is electron interaction. In addition, among all the NVPu

formation energies of X-vacancy clusters, Ef

FVO

(Pu3O8N) is the largest, whereas Ef

(Pu4O7F)

is the smallest. The latter can be well explained by the fact that FVO cluster is calculated to be thermodynamically stable. For the NVPu cluster, the relatively larger incorporation energy, formation energy of Pu vacancy and size mismatch between N atom and Pu vacancy together result in the instability of the cluster. Another widely discussed energy related to impurity atoms, especially RG atoms, is the solution energy EX s , which is important in the formation of gas bubbles. Generally, a larger solution energy for an impurity atom indicates that it is less stable, facilitating the formation of other defect configurations or gas bubbles. In term of the point defect model,67 the solution energy EX s can be expressed as follows:


18

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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


X X EX s = Ei + Ea ;

(10)

where EX a is the apparent energy defined in the point defect model. The apparent energy depends on temperature, defect concentration and the deviation from stoichiometry (such as x in PuO2-x or PuO2+x). However, previous studies have demonstrated that EX i is still the dominant term even when the above dependences are considered.26 For the sake of brevity, we discuss here the solution energies of only the most widely studied RG atoms based on incorporation energy. Clearly, the small incorporation energy of a He atom implies that it may lie at the edge of solubility and at the formation threshold for He bubbles in PuO2. In comparison with the experimental and atomic-scale simulation of the effects of He atom in fcc metallic δ-Pu,37,38,66 we find that He bubbles in metallic Pu form more easily than in PuO2. The difference arises because the octahedral interstitial volume in metallic Pu (lattice parameter a0 = 4.637 Å) is smaller than in PuO2 (a0 = 5.396 Å); therefore, the size effect of a He atom in the former is larger. In fact, the available incorporation energy of a He atom in metallic Pu is larger than the value calculated in this work. From Figures 2 and 4, one can find that the incorporation energies of RG atoms in Pu4O8 increase substantially with increasing atomic number, especially in the case of RG atoms X at octahedral interstitial sites. Consequently, the large EX i and Es values corresponding to high

atomic number signify that the formation of gas bubbles is favorable, which is in reasonable agreement with experimental observations of oxide-type nuclear fuels.7

3.3. Lattice volume of the relaxed structures In general, size effects of impurity atoms are of central importance to energetics, as discussed above. To illustrate this size effect, we investigate the structural changes of the defect models containing impurity atoms. First, our previous calculations, which were obtained using a complete relaxation scheme, showed that the AFM states of both U4O8 and Pu4O8 reduce the


19


cubic symmetry of the fluorite structures to tetragonal structures; in the latter structure the lattice parameter c slightly differs from a and b. In addition, the lattice contraction with incorporation of an octahedral interstitial O atom into U4O8 or Pu4O8 is in good agreement with experimental findings.68 However, the anisotropic distortion of defect models containing impurity atoms increase with the introduction of Pu and O vacancies and with increasing atomic radius of the impurity atom. Here, we do not intend to analyze the distortion in detail, but only provide the relaxed lattice volume of the defect models for the purpose of explaining the general size-effect trend, as plotted in Figure 5. 220

Pu4O8X

210

Pu4O7X

200

Pu3O8X

190

3

Volume (Å )

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

Page 20 of 38

180 170 160

Pu4O7 Pu4O8

150

Pu3O8

140 H

He

B

C

N

O

F

Ne Cl

Ar

Kr Xe

X

Figure 5. Lattice volumes of relaxed defect models containing impurity X atom at octahedral interstitial (Pu4O8X), O vacancy (Pu4O7X) and Pu vacancy (Pu3O8X) sites. From Figure 5, we find that, for each type of defect model (i.e., Pu4O8X, Pu4O7X or Pu3O8X), the lattice volume generally increases with increasing atomic radius. This trend always holds true for the models containing RG atoms because the size effect is the dominant factor; it also generally holds true for Pu4O8X models because the octahedral interstitial atoms weakly perturb


20

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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


electron interactions. As is well known, atomic radius is not a fixed parameter, but instead depends on the chemical environment. In comparison with a neutral-charge atom, electron absorption from, or loss to the surroundings results in increasing or decreasing atomic radius, respectively. The charge-transfer effects are more prominent for chemically active atoms than for RG atoms, which is addressed in the discussion of electron interactions. Interestingly, the volume of Pu4O7 is larger than that of Pu4O8. In fact, the phenomenon can be viewed as the sum of two opposing components: (expansive) size effects and (contractile) charge-transfer effects; similarly, the volume of Pu4O9 is slightly smaller than that of Pu4O8. When an O atom is removed from Pu4O8, f electrons in Pu become more localized, facilitating the formation of a lower-valence Pu ion with larger atomic radius. If charge-transfer effects prevail over size effects, the models contract and vice versa.32 Taking Pu3O8 as another example, removing one Pu atom from Pu4O8 makes the supercell contract, in part because the atomic radius of Pu is larger than that of O. Based on this analysis, one can understand why the volume of Pu4O7X is generally the largest, followed by Pu4O8X and Pu3O8X. However, some abnormalities occur in the volume data of Pu4O7X and Pu4O8X that can be understood in terms of charge-transfer effects, as will be addressed in the following section.

3.4. Charge transfer The interpretations of the energetics and the relative stability of the defect models containing impurity X atoms are further substantiated by the analysis of electronic structures. To obtain a better understanding of electronic structures, we first present the results of charge accumulation or depletion by impurity X atoms through the calculation method of Bader charge analysis,69 as shown in Figure 6. Certainly, the charge accumulation or depletion of the host (Pu4O8, Pu4O7 or Pu3O8) is opposite to the respective charge accumulation or depletion of X. According to the


21


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Page 22 of 38

atomic ratio of O to Pu, the formal charge of Pu in Pu4O8, Pu4O7 and Pu3O8 is +4, +3.5, and 5.33, respectively; note, however, that the formation of Pu ions with valence states higher than +4 in Pu oxide is much more difficult than that below +4.36 Pu4O7 and Pu3O8 can be viewed as electron-rich and electron-poor defect models for Pu ions in comparison with electron-matched Pu4O8. As a result, Pu ions in Pu4O7 accept or donate electrons from their chemical surroundings, including incorporated impurity atoms, whereas Pu ions in Pu3O8 spontaneously donate electrons. From Figure 6, we find that impurity X atoms generally gain the most amount of charge from the Pu4O7X host material, followed by Pu4O8X and Pu3O8X. In fact, almost all X in Pu3O8X transfers a certain amount of charge to the host, with the exception that the strongest oxidant, F, absorbs a small amount of charge from the host. This general trend is in reasonable agreement with the above analysis on the formal charge of Pu in the three defect models. Any deviation from the trend mainly occurs in the case of RG atoms. As the result of their closed-shell electron configuration, RG atoms were long considered to exhibit no noticeable charge transfer or chemical bonding with other materials. However, increasingly more experimental and theoretical studies have provided evidence for chemical bonding of RG atoms with other materials, including actinide-based materials. The amount of charge-transfer strongly depends on the properties of RG atoms and their chemical surroundings. In the present studies, we find that RG atoms exhibit the tendency to donate more electrons to the hosts with increasing atomic number of the RG atoms and increasing electron-poor extent of Pu ions in the hosts. Although the amount of charge transfer between the three hosts and light RG atoms such as He and Ne is basically negligible, heavy RG atoms such as Kr and Xe can transfer a small amount of electrons to Pu4O8 and Pu4O7. For the case of Pu3O8, even the relatively light RG atom Ar can transfer a small amount of electrons to the host, and the heaviest RG atom Xe in the calculations donates


22

Page 23 of 38

1.21 e, the same electron-transfer amount of each O atom in perfect Pu4O8, characterizing noticeable chemical bonding between the Xe atom and the Pu3O8 host. The results are in good agreement with research results describing chemical bonding of RG atoms with solid materials.39−42 With increasing atomic number of RG atoms, the valence electrons can be polarized more easily, facilitating chemical bonding with their chemical surroundings and the possible formation of RG chemical compounds.

Electron transfer (e)

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


1.6 1.4 1.2 1.0 0.8 0.6 0.4 0.2 0.0 -0.2 -0.4 -0.6 -0.8 -1.0 -1.2 -1.4 -1.6

Pu4O8X Pu4O7X Pu3O8X

H

He

B

C

N

O

F

Ne Cl Ar

Kr Xe

X

Figure 6. Electron transfer of impurity X atoms at the octahedral interstitial (Pu4O8X), O vacancy (Pu4O7X) and Pu vacancy (Pu3O8X) sites. Positive or negative values represent the increase or decrease in charge, respectively.

3.5. Electron structures We now turn to the electron structure analysis of the defect models. First, we briefly discuss the basic features of the electron structure of Pu metal and Pu-based compounds. The valence configuration of Pu is widely accepted to be 5f67s2 despite the fact that very small energy


23


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Page 24 of 38

differences between Pu 5f and 6d orbitals cause it partial 5f coverage; electrons fluctuate between the 5f and 6d orbitals and the quantity of 5f electron is considered to be non-integer (i.e., neither 5 nor 6). In fact, accumulated theoretical and experimental findings suggest a 5f count near 5, with 5.4 being a reasonable upper limit.27 The most remarkable feature of the electron structure of metallic Pu is the presence of strong localized 5f states just below the Fermi energy (EF), indicating that the localized 5f states do not contribute to chemical bonding or hybridization with other states in the metallic phase.70,71 However, the localized 5f electrons may exhibit more or less delocalized character depending on their chemical surroundings, a conclusion that is supported by both theoretical and experimental research on Pu compounds, especially Pu oxides.32,72-74 With the Pu2O3 → PuO1.75 → PuO2 → PuO2.25 transition of increasing Pu ion valence state, Pu 5f electrons become more delocalized with the typical outcome of fewer 5f states below EF. Here, reflecting the interesting findings in the area of chemical bonding of RG atoms, we divide our electron structure analysis into two thrusts: defect models containing RG atoms and the remaining impurity atoms considered in the calculations. The total and projected density of states (TDOS and PDOS) of defect models containing RG atoms, in comparison with the respective models without RG atoms, are presented in Figure 7. As expected, Pu4O8 is predicted to exhibit a semiconducting ground state with a band gap of approximately 1.6 eV, which is consistent with other theoretical results that use similar DFT + U methods.28 Clearly, the Pu 5f electrons in Pu4O8 are less localized than those in metallic Pu. After removing an O atom from Pu4O8 to form Pu4O7, the surplus Pu 5f electrons become localized and typically feature narrow and sharp DOS peaks just below EF, as shown in Figure 7(b). The valence bands (VBs) and conduct bands (CBs) are still well separated as more O p electrons participate in chemical bonding; therefore, no unoccupied O p electron state appears


24

Page 25 of 38

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


above EF. In contrast, after removing a Pu atom from Pu4O8 to form Pu3O8, Pu 5f electrons become more delocalized with the characters of very flat DOS peaks below EF, as shown in Figure 7(c). However, unlike the cases of Pu4O8 and Pu4O7, the surplus O p electrons traverse EF, forming unoccupied electron states and resulting in a conducting ground state. In addition, the shift of TDOS of both Pu4O7 and Pu3O8 to EF implies that the formation of Pu and O vacancies in Pu4O8 is energetically unfavorable. After incorporating the RG atoms into Pu4O8, Pu4O7 and Pu3O8, some noticeable changes appear in their respective DOS. Generally, owing to their closed-shell behavior, RG atoms induce the weak perturbations in the electronic structure of the hosts. For example, the PDOS of He atoms in the three models lie in a deep energy level, far away from EF. However, the degrees of perturbation in the DOS of hosts increase with increasing atomic number of RG atoms. In the case of Pu4O8X, the contributions from RG atoms to the total DOS are very limited. In fact, Pu4O8X (X: He, Ne, Ar) remain in the semiconducting state despite the fact that their respective band gaps are slightly reduced with increasing atomic number. Interestingly, in the cases of Pu4O8Kr and Pu4O8Xe, a small amount of Pu 5f electrons traverse EF, resulting in the disappearance of band gaps. Electron transfer and structure distortion are thought to be the two main reasons for the deviation of their DOS from the hosts. In fact, the valence-electron states of RG atoms move closer to EF from Pu4O8He to Pu4O8Xe; in particular, a very small number of electron states of Xe lie below EF, giving rise to the very weak hybridization interaction with Pu 5f and O 2p electrons. The general trends of the TDOS and PDOS of Pu4O7X and Pu3O8X are similar to those of Pu4O8X. However, all Pu4O7X compounds exhibit semiconducting ground states, whereas all Pu3O8X compounds exhibit conducting ground states. For Pu4O7 with electron-rich Pu ions, the incorporation of RG atoms cannot change the basic properties of the


25


localized 5f electrons. For Pu3O8 with electron-poor Pu ions, the incorporation of RG atoms cannot change the basic properties of the surplus O 2p electrons traversing EF. As addressed above, the donor-like RG atoms can transfer more electrons to the hosts as the atomic number increases. For Pu3O8Xe, the Xe atom provides electrons to the host and balances the surplus O 2p electrons, facilitating chemical bonding between Pu and O. Therefore, almost no O 2p electrons traverse EF and the electron states located at EF arise primarily from hybridization interactions between Pu f and Xe p electrons. In Figure 7(c), one can observe that the main Xe PDOS are farther away from EF in comparison with the main Kr PDOS—behavior that seems to deviate from the trend described above. In fact, because the O 2p electron states do not traverse EF, the width of the VBs becomes narrower in comparison with Pu3O8Kr, as illustrated by the red lines with arrows in Figure 7(c). spin up

Pu4O8

Pu4O7

Pu3O8

Total Pu f Op

spin down

Pu4O8He

Pu4O7He

He s

Ne p

Ne p

Ar p

Ar p

Kr p

3 8

Kr p

Kr p

Pu4O7Xe

EF

Xe p

-4

Energy (eV)

(a)

Ar p

Pu O Kr

4 7

Pu4O8Xe

-6

Ne p

Pu3O8Ar

Pu O Kr

4 8

-8

Pu3O8Ne

Pu4O7Ar

Pu O Kr

-10

He s

Pu4O7Ne

Pu4O8Ar

-12

Pu3O8He

He s

Pu4O8Ne

DOS (arb. units)

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

Page 26 of 38

-2

Pu3O8Xe

Xe p

0

2

-14

-12

-10

Xe p

-8

-6

-4

-2

0

2

Energy (eV)

(b)


-9

-8

-7

-6

-5

-4

-3

-2

-1

0

1

2

3

Energy (eV)

(c)

26

Page 27 of 38

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


Figure 7. Total and projected density of states (TDOS and PDOS) of the defect models containing impurity X atoms (X: He, Ne, Ar, Kr, Xe). (a) Pu4O8X, (b) Pu4O7X, (c) Pu3O8X. The Fermi energy (EF) is scaled to zero and marked by the black dotted line. The TDOS and PDOS of the defect models containing the remaining impurity X atoms (X: H, B, C, N, O, F, Cl), in comparison with the respective models without impurity atoms are presented in Figure 8. Generally, these impurity atoms result in relatively stronger perturbation of the electronic structure of the hosts than the RG atoms. For the case of Pu4O8X compounds, the most remarkable change (from a stability point of view) is the upward shifting of EF in some models such as X = B, C, N and O. Taking C and O atoms as examples, although the VBs and CBs of Pu4O8C and Pu4O9 are well separated, the gap states induced by the incorporated atoms are clearly visible, forming n-type and p-type semiconductors, respectively. This pinning effect, well-known in the field of semiconductor doping, implies that octahedral interstitial C and O atom generate unoccupied states and thus reduce chemical bonding and stability. However, for Pu4O8F and Pu4O8Cl, in which F and Cl atoms have a formal charge of –1, there are no unoccupied states resulting from F and Cl atoms, indicating that each chemically binds with the Pu4O8 host. The results strongly demonstrate that Pu4O8X, in which the formal charge of X is –1, is relatively more stable and that the valence state of Pu in Pu4O8X can reach +5. As concluded from the energetics of impurity atoms, incorporating an F atom into Pu4O8 is energetically feasible. Though the Cl atom satisfies the charge requirement in forming a Pu5+ ion and no obvious shifting of EF induced by the Cl atom is observed in Pu4O8Cl, the relatively large size effect results in the instability of Pu4O8Cl relative to Pu4O8 and Cl2. These explanations of DOS trends are consistent with calculated charge-transfer results and can be logically extended to the calculated DOS of Pu4O7X and Pu3O8X.


27


spin up

Pu4O8H

Total Pu f

Op

Pu4O7H

Pu3O8H

Hs

spin down

Hs

Hs

Pu4O7B

Pu4O8B

Pu3O8B

B p

B p

B p

Pu4O7C

Pu4O8C

Pu3O8C

C p

C p

DOS (arb. units)

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

Page 28 of 38

C p

Pu4O7N

Pu4O8N

Pu3O8N

N p

N p Pu4O9

N p

Pu4O7

Pu3O8

Pu4O7F

Pu3O8F

Octahedral O p Pu4O8F

F p

F p

Pu4O7Cl

Pu4O8Cl

EF

Cl p

-7

-6

F p

-5

-4

-3

-2

-1

0

Pu3O8Cl

Cl p

1

2

3 -7

-6

-5

Cl p

-4

-3

-2

-1

Energy (eV)

Energy (eV)

(a)

(b)

0

1

2

3 -7

-6

-5

-4

-3

-2

-1

0

1

2

3

Energy (eV)

(c)

Figure 8. Total and projected density of states (TDOS and PDOS) of the defect models containing impurity X atoms (X: H, B, C, N, O, F, Cl). (a) Pu4O8X, (b) Pu4O7X, (c) Pu3O8X. The Fermi energy (EF) is scaled to zero and marked by the black dotted line.

4. CONCLUSION To understand the behavior of point defects in PuO2, we have performed calculations using a DFT + U approach to investigate the energetics and electron structures of PuO2 containing a series of impurity atoms: H, He, B, C, N, O, F, Ne, Cl, Ar, Kr and Xe. Three incorporation sites are considered: the octahedral interstitial, O vacancy, and Pu vacancy. Essentially all impurity atoms presented here are energetically unfavorable at the three incorporation sites, with the


28

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exception of the F atom at the octahedral interstitial site and the O vacancy. The swelling of the hosts, the relative stability and the amount of electron transfer of the impurity atoms in the hosts depend strongly on the incorporation sites and properties of impurity atoms such as their atomic radii and electron affinities. Impurity atoms at Pu vacancies constitute the most unstable defect configuration, mainly because of the very large formation energy of a Pu vacancy; the O vacancy is a more energetically favorable site for accommodating an impurity atom. The incorporation energies of impurity atoms at octahedral interstitial sites are generally proportional to their atomic radii and inversely proportional to their electron affinities. Charge-transfer analysis indicates that an impurity atom at an O vacancy generally gains the most amount of charge from the host, followed by an octahedral site and a Pu vacancy, owing to their electron-rich, electronneutral and electron-poor properties of Pu ions in the hosts, respectively. The electronic structures of these systems containing impurity atoms also exhibit general trends in terms of relative stability and quantity of electron transfer. In particular, the results of electron transfer and electron structures related to the incorporation of RG atoms into PuO2 demonstrate that the polarization of their closed-shell valence electrons and their participation in chemical bonding increase with increasing atomic number, implying the possible existence of compounds of a RG and Pu. It is concluded that the general trends obtained from the calculations are applicable to other impurity atoms in PuO2.

ASSOCIATED CONTENT AUTHOR INFORMATION Corresponding Author *Email address: [email protected].


29


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Page 30 of 38

Notes The authors declare no competing financial interest.

ACKNOWLEDGMENTS Many thanks go to X. Tian and B. Sun for fruitful discussions in the use of VASP code, and to P. Zhao for proof reading the manuscript. The research was supported by the National Natural Science Foundation of China (No. 21371160, 11305147, 21401173 and 11404299), and the 863 Program of China (No. SQ2015AA0100069), and the Foundation of President of China Academy of Engineering Physics (No. 2014-1-58). We acknowledge the computer facility received from Institute of Computer Applications of China Academy of Engineering Physics.

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2007. (5) Cooper, N. G. (ed.) Challenges in Plutonium Science, Los Alamos Sci. 26, Los Alamos National Laboratory, 2000.


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(6) Ao, B.; Chen, P.; Shi, P.; Wang, X.; Hu, W.; Wang, L. Computer Simulation of Helium Effects in Plutonium during the Aging Process of Self-Radiation Damage. Commun. Comput. Phys. 2012, 11, 1205–1225. (7) Frost, B. R. T. Nuclear Materials. Volumes 10A and 10B of Materials Science and Technology–A Comprehensive Treatment, edited by Cahn, R. W.; Huusen, P.; Kramer, E. J. Wiley-VCH Verlag, Weinheim, 1994. (8) El-Genk, M. S.; Tournier, J. M. Estimates of Helium Gas Release in

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37


For Table of Contents Only 1.08

1.0

EXi(Pu4O8X)

0.9

Unit: eV 10.90 10.9 9.65 9.65 8.65 8.65 7.65 7.65 6.65 6.65 5.65 5.65 4.65 4.65 3.65 3.65 2.65 2.65 1.65 1.65 0.650 0.65 -0.350 -0.35 -1.35 -1.35

0.8

r (Å)

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

Page 38 of 38

0.7 0.6 0.5 0.4 0.3 0

50

100

150

200

250

300

349

EEA (KJ/mol)

(a) The incorporation energies of impurity X atoms in Pu4O8 are generally proportional to the atomic radii r but inversely proportional to the electron affinities EEA. (b) The qualitative trends are expected to be transferable for the behaviors of other impurity atoms in Pu4O8 not considered here.


38

First-Principles Energetics of Some Nonmetallic Impurity Atoms in

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