First-principles DFT + U calculations on the energetics of Ga in Pu, Pu2O3 and PuO2

Computational Materials Science 122 (2016) 263–271

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First-principles DFT + U calculations on the energetics of Ga in Pu, Pu2O3 and PuO2 Bingyun Ao ⇑, Ruizhi Qiu, Haiyan Lu, Piheng Chen ⇑ Science and Technology on Surface Physics and Chemistry Laboratory, P.O. Box 9071-35, Jiangyou 621907, China

a r t i c l e

i n f o

Article history: Received 25 April 2016 Received in revised form 27 May 2016 Accepted 29 May 2016

Keywords: Plutonium oxides Gallium Interface Density functional theory Electronic structure

a b s t r a c t First-principles density functional theory–generalized gradient approximation methods are used to calculate the energetics of Ga in Ga-stabilized d phase Pu, Pu2O3 and PuO2, in order to elucidate the relative stability of Ga in the Pu oxide layers. The Hubbard parameter U is used to describe the strongly correlated electron behavior of Pu 5f electrons. Three incorporation sites for Ga, i.e., interstitial site, Pu and O vacancies, are considered. The results indicate that the energetics of Ga significantly depend on the inherent properties of the host materials and the incorporation sites in them. Ga incorporation into interstitial sites and O vacancies of both Pu2O3 and PuO2 are energetically unfavorable. Ga incorporation into Pu vacancy of PuO2 is the most energetically favorable, followed by Ga incorporation into Pu vacancies of Pu2O3 and Pu. However, this does not mean that there would be the highest concentration of Ga in PuO2 among these three Ga-stabilized Pu substances because it is most difficult for Pu vacancy formation in PuO2. The distribution of Ga in the Pu oxide layers is proposed to be strongly dependent on the distribution and the concentration of Pu vacancy, as a result, Ga concentration likely decrease with the transitions of Pu ? Pu2O3 ? PuO2. Ó 2016 Elsevier B.V. All rights reserved.

1. Introduction Plutonium (Pu) has been considered the most complicated and mysterious element in the Periodic Table because it exhibits many unusual physical and chemical properties which are rooted from its extremely complex 5f electronic states. Taking phase stability for an example, Pu has at least six stable allotropes with great density changes from room temperature to its very low melting temperature (913 K) at atmospheric pressure. From the technologic application point of view, there are more advantages to studying the high-temperature cubic d phase Pu than the roomtemperature monoclinic a phase Pu. In fact, for many years it has been known that the addition of low concentration of gallium (Ga) can stabilize d-Pu at room temperature. Despite a thorough understanding of the stabilization mechanism is still not available, d phase Pu–Ga alloy has proven to be technologically the most useful phase and be kinetically stable for a long time; therefore, this alloy has been the most concerned among all the Pu-based materials. However, modern-day problems regarding Pu–Ga alloy involve understanding and predicting the properties changes for the safe handling, use and long-term storage; among them, the properties

⇑ Corresponding authors. E-mail addresses: [email protected] (B. Ao), [email protected] (P. Chen). http://dx.doi.org/10.1016/j.commatsci.2016.05.038 0927-0256/Ó 2016 Elsevier B.V. All rights reserved.

relative to surface reaction and corrosion are the focus of attention because Pu is highly reactive and very sensitive to its chemical surroundings [1–3]. The changes in surface structure and composition of Pu–Ga alloy may play a crucial role in the practical applications. Consequently, extensive studies have been conducted on the surfacerelated properties (e.g., surface atomic and electronic structure, composition, reaction thermodynamics and kinetics, etc.). Although, more and more results have provided new insights into understanding the complicated surface phenomena of Pu–Ga alloy, some underlying mechanisms remain in controversy and further more systematic and quantitative studies are required to obtain precise parameters regarding the chemical kinetics of this radioactive and toxic material. It is worth noting that the basic process of surface oxidation and the rough oxide structure and composition have been well determined or understood. Owing to the highly reactive properties of Pu, an oxide film always exists on the surface of Pu–Ga alloy even in the very strict conditions of a high quality inert gas glove box or an ultra high vacuum (UHV) container. The initial oxidation of Pu occurs via a trivalent sesquioxide (Pu2O3) followed by a tetravalent dioxide (PuO2). Moreover, PuO2 cannot coexist with metallic Pu because the reduction of PuO2 with the participation of Pu to Pu2O3 (i.e., 3PuO2 + Pu ? 2Pu2O3) is thermodynamically favorable, such that a Pu2O3/Pu interface will always

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form. These are the well-accepted simplistic descriptions of Pu oxide layers despite other non-stoichiometric Pu oxides (i.e., PuO2
x, 0 < x < 0.5) may also form and the ratio of Pu2O3 to PuO2 is very sensitive to external conditions such as temperature and O2 partial pressure [1,4,5]. Interestingly, Pu2O3 and PuO2 may play completely different roles in the further surface reaction; for a typical example, Pu2O3 can accelerate hydriding reaction whereas PuO2 can inhibit the reaction [6]. The influences of oxide structure and composition on the surface reaction of Pu have long been the focus in the field of Pu surface science. However, seldom works have considered the roles of Ga in the surface-related issues despite most of experimental samples use Pu–Ga alloy instead of unalloyed Pu. It is worth pointing out that many experimental and theoretical studies have been conducted on the fine structures of Pu–Ga alloy to understand the roles of Ga in the stabilization mechanism of this alloy. The incorporation site of Ga, bonding interaction between Pu and Ga, and the potential phase transformations (i.e., from d phase alloy to a phase and other intermetallic compounds such as Pu3Ga) have been at least partially understood [1,2,7–9]. Knowledge from oxidation behavior of Pu shows that the oxidation rate of Pu–Ga alloy can be generally slower than that of unalloyed Pu. Nevertheless, some experimental results showed that Ga impurity can either enhance or hinder the oxidation rate of d-Pu when compared to unalloyed Pu [10,11]; this is mainly because the initial stages of oxidation are inherently a surface phenomenon, thus the external environment, the chemical states and the occupied sites of Ga can be the influence factors in oxidation rate. Up till now, the underlying reasons for the rate change resulted from Ga have not been well understood. The quantitative analysis of Ga at the oxide layers, which requires surface-sensitive techniques and high quality Pu samples, may be one of important cause of the difficulty. From the available experimental results we can find whether Ga can be stabilized at the oxide layers, the existence states and the incorporation sites of Ga remain unclear. Among them, the classic works by Pugmire et al. preliminary studied the roles of Ga during the oxidation of Pu–Ga alloy by combining high-resolution X-ray photoelectron spectroscopy (XPS), Auger electron spectroscopy (AES) and electron-probe microanalysis (EPMA) techniques [12]. The results showed that the Ga concentration was very sensitive to the thickness of oxide film. The Ga concentration at a 30 nmthick oxide film showed an approximate Ga concentration in bulk, whereas the Ga concentration at a 300 nm-thick oxide film significantly reduced. AES depth-profile of oxide film indicated the presence of a Ga-depleted region at the surface and a Ga-rich region at the oxide/metal interface. Therefore, the authors concluded that the Ga-rich region at the oxide/metal interface could significantly reduce the number of Pu atoms, thereby reducing the oxidation rate as the increasing thickness of oxide film. Although, the experimental results help understand the basic macroscopical behavior of Ga in the Pu–Ga alloy oxide layers, further studies are required to obtain the microscopic behavior of Ga and the inherent mechanism of Ga on the oxidation of Pu. A possible solution that compliments experiments and serves as a powerful tool in studying the behavior of Ga in the Pu oxide layers is the use of first-principles calculations in the framework of density functional theory (DFT). Indeed, first-principles calculations have contributed to our understanding of the microscopic behavior of point defects and impurities for the past twenty years [13,14]. In the context of Pu-based materials, however, many theoretical attempts by means of DFT-based methods have been conducted on their ground-state properties to understand the complicated 5f electronic states and the unusual properties of these materials [3,15–19]. To our knowledge, the behaviors of point defects and impurities in Pu-based materials have only rarely been reported. Limited theoretical reports on the topic have

focused only on the defect formation energy of Ga in d-Pu, and rare gases such as He and Xe in PuO2 [20–26]. For Ga in PuO2 and Pu2O3, no any theoretical report is available; one scarcity can be attributed to the difficulty in the computational efficiency of Pu2O3 containing 80 atoms per unit cell which is a very large computational system from the point view of electronic structure calculations. Some available theoretical attempts on Pu2O3 have focused only on the ground-state electronic structure of its bulk and surface, and on the reaction energy between PuO2 and Pu2O3 [15,27–30]. Recently, Hernandez et al. calculated the formation energy of hydrogen-vacancy complex in Pu–Ga alloy and the atomic oxygen adsorption on Ga stabilized d-Pu (1 1 1) surface by means of an all-electron DFT method [11,31]. The former calculation results showed that hydrogen could stabilize Pu vacancy and drive the formation of superabundant vacancies (SAV) which is very common phenomenon in metal-hydrogen systems [32,33]. Additionally, the hydrogen atom prefers to interact much more strongly to the Pu atom than the Ga atom in the hydrogenvacancy complex [31]. The latter calculation results suggested that the presence of Ga in a Pu matrix could slow down the growth of Pu oxide layers [11], judged from the energetics of O atom at different sites (i.e., top of Ga, bridge between Pu and Ga, hollow sites, and interstitial site.). In our previous theoretical studies on PuO2 by means of wellestablished DFT + U method (U is Hubbard parameter for describing strongly correlated electron behavior of Pu 5f electrons.), we calculated the energetics of some typical nonmetallic impurity atoms (i.e., H, He, B, C, N, O, F, Ne, Cl, Ar, Kr and Xe) in PuO2 [34,35]. A general trend in the relative stability of the impurity atoms was obtained by the comparison of atomic basic properties (i.e., atomic radius and electron affinity) with the calculated energetics and electronic states. In the current theoretical works, we extend our studies to focus on the relative stability and electronic states of Ga in Pu, Pu2O3 and PuO2. The main results show that the relative stability of Ga is strongly dependent on the inherent properties of hot materials and the incorporation sites for Ga in them. To the best of our knowledge, this is the first theoretical attempt to study the relative stability of Ga in the Pu oxide layers. We expect that the theoretical results are referable in the further investigation on the roles of Ga in the oxidation of Pu–Ga alloy.

2. Computational details Delta-Pu has the face-centered cubic (fcc) structure with a lattice parameter of 4.64 Å. In order to reasonably reflect the experimental Ga concentration in the Ga-stabilized d-Pu alloy, here we use its 2  2  2 supercell containing 32 Pu atoms to build the computational configurations. It has been demonstrated that one Ga atom occupies one Pu lattice site in the Ga-stabilized d-Pu alloy; thus, the Ga concentration is 3.125 at.% for the calculation model Pu31Ga, which is basically consistent with the Pu–Ga alloy in practical use [1]. Other configurations with different Ga concentrations are not considered in the present work. PuO2 also crystallizes in the
fcc fluorite structure (space group: 225=Fm3m, lattice parameter: 5.39 Å). Here, we also use its 2  2  2 supercell containing 32 Pu atoms and 64 O atoms (i.e., Pu32O64) to build the computational configurations. Three incorporation sites for Ga, i.e., octahedral interstitial, Pu vacancy and O vacancy, are considered, corresponding to Pu32O64Ga, Pu31O64Ga and Pu32O63Ga, respectively. These three sites are the ones most widely studied in electronic structure calculations concerning the basic behaviors of impurity atoms in oxide-type nuclear fuels. More complicated defects, such as divacancies, multi-vacancies, or other defect clusters which might accommodate Ga and require a larger supercell to build the defect configurations, are currently not considered. For Pu2O3, it

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crystallizes into a cubic Mn2O3 structure or a hexagonal La2O3 structure. The cubic crystal is known as a-Pu2O3. It contains 80 atoms (32 Pu and 48 O atoms, i.e., Pu32O48) per unit cell (16 formula units) and is stable below 600 K. Ideal a-Pu2O3 can be derived from a 2  2  2 supercell of the fluorite PuO2 structure by removing 25% of O atoms to create structural vacancies. Due to missing of 25% O atoms, the symmetry of a-Pu2O3 is lower than PuO2, and
with a lattice parameter of belongs to the space group 206=Ia3 11.06 Å. The hexagonal crystal is denoted as b-Pu2O3. From the point view of practical application, we decide to leave the high temperature b-Pu2O3 outside of scope for the present calculations. Hereafter, a-Pu2O3 is referred to as Pu2O3. The calculation configurations of PuO2 and Pu2O3 are shown in Fig. 1. For their magnetic orders of cubic d-Pu and PuO2, our DFT + U calculations and other similar calculations by other researchers show that the collinear 1
k antiferromagnetic (AFM) states along (1 0 0) lattice direction are energetically more favorable than nonmagnetic (NM) and ferromagnetic (FM) states. For Pu2O3, we compare the total energy of the so-called 1
k AFM configuration (AFM-1) mentioned above and the magnetic configuration (AFM-2) proposed by Regulski et al. [36]; in the latter configuration, its spin arrangements have four sublattices I, II, III and IV, as shown in Fig. 1(c). We find that the total energy of AFM-1 and AFM-2 Pu2O3 are almost degenerated; therefore, only AFM-1 Pu2O3 is considered in the studies of Ga incorporation into the oxide for the sake of computational efficiency. Similar to the case of PuO2, three incorporation sites of Ga incorporation sites, i.e., interstitial, Pu vacancy and O vacancy, are

considered, corresponding to Pu32O48Ga, Pu31O48Ga and Pu32O47Ga, respectively. Total energy calculations are performed with VASP code, the projector augmented wave (PAW) method, and relativistic effective core potentials (ECPs) [37–39]. Pu 6s27s26p66d25f4, O 2s22p4 and Ga 3d104s24p1 are treated as valence electrons. 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 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 [40]. 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 Pu 5f electrons. This value has been demonstrated 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 the formation of hyperstoichiometric Pu oxides [34,35]. Additionally, we test U values in the range of 3–6 eV for calculations related to PuO2 and PuO2.25. The U value has a significant influence on the band gap and total energy of the calculated configurations. However, we find that the variation arising from using different U values for the energetics of O can be neglected. Thus, the U value is expected to play an insignificant role in the calculations of

Spin down Spin up

(b) Pu2 O 3 (AFM -1)

(a) PuO 2 (AFM)

I

II

III

IV

(c) Pu 2 O 3 (AFM-2) Fig. 1. Calculation configurations of PuO2 and Pu2O3. (a) AFM PuO2 with the magnetic order along (1 0 0) lattice direction; (b) AFM-1 Pu2O3 with the magnetic order along (1 0 0) lattice direction; (c) AFM-2 Pu2O3 with four magnetic sublattices I, II, III and IV. In Fig. (a) and (b), the blue and grey balls designate Pu and O atoms, respectively. In Fig. (c), O atoms are removed for the sake of a clear indication of Pu magnetic order. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

B. Ao et al. / Computational Materials Science 122 (2016) 263–271

3. Results and discussion 3.1. Lattice volume of the relaxed configurations Knowledge from DFT calculation shows that relaxation scheme is very sensitive to the materials containing defects. An outstanding example for the actinide-based materials is the most widely calculated incorporation energy of octahedral interstitial O in UO2, which spans from largely negative
2.44 eV to slightly positive 0.1 eV in the literature [44–46]. 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 required for the configurations containing defects because of the possibility of anisotropic distortion. Our previous GGA + U calculations using a complete relaxation scheme on the conventional cells of both PuO2 and UO2, i.e., Pu4O8 and U4O8, indicated that their AFM configurations reduce the cubic symmetry of the fluorite structures to tetragonal structures; that is, lattice parameter c slightly differs from a and b. This is in consistency with other theoretical results using a similar complete relaxation scheme on cubic actinide dioxides. In the present complete relaxation on the supercells of Pu, PuO2 and Pu2O3, we find the similar reduction of symmetry and very slight anisotropic distortion. However, such anisotropic distortion increases with the introduction of point defects (i.e., Ga impurity, Pu vacancy and O vacancy). 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 models for the purpose of elucidating the general trend resultant from point defects,

1500 Pu2O3

1400 PuO2

1300 3

energetics of impurity atoms. Moreover, similar conclusions have been drawn from our previous calculations regarding the influences of other calculation parameters (i.e., spin–orbit coupling and more complicated non-collinear AFM configurations) on the energetics of impurity atoms in PuO2. 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. Complete relaxation without symmetry constraints is adopted. 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. 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 5  5  5 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 [41]. Pure spin-polarized DFT calculations are performed to determine the total energy of an O atom in molecular state. We use half the total energy of an O2 molecule as the total energy of an O atom. Owing to the well-known disadvantages of pure DFT in describing molecule, the scheme selected to calculate the total energy of an O2 molecule is similar to the one proposed by Korzhavyi et al. [42]. The total energy of an O2 molecule is obtained by the sum of the energy of free O atom and the well-established dimerization energy (i.e., the reaction energy of 2O = O2) [43]. The total energy of a free O atom is calculated by using a periodic cubic cell with a lattice constant of 15 Å and only one k point C in the framework of spin-polarized DFT. Moreover, pure spin-polarized DFT method is used to calculate the total energy of a-Ga crystallized in orthorhombic structure to obtain the energy of a Ga atom [11].

Volume (Å )

266

1200 1100 1000 Pu

900 800 A1 A2 A3 A4 A5 B1 B2 B3 B4 B5 C1 C2

C3

Calculation configuration Fig. 2. Lattice volumes of fully relaxed calculation configurations. The configurations are denoted as follows: A1
Pu32O63, A2
Pu31O64, A3
Pu32O64Ga, A4
Pu32O63Ga, A5
Pu31O64Ga, B1
Pu32O47, B2
Pu31O48, B3
Pu32O48Ga, B4
Pu32O47Ga, B5
Pu31O48Ga, C1
Pu32Ga, C2
Pu31, C3
Pu31Ga. The lattice volumes of fully relaxed PuO2 (Pu32O64), Pu2O3 (Pu32O48) and Pu (Pu32) are marked by the transverse dotted lines for comparison.

as plotted in Fig. 2. Some general features can be clearly found from the figure. First, the errors of theoretical lattice volumes with comparison to experimental observations are 7.55%, 3.13% and 3.24% for perfect Pu, PuO2 and Pu2O3, respectively. Considering the wide range of available theoretical lattice volumes by means of different DFT-based methods, particularly for d-Pu, the present DFT + U results are basically reasonable. In principle, the theoretical lattice volume of Pu could be improved by using smaller Hubbard U value because U value characterizes the repulsive interaction. However, in order to satisfy the consistency in the calculations of energetics of Ga in the Pu oxide layers, we insist on the same U value for all the configurations considered here because this value has a significant influence on the total energies. Second, Pu-based configurations have the smallest volumes, followed by PuO2- and Pu2O3- based configurations, no matter which defect the configurations contain. This is in consistency with the lattice volumes of perfect Pu, PuO2 and Pu2O3, mainly due to the fact that point defects usually induce a relatively small volume change in the host materials. Interestingly, the volume of Pu2O3 is larger than that of PuO2 despite that the total number of O atom in the former is 25% less than that of the latter. In fact, the unusual phenomenon can be viewed as the sum of two opposing components: expansive size effects and contractile electron-interaction effects. When O atoms are removed from PuO2 to form Pu2O3, Pu 5f electrons become more localized, in other words, less 5f electrons take participation in the chemical bonding, facilitating the formation of a lower valence Pu ion with larger atomic radius. If electroninteraction effects prevail over size effects, the configurations contract and vice versa. As shown in the figure, the lattice volumes of Pu32O63 and Pu32O47 are slightly larger, whereas the lattice volumes of Pu31O64 and Pu31O48 are slightly lower, than those of Pu32O64 and Pu32O48, respectively. Removing one Pu atom from either PuO2 or Pu2O3 makes the configuration contract, in part because the atomic radius of Pu is larger than that of O. Our previous DFT + U calculations on Pu hydrides and hyperstoichiometric Pu oxides also showed this unusual volume changes and the delocalization–localization transition of Pu 5f electrons was proposed to be the major reason [17,34,47]. Third, the similar conclusions as addressed above can be drawn from the volumes of the configurations with the incorporation of Ga. The lattice volumes of Pu32O64Ga (Ga at interstitial site) and Pu32O63Ga (Ga at O vacancy) are slightly larger than those of Pu32O64 and Pu32O63, respectively.

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3.2. Energetics of Ga in Pu, Pu2O3 and PuO2 From the point view of first-principles calculations, defect energetics are the most important results for describing the relative stability of defects in solid state materials. 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 configurations. 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 interstitial impurity atom. For a configuration containing a Ga atom and a Pu or an O vacancy, Ef does not equal Ei because the former contains the formation energy of a vacancy as well. The expressions of incorporation energies related to point defects (Ga, O and Pu vacancies) in PuO2 (i.e., Pu32O64) configurations are listed as follows:

EGa i ðPu32 O64 GaÞ ¼ Etot ðPu32 O64 GaÞ
Etot ðPu32 O64 Þ
Etot ðGaÞ;

ð1Þ

EGa i ðPu32 O63 GaÞ ¼ Etot ðPu32 O63 GaÞ
Etot ðPu32 O63 Þ
Etot ðGaÞ;

ð2Þ

EGa i ðPu31 O64 GaÞ ¼ Etot ðPu31 O64 GaÞ
Etot ðPu31 O64 Þ
Etot ðGaÞ;

ð3Þ

EVi O ðPu32 O63 Þ  EVf O ðPu32 O63 Þ ¼ Etot ðPu32 O63 Þ þ Etot ðOÞ
Etot ðPu32 O64 Þ;

ð4Þ

EVi Pu ðPu31 O64 Þ  EVf Pu ðPu31 O64 Þ ¼ Etot ðPu31 O64 Þ þ Etot ðPuÞ
Etot ðPu32 O64 Þ;

ð5Þ

where VO and VPu denote O and Pu vacancies in Pu32O64, respectively. According to the definitions of defect energetics in PuO2, one can easily obtain the energetics expressions related to point defects in Pu2O3 (i.e., Pu32O48) and Pu (i.e., Pu32) configurations. Here, for the sake of brevity, the expressions of incorporation energies related to point defects in Pu2O3 and Pu are not listed. The vacancy formation energy in d-Pu is calculated to be 0.70 eV, which is rather low in comparison with other cubic metals. This is primarily because metallic Pu is a soft metal with very low melting point and very low stiffness, facilitating the formation of vacancy. It is worth mentioning that vacancy formation energy is one of key parameters for the development of interatomic potentials, which is required for the atomic-scale molecular dynamics simulation on the self-radiation damage of Pu. However, to our knowledge, the experimental result of vacancy formation energy of d-Pu is not available. Other theoretical results derived from multi-scale computational methods showed a relatively wide range of vacancy formation energy, i.e., from 0.44 eV to 1.34 eV [48–51]. Interestingly, the present calculated vacancy formation energy is in good agreement with the result evaluated using a simple scaling rule with melting temperature of Pu [52]. The formation energies of Pu and O vacancies in PuO2 are calculated to be 10.64 eV and 3.76 eV, respectively. The larger vacancy formation energy corresponds to the high melting point and the high stiffness of PuO2, which is a common property for most ionic type metal oxides. The incorporation energy of Ga in Pu31Ga configuration is

calculated to be
0.16 eV. This relatively small value is expected to be in consistency with the well-accepted viewpoint that the Ga-stabilized d-Pu alloys are actually metastable [1,2]. However, the Ga-stabilized d-Pu alloys can be casted and exist in the common conditions mainly due to the fact that the decomposition of the alloys is dynamically controlled and requires very long time to take place. Additionally, the reaction energy of PuO2 formation, i.e., Pu + O2 = PuO2, is calculated to be
1049.48 kJ/mol, which agrees well with the experimental value of
1056.27 kJ/mol in the standard condition [1]. Based on the above results of the basic behaviors of vacancies and Ga in Pu and Pu–Ga alloy, we consider that the present calculation methods are basically reasonable in describing the energetics of simple defects in Pu oxides and alloys in spite of the inherent deficiency of DFT + U method in exactly capturing the electron structures. Therefore, the incorporation energies of Ga and other relevant point defects in the Pu oxide layers (i.e., Pu, Pu2O3 and PuO2) are calculated, as shown in Fig. 3. Some general conclusions about the behaviors of point defects can be drawn from the figure. First, one can find that the formation energy of Pu vacancy in Pu2O3 is about half of that in PuO2, whilst the formation energy (i.e., the incorporation energy in the figure) of O vacancy in Pu2O3 is about double of that in PuO2. This imply that, for the Pu–O binary system in the normal condition, it is rather difficult for the formation of Pu ion higher than +4 valence, whilst the formation of Pu ion between +3 and +4 valences is relatively favorable. Despite the formation energy of Pu vacancies in both PuO2 and Pu2O3 are largely positive, Pu vacancies could form in some non-equilibrium conditions such as continuous radiation damage, as will be addressed later. Second, Ga atoms incorporation into the interstitial site and O vacancy of both Pu2O3 and PuO2 are energetically unfavorable. Size effect and electron interaction are proposed to be the two main reasons for the incompatibility of Ga with the two defect sites, despite that we cannot determine the dominant effect in the meantime. For the case of interstitial Ga atom, it can be well understood because the Ga atom induces relatively remarkable lattice distortion and makes the system energy increase. In fact, this conclusion holds true for most of solid state materials containing interstitial impurity atoms. For the case of Ga atom at O vacancy, despite that the inclusion of Ga atom could offset, at least to some extent, the size effect resulted from removing an O atom, the electron interaction plays an important role in the stability of Ga atom. This is primarily

Incorporation energy ofpoint defect (eV)

However, the lattice volume of Pu31O64Ga is slightly lower than that of Pu31O64, which is supposed to be resulted from the electron-interaction of Ga with the host materials. The similar trends are observed for Pu2O3 with the incorporation of Ga and for Pu with the substitutional Ga (i.e., Pu31Ga), which will be addressed in the discussion of electron structures.

16 14 V Ei Pu(Pu31O64 ) 12 10 V Ei Pu (Pu31O48 ) 8 Ga 6 V Ei O(Pu32O63) Ei (Pu32O63Ga) EVO(Pu O ) EGa(Pu O Ga) 32 47 i i 32 48 4 Ga Ga Ei (Pu32Ga) EVi Pu(Pu31) Ga 2 (Pu O Ga) E i 32 47 Ei (Pu32O64Ga) 0 Ga E i (Pu 31Ga) -2 Ga -4 E i (Pu31O48Ga) Ga Ei (Pu31O64 Ga) -6 -8 -10 A1 A2 A3 A4 A5 B1 B2 B3 B4 B5 C1 C2 C3

Calculation configuration Fig. 3. Incorporation energies of point defects (Ga, Pu vacancy and O vacancy) in Pu, Pu2O3 and PuO2. The nomenclatures of the calculation configurations can be referred to Fig. 2. Note that the widely used terminology ‘‘formation energy” is the same as incorporation energy for the configuration containing only one point defect (see the text). Positive or negative values mean energetically favorable or unfavorable, respectively.

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because O atom in the host materials acts as electron acceptor, whereas Ga atom is electron donor. Therefore, the mismatch between Ga and O makes the system unstable. Third, the incorporation energies of Ga atoms incorporation into Pu vacancies of Pu, Pu2O3 and PuO2 are negative, implying the relative stability of Ga atoms at Pu vacancies. Among them, the incorporation energy of Ga at Pu vacancy of PuO2 is the largest negative, followed by those of Pu2O3 and Pu. According to the previous analysis on the stability of Ga atom at O vacancy, Ga atoms at Pu vacancies generally have favorable size and electron-interaction effects. In fact, the formation of Pu–Ga alloy by substituting a Pu atom for a Ga atom is a good example for the two effects. The Ga-vacancy (GaVPu or GaVO) complex containing two point defects is the simplest defect cluster in the configurations considered here and the formation energy of a complex characterizes the stability of the defect configuration. The formation energy of the complexes in PuO2 (i.e., Pu32O64) can be calculated as follows: Pu EGaV ðPu31 O64 GaÞ ¼ Etot ðPu31 O64 GaÞ þ Etot ðPuÞ f


Etot ðPu32 O64 Þ
Etot ðGaÞ;

ð6Þ

O EGaV ðPu32 O63 GaÞ ¼ Etot ðPu32 O63 GaÞ þ Etot ðOÞ
Etot ðPu32 O64 Þ f


Etot ðGaÞ:

ð7Þ

For the defect complex, the binding energy Eb is widely used to characterize the binding ability of an impurity atom to vacancy. Here, we define Eb as the energy difference between the formation energy of Ga at the octahedral interstitial site and at the vacancy. The binding energy of Ga to VPu or VO in PuO2 (i.e., Pu32O64) can be expressed as follows: Ga Pu EGaV ðPu31 O64 GaÞ ¼ EGa i ðPu32 O64 GaÞ
Ei ðPu31 O64 GaÞ; b

ð8Þ

Ga O EGaV ðPu32 O63 GaÞ ¼ EGa i ðPu32 O64 GaÞ
Ei ðPu32 O63 GaÞ: b

ð9Þ

10 8

GaVPu (Pu31O64Ga)

Eb

10

GaVO (Pu32O47Ga)

Ef

GaV Ef O(Pu32O63Ga) GaVPu

Ef

8 GaVPu (Pu31O48Ga)

Eb

(Pu 31O64Ga)

6

6 GaV E f Pu(Pu31O48Ga)

4 2 0 -2

4

GaV Eb Pu(Pu31Ga)

GaVPu (Pu

Ef

GaVO (Pu32O47Ga)

Eb GaV Eb O(Pu32O63Ga)

A4

31Ga)

2 0 -2

A5

B4

B5

Binding energy of Ga to vacancy (eV)

Foramtion energy of GaV complex (eV)

Here, for the sake of similarity, the expressions of formation energy and binding energy related to Ga-vacancy complexes in Pu2O3 and Pu can be logically obtained, such that they are not listed. Note that the positive binding energy represents the favorable binding ability of Ga to vacancy according to the current definition. The formation energy and binding energy of Ga-vacancy complexes in Pu, Pu2O3 and PuO2 are given in Fig. 4. Clearly, the formation energies of all the Ga-vacancy complexes considered here are positive, implying that the complexes are energetically

C2

Calculation configuration Fig. 4. Formation energies and binding energies of Ga-vacancy complex in Pu, Pu2O3 and PuO2. The nomenclatures of the calculation configurations can be referred to Fig. 2. Note that the positive binding energy represents the favorable binding ability of Ga to vacancy.

unfavorable under normal conditions. However, one can find that the formation energies of GaVPu complexes in both Pu2O3 and PuO2 are lower than the formation energies of single Pu vacancy in them. This makes clear that Ga can stabilize Pu vacancies in both Pu2O3 and PuO2. In fact, the stabilizing effects can be easily understood from the calculated binding energy. As shown in Fig. 4, the binding energies of Ga to Pu vacancies in both Pu2O3 and PuO2 are largely positive, whereas the binding energies of Ga to O vacancies in PuO2 or Pu2O3 are slightly negative or slightly positive, respectively. This is consistent with the previous conclusion that both Pu and O vacancies can offset (to a certain extend) elastic perturbation induced by the size effects of Ga atoms; however, Pu vacancies are more favorable with regard to electron interactions and can act as trapping sites for metallic Ga atoms in condition of the formation of Pu vacancies before incorporating Ga atoms. This stabilizing effect still holds true for the case of Ga atom at Pu vacancy in metallic Pu despite that the binding energy of Ga to Pu vacancy is slightly positive. Therefore, we conclude that electron interaction, instead of size effect, plays the dominant role in the relative stability of Ga atom. We now focus on the discussion of the potential existence of Ga in the oxide layers of Ga-stabilized d-Pu alloy from the calculated energetics since there is no any quantitative experimental data in the literature on the issue. It is apparent that Ga atoms are unstable in the perfect Pu, Pu2O3 and PuO2 lattices, and in Pu2O3 and PuO2 lattices containing only O vacancies. This is because the incorporation energies of Ga atoms in the above configurations are positive. Experimental observations have demonstrated that Ga atom always occupies the Pu lattice site (i.e., Pu vacancy in the present work), instead of interstitial site, in the Ga-stabilized d-Pu alloy [1,2,9]. In fact, we can find that the properties of Pu vacancies in the Pu oxide layer play the dominant role in the relative stability of Ga. With the pre-existence of Pu vacancies, from the incorporation energies one can find that Ga is relatively most stable in PuO2, followed by Pu2O3 and Pu. This is mainly due to the fact that Pu vacancy in PuO2 is most unstable, thus the stabilization role played by Ga is most significant, followed by Pu2O3 and Pu. However, this does not mean that Ga can easily accumulate in PuO2 layer. We suggest that Ga concentration in the Pu oxide layers would be strongly dependent on the concentration of Pu vacancy. In the dilute limit, the concentration of a point defect in crystal is well determined by the defect formation energy Ef through a Boltzmann expression:

c ¼ A expð
Ef =kB TÞ;

ð10Þ

where A is a constant for a specific material, Ef the formation energy of a point defect, kB the Boltzmann constant, and T the temperature. Note that this expression assumes thermodynamic equilibrium. One can easily find that the concentration of Pu vacancy in PuO2 is the lowest, followed by Pu2O3 and Pu. In fact, very small vacancy formation energy for metallic Pu is in consistency with the formation of Pu–Ga alloy by substituting a Pu atom for a Ga atom. On the other hand, it is difficult for a Ga atom to replace a Pu atom in Pu2O3 or PuO2, especially for the latter. However, apart from equilibrium defects, non-equilibrium defects including vacancy and vacancy-related extended defects such as dislocation and grain boundary are unavoidable in the Pu-based materials. As well known, a part of the non-equilibrium defects form during their conventional fabrication, oxidation and storage. More importantly, Pu is a radioactive element, decaying to U nucleus with a high recoilenergy of about 86 keV by emitting a particle with a high kinetic energy of about 5 MeV [1,53]. Knowledge from this so-called selfradiation damage effect has demonstrated the inevitable formation of various kinds of defects despite that most of defects can recover by defect annihilating mechanism. The radiation-induced Pu vacancies, vacancy clusters and vacancy-rich extended defects are the potential sites for accommodating Ga atoms. It is worth pointing

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B. Ao et al. / Computational Materials Science 122 (2016) 263–271

(a) Pu 32O64 (PuO2)

160 120 80 40 0

(b) Pu 32O63

160 120 80 40 0

(c) Pu31O64

160 120

DOS (states/eV)

out that radiation effects can enhance the diffusion of Ga atoms from bulk Pu–Ga alloy to other region, facilitating the formation of intermetallic compound, i.e., Pu3Ga or other potential intermetallic compounds with lower Ga composition [54]. Although the diffusion dynamics of Ga atom is beyond the scope of the current calculations, the diffusion of Ga from bulk Pu–Ga alloy to the Pu oxide layers is still expected owing to the significant concentration difference of Ga in the different layer. Moreover, the real structures of Pu oxide layers are more complicated than the simplified sandwich-like structures. The Pu/Pu2O3 and Pu2O3/PuO2 interfaces are usually far from ideal lattice-matched structures. This is primarily because initial Pu surface before oxidation is usually far from perfect surface structure and the mismatch of lattice parameters can result in the distortion of interfaces. Additionally, apart from the two Pu oxides, the complicated Pu–O phase diagram shows the Pu2O3–PuO2 region consists of widely nonstoichiometric Pu oxides (i.e., PuO2-x, 0 < x < 0.5) [1]. Recently, even amorphous Pu oxides in the Pu oxide layers were observed [55]. Generally, the complicated oxide-layer structures mentioned above favor the formation of vacancy or vacancy-rich defects. We consider that Ga could distribute into the whole Pu oxide layers and Ga concentration is relative to the concentration of Pu vacancy. The formation energy of Pu vacancy increases with the transition of Pu ? Pu2O3 ? PuO2, suggesting the decreasing concentrations of Pu vacancy and Ga with the transition. This is basically in agreement with the available experimental observations despite that the concentration profile of Ga in the Pu oxide layers cannot be quantitatively determined in the current calculations.

80 40 0

(d) Pu 32O63Ga

160 120 80 40 0

(e) Pu 31O64Ga

160 120 80 40 0

Total Pu f Op Ga p Ga p (×32)

(f) Pu 32O64Ga

160 120 80

EF

40 0

3.3. Electron structure

-7

-6

-5

-4

-3

-2

-1

0

1

2

3

4

5

Energy (eV) The basic behavior of Ga in the Pu oxide layers discussed above is also identified by the calculated electronic structure of all the configurations considered here. Above all, in terms of other researchers’ and our previous calculations on Pu-based materials, especially on Pu oxides [3,15,34,35,56–58], we briefly discuss the general features of the electronic structures of Pu, Pu2O3 and PuO2 with or without impurity atoms. The most remarkable feature of the electronic structure of metallic Pu lies in 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 electronic states. However, the localized 5f electrons may exhibit more or less delocalized characters depending on the chemical surroundings, a conclusion that is support by both experimental and theoretical studies on Pu compounds. Taking Pu–O system for an example, with the Pu ? Pu2O3 ? PuO2 transition of increasing Pu ion valence states, Pu 5f electrons become more delocalized with the typical feature of fewer 5f states below EF. Solid state PuO2 with nominal Pu4+ ion has long been recognized as the highest composition binary oxide despite that many attempts have been made to search hyperstoichiometric Pu oxides with Pu ion valence higher than +4. Generally, hyperstoichiometric Pu oxides might form only under some special long-term storage environment containing highly-reactive free radicals resultant from radiolysis water. Therefore, in most cases regarding the issue of Pu surface science, hyperstoichiometric Pu oxides are usually excluded from the discussion. For the influencing effects of impurity atoms in Pu oxides, our previous calculations on a series of nonmetallic impurity atoms in PuO2 showed that the perturbation from most of the impurity atoms could result in instability of the host, and only the strongest oxidant F with small atomic radius and large electron affinity could stabilize the host [35]. The total and projected density of states (TDOS and PDOS) of PuO2 and Pu2O3 related configurations are presented in Fig. 5 and Fig. 6, respectively. As expected, PuO2 and Pu2O3 are predicted to

Fig. 5. Total and projected density of states (TDOS and PDOS) of PuO2-related configurations. The Fermi energy (EF) is scaled to zero and marked by the grey dash line. All of the PDOS of Ga p states are also amplified to 32 Ga atoms for the sake of clarity.

exhibit semiconducting ground states with the band gaps of approximately 1.6 eV and 2.0 eV, respectively, which is consistent with experimental observations and other theoretical results from similar GGA + U methods. For PuO2, the Pu 5f and O 2p states show strong hybridizing features, covering a wide energy range (5 eV) below EF. As for Pu2O3, there are two hybridizing energy ranges for Pu 5f and O 2p states. The first range is from EF to
1.0 eV where 5f states are dominant. In fact, the Pu 5f states with narrow and sharp DOS peaks just below EF are the typical feature of localization. The second range is from
2.0 eV to
4.5 eV where O 2p states are dominant. In terms of the DOS of the two oxides, we can find that Pu 5f states in Pu2O3 become more localized as a result of missing O atoms; therefore, the bonding strength becomes weaker, and correspondingly, the lattice volume expands as discussed previously. After removing an O atom or a Pu atom from the two oxides, some noticeable changes occur in their respective DOS spectra. For Pu32O63, as shown in Fig. 5(b), the valence bands (VBs) and conduct bands (CBs) are still well separated despite that the band gap decreases with comparison to PuO2. The surplus Pu 5f electrons become localized and typically feature narrow and sharp DOS peaks just below EF, which also induces a slight lattice expansion. For Pu31O64, as shown in Fig. 5(c), although the VBs and CBs are still well separated, a small amount of electronic states resulted from the hybridization of surplus O 2p states with Pu 5f states traverse EF, giving rise to a conducting ground state. In contrast to Pu32O63, Pu31O64 can be viewed as electron-poor configuration for Pu ions in comparison with electron-matched Pu32O64. The electrons of Pu that participate in chemical bonding in Pu31O64 are more than those in Pu32O64, resulting in a slight lattice contraction. For the

B. Ao et al. / Computational Materials Science 122 (2016) 263–271

(a) Pu 32O48 (Pu2O3)

160 120 80 40 0

(b) Pu 32O47

160 120 80 40 0

(c) Pu 31O48

160

DOS (states/eV)

120 80 40 0

(d) Pu 32O47Ga

160 120 80 40 0

(e) Pu 31O48Ga

160 120 80 40 0

Total Pu f Op Ga p Ga p (×32)

(f) Pu 32 O48Ga

160 120 80

EF

40 0

-7

-6

-5

-4

-3

-2

-1

0

1

2

3

4

5

Energy (eV) Fig. 6. Total and projected density of states (TDOS and PDOS) of Pu2O3-related configurations. The Fermi energy (EF) is scaled to zero and marked by the grey dash line. All of the PDOS of Ga p states are also amplified to 32 Ga atoms for the sake of clarity.

cases of O vacancy and Pu vacancy in Pu2O3, the electronic structures can be logically described based on the analysis of DOS spectra of Pu32O63 and Pu31O64. Note that Pu31O48 remains the semiconducting state and no any unoccupied state occurs above EF. This is primarily because the valence of Pu ion in Pu2O3 is much lower than that in PuO2, i.e., Pu ion in the former is electron-rich configuration; therefore, removing a Pu ion from Pu2O3 just slightly increases the valence of Pu and cannot induce the occurrence of surplus O 2p states. However, the valence of Pu ion in PuO2 is +4, the highest valence state in Pu–O binary system; therefore, removing a Pu ion from PuO2 results in a chemically unreasonable configuration. After incorporating a Ga atom into PuO2 and Pu2O3, some small perturbations occur on the respective DOS spectra. Note that Ga atomic concentration is very low in the current Pu oxide configurations and the DOS contribution from Ga is insignificant. For PuO2 with a Ga atom incorporated into O vacancy (Pu32O63Ga), or Pu vacancy (Pu31O64Ga), or interstitial site (Pu32O64Ga), the semiconducting states still exist. However, the EF levels of both Pu32O63Ga and Pu32O64Ga shift to higher energy with comparison to Pu32O64. This is primarily because of electronic incompatibility of Ga atom at the two sites. As addressed above, Pu32O64 is an electronmatched configuration and Pu32O63 is an electron-rich one, such that the incorporation of Ga (i.e., an electron donator) into Pu32O64 or Pu32O63 makes the electron states deviate from the host. For Pu31O64, i.e., the electron-poor configuration, the incorporation of Ga into it is in favor of maintaining the electronic structure of Pu32O64, as shown in Fig. 5. Such explanations based on electron match also generally hold true for the cases of Ga incorporation

into Pu2O3, as can be found in Fig. 6. As expected, the incorporation of Ga into Pu31O48 yields an insignificant perturbation to the electronic states of Pu32O48. Meanwhile, the incorporation of Ga into both Pu32O47 and Pu32O48 result in the shift of EF to higher energy. However, for Pu32O47Ga and Pu32O48Ga configurations, the electronic states mainly induced by Ga pin on EF, suggesting the occurrence of surplus Ga electrons in the hosts. In fact, in comparison with the cases of Ga incorporation into PuO2, such phenomena can be explained by the fact that Pu2O3 is essentially an electronrich configuration on the premise of electron-matched PuO2 configuration. Therefore, it is more difficult for Pu32O47 and Pu32O48 to absorb Ga electrons to participate in chemical bonding. In order to analyze the bonding interaction of Ga with the hosts in detail, the PDOS of all the electronic states of Pu, O and Ga in the three relatively stable configurations for Ga (i.e., Pu31Ga, Pu31O64Ga and Pu31O48Ga) are presented, as shown in Fig. 7. Here, only the first nearest neighboring (1nn) Pu atom and the 1nn O atom are selected for the sake of clarity since the bonding interactions between Ga atom and other Pu atoms or O atoms become negligible. Note that symmetry of the crystals is broken, therefore, Ga has only one 1nn Pu atom, instead of 12nn Pu atoms in the perfect fcc crystal. For the metallic state Pu31Ga configuration, almost all the electronic states of Pu and Ga traverse EF, as shown in Fig. 7(a). The electronic states at EF contributed from 1nn Pu 5f states are relatively weak. In fact, Pu 5f states of other Pu atoms away from 1nn Pu atom contribute the main electronic states around EF. Additionally, one can find that there are discernable hybridization interactions between Ga 4p and Pu 6d electronic states. This is shown by similarities in the position and shape of the DOS peaks in their respective PDOS. Therefore, the Pu atom in Pu–Ga alloy tends to have some d-bonding with the Ga 4p electrons, which agrees well with other findings [26]. The local bonding interactions between Ga atom and Pu oxides become relatively more complicated, as shown in Fig. 7(b) and (c). Generally, there exist the combined hybridization interactions among Ga 4p, Pu 5f, Pu 6d and O 2p electronic states. The very small Pu 5f DOS contributions around

(a) Pu 31Ga

0.8 0.6 0.4 0.2 0.0

DOS (states/eV)

270

(b) Pu 31O 64Ga

0.8 0.6 0.4 0.2 0.0 0.8

1nn Pu f 1nn Pu d 1nn Pu p 1nn Pu s Ga p Ga s 1nn O p 1nn O s

(c) Pu 31O48Ga

0.6 0.4

EF

0.2 0.0 -7

-6

-5

-4

-3

-2

-1

0

1

2

3

4

5

Energy (eV) Fig. 7. Projected density of states (PDOS) of the Ga atom in Pu vacancy, and the first nearest neighboring (1nn) Pu atom, and the 1nn O atom. Note that symmetry of the crystals is broken, therefore, Ga has only one 1nn Pu atom, instead of 12nn Pu atoms in the perfect fcc crystal. Other Pu atoms (not shown in the figure) have the overwhelming major contribution to the total 5f states. The Fermi energy (EF) is scaled to zero and marked by the grey dash line.

B. Ao et al. / Computational Materials Science 122 (2016) 263–271

EF are mainly responsible for their electron-poor behavior, resulting in the enhanced chemical bonding or electron transfer with relation to Pu 5f electrons. 4. Conclusions We have conducted the GGA + U methods to calculate the energetics of Ga atom in the three main materials of Pu oxide layers, i.e., Pu, Pu2O3 and PuO2, for the purpose of understanding the relative stability and the potential occupying sites of Ga. Two incorporation sites for Pu (interstitial and Pu vacancy) and three incorporation sites for both Pu2O3 and PuO2 (interstitial, Pu and O vacancies) are considered for the calculations of formation energy, incorporation energy and binding energy with relation to Ga. Essentially, Ga atom is energetically unfavorable at almost all of the incorporation sites with comparison to their corresponding perfect lattices in terms of the calculated defect formation energy. The only exception is the potentially stable configuration of Ga in Pu vacancy of Pu, in which the defect (Ga-vacancy complex) formation energy is slightly positive. However, Ga atom is energetically favorable at Pu vacancies of Pu, Pu2O3 and PuO2 with the preexistence of the Pu vacancies. This is mainly because the incorporation energies of Ga at Pu vacancies of the three materials are negative, and the binding energies of Ga to Pu vacancies are positive, a typical feature of the stabilization of Pu vacancies by Ga. For the cases of Ga at O vacancies of Pu2O3 and PuO2, all the calculated energies show the instability of Ga. Therefore, we conclude that the concentration of Pu vacancy in the Pu oxide layers plays the decisive role in controlling the distribution of Ga during the oxidation process of Pu–Ga alloy. According to the possible formation processes of Pu vacancies in the real situations, we propose that Ga could distribute into the Pu oxide layers and the Ga concentration decreases with the transition of Pu ? Pu2O3 ? PuO2. This is mainly due to the fact that the formation energy of Pu vacancy of PuO2 is the largest, followed by Pu2O3 and Pu. Electronic structure analysis indicates that the influences of Ga on the hosts are strongly dependent on the incorporation sites, i.e., Pu vacancy or O vacancy; one typical feature is that Ga at Pu vacancy can retain the main behavior of electronic states of the hosts, whereas the electronic states of Ga at O vacancy deviate from the hosts, yielding the shift of Fermi energy level to higher energy or the occurrence of the isolated unoccupied Ga 4p states. This is generally in consistency with the conclusion on the energetic stability of Ga at the two different incorporation sites. Acknowledgements Many thanks go to Prof. Jun Chen for proof reading the manuscript. The research was supported by the National Natural Science Foundation of China (Nos. 21371160, 11305147, 21401173 and 11404299), the 863 Program of China (No. 2015AA01A304), and the Foundation of President of China Academy of Engineering Physics (No. 2014-1-58). References [1] N.G. Cooper (Ed.), Challenges in Plutonium Science, Los Alamos Sci. 26, Los Alamos National Laboratory, 2000. [2] A.J. Schwartz, H. Cynn, K.J.M. Blobaum, M.A. Wall, K.T. Moore, W.J. Evans, D.L. Farber, J.R. Jeffries, T.B. Massalski, Prog. Mater Sci. 54 (2009) 909–943. [3] K.T. Moore, G.V. Laan, Rev. Mod. Phys. 81 (2009) 235–298. [4] V. Alexandrov, T.Y. Shvareva, S. Hayun, M. Asta, A. Navrotsky, J. Phys. Chem. Lett. 2 (2011) 3130–3134. [5] A.J. Nelson, P. Roussel, J. Vac. Sci. Technol., A 31 (2013) 031406. [6] L.N. Dinh, J.M. Haschke, C.K. Saw, P.G. Allen, W. McLean II, J. Nucl. Mater. 408 (2011) 171–175.

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