Journal of Nuclear Materials 426 (2012) 139–147

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Journal of Nuclear Materials

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First-principles study of surface properties of PuO2: Effects of thickness andO-vacancy on surface stability and chemical activity

Bo Sun ⇑, Haifeng Liu, Haifeng Song, Guangcai Zhang, Hui Zheng, Xiangeng Zhao, Ping Zhang ⇑Institute of Applied Physics and Computational Mathematics, Beijing 100088, People’s Republic of China

a r t i c l e i n f o a b s t r a c t

Article history:Received 23 December 2011Accepted 24 February 2012Available online 13 March 2012

0022-3115/$ - see front matter � 2012 Elsevier B.V. Ahttp://dx.doi.org/10.1016/j.jnucmat.2012.02.029

⇑ Corresponding authors. Tel.: +86 10 59872411.E-mail addresses: sun_bo@iapcm.ac.cn (B. Sun),

Zhang).

The (111), (110), and (001) surfaces properties of PuO2 are studied by using density-functional the-ory + U method. The total-energy static calculations determine the relative order of stability for low-index PuO2 surfaces, namely, O-terminated (111) > (110) > defective (001) > polar (001). The effect ofthickness is shown to modestly modulate the surface stability and chemical activity of the (110) surface.The high work function U of 6.19 eV indicates the chemical inertia of the most stable (111) surface, andthe surface O-vacancy with concentration CV = 25% can efficiently lower U to 4.35 eV, which is a crucialindicator of the difference in the surface chemical activities between PuO2 and a-Pu2O3. For the polar(001) surface, 50% on-surface O-vacancy can effectively quench the dipole moment and stabilize the sur-face structure, where the residual surface oxygen atoms are arranged in a zigzag manner along the h100idirection. We also investigate the relative stability of PuO2 surfaces in an oxygen environment. Underoxygen-rich conditions, the stoichiometric O-terminated (111) is found to be the most stable surface.Whereas under O-reducing conditions, the on-surface O-vacancy of CV = 1/9 is stable, and for high reduc-ing conditions, the (111) surface with nearly one monolayer subsurface oxygen removed (CV = 8/9)becomes most stable.

� 2012 Elsevier B.V. All rights reserved.

1. Introduction

Plutonium dioxide (PuO2) is of high importance in the nuclearfuel cycle and is particularly crucial in long-term storage of Pu-based radioactive waste. Besides playing an important role in bothtechnological applications and environmental issues, Pu metal andits oxides show many intricate physical behaviors due to the com-plex electronic structure properties of 5f states [1–4]. Therefore, athorough understanding of the physical and chemical properties ofPuO2 is of great significance, full of challenges and has always at-tracted attention. Recently, there have occurred in the literaturea series of experimental reports [5–7] on the strategies of storageof Pu-based waste. When exposed to air and moisture, metallicplutonium surface rapidly oxidizes to PuO2 [8,9]. Under specialaqueous condition, the interaction of PuO2 surface with adsorbedwater can generate non-stoichiometric PuO2+x (x 6 0.27) [5] viaan overall reaction, namely, PuO2 + xH2O ? PuO2+x + xH2. However,the oxidation of PuO2 has been proved to be strongly endothermicby subsequent first-principles theoretical calculation [10,11]. Totest the possible existence of surface PuO2+x, recent photoemissionstudy [7] has been carried out and found that PuO2 is only coveredby a chemisorbed layer of oxygen and can be easily desorbed at

ll rights reserved.

zhang_ping@iapcm.ac.cn (P.

elevated temperature. Thus, PuO2 is generally acknowledged asthe highest stable Pu-oxide under ambient conditions. However,under oxygen-lean conditions (in the vacuum or inert gas), thePuO2-layer can be reduced to sesquioxides (Pu2O3), which can pro-mote the corrosion of the Pu-metal by hydrogen [8]. As we know,the low-temperature phase of Pu-sesquioxide is a phase with spacegroup Ia�3 (No. 206), which is similar in the crystal structure to thecubic PuO2 (Fm�3m, No. 225) with the 25% O vacancy located in the16c (0.25, 0.25, 0.25) sites. The above mentioned experimentalobservations indicate that the surface of PuO2 is to some extentchemically inactive, however, the formation of O vacancies canprominently modify the electronic structure properties of boththe bulk and the surface of PuO2. As a matter of fact, the surfacelayers are directly involved in the significant corrosion processesand many technological applications of the actinide oxides, thusa deep understanding of the physical and chemical properties ofPuO2 surfaces is always desirable. However, due to the radioactiv-ity and toxicity of Pu and the complexity of the Pu element and Pu–O system, it is extraordinarily difficult to experimentally explorethe surface atomic and electronic structure properties of the Pu-oxides, and particularly so for a single phase compound.

From the theoretical point of view, conventional density-func-tional theory (DFT) that applies the local density approximation(LDA) or generalized gradient approximation (GGA) underestimatesthe strong on-site Coulomb repulsion of the 5f electrons and, conse-quently, describes PuO2 as incorrect ferromagnetic FM conductor

140 B. Sun et al. / Journal of Nuclear Materials 426 (2012) 139–147

[12] instead of antiferromagnetic AFM Mott insulator reported byexperiment [13]. Similar problems have been confirmed in studyingother correlated materials within the pure LDA/GGA schemes. For-tunately, several approaches, including the LDA/GGA + U [14–16],the hybrid density functional of (Heyd, Scuseria, and Enzerhof)HSE [17], the self-interaction corrected local spin density SIC-LSD[18], and LDA combined dynamical mean-field theory DMFT [19],have been developed to correct these failures in calculations of acti-nide compounds. The effective modification of pure DFT by LDA/GGA + U formalisms has been confirmed widely in study of PuO2

[20–25]. By tuning the effective Hubbard parameter in a reasonablerange, the AFM Mott insulator feature was correctly calculated andthe structural parameters as well as the electronic structure are wellin accord with experiments. However, those increasing theoreticalresearches have been focusing on the bulk properties of PuO2, andvery little is known regarding its surface physical and chemicalproperties, which is in sharp contrast to the depth and comprehen-siveness of researches conducted upon the transition metal and rareearth oxides [26]. As far as we are aware, few DFT studies of thePuO2(100) and (110) surfaces have been presented in the literature[27,28]. In addition, one of the most important issues, i.e., the possi-ble formation of O vacancies and their effect on the atomic and elec-tronic structures of PuO2 surfaces, remains completely unexplored.

Motivated by the above mentioned facts, in this paper, we sys-tematically study the surface properties of PuO2. Specifically, wehave addressed (i) the structural stabilities of the low-indexPuO2(111), (110), and (001) surfaces based on the calculationsof surface energies and surface relaxations, (ii) the surfaceelectronic properties such as the surface work function andlayer-projected density of the state (PDOS), and (iii) the effects ofPu-oxide thickness and O-vacancy on the surface stabilities andelectronic structure properties.

This paper is organized as follows. The details of our calcula-tions are described in Section 2. In Section 3 we present and dis-cuss the results. In Section 4, we summarize our main conclusions.

(a) (b) (c) (d)Fig. 1. Low-index PuO2 surface models: (a) ideal oxygen-terminated (111) unitcell; (b) (110) unit cell; (c) ð

ffiffiffi2p�

ffiffiffi2pÞR45� super-cell of ideal oxygen-terminated

(001); and (d) the defective (001) surface with four different distributions of 50%O-vacancy on the bottom and top faces, namely, surf-1, surf-2, surf-3 and surf-4.The blue, red and white spheres denote Pu-atom, O-atom and O-vacancy,respectively. In the side-views of three ideal surface, the labels of different Pu-cation/O-anion [+ +/�] stacking sequences are also indicated at the lower part of thegraphs. (For interpretation of the references to color in this figure legend, the readeris referred to the web version of this article.)

2. Methodology

2.1. DFT calculations

The DFT calculations are carried out using the Vienna ab initiosimulation package [29] with the frozen-core projector-augmentedwave (PAW) pseudopotentials [30,31] and plane-wave set. For theplane-wave set, a cut-off energy of 400 eV is used. The plutonium6s27s26p66d25f4, and the oxygen 2s22p4 electrons are treated as va-lence electrons. The exchange and correlation effects are treated inboth the LDA and the GGA [32], based on which the strong on-siteCoulomb repulsion among the localized Pu 5f electrons is de-scribed by using the LDA/GGA + U formalisms formulated by Duda-rev et al. [14–16]. As concluded in some previous DFT studies[20,21,23,25], although the pure LDA and GGA fail to depict theelectronic structure, especially the insulating nature and the occu-pied-state character of bulk AFM PuO2, the LDA/GGA + U ap-proaches can capture the Mott insulating properties of thestrongly correlated Pu 5f electrons adequately and well reproduceexperimental ground-state parameters by tuning the effectiveHubbard parameter Ueff at �4 eV. In this paper, the sphericallyaveraged screened Coulomb energy U and the exchange energy Jfor the Pu 5f orbitals are set to be 4.75 and 0.75 eV respectively,which have been tested and applied in our previous studies of plu-tonium oxides [20,21,25]. For fluorite structure PuO2 of AFM, ourcalculated equilibrium lattice parameter a0 = 5.466 Å withinGGA + U or a0 = 5.362 Å within LDA + U is in good agreementwith the experimental value of 5.398 Å [5]. Our extensive testcalculations in this work indicate that the choice of Ueff can alter

the electronic-structure properties of PuO2 surfaces, as well asthose of bulk PuO2. Specifically, when Ueff is less than 2.0 eV, theresults of the electronic density of state (DOS) indicate that PuO2

surfaces are metallic FM-conductor instead of the AFM Mott-insu-lators. The combination of U = 4.75 and J = 0.75eV is also the opti-mum to well describe the electronic structure properties of thesurfaces of PuO2, although the atomic structural optimizationsseem to be insensitive to the choice of Ueff.

The low-index surfaces of PuO2 are modeled by finite-sizedperiodic supercells, consisting of a number of oxide layers infinitein x and y directions and separated in the z direction by a vacuumof 30 Å. The Brillouin zone (BZ) integration is performed using theMonkhorst–Pack (MP) k-point mesh [33]. Specifically, the two-dimensional (2D) unit (1 � 1) cell with a 11 � 11 � 1 k-point MPgrid is employed for the defect-free (ideal) PuO2(111) and (110)surfaces, and a ð

ffiffiffi2p�

ffiffiffi2pÞR45� supercell with a 7 � 7 � 1 k-point

grid is used for the (001) surface. Examples of the initial slab con-figurations used in the calculation are shown in Fig. 1a–c, whichare obtained by truncating bulk PuO2 along the [111], [110] and[001] orientations, respectively. In the spin-polarized calculationswith the AFM order set to be in a simple ‘‘"; "; ’’ alternative man-ner along the z direction, all atoms are fully relaxed until the Hell-mann–Feynman forces are less than 0.01 eV/Å. Variousconvergence tests have been performed to ensure the above men-tioned input parameters and models feasible and reasonable in ourcurrent calculations. The result thereof shows that the surface en-ergy of a slab with certain thickness is converged within 3 meV/Å2.In this paper, for the convenience of depiction and plotting, we areusing the number of Pu-cation layer N in a PuO2 slab to representits thickness. Thus, one can see in Fig. 1a–c that the ideal (111),(110), and (001) slabs have the same thickness tag, namely,N = 6, and it is worth noting that in practice these slabs consist of18, 6 and 13 atomic monolayers (MLs), respectively.

According to Tasker’s conclusion [34] on the surface stabilitiesof ionic crystals, the side-view of three low-index PuO2 surfacesin Fig. 1 can reveal that the oxygen-terminated (111) surface, con-sisting of successive and electrically neutral ‘‘O–Pu–O’’ blocks, isthe ‘‘Tasker-type-II ’’ surface, the (110) is the typical ‘‘type-I ’’ sur-face stacked with identical neutral planes fulfilling the PuO2 stoi-chiometry, and the (001) is the typical ‘‘type-III ’’ surface,consisting of oppositely charged planes. Generally, type-I and

B. Sun et al. / Journal of Nuclear Materials 426 (2012) 139–147 141

type-II are stable non-polar surfaces, while type-III is unstable po-lar surface due to the dipole moment of the repeated unit in zdirection. The dipole moment may be quenched and the polar sur-face stabilized by a variety of methods [35–38], including surfacereconstruction, the presence of adsorbates, and changes in thesurface electronic structure. In our present work, the polar (001)surface is modeled as two oxygen-terminated surfaces with 50%oxygen vacancies to fulfill the stoichiometric formula, and the dif-ferent distributions of the 50% O-vacancy considered here areshowed in Fig. 1d. Besides above-mentioned three low-index sur-faces, the Pu-terminated (111) surface generated by removingthe outmost O layers of the O-terminated (111) surface has beenfound to be quite unstable and eventually become O-terminatedthrough a significant reconstruction in the surface region due tothe intense dipole–dipole interaction. In such stable structure,the upper layers resemble the b-Pu2O3(0001) surface. Thus, weexclude the Pu-terminated (111) slab model and briefly namethe O-terminated PuO2(111) surface as (111) surface if not men-tioned differently.

The surface energy Es is the energy needed to produce a unitsurface from a 3D infinite crystal and is one central quantity inthe studies of the relative stability of different surfaces. In theDFT total-energy calculations of repeated slab-supercell geome-tries, Es can be written as

Erelax=unrelaxs ¼ 1

2AErelax=unrelax

slab � Ebulk

� �; ð1Þ

where Esrelax=unrelaxslab is the total energy of the supercell with relaxed/

unrelaxed slab, Ebulk is the energy of the reference bulk with thesame number of atoms, and the denominator 2A is the total areaof both surfaces of the slab with a finite thickness. Here, the conver-gence of the Es (i.e., Erelax

s in Eq. (1)) is mainly determined by twocorrelated factors, namely, the atomic structural relaxations in sev-eral outmost layers and the thickness of the slab model. For the sur-face structural relaxations, one can simply evaluate its contributionto Es by calculating the surface relaxation energyDEs ¼ � Erelax

s � Eunrelaxs

� �. The effect of the slab thickness should be

highlighted especially when the slab consists of the complicatedcompounds such as the actinide oxides, and in addition, the workfunctions calculated with slab approximations are known to bedepending on the slab thickness. Thus, in this work, both factorswill be considered and discussed in detail.

2.2. Thermodynamic considerations

The DFT total-energy calculation gives Es only at zero tempera-ture T = 0, zero pressure P = 0, and for the surface in contact withvacuum, which cannot be used to study the influence of the realis-tic environmental conditions at a specific T and P. To further studythe relative stability of the PuO2 surfaces with various concentra-tions of surface vacancy (CV) at finite T and gas partial P of the sur-rounding environment, we take the approach of ‘‘ab initio atomicthermodynamics’’ [39,40] to get the surface Gibbs free energy c(T, P), with the general expression given by

cðT; PÞ ¼ 12A

GðT; P; fnigÞ �P

iniliðT;piÞ

� �; ð2Þ

where G is the Gibbs free energy of the solid with the surface ofinterest, 2A is the total surface area, ni, li and pi are the particlenumber, the chemical potentials and the partial pressures of thevarious species. Here, the focus of our work is the relative stabilityof O-terminated PuO2 surfaces with different O-vacancy concentra-tions, thus only two chemical species need to be considered, namelyi = Pu and O. In practice, the surface Gibbs energy difference Dc (T,P) between a defective PuO2 surface and the corresponding

defect-free (ideal) surface is the important quantity required, whichcan be written as

DcðT; PÞ ¼ 12A½GdefectðT; P;NVÞ � GidealðT; PÞ þ NVlOðT;pO2

Þ�; ð3Þ

where Gdefect and Gideal are the Gibbs free energies of the supercellswith the defective and ideal PuO2 surfaces, respectively, and NV isthe total number of O vacancies on the PuO2 surface. In the presentsituation, the entropy and volume effects are small compared to theband energy in the Gibbs free energy and thus are neglected in ourcalculations. lOðT;pO2

Þ in Eq. (3) is the oxygen chemical potentialunder partial pressure pO2

and for ideal oxygen-gase we can usethe well-known thermodynamic expression [40]

lOðT;pO2Þ ¼ 1

2ðEO2 þ ~lO2 ðT;p0Þ þ kBT lnðpO2

=p0ÞÞ; ð4Þ

where EO2 is the total energy of the oxygen molecule. For the stan-dard pressure p0 = 1 atm, the values of ~lO2 ðT;p0Þ have been tabu-lated in Ref. [41]. If we refer the lO to 1

2 EO2 , then the allowedrange for the DlO ¼ lO � 1

2 EO2 is given by

�12

Ef 6 DlO 6 0; ð5Þ

where Ef is the formation energy of bulk PuO2, namely,Ef ¼ jEPuO2 � Ed�Pu � EO2 j.

To determine reasonable ranges of DlO, the d-Pu is considered asreference system to calculate the formation energy Ef of bulk PuO2.Since the spin–orbit coupling (SOC) is important for certain proper-ties of heavy-metal compounds, we also include SOC effect in thecalculations of EPuO2 and Ed�Pu. Finally, we restrict DlO to�4.89 eV 6DlO 6 0 based on the GGA + U and�4.83 eV 6 DlO 6 0based on the GGA + U + SOC. The effect of spin polarization has beenincluded in calculating EO2 .

3. Results and discussion

3.1. Surface energy and structural relaxation

First, the relative stability of the low-index PuO2 surfaces isstudied based on the systematic calculation of surface energy Es

and the detailed analysis of structural relaxation. Furthermore,the effects of slab thickness on both surface stability and relaxationare considered and discussed. In the following text, we first presentthe results of non-polar (111) and (110) surfaces, and then the po-lar (001) surface.

The calculated surface energy for fully relaxed (111) and (110)slabs as a function of the thickness is illustrated in Fig. 2a. Obvi-ously, both the GGA + U and LDA + U calculations give the consis-tent results that the (110) surface energy is much higher thanthe (111) surface energy. Generally, the calculated Es for (110) is42% with GGA + U (or 33% with LDA + U) higher than for (111).Therefore, the PuO2(111) surface is much more stable than the‘‘more open’’ (110) surface with relatively higher concentrationof the surface dangling bonds. For these two non-polar surfaces,Fig. 2a furthermore shows two points worthy of special noticeand further discussion: (i) despite the large difference in theirrespective Es between GGA + U and LDA + U calculations, the uppervalue (i.e., the LDA + U result) of the (111) surface is notably smal-ler than the lower value (i.e., the GGA + U result) of the (110) sur-face; (ii) the Es of the (111) surface is insensitive to the thicknesswith steady values (0.045 eV/Å2 for GGA + U and 0.065 eV/Å2 forLDA + U), whereas for the (110) surface the evolution of Es as afunction of slab thickness shows an oscillating behavior, whichindicates excellent agreement between LDA + U and GGA + U.

For the DFT energetic studies of solid materials, it is well knownthat the GGA calculation usually underestimates the experimental

(a) (b)

Fig. 2. The surface energy Es as a function of the PuO2 slab thickness: (a) Erelaxs (solid sphere) of (111) surface, Erelax

s (solid square) and Eunrelaxs (open square) of the (110) surface

and (b) Erelaxs (solid sphere) and Eunrelax

s (open circle) of defect-(001) surfaces. Note that the slab thickness is defined by the number N of the Pu-cation layers. Four differentterminations of defect-(001) slabs in (b) are described in Fig. 1d.

142 B. Sun et al. / Journal of Nuclear Materials 426 (2012) 139–147

value and on the contrary the LDA often reports overestimatedresults for many physical quantities, amongst which the surfaceenergy is a typical one. These opposite deviations from the exper-imental measurement have been attributed to the ‘‘overbinding’’character of LDA and the consequent overcorrection of this defectin GGA [42,43]. However, we are more interested in comparingthe relative stabilities of different surfaces than in assessing thedifferent performances of LDA and GGA functionals, especially inthe absence of the experimental data. As far as we are aware, afew existing DFT calculations have given a similar trend in LDA-and GGA-Es results of metal oxides. For example, the LDA-Es resultsare 35% and 22% higher than the GGA results for CeO2(111) and(110) surfaces [46], respectively, while for MgO (001) surfacethe LDA-Es is 25.8% higher than the GGA-Es with the experimentalvalues positioned in between. Here, based on the above-mentionedpoint (i), we are positive that the experimental observation willagree on the prominent stability of the PuO2(111) surface.

We now turn our attention to the evolution with the slab thick-ness of the surface energies in Fig. 2a. As is known, for a certaincleaved surface, the consequent structural relaxation is an effectiveway to minimize the surface cleavage energy, corresponding to theEunrelax

s , with the contribution defined as the surface relaxation en-ergy DEs ¼ � Erelax

s � Eunrelaxs

� �. For (111) surface, the Eunrelax

s (notplotted here) is very close to the Erelax

s , producing a quite smallDEs less than 1.0 meV/Å2, and the thickness effect on the surfacerelaxation can be neglected. From Fig. 2a, one can see that theEunrelax

s of (110) surface is clearly larger than the correspondingErelax

s with their difference (DEs) being higher than 10 meV/Å2.Additionally, we find that the Eunrelax

s is to some extent insensitiveto the slab thickness, thus the oscillating behavior of Erelax

s is tiedup to the dependence of DEs upon the slab thickness.

In order to draw a clear comparison of the surface relaxation be-tween (111) and (110) surfaces and gain a detailed understandingof the oscillating behavior of (110)-Erelax

s , it proves to be quite nec-essary to discuss the surface structures undergoing full relaxations.Fig. 3a and b shows the interlayer relaxations along the directionsperpendicular to the (111) and (110) surfaces respectively. Herethe interlayer relaxation Di+1, i is given by the optimized interlayerdistance di+1, i in a relaxed slab compared to the bulk interlayer dis-tance d0

iþ1;i along the corresponding direction. Obviously, the signs+ and � of Di+1,i indicate expansion and contraction of the

interlayer spacing respectively. The stacking sequence of the(111) slab with N = 9 consists of 9 ‘‘O–Pu–O’’ blocks, and thereforethis (111) slab contains totally 27 atomic monolayers (MLs). Onecan see from Fig. 3a that the interlayer relaxations are really small,so that the shrinkage ratio of the thickness is only �0.25%. The(110) slabs used in Fig. 3b contain nine atomic MLs with two oxy-gen and one plutonium atoms per 1 � 1 cell being coplanar. Fig. 3bshows that (i) the interlayer relaxations in the (110) surface regionof a few atomic layers are prominently larger than those of the(111) surface in Fig. 3a; (ii) the interlayer relaxations of Pu sublat-tice are larger than the oxygen sublattice, which is especiallyapparent in the outmost two layers. Such mismatch of the relax-ations between O- and Pu-sublattices gives rise to the vertical dis-placement dPu–O between O and Pu atoms which are coplanar inthe unrelaxed (110) slab. Fig. 3c gives a sketch map of the dPu–O

in the surface and subsurface layers as a result of the mentionedmismatch: D2,1-Pu – D2,1-O. One can see that due to the nonzerodPu–O, cation–anion dipoles with inverse orientations are generatedin the surface and subsurface respectively. Strictly speaking, the re-laxed (110) surface is now not a non-polar surface for Pu and Ospecies. As we are aware, this observable surface polarization ofPuO2(110) slab induced by the structural relaxation is in goodagreement with previous DFT calculation [28]. Besides the inter-layer (vertical) relaxation, the inplane (lateral) relaxation of thesurface layer (see Fig. 4a) tends to shorten the Pu–O bond on thesurface by driving two nearest-neighbor oxygen atoms (bondingto the same Pu atom) to close up by �0.22 Å, leading to the forma-tion of O–O dimers on the (110) surface. Furthermore, we havefound that the vertical displacement dPu–O shows an oscillatingbehavior with the increasing slab thickness while the structure ofthe inplane O–O dimers is to some extent insensitive to the slabthickness. To reveal a clear-cut relationship between the structuralrelaxation and the corresponding released energy DEs, we plot thedPu–O (in both surface and subsurface) and DEs as functions of theslab thickness N in Fig. 3d. One can see that the oscillating behav-iors of dPu–O and DEs are quite in-phase, indicating that the oscilla-tions of Es of (110) surface as a function of slab thickness originatefrom the interlayer relaxation.

The ideal PuO2(001) surface (see Fig. 1c) is an unstable polarsurface with an overall dipole field. However, it is found that 50%surface O vacancies in our defective (001) slab models (see

(a)

(b)

(d)

(c)

Fig. 3. The interlayer relaxation Di+1,i of (a) the (111) slab and (b) (110) slab with N = 9. (c) Sketch map of the vertical displacement dPu–O in the surface and subsurface of therelaxed (110) slab due to the mismatch D2,1-Pu – D2,1-O. (d) The dPu–O in both surface and subsurface of (110) slab and the relaxation surface energy DEs as a function of theslab thickness.

Fig. 4. The top view of the surface structures of the relaxed: (a) (110) slab, and the defect-(001) slabs, (b) surf-1/surf-2 slabs and (c) surf-1/surf-2 slabs. The white arrows(not to scale) indicate the directions of the inpane lateral movements of the surface O atoms in (a) and of the subsurface Pu-atoms in (b).

B. Sun et al. / Journal of Nuclear Materials 426 (2012) 139–147 143

Fig. 1d) can effectively quench the dipole field and stabilize thesurface. Considering that a half oxygen vacancies can usually in-duce the significant surface reconstruction, here we first carryout the first-principles molecular dynamic (FPMD) simulationsbased on GGA + U within the micro-canonical ensemble to suffi-ciently optimize the defect-(001) surface structures and then cal-culate their zero-temperature surface energies. From the Es result(including Erelax

s and Eunrelaxs ) presented in Fig. 2b as a function of

the slab thickness N, one can see that with increasing N, the Erelaxs

for the four defect-(001) surface models converges to �0.11 eV/Å2, which is still notably larger than that of the (110) surface.Interestingly, according to the results of Erelax

s , surf-3 and surf-4slab models are a bit less stable than surf-1 and surf-2 in the wholerange of slab thickness that we considered. However, the values of

Eunrelaxs for surf-3 and surf-4 models are lower than those for surf-1

and surf-2 models mainly due to the two different distributions ofthe surface oxygen vacancies, namely, the missing-row and uni-form types in surf-1/surf-2 and surf-3/surf-4 respectively.

After the structural optimization by the FPMD simulations, forall four defect-(001) surface models with N = 8, the surface oxy-gens as well as the subsurface oxygens beneath relax inward by0.26 Å and 0.14 Å respectively, while the subsurface oxygens with-out surface oxygen above relax outward by �0.17 Å. For surf-1/surf-2, the Pu-sublattice relaxes inward by �0.02 Å, on the con-trary, the Pu-sublattice relaxes outwards by 0.05 Å for surf-3/surf-4. Accompanied with a slight discrepancy in vertical relax-ations of the Pu-sublattice for surf-1/surf-2 and surf-3/surf-4, it isfound that the difference in DEs for these two types of (001)

(a)

(b)

(c)

(d)

Fig. 5. The atom-projected (orbital resolved) DOS for (a) bulk PuO2, (b) (111)surface, (c) (110) surface, and (d) defect-(001) surface. The Fermi level is indicatedby the vertical dashed line at 0 eV.

144 B. Sun et al. / Journal of Nuclear Materials 426 (2012) 139–147

terminations is mainly caused by the distinguishing inplane (lat-eral) relaxations of subsurface Pu-sublattices, which are sketchedin Fig. 4b and c. For surf-1/surf-2, the Pu atoms bonding to thesame surface oxygen atom relax to close up by �0.45 Å and thisperiodic lattice distortion consequently provoke the zigzag mannerreconstruction of surface oxygen-lattice from the initial linearchain. Interestingly, this peculiar reconstruction was experimen-tally observed in the defective polar (001) surface of uraniumdioxide UO2 with 50% oxygen vacancies [44]. However, becauseof the uniform distribution of the surface O-vacancies, the Pu andO atoms in surf-3/surf-4 keep lateral inaction. For the defective(001) surfaces, our current results show that both the slab thick-ness and the distributions of the surface O-vacancies can notablyimpact the surface stability, and there may be several more stabi-lizing mechanisms coexisting on the polar (001) surface.

To briefly summarize our results in this section, we give the rel-ative order of stability for low-index PuO2 surfaces, namely,(111) > (110) > defect-(001) > polar-(001), which is well consis-tent with that of CeO2 [45,46] and UO2 [47], which are of the samefluorite structure as PuO2.

3.2. Surface electronic structure and work function

The bulk PuO2 is considered to be the AFM Mott insulatoraccording to the experimental report [13]. Here the atom-projecteddensity of the electronic states (PDOSs) for the Pu and oxygenatoms in the bulk PuO2 and on the relaxed (111), (110), and de-fect-(001) surfaces are shown in Fig. 5. Since the GGA + U andLDA + U give the similar description of the PDOS, here we only plotthe GGA + U results. The orbital-resolved PDOS of the bulk PuO2 atthe ground state has been calculated and analyzed in detail by pre-vious DFT + U [20,22,23,25] and hybrid DFT [9,17] studies, andthose theoretical results of DOS are usually tested by comparingwith the experimental photoelectron spectroscopy (PES) measure-ments [6,7].

Here, we replot the PDOS of the bulk PuO2 with AFM phase as abenchmark for those of the Pu–O atoms on different PuO2 surfaces,aiming at finding significant influence in the electronic structureby the inclusion of surface effect. The PDOS of bulk PuO2 inFig. 5a demonstrates the following features: (i) above the Fermi le-vel, the insulating band gap is about 1.8 eV, which is in good agree-ment with the experimental measurement [6]; (ii) below the Fermilevel the highest occupied band (HOB) with a range of �5 to 0 eV ismainly the 5f(Pu)-2p(O) hybridization, with little contributionsfrom 6p and 6d states of Pu; and (iii) the lower occupied band(LOB) with a range of �21 to �13 eV consists of Pu-6p and O-2sstates.

From the surface DOS in Fig. 5, one can see that the PDOS distri-bution for the (111) surface shows a close resemblance to the caseof the bulk PuO2, specifically, the similarities in the insulating bandgap and the structures of Pu-5f state with two pronounced peaksare so strong that the slight contraction and shift-up of the HOBare almost covered up. For the (110) surface, the insulating bandgap reduces to �1.6 eV, and particularly, the two-peak structureof Pu-5f disappears mainly due to the existing surface polarizationwith nonzero dPu–O, which modifies the crystal symmetry of theoxide surface layer. For the (001) surface, since the surface layerof surf-1 slab model used in Fig. 5d is not the stoichiometricPuO2 but the ‘Pu–O’, the insulating band gap further reduces to�1.4 eV, and a sharp peak of Pu-5f state emerges below the Fermilevel, which implies the increase in the localized correlation of thePu-5f electronic state due to the presence of oxygen vacancies.These facts suggest that the surface effect of PuO2 upon the elec-tronic structure of the bulk phase appears to be insignificant forthe stable (111) surface, to some extent significant for the (110)surface, and remarkable for the defect-(001) surface. In order to

be able to theoretically reproduce the whole PES spectra of PuO2

layers by the right description of the complex behavior of Pu-5fstate, there is clearly much left to be done.

In addition to the PDOS, we have also calculated the work func-tion U of low-index PuO2 surfaces, and plotted them in Fig. 6. Thework function U is the minimum energy required to remove anelectron from the surface to the vacuum and can be written asU = Vvacuum � EF, where Vvacuum is the planar-averaged electrostaticpotential in the middle of the vacuum and EF is the Fermi energy ofthe system. Therefore, work function is one fundamental physicalquantity for the surface reactivity. Furthermore, a modified or tun-able U can be useful for applications such as catalysis, because aslight change in the energy scale is exponentially amplified forchemical reactions.

From Fig. 6a, one can see that the U of stable (111) surface withan average value of �6.1 eV (GGA + U) or �6.3 eV (LDA + U) ismuch higher than that of the (110) surface with an average valueof �4.7 eV (GGA + U) or �4.8 eV (LDA + U). Thus, for non-polar sur-faces, stable (111) surface will show its inertness in the surfacechemical reactions, and the more open (110) surface is expectedto be chemically active. Fig. 6a also demonstrates the convergencebehavior of U as a function of the slab thickness. Here, it is foundthat the GGA + U and LDA + U results of U are in general agree-ment. For the stable (111) surface, the work function shows less

(a) (b)

Fig. 6. The calculated work function U as a function of the slab thickness: (a) PuO2(111) and (110) surfaces, (b) the ideal (001) and the four defect-(001) surfaces.

Table 1The calculated work function U (in eV) of PuO2(111), (110) and (001) surfaces.

CV = 0 CV = 1/9 CV = 1/4 CV = 1/2 CV = 3/4 CV = 1

(111): On-surface 6.19 5.09 4.35 4.07 – –(111): Subsurface 6.19 5.36 5.18 4.87 4.49 2.57(110): On-surface 4.70 – 3.84 3.57 2.80 2.44(001): On-surface 7.93 – 7.24 6.63 4.68 3.25

B. Sun et al. / Journal of Nuclear Materials 426 (2012) 139–147 145

responsiveness to the thickness effect, as well as its surface energyEs in Fig. 2a. On the contrary, both U and Es of the (110) surface aresensitive to the slab thickness with a convergent oscillation. Com-bining with the surface relaxation results given in Fig. 3d, one canconclude that the thickness effect modifies both the surface stabil-ity and surface chemical activity through the structural relaxations.Usually, the thickness of the oxide film formed on Pu metal duringstockpile process is typically of nanometer scale. Thus, our presentfinding of thickness-selective surface activity may help to deepenthe understanding of the microscopic mechanisms for the chemicalreaction of small molecules (such as water) on oxidized Pu sur-faces, which is fundamental to the safety issue of nuclear industry.Interestingly, a recent DFT study [48] has reported that the thick-ness effect of MgO film can be used to control the dissociation ofwater molecule on surface.

For the case of the polar (001) surface shown in Fig. 5b, thework function is mainly dominated by the strength of the anion-cation dipole, which impedes the escape of electrons. Therefore,one can see that the work function of the ideal (001) surface isclose to 8 eV, which is much higher than that of the defect-(001)surfaces with an average value of �6.4 eV. Due to the significantinfluence of the existing dipole on the (001) surface, it is not rea-sonable to compare its surface chemical activity with ideal (110)or (111) non-polar surface merely via the surface work function.

3.3. Effect of oxygen vacancy

In this section, we focus on the effect of O-vacancy with variousconcentrations upon the surface activity and surface relative sta-bility by using the static GGA + U calculation and the approach of‘‘ab initio atomistic thermodynamics’’. Here, our current study ismainly driven by the following motivations: (i) to explain the dif-ference in the surface chemical activity between PuO2 and a-Pu2

O3, as mentioned in Section 1; (ii) to discuss the mechanism of cre-ating surface oxygen-vacancy in the cancelation of the polarity forPuO2(001) surface; and (iii) to explore the stable surface phase ofPuO2 in an oxidizing environment. Amongst these listed issues, theO-vacancy is obviously the major factor.

In the calculation, to eliminate the thickness effect of the PuO2

slab, we employ (111), (110), and (001) slabs with N = 6, 8, and 8respectively. The various concentrations of oxygen vacancy (CV) aremodeled by removing different amounts of oxygen atoms from

ideal slabs with a series of surface unit cells. Here, CV is the ratiobetween the number of O-vacancies and the total number of Oatoms on the ideal surface layer. Specifically, for the (111) surface,slabs of (2 � 2) and (3 � 3) unit cells are employed to create CV of19 ;

14 ;

12 ;

34 ;

89, and 1.0. For the (110) surface, slab of (1 � 2) unit cells is

used to create CV of 14 ;

12 ;

34, and 1.0. For the (001) surface, slab of

ðffiffiffi2p�

ffiffiffi2pÞR45� unit cells can create CV of 1

4 ;12 ;

34, and 1.0.

Before the discussion on the evolution of work function as afunction of CV, we first present the O-vacancy effect upon the struc-tural relaxation of the (111) slab. The static calculation demon-strates that the (111) surface with on-surface O-vacancy isslightly preferred in total energy when CV 6 1/2. However, when1/2 < CV 6 1, the subsurface oxygen atoms, each of which sharingthe same unit surface cell with one certain surface oxygen, willbreak through the above Pu-terminated layer to form a completeO-terminated surface, leaving the subsurface O-vacancies at theirformer sites. Therefore, when CV > 1/2, all the on-surface O-vacan-cies will convert to be the subsurface O-vacancies by a significantreconstruction.

The GGA + U calculated work function U of (111), (110), and(001) surfaces for different values of CV is listed in Table 1, wherethe ‘‘on-surface’’ and the ‘‘subsurface’’ denote the initial pure on-surface and subsurface distributions of O-vacancies for the (111)surface. One can see from Table 1 that for all three surfaces thework function will monotonically reduce with increasing CV.Therefore, the introduction of O-vacancy can prominently enhancethe surface chemical activity of non-polar (111) and (110) sur-faces. For instance, the work function of the ideal (111) surfaceis 6.19 eV, while a low CV = 1/9(1/4) of on-surface O-vacancy caneffectively depress the work function by 1.1 (1.84) eV and effi-ciently amplify the probability of the chemical reaction betweenthe PuO2(111) surface and other small gaseous molecules suchas H2 and H2O, which will be investigated in our next work. This

146 B. Sun et al. / Journal of Nuclear Materials 426 (2012) 139–147

result can be also extended to explain the significant difference inthe chemical activities between PuO2 and a-Pu2O3, the latter hasbeen found in experiment [8] to be more active in interacting withsmall molecules.

Assuming that the PuO2 surface is in equilibrium with an exter-nal oxygen environment and translating the oxygen chemical po-tential into temperature and pressure conditions according toEqs. (3) and (4) respectively, we first discuss effect of the O-va-cancy upon the relative stability of one certain surface. Fig. 7a–cpresent the Gibbs surface free energy difference Dc of (111),(110) and (001) surfaces respectively. Here the Dc is calculatedby Eq. (3) with the corresponding ideal surface as the referencesystem. For the (111) surface, from Fig. 7a one can see that (i)the ideal, vacancy-free (111) surface is the most stable structureunder the oxygen rich conditions with DlO P �2.49 eV; (ii) thendefect-(111) surface with on-surface O-vacancy of CV = 1/9 be-comes stable within a very narrow range of�2.63 6DlO < �2.49 eV; (iii) for further reducing environmentwith DlO 6 �2.63 eV, the defect-(111) surface with subsurfaceO-vacancy of high CV = 8/9 becomes the most stable.

For the (110) surface, Fig. 7b shows that (i) the ideal (110) sur-face is most stable within the range of the DlO P �1.96 eV; (ii) thedefect surface with CV = 1/4 becomes most stable within�2.54 6DlO < �1.96 eV; (iii) the defect surface with CV = 1/2 insuccession becomes most stable when �2.93 6DlO < �2.54 eV;and (iv) the defect surface with CV = 3/4 becomes most stable when�3.50 6 DlO < �2.93 eV, and the Pu-terminated (110) surfacewith CV = 1 is not a stable surface phase in the whole range ofthe allowed DlO.

(a)

(c)

Fig. 7. Surface free energy difference Dc of (a) PuO2(111), (b) (110) and (c) (001) surfacpotential DlO, with the corresponding pressure lines at T = 300 K and T = 600 K. The lowgathered in (d) with the ideal (111) surface as the reference configuration.

From the results of polar-(001) surface in Fig. 7c, we have foundthat (i) under the O-rich conditions, the ideal (001) surface is unsta-ble, however the 50% surface O-vacancies can efficiently stabilize thepolar surface; (ii) when DlO 6 �1.69 eV, the defect-(001) surfacewith CV = 3/4 is the optimal surface structure; and (iii) within thewhole allowed range of DlO, the Pu-terminated (001) surface isunstable so as the vacancy-free O-terminated (001) surface.

We collect all the stable surface phases from Fig. 7a–c, and sum-marize them in Fig. 7d by taking the ideal (111) surface as the ref-erence structure. One can see that the ideal (111) surface, defect-(111) surface with low on-surface O-vacancy concentration ofCV = 1/9 and with high sub-surface CV = 8/9 are the stable surfacestructures. That is to say, the ideal (111) surface is stable underthe oxygen-rich conditions, while for an oxygen-reducing environ-ment the (111) surface with nearly one monolayer subsurface oxy-gen removed become stable, and the on-surface oxygen vacancywith low CV of 1/9 can minimize the Gibbs surface energy in a verynarrow range of DlO.

In Table 2, we have listed the O-vacancy formation energies EV,

which can be defined as Ev ¼ 1NO—V

Edefectslab � Eideal

slab þ NO—V � 12 EO2

h i,

where NO–V is the total number of the O-vacancy in a defective slab,

Edefectslab ; Eideal

slab and EO2 are the total energies of the defective slab, idealslab and a free oxygen molecule, respectively. One can see for the(111) surface that the EV does not show considerable change ex-cept in the extreme case of CV = 1 with a maximum valueEV = 3.20 eV. On the contrary, the EV of the (110) surface is sensi-tive to the CV, namely, the EV monotonically increases with increas-ing CV, indicating a notable interaction between the vacancies.

(b)

(d)

es with various concentrations of O-vacancy Cv as a function of the oxygen chemical-energy surface terminations are drawn with the thick lines in (a)–(c), which are

Table 2The calculated formation energy of the O-vacancy Ev (in eV/atom).

CV = 1/9

CV = 1/4

CV = 1/2

CV = 3/4

CV = 8/9

CV = 1

(111): On-surface

2.49 2.85 2.83 – – –

(111):Subsurface

2.54 2.89 2.87 2.63 2.63 3.20

(110): On-surface

– 1.96 2.54 2.93 – 3.50

(001): On-surface

– �3.38 �1.93 �0.73 – 1.11

B. Sun et al. / Journal of Nuclear Materials 426 (2012) 139–147 147

Finally, the polar (001) surface is a special case. The minus EV indi-cates that the formation of surface O-vacancy is an exothermic pro-cess, and at the same time stabilizes the polar surface. However theEV also monotonically increases with the CV and rises to +1.11 eVwhen CV = 1.

4. Conclusions

To conclude, we have systematically studied the basic surfaceproperties of low-index PuO2(111), (110), and (001) surface bymeans of the first-principles DFT calculations within the LDA + Uand GGA + U frameworks. The defect-free O-terminated (111) sur-face is found to be most stable, possessing the lowest Es that isinsensitive to the thickness of the film. The surface energy of thenon-polar (110) surface is 33–42% higher than that of the (111)surface, accompanying with an oscillating behavior with the filmthickness. The polar (001) surface has been modeled using 50%oxygen vacancies to cancel the polarity. The residual surface oxy-gen atoms have been found to reconstruct in a zigzag manneralong the h100i direction. In connected with the relative order ofstability for these three low-index surfaces, our calculated surfaceelectronic structures have displayed from insignificant to remark-able deviation from the bulk case. The work function U has alsobeen systematically investigated, and a high value of about6.19 eV for the most stable (111) surface indicates its low chemicalactivity. Remarkably, this value can be reduced to 4.35 eV with 25%oxygen-vacancy present on the surface. This conclusion can beused to explain the difference in the surface chemical activities be-tween PuO2 and a-Pu2O3.

We have also investigated the surface thermodynamics in anoxygen environment. Our results have indicated that under oxy-gen-rich conditions, the stoichiometric (111) surface is most sta-ble. Under oxygen-reducing conditions, the on-surface O-vacancyof low concentration CV = 1/9 can slightly minimize the Gibbs sur-face energy c of (111) in a narrow range of the oxygen chemicalpotential DlO. For the highly reducing conditions, the (111) sur-face with nearly one monolayer subsurface oxygen removed(CV = 8/9) becomes most stable, where the upper layers resemblethe b-Pu2O3(0001) surface. Based on these systematic results, ourcurrent study may provide a guiding line to understand variouschemical properties and processes occurred on PuO2 surfaces.

Acknowledgments

This work was supported by NSFC under Grant No. 51071032,and by the Foundations for Development of Science and Technol-ogy of China Academy of Engineering Physics under Grant Nos.2010B0301048 and 2011A0301016.

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