Density-functional theory investigation of oxidative corrosion of UO2

Computational and Theoretical Chemistry 987 (2012) 90–102

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Density-functional theory investigation of oxidative corrosion of UO2 Anne M. Chaka a,⇑, Gloria A.E. Oxford a, Joanne E. Stubbs b, Peter J. Eng b, John R. Bargar c a

Physical Measurement Laboratory, National Institute of Standards and Technology, Gaithersburg, MD 20899, USA Consortium for Advanced Radiation Sources, The University of Chicago, Chicago, IL 60637, USA c Stanford Synchrotron Radiation Lightsource, Menlo Park, CA 94025, USA b

a r t i c l e

i n f o

Article history: Received 23 June 2011 Accepted 17 November 2011 Available online 26 November 2011 Keywords: Uranium dioxide Density functional theory Ab initio thermodynamics Oxidation Corrosion Surface

a b s t r a c t Corrosion and weathering of uranium dioxide (UO2) is a serious concern in a broad range of technological and environmental systems. Oxidation of UO2 can compromise the integrity of nuclear fuel rods, as well as result in the bioavailability of uranium in contaminated ground water at mines, mills, and nuclear waste storage facilities. How the oxidation proceeds, however, is not well understood. In this work, density-functional theory and ab initio thermodynamics are used to delineate the initial stages of surface and subsurface oxidation of UO2 at the (1 1 1) surface as a function of temperature and oxygen pressure. Initially, chemisorption of oxygen on the clean stoichiometric surface results in formation of highly stable triple-bonded uranyl groups and oxidation of the topmost uranium atoms to U6+ at a minimal p(O2) near 0 K. Once the surface is saturated with uranyl groups and the oxygen chemical potential increases above 1.0 eV, subsurface oxidation becomes thermodynamically favored. The degree of oxidation of the subsurface uranium atoms is determined by quantifying the transfer of electrons from the localized U 5f bands to those dominated by the delocalized O 2p bands as oxygen atoms occupy octahedral interstitial sites in the UO2 lattice. Occupation of the octahedral site nearest the surface results in an expansion of the lattice, whereas movement of the oxygen interstitial to deeper sites results in a net contraction. Ó 2011 Published by Elsevier B.V.

1. Introduction Corrosion and weathering of uranium dioxide (UO2) is a serious concern in a broad range of technological and environmental systems. Uranium dioxide, also known as uraninite, is a key material for the nuclear power industry and weapons systems, as it constitutes the most common component of nuclear fuel rods and is a corrosion product of depleted uranium (DU) penetrators used in munition systems. Corrosion can compromise the integrity of fuel rods in a reactor or in nuclear waste storage facilities, as the volume of oxidized UO2 can expand by as much as 38% [1–4]. Oxidation of uranium oxide fuel is also the primary loss mechanism for uranium and transuranium actinides to the environment from spent fuel matrices. In recent conflicts in the Persian Gulf and the Balkans where DU was widely used, submicron to micron-sized particles consisting primarily of uranium dioxide were found in sand, soil, and on the surface of targets, thus representing an environmental and respiratory hazard [5]. Uraninite nanoparticles, precipitated by bacteria, are also of intense interest as a means to stabilize uranium in contaminated aquifers [6,7]. Oxidative corrosion and weathering can occur when UO2 is exposed to air or radiolytic oxidants such as H2O2, OH, or HO2, leading to degradation of the material and release into the environment [4,8–12]. ⇑ Corresponding author. Tel.: +1 301 975 2481; fax: +1 301 975 6991. E-mail address: [email protected] (A.M. Chaka). 2210-271X/$ - see front matter Ó 2011 Published by Elsevier B.V. doi:10.1016/j.comptc.2011.11.028

Bioremediation efforts for uranium-contaminated groundwater focus on UO2 nanoparticles as a biogenic product, so understanding long-term stability in the environment is critically important [6]. In this work we present the results of electronic structure calculations and an ab initio thermodynamics framework to delineate the initial stages of UO2 surface and subsurface oxidation as a function of temperature and oxygen partial pressure pO2. Uranium exhibits a rich redox chemistry, with oxidation states ranging from 3+ to 6+. Nonstoichiometry for uranium oxides is more common than stoichiometry, with the UO2 lattice capable of adsorbing at least 10% oxygen interstitially to form UO2.25 with a concomitant decrease in the lattice parameter of approximately 0.5% [13]. UO2 has an open cubic fluorite structure in the space group Fm3m shown in Fig. 1, with a face-centered cubic arrangement of uranium atoms enclosing a cubic arrangement of oxygen atoms [14]. Uranium atoms exhibit 8-fold coordination and oxygen 4-fold tetrahedral coordination. The fluorite lattice is characterized by four large interstitial vacancies for each unit cell at (0.5, 0, 0), (0, 0.5, 0), (0, 0, 0.5), and (0.5, 0.5, 0.5). These are often referred to as ‘‘octahedral holes’’ because they are surrounded by six uranium atoms in a slightly distorted octahedral arrangement, even though the cubic cage of eight oxygen atoms is closer. Both temperature and oxygen partial pressure p(O2) have been shown to play a critical role in the oxidation of UO2 [2–5,11,13,15– 24]. Early experiments indicated that oxygen becomes mobile in the interior of the UO2 lattice above approximately 343 K, and that

A.M. Chaka et al. / Computational and Theoretical Chemistry 987 (2012) 90–102

Fig. 1. Magnetic structure of UO2. Uranium and oxygen atoms are in blue (smaller) and red (larger), respectively. The lines do not represent chemical bonds. In the 3k structure, the moments lie along h1 1 1i [73,78]. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

single layer chemisorption occurs at temperatures above about 173 K although the nature of the adsorbed oxygen species could not be determined [13,15,16,18,25]. Theoretical calculations [26– 30] have supported the experimental evidence that oxygen interstitials are reasonably mobile within the bulk UO2 lattice. Experimental and computational investigations of oxygen transport in bulk UO2 by Dorato and coworkers are consistent with an interstitial hopping mechanism; the calculated activation barrier of 0.88 eV compared favorably with the most recently measured experimental diffusion activation barrier of 0.75 ± 0.08 eV [27]. Within the temperature range of 173–343 K it has been established that the rate of bulk oxidation of UO2 is proportional to the oxygen pressure [18]. Experiments on UO2 single crystals under oxidative conditions [2,3,11,18,20–23] and on micron-sized UO2 particles examined in Kuwait and Kosovo [5] provide evidence of complicated transformations as oxygen is incorporated into the lattice. Incorporation and clustering of subsurface interstitial oxygen atoms has been proposed as a key mechanism for the ultimate breakdown, cracking, and spallation of the UO2 surface, but is not well understood [2,12]. In recent years there have been several investigations into bulk defects of stoichiometric UO2 using density-functional theory (DFT) [31–43]. With the exception of the GGA + U method (generalized gradient approximation plus Hubbard correction U, see Section 2.2) and at least one hybrid functional [32], the formation energy of a single oxygen insertion into the central octahedral interstitial in bulk UO2 has been calculated to be highly favorable, with DFT values ranging from 2.9 eV to 1.34 eV depending on the type of functional and core electron treatment [33,34,36,38,41]. (It should be noted that the GGA + U method, and at least one of the hybrid functionals, which improve the description of the band structure and insulating nature of UO2, unfortunately yield an endothermic value for the oxygen interstitial formation energy that is not consistent with experimental observations of exothermic oxygen absorption.) Geng and coworkers used the local spin-density approximation plus the Hubbard correction (LSDA + U) method to examine ‘‘clustering’’ of oxygen interstitials in bulk UO2 by creating supercells with adjacent cells filled or vacant, so that closest OAO interstitial distances were a lattice vector (5.445 Å) apart [38]. Single oxygen interstitials were placed in the center of every fluorite 1  1  1 conventional lattice with an energy of 1.39 eV, which is slightly higher than the formation energy of (1.64 eV)

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for placing a single O2 molecule into a 2  2  1 supercell. To our knowledge no one has yet investigated the energetics, redox behavior, and interactions of oxygen occupying any of the three octahedral interstitial locations in addition to the central site, and none in a subsurface context. In the absence of water, the most stable surface of UO2 is the (1 1 1); the structure of the clean surface has been the subject of several experimental investigations [2,44–51]. The natural cleavage plane for the fluorite structure is between the oxygen layers separating OAUAO stoichiometric units, which generates a nonpolar, three-coordinate oxygen termination. The topmost uranium atoms just below the first layer of oxygen atoms exhibit 7-fold coordination. The OAUAO layers continue into the bulk with a spacing of 3.157 Å. Early low-energy electron diffraction (LEED) experiments by Ellis and coworkers observed that the 1  1 UO2 (1 1 1) surface diffraction pattern is consistent with atoms in their unmodified bulk positions [44,52]. Ellis and Taylor observed an oxygen termination with O atoms in positions consistent with the bulk sequence using low-energy He+ ion scattering spectroscopy and low-energy electron diffraction [47,48]. Castell and coworkers used high temperature scanning tunneling microscopy, Auger electron spectroscopy, and LEED analysis to determine that the UO2 (1 1 1) surface forms clean, well-ordered 1  1 surfaces with minimal relaxation upon cleavage [50,53]. Rutherford backscattering experiments have indicated an outward relaxation of 0.19 ± 0.01 Å of the uranium cations [45]. The stability and reactivity of the UO2 (1 1 1) surface with respect to water and molecular oxygen has been explored using computational methods based on empirical pair potentials [54–58] and DFT calculations [58–62]. The empirical methods have been consistent with the trends established by more accurate quantum-mechanical calculations for the relative ordering of the clean and hydroxylated surfaces [55–58,61]. Boettger and Ray used spin-polarized GGA scalar relativistic calculations to examine the role of 5f electrons in the bonding of the lattice and in the surface chemistry with respect to dissociation of water [61]. Density of states (DOS) analysis using non-spin polarized calculations of a dissociated water monolayer on the (1 1 1) UO2 surface indicated no participation of the uranium f electrons, despite the metallic character obtained for their GGA calculation; hence the authors concluded that f electrons do not appear to serve as a reservoir for donating and accepting electrons from adsorbates and thus do not significantly impact the surface chemistry. Adsorption energy for one dissociated water molecule was calculated to be 1 eV. Skomurski and coworkers utilized a plane-wave pseudopotential method and spin-polarized GGA (PW91) on two-layer ferromagnetic slabs to determine that molecular water was more stable than dissociated water, and that water accelerated the oxidation of surface uranium atoms by adsorption of atomic oxygen. Adsorption of oxygen onto the UO2 (1 1 1) surface was first considered theoretically by Skomurski and coworkers, where they examined atomic and molecular oxygen located atop surface uranium atoms, and co-adsorption energies with dissociated and physisorbed water on two-layer slabs [62]. In this work we term the chemical entity of atomic oxygen absorbed onto a surface uranium atom as a ‘‘uranyl group’’ with a triple U„O bond. The term is analogous to double bonded oxygen-transition metal groups such as ferryl, chromyl, and vanadyl, and distinct from the water-soluble uranyl molecular cation [O„U„O]+2. The atomistic details and energetics of the initial subsurface oxidation of UO2 have remained elusive, as individual oxygen atoms that migrate below the surface in a random fashion are very difficult to detect experimentally but are ideally suited for investigation by atomistic simulation. In this work we investigate how the most stable UO2 surface – the (1 1 1) – absorbs oxygen. Of particular interest is to determine how readily uranium in UO2 can be

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oxidized from its 4+ state to 5+ and eventually the 6+ state, from which at alkaline pH it can readily form the (UO2)2+ uranyl molecular cation or carbonate complexes that are water soluble, highly mobile, and easily absorbed biologically [6,7]. We will also present a detailed analysis of the electronic structure and bonding and how it changes during the oxidation process caused by absorption of subsurface oxygen. 2. Computational methodology 2.1. Bulk structure From a theoretical perspective, the strongly correlated electrons and relativistic effects of uranium oxides continue to present a challenge. The ground state of the uranium atom is 5f36d17s2, and in UO2 it is 5f2. Over the past decade, GGA with relativistic pseudopotentials has been shown to provide an accurate description of the crystal structure, cohesive energy, and bulk modulus for uranium and other early actinides[34,60,63–66] and their oxides [34,35,58,61], which constituted a significant improvement over LDA [34]. Inclusion of spin-orbit coupling has been demonstrated to have a negligible impact on the structural ground state and elastic properties of a-uranium [63], on the band gap of UO2[67], or on the structure and cohesive properties of the UO2 hydroxylated surface [61]. 2.2. Magnetism and conductivity Although GGA provides a good description of the bonding in uranium dioxide as evidenced by structure, bulk moduli, and relative surface energies, certain aspects of the electronic structure have remained challenging. UO2 is a semi-conductor with a band gap on the order of 2–2.7 eV [68–71], and an antiferromagnetic (AFM) ground state [72–78] with a Néel temperature of 30.8 K [14,69,72]. It has a noncollinear 3k magnetic structure with the moments oriented along the h1 1 1i directions of the cubic unit cell, shown in Fig. 1 [73,75]. The 5f2 bands are isolated in the middle of a 5–6 eV p–d gap between the valence and conduction bands [70,79]. GGA in previous work, however, has predicted that UO2 is a metal with a ferromagnetic (FM) ground state [33,34,66]. Many approaches have been utilized to address these issues, including hybrid functionals and the self-interaction correction [67,80–85]. In recent years, the most widely utilized approach has been to add a Coulombic correction (DFT + U) to improve the localized description of the f electrons and produce a more accurate calculation of the band gap, magnetic state, and photoemission spectra [26,27,34,36,37,40,42,53,86,87]. Using the DFT + U formalism requires imposing the presence of U5+ or U3+ cations in studying defects and careful control of 5f occupation matrices to avoid being trapped in a metastable minimum, which can be several eVs above the ground state [26,27,34,42]. There is some concern, however, as to how well the DFT + U approach describes absorption of oxygen interstitials that underlies oxidative corrosion, which is the focus of this work. Dorato and coworkers found that using GGA + U adsorption of a single oxygen atom into a 97-atom UO2 supercell (UO2.031) is endothermic by 0.10 eV [27]. Reoptimization of the lattice constants after addition of the oxygen interstitial resulted in a lowering of the oxygen interstitial formation energy to a slightly exothermic value of 0.05 eV [26]. These high oxygen interstitial formation energies are not consistent with the experimental observations that UO2 can absorb up to 10% oxygen with only a minimal change in lattice volume [13], and readily achieves hyperstoichiometry up to UO2.25. GGA, in contrast, yields an oxygen interstitial formation energy of 2.5 eV in a 24 atom supercell which is consistent with the known proclivity of UO2 to absorb oxygen. The oxygen interstitial energy found by

Freyss et al. for a 12-atom super was slightly lower at 2.6 eV, indicating the OAO interstitial repulsion at these distances is well-screened by the highly charged uranium cations [34]. It may be that the U term that is optimized to yield the correct band gap in DFT + U methods over-emphasizes Coulombic repulsions between electrons and thus raises the formation energy for anionic interstitials such as oxygen. The recently developed local hybrid functional on correlated electron method (LHFCE) provides an improved description of the band gap and magnetic ground state of UO2 over GGA [32,85], but appears to exhibit some of the same issues as DFT + U with respect to the formation energy of oxygen interstitials. Calculation of a phase diagram of bulk UO2 as a function of p(O2) using LHFCE by Crocombette and coworkers found that the oxygen interstitial formation energy was so high, the only way to achieve hyperstoichiometric UO2+x was to introduce uranium vacancies [32]. We tested the generalized gradient approximation (GGA) of Perdew, Burke, and Ernzerhof [88] as implemented in DMol3 using atom-centered numerical basis sets with relativistic effective core potentials for uranium and all-electron treatment of oxygen atoms [89–93]. The valence electrons explicitly treated in the double numeric (analogous to double zeta) plus polarization (dnp–ecp) uranium basis set consist of 5spdf, 6spd, and 7sp, which includes polarization functions for 5f and 6d electrons. A real-space cutoff of 5.1 Å was utilized for basis functions on both uranium and oxygen atoms. The optimized lattice constant (5.459 Å) was within 0.2% of the experimental value of 5.47 Å [14]. In contrast to previous theoretical work but consistent with experiment, the 3k AFM electronic state was found to be the ground state, followed by the 2k layered structure, the 1k, and then the FM state. As shown in Table 1, the 3k AFM ground state exhibits a small bandgap of 0.38 eV, which decreases with lower order magnetic states. The FM ground state was indeed a metal, but 0.43 eV higher in energy per UO2 formula unit. Hence in view of all these factors – good GGA results for bulk structural and cohesive properties, unphysical formation energy for oxygen interstitials and difficulty achieving selfconsistent field convergence to the ground state with GGA + U, and correct magnetic ground state and finite (albeit small) bandgap using the implementation of GGA (PBE), core potentials, and numerical basis sets in DMol3 – we have utilized the GGA approach throughout this study. 2.3. Surface models For surface models it is desirable that the surface energy for clean surfaces is converged with respect to slab thickness. Skomurski and coworkers tested (1 1 1) surface energy versus slab thickness from 2 to 6 FM UO2 layers using GGA (PW91) [94,95], and did not find convergence; the surface energy decreased by approximately half, from 37 meV/Å2 to 17 meV/Å2 (0.6 J/m2 to 0.3 J/m2) [58]. To test for surface energy convergence for both FM and AFM, slabs consisting of 5–11 UO2 layers (15–33 atomic layers with an OAUAO sequence) were constructed maintaining only inversion symmetry. All atoms were free to relax using 8  8  1 k-point sampling. More than 50 Å of vacuum was maintained between the slabs in all cases. Given the computational limitations of the 3k AFM structure which requires a 2  2  2 super Table 1 Calculated magnetic configurations and band gaps. Magnetic configuration

DE (eV) per UO2

Band gap (eV)

AFM 3k AFM 2k AFM 1k FM

0.0 +0.17 +0.36 +0.43

0.38 0.18 0.09 Metal

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cell, we tested only the 1k AFM structure on 1  1 surface unit cells, with the spins on uranium atoms alternating in layers parallel to the (1 1 1) surface. The slab thickness test results are shown in Table 2. The surface energy for the 1k AFM slab is converged already at five layers. The surface exhibits conducting states which are confined to the surface and do not delocalize over the bulk of the slab. The surface energy for the FM slab required nine layers to converge, with the surface energy decreasing significantly from 50.0 meV/Å2 to 41.8 meV/Å2 as the slab thickness increases from 5 to 11 UO2 layers, respectively. The metallic electronic structure of the FM slab enables the surface states to interact with the bulk and hence are more sensitive to slab thickness. The relaxations values for the 1k AFM and FM stoichiometric and uranyl-terminated 7-layer slabs are shown in Table 3. For the clean surfaces, there is negligible relaxation of the (1 1 1) surfaces, which is consistent with Skomurski and coworkers [62]. The 7-layer 1k AFM slab model is used for all subsequent oxidation calculations. 2.4. Ab initio thermodynamics‘ The theory of ab initio thermodynamics has been presented in detail elsewhere [96–98]. Here, we summarize the theory in the context of the UO2 system. The surface free energy c is defined based on the assumption that the two equivalent surfaces of the slab are in equilibrium with the bulk oxide and an oxygen reservoir at constant temperature and pressure.

( ) X 1 Gslab ðT; p; Ni Þ  cðT; pÞ ¼ Ni li ðT; pÞ 2A i

ð1Þ

where A is the surface area, Gslab is Gibbs free energy of the slab, and Ni and li are the number and chemical potential of atom type i, respectively. The Gibbs free energy of the slab is simply equal to the sum of the DFT total energy of the slab at 0 K Eslab,0K and the vibrational energy contributions at finite temperature DGvib. The chemical potentials of uranium and oxygen, lU and lO, respectively, are determined from the Gibbs free energy of the components of the system.

lU þ 2lO ¼

Gbulk UO2

ð2Þ

1 2

lO ¼ Ggas O2

ð3Þ

In these equations, Gbulk UO2 is the Gibbs free energy of bulk UO2, and Ggas O2 is the Gibbs free energy of gas-phase oxygen. Eq. (1) then becomes

cðT; pÞ ¼

o 1 n Eslab;0K þ DGvib  NU Gbulk UO2 ðT; pÞ þ ð2N U  N O ÞlO ðT; pÞ ; 2A ð4Þ

Reuter and Scheffler demonstrated that for RuO2, the difference between vibrational energy contributions to DGvib and Gbulk is no more than 10 meV/Å2 below 1000 K [97]. This contribution to c Table 2 Surface energies as a function of slab thickness (meV/Å2).

a

Number of UO2 units in slab

FMa

FM

AFM

2 3 4 5 6 7 9 11

36.8 31.8 28.7 20.6 16.9 – – –

– – – 50.0 50.8 45.8 41.6 41.8

– – – 55.4 57.8 55.4 62.8 56.0

Ref. [58].

is expected to be even smaller for the clean UO2 surface due to the mass of uranium. However, the uranyl-terminated surface does not have a counter part in the bulk and may have larger vibrational energy than the clean surface so that DGvib and Gbulk UO2 may not effectively cancel. Including the entropy from the calculated vibrational frequency of 1081 cm1 for the U„O stretch of the UO2þ 2 ion lowered c by less than 8 meV/Å2 at 1000 K. Therefore, cancellation of DGvib and Gbulk UO2 is a reasonable approximation that was used in this work. The vibrational energy contributions to lO were calculated using experimental data from the NIST–JANAF tables [99] for the temperature dependence and the following equation for the pressure dependence,

1 2

lO ðT; pÞ ¼ lO ðT; p Þ þ kT ln

  p p

ð5Þ

where p° is the standard state pressure. We are interested in UO2 surface and subsurface oxidation as a function of temperature and oxygen partial pressure pO2, and the range of lO that is investigated has explicit physical limits. The maximum oxygen concentration lO,max consists of condensed O2 at the surface at 0 K. Ignoring the extremely weak intermolecular interactions between condensed oxygen molecules, lO,max is effectively defined by the Gibbs free energy of the O2 molecule in Eq. (3) above. The minimum oxygen chemical potential depends on the heat of formation of the oxide, and is defined by the point where all the oxygen is bound in the oxide and none exists in the gas phase above the surface. Going below lO,min would result in uranium metal forming on the surface as oxygen is removed from the lattice. Hence

lO;min ¼

 1  bulk GUO2  Gbulk U 2

ð6Þ

where Gbulk is the Gibbs free energy of bulk uranium metal. This U quantity was calculated for a-uranium using GGA optimized lattice constants from the literature [63] and a 9  4  5 k-point grid. The range of accessible lO values is rescaled so that the maximum occurs at 0 eV:

1 bulk 1 DG < lO  GO2 < 0 2 f ;UO2 2

ð7Þ

where DGbulk f ;UO2 is the Gibbs free energy of formation of the bulk oxide. For UO2, the range was determined to be 5.43 eV. 2.5. Error in GGA O2 calculation An assessment of the errors associated with the methodology is critical. The O2 molecule presents a challenge for DFT because of its short bond length and triplet ground state. The atomization energy of O2 provides a means to determine the error in the O2 DFT energy. The absolute error in the atomization energy calculated in this study is 0.84 eV, which is similar to the error calculated in other GGA studies using all-electron basis sets [88,98]. To evaluate if the error in the UO2 DFT energy cancels with that in the O2 DFT energy, the Gibbs free energy of formation of bulk UO2 was calculated at 0 K, at which temperature the Gibbs free energy of formation becomes equal to the enthalpy of formation, DHf U02 (0 K). Given the limited thermochemical data for bulk UO2, the experimental DHf (0 K) was determined to be 11.2 eV [100] as calculated from

DHf ;UO2 ð298:15 KÞ  DHf ;UO2 ð0 KÞ ¼ fHUO2 ð298:15 KÞ  HUO2 ð0 KÞg  fHU ð298:15 KÞ  HU ð0 KÞg  fHO2 ð298:15 KÞ  HO2 ð0 KÞg HUO2 ,

HU ,

HO2

ð8Þ

where and are the enthalpies of bulk UO2, a-uranium, and gaseous O2, respectively. The average error in the calculated

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Table 3 Relaxations of UO2 (1 1 1) surface for 7-layer slabs. Layersa

Antiferromagnetic Clean Å

i–1 1–2 2–3 3–4 4–5 5–6 6–7 7–8 8–9 9–10 10–11

OURAO1 O1AU1 U1AO2 O2AO3 O3AU2 U2AO4 O4AO5 O5AU3 U3AO6 O6AO7 O7AU4

0.781 0.801 1.546 0.782 0.781 1.584 0.766 0.782 1.563 0.778

Ferromagnetic Uranyl

Clean

D%

Å

D%

0.9 3.6 3.7 1.1 1.0 1.3 1.0 1.1 2.6 0.6

1.530 0.281 0.859 1.459 0.770 0.782 1.587 0.771 0.783 1.578 0.771

4.7 63.7 11.1 9.1 0.5 1.1 1.1 0.3 1.2 1.7 0.4

Å 0.778 0.798 1.536 0.779 0.782 1.578 0.761 0.794 1.542 0.786

Uranyl

D%

Å

D%

1.3 1.2 2.4 1.2 0.9 0.3 3.5 0.7 2.0 0.4

1.529 0.281 0.855 1.452 0.780 0.761 1.574 0.787 0.756 1.569 0.803

2.8 64.4 8.3 7.7 1.1 3.6 0.0 0.2 4.1 0.3 1.7

a Layers indicated are shown in Fig. 2. Relaxations indicated are with respect to the bulk layer spacings for the optimized 1k AFM lattice (0.773 Å and 1.605 Å) and for the FM lattice (0.779 Å and 1.573 Å).

Fig. 2. Half of the 7-layer UO2 (1 1 1) surface slabs. Uranium atoms are the small blue circles, and lattice oxygen are the larger red circles. Pink atoms are the oxygen interstitials at positions (c) P1, (d) P2, and (e) P3. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

values of DHf (0 K) using DFT total energies is 10.8% for AFM and FM UO2. By adding an energy correction of 0.84 eV to the DFT energy of O2, the error in DHf (0 K) is reduced to only 3.25%. This result indicates that the majority of the error in DHf (0 K) is associated with the error in the DFT energy of O2. Therefore, the energy correction of 0.84 eV was applied to the O2 DFT energy in all surface free energy calculations. It should be noted that fortuitous cancellation of errors in an LDA study led to a calculated DHf (0 K) value of 11.0 eV, in close agreement with the experimental value [33]. 3. Results and discussion In this section we discuss first the thermodynamics of surface and subsurface oxidation, followed by the structural aspects, and lastly a detailed analysis of the electronic structure and redox chemistry. 3.1. Energies of formation and ab initio thermodynamics 3.1.1. Surface oxidation The exposed uranium atom on the clean (1 1 1) surface, designated U1 in Fig. 2, is under-coordinated and the most probable site for initial oxidation. We find that oxidation by dissociation of

molecular oxygen to form a uranyl group is calculated to have highly favorable formation energy of 2.49 eV at 0 K for the 7layer AFM slab, defined as the difference in total DFT energy between the slab with the uranyl group and the clean slab plus an isolated O2 molecule including the DFT energy correction. This formation energy is significantly more favorable than the 1.15 eV obtained by Skomurski and coworkers for the 2-layer FM (1 1 1) slab [62]. The ab initio thermodynamics results, which provide the temperature and pressure dependence of the surface free energies, are shown in Figs. 3 and 4. At low lO the clean stoichiometric surface is the most stable surface at thermodynamic equilibrium with a surface free energy of c = 55.4 meV/Å2. The thermodynamic crossover from the clean stoichiometric surface to the oxidized uranyl structure is predicted to occur at a very low oxygen chemical potential lO of 2.49 eV, consistent with the high binding energy of the uranyl oxygen. From Fig. 4 it can be seen that a temperature higher than 1000 K and a p(O2) below 1011 mbar is required for the clean stoichiometric surface to have a lower surface free energy than the oxidized uranyl structure. Thermodynamically, the uranyl group should form spontaneously with even trace amounts of O2 in the system, i.e. a p(O2) below 1030 bar, even at temperatures approaching 0 K. This is consistent with early oxidation studies on freshly crushed and reduced UO2 crystals that exhibited surface chemisorption of oxygen spontaneously

A.M. Chaka et al. / Computational and Theoretical Chemistry 987 (2012) 90–102

Fig. 3. Ab initio thermodynamics result for the UO2 (1 1 1) surface showing surface free energies c as a function of oxygen chemical potential lO. Solid vertical lines represent the physical limits for the range of lO corrected for the error in the GGA O2 dissociation energy. The gray vertical line at 5.0 eV represents the uncorrected value for lO,min.

Fig. 4. Temperature–pressure phase diagram for oxidation of UO2 (1 1 1) slabs. Experimental data point by Blackburn at 473 K and 0.7 mbar indicated. [17].

at 90 K [15]. At oxygen pressures above 13 mbar, equilibration of surface oxidation would occur within minutes; below 1.3 mbar equilibration required 30 minutes. Ferguson and McConnell measured the heat of oxygen chemisorption under the same conditions and obtained a value of 2.38 ± 0.08 eV [16]. Although the nature of the oxidized surfaces were not identified, and the experiments were conducted on a complex powder, the highly exothermic formation energy calculated for the uranyl structure on the (1 1 1) surface is consistent with these early experiments and may explain their observations.

3.1.2. Subsurface oxidation In a 7-layer slab, there are three unique octahedral holes that can accommodate an oxygen atom, labeled P1, P2, and P3, shown in Fig. 2a. The successive octahedral holes are separated by a distance of 3.72 Å in the clean, relaxed surface slab. The density of interstitial oxygen atoms in these sites, and hence the degree of oxidation, is much higher than the density typically investigated in studies of bulk oxygen interstitials where only the central octahedral holes in the conventional cubic fluorite unit cell structure have been considered.

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Oxidation of the first subsurface site P1 was considered in both the presence and absence of the surface uranyl group. The formation energy for the P1 oxygen interstitial for the clean surface was found to be 0.77 eV. This value is considerably smaller than the 2.49 eV formation energy for the surface uranyl group, indicating that P1 occupation is much less favorable than the surface oxidation. This is clearly illustrated in Fig. 3 where the free energy for oxidation at P1 is on the order of 133 meV/Å2 higher across the entire range of lO. Once the uranyl group is formed, however, subsequent oxidation of the P1 interstitial is still favorable with a formation energy of 0.65 eV. Occupation of the P2 site is even more favorable, with a formation energy of 1.03 eV relative to the energy of the uranyl surface slab. As the oxygen interstitial is moved deeper into slab at the P3 site, however, the formation energy decreases slightly to 0.84 eV. This increase is due to the repulsive interaction of the P3 interstitial with its inverse P(-3) in the 7-layer slab, as illustrated in Fig. 2e. The distance between P3 and P(3) is only 3.850 Å, compared to 9.748 Å for P2 and P(2). The interstitials at P1, P2, and P3 are also surrounded by their four counterparts in neighboring unit cells at a distance of 3.86 Å. The exothermic formation energy for the oxygen interstitials is consistent with the high density of oxygen absorption observed experimentally for bulk UO2, and indicates that locally a higher density is possible than the 5.445 Å separation for bulk interstitial oxygens placed at the center of the conventional fluorite unit cells that has previously been considered [33,34,36,38,41]. The relative strengths of binding of the surface uranyl oxygen compared to the subsurface sites are consistent with the experimental results of Roberts [15], Alberman and Anderson [13], and Ferguson and McConnell [16] who concluded that the chemisorbed oxygen is more tightly bound at the surface than the interstitially absorbed oxygen in the lattice. The results in Fig. 3 indicate that the subsurface interstitials begin to become occupied when the oxygen chemical potential increases to 1.0 eV. In terms of temperature and pressure, Fig. 4 shows that the highest energy interstitial P1 requires the lowest temperatures and highest oxygen partial pressures to become occupied. As P1 is the first position that oxygen must occupy as it migrates into a UO2 single crystal from the (1 1 1) direction, the ‘‘uranyl + P1’’ line in Fig. 4 represents a thermodynamic threshold for subsurface oxidation. Although many experiments have been conducted on UO2 oxidation and the complex structural changes that result [2,3,5,11,13,18,20–23,25], the number in which both temperature and pressure have been systematically varied to probe this threshold is limited. In 1957 Blackburn and coworkers systematically varied pO2 while measuring the parabolic rate constants for oxygen absorption gravimetrically on crushed, reduced near-stoichiometric crystals at 473 K [17]. At this temperature the rapid oxidation rate remained constant as long as the pO2 remained between 0.7 mbar and 1 bar (20–101 kPa), but slowed appreciably below 0.7 mbar. This point at 473 K and 0.7 mbar is indicated in Fig. 4, which is in fortuitously excellent agreement with the P1 oxidation threshold line for subsurface oxidation at the UO2 (1 1 1). This result, plus the low barriers measured and calculated for oxygen transport within UO2 suggest that the oxidation threshold observed by Blackburn is thermodynamic rather than kinetic. 3.2. Structural impacts of oxidation The relaxations for the clean and oxidized UO2 (1 1 1) surface structures shown in Figs. 2 and 5 are in Tables 3 and 4. The uranyl group has a very short UAO bond length of 1.81 Å, which is equivalent to the 1.80 Å distance obtained by Skomurski and coworkers, and independent of the subsurface oxidation. This UAO bond distance is consistent with what is observed for U6+ in [UO2]2+ crystal structures [101,102]. Burns conducted a systematic investigation

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Fig. 5. Local bonding environments for interstitial oxygen atoms P1, P2, and P3, shown in pink. Atom names correspond to those indicated in Fig. 2.

Table 4 Relaxations for UO2 (1 1 1) with subsurface oxidation interstitials at positions P1, P2, and P3, shown in Fig. 5. Layersa

i–1 1–2 2–3 3–4 4–5 5–6 6–7 7–8 8–9 9–10 10–11 11–12

P1

OUR AO1 O1AU1 U1AO2 O2AP1 P1AU2 U2AO3 O3AO4 O4AO5 O5AU3 U3AO6 O6AO7 O7AU4

P2 Å

D%

1.469 0.345 0.960 1.550 0.746 0.304 1.555 1.537 0.389 0.871 1.470 0.750

8.4 55.4 24.1

139.3b 4.2 47.9 12.6 8.4 3.0

OUR AO1 O1AU1 U1AO2 O2AO3 O3AU2 U2AO4 O4AP2 P2AO5 O5AU3 U3AO6 O6AO7 O7AU4

P3 Å

D%

1.540 0.268 0.900 1.263 0.943 0.398 1.180 0.973 0.281 1.188 1.319 0.715

4.1 65.4 16.3 21.3 21.9 48.5

63.7 53.6 17.8 7.5

OUR AO1 O1AU1 U1AO2 O2AO3 O3AU2 U2AO4 O4AO5 O5AU3 U3AO6 O6AP3 P3AO7 O7AU4

Å

D%

1.533 0.278 0.860 1.429 0.792 0.716 1.331 1.141 0.257 1.087 0.761 1.533

4.5 64.1 11.2 10.9 2.4 7.4 17.1 47.5 66.7

4.6

a

Layer numbers differ from those indicated for the stoichiometric surface shown in Fig. 2a due to the insertion of oxygen interstitials. Relative relaxations are with respect to the 1k AFM bulk lattice. b In the P1 slab, U2 has moved above O3 closer to the surface, making the ordering of atoms in the P1 case different from the bulk sequence where U2 is below O3.

of 368 U6+ mineral and inorganic compound crystal structures and determined that UAO distances fall into two distinct distributions [102]. The short, axial uranyl [O„U„O]2+ triple bonds range from 1.7 Å to 1.9 Å with an average of 1.793 Å and a standard deviation of 0.035 Å. In the equatorial position, U6+ can accommodate four to six oxygen ligands with an irregular distribution and an average UAO distance of 2.460 Å and a standard deviation of 0.107 Å. XPS measurements by Veal and coworkers indicate that these longer UAO distances on the order of 2 Å and longer in the equatorial plane of uranyl molecular compounds and complexes, as well as in bulk UO2, do not exhibit multiple bond ‘‘uranyl’’ character [101]. The O3 oxygen atom directly below the U1 cation at a distance of 2.32 Å away in Fig. 2 is constrained by its proximity and interactions with its neighboring bulk uranium atoms and does not exhibit triple bond uranyl character (see the density of states (DOS) and bonding analysis discussed in Section 3.3), and is comparable to other bulk UAO interactions in uraninite. Hence the oxidized surface uranium atom exhibits an unusual coordination and bonding environment – half uranyl and half bulk UO2 – and might be more accurately termed a ‘‘hemi-uranyl’’. Expansion and contraction of the UO2 lattice is an important consideration for oxidative corrosion UO2 in fuel rods, contaminated sites, and micron-sized DU particles released upon impact in the battlefield. For the 7-layer slab calculations shown in Fig. 2, the extent of the net relaxation can be compared by considering the relative distances between the topmost uranium atoms (U1) and those at the center of the slabs (U4). The clean stoichiometric 1k AFM surface slab exhibits a minimal contraction of 0.74% between U1 and U4 relative to the corresponding distance in the bulk. Addition of the surface uranyl oxygen results in a small

increase in the amount of contraction to 1.02% of the overall U1AU4 distance. The contraction of layers is localized primarily at the surface, as indicated in Fig. 2 by the contraction between the surface O1 and O4 atoms to 4.15 Å from 4.69 Å in the clean surface, and the U2AU3 separation remaining essentially unchanged at 4.7 Å. Table 3 shows that with the presence of the uranyl group, the next topmost oxygen at O1 relaxes into the surface by 63.7% Subsurface oxygen absorption at the P1 site results in a significant net expansion of the U1AU4 distance by 7.1%. The expansion is primarily localized in the upper layers, with the O1AO4 distance increasing to 5.46 Å from 4.69 Å for the clean surface. In contrast, occupation of the P2 and P3 oxygen interstitial sites result in a net contraction of the overall slab thickness by 3.1% and 2.9%, respectively. Fig. 5 illustrates the local environment for each oxygen interstitial. All three interstitials maintain a distorted octahedral environment with respect to the uranium atoms, with three longer distances to the upper layer of uranium atoms and three shorter distances to the lower uranium layer. P1’s proximity to the surface and the uranyl group results in the greatest asymmetry and octahedral distortion with the longest distances to the three topmost U1 layer atoms ranging from 3.35 Å to 3.43 Å, and from 2.34 Å to 2.36 Å to the U2 layer atoms. P2 and P3 have comparable distances to the uranium atoms located in the layer above them, 2.73 Å to the U2 and U3 atoms, respectively. The proximity of P3 to P(3) and their mutual repulsion, however, results in a slightly longer distance (2.60 Å) to the layer of U4 atoms between them compared to the 2.56 Å between P2 and the U3 atoms in the layer below. The cubic arrangement of oxygen atoms surrounding each interstitial is also distorted, with four long and four short distances.

A.M. Chaka et al. / Computational and Theoretical Chemistry 987 (2012) 90–102

97

Fig. 7. PDOS of the (a) FM clean surface, (b) AFM clean surface, and (c) AFM oxidized surface with uranyl groups showing U7s, 7p, 6d, and 5f and O 2p interactions.

These groups of four long or short distance oxygen atoms do not lie in a single plane of the cube, however. Three of the four lie in a plane parallel to the (1 1 1) surface between the interstitial and its layers of nearest neighbor uranium atoms, and one of the four lies outside this uranium atom plane directly above or below the interstitial. Again, P1 has the greatest asymmetry, with distances to the three O2 oxygen atoms that are just below the U1 uranium atom layer at 2.70 Å to 2.72 Å, and at 2.85 Å to the surface O1 atom above them. Three of the lower layer O3 atoms range from 2.45 Å to 2.48 Å away, and the nearest neighbor oxygen atom in O4 is 2.61 Å away. For P2 the distance to the four oxygen atoms above

(one in layer O3 and three in layer O4) is essentially the same at 2.52 Å. The distance from P2 to the four oxygen atoms below (three in layer O5 and one in layer O6) is somewhat shorter at 2.43 Å. In P3, the relative distances to the oxygen atoms above and below is reversed from those surrounding P2, at 2.36 Å and 2.48 Å, respectively. This longer distance from P3 to the oxygen atoms in layers O7 and O8 is again due to the repulsion between P3 and its inversion center image at P(3). In the 1  1 surface models employed in this study there is negligible lateral relaxation observed. Lateral relaxations may occur if larger supercells are employed. With the exception of P1, a low

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symmetry structure, oxygen interstitials placed off center for initial positions returned to the center of the octahedral site.

3.3. Density of states and bonding analysis Previous GGA band structure calculations on bulk UO2 have shown a relatively flat band for U5f2 electrons, indicating little participation in bonding in the lattice [Boettger02]. In this section we examine the density of states to determine the character of the bonding for the clean and uranyl-terminated UO2 (1 1 1) surfaces for both the FM and AFM magnetic states. Examination of the density of states at the Fermi level (EF) also provides information regarding the degree of conductivity of a solid. Fig. 7 shows comparisons of partial density of states (PDOS) between surface and bulk uranium (U1 and U4, respectively) in the FM and AFM stoichiometric and AFM uranyl-terminated surface slabs. Near EF, the uranium 5f states dominate the DOS. As shown in Fig. 7a and b, U1 has more than four times as many states at the Fermi level as U4 does in the FM stoichiometric surface slab. A similar situation is observed for the AFM clean and oxidized surfaces (Fig. 7c–f) where two and four times as many states, respectively, are observed at EF for U1 compared to U4. These results demonstrate that the conducting states are mostly localized on the surface for the FM and AFM stoichiometric and AFM oxidized surfaces. While the shape of the U1 PDOS is similar for the FM and AFM stoichiometric surface below the Fermi level (Fig. 6a and c, respectively), the AFM uranyl-terminated surface U1 (Fig. 6e) has few 5f states directly below EF but more than twice as many total 5f states below EF as calculated from the integrated PDOS. The increase in 5f states well below EF for the AFM oxidized surface U1 results from greater interaction with the O 2p states of the uranyl oxygen OUR due to the short UAO bond length to form the triple bond (see Fig. 7) and is indicative of U1 oxidation to 6+ (see discussion in Section 3.4). Interestingly, U4 in the AFM clean and oxidized surface slabs differ in the shape of the PDOS directly below EF (see Fig. 6d and f), showing that effects of surface oxidation propagate to the middle of the slab. In all surfaces, the U1 PDOS shift to higher energies relative to the U4 PDOS in the range of 8 to 3 eV below EF. The variations between the U1 and U4 PDOS in this region reveal the different bonding environment that the uranium atoms experience at the surface compared to the bulk because this range contains the overlap between O 2p and U orbitals (see discussion below). U4 atoms in each surface slab have slightly more 5f states mixing with the O 2p states than do U1 atoms in the FM and AFM clean surface, likely due to an additional oxygen within the U4 coordination sphere with which to interact. The overlap in the PDOS of U1 and its oxygen nearest neighbors is presented in greater detail to delineate the covalent nature of the bonding, which is observed throughout the surface slabs. For the clean surfaces, the covalent interactions are mostly confined to the region between 8 eV and 2 eV. This region is comprised of U 7s, 7p, 6d, and 5f orbital interactions with the O 2p orbitals (Fig. 7). In Fig. 8a, the PDOS of surface and subsurface atoms in the FM stoichiometric surface is given between 8 eV and 0 eV below EF. The most significant orbital mixing in this region involves U 5f and O 2p orbitals between 4 eV and 3 eV. The peaks in the O1 2p DOS at -3.95 eV, 3.75 eV, and 3.28 eV correspond exactly with peaks in the U15f DOS and are closely matched with peaks in the 2p DOS of O2. The peak at 3.28 eV also shows some small contributions from O3 2p orbitals. The U1 7s, 7p, and 6d states undergo some mixing with the 5f states over the region of interest (Fig. 7a). Between 7 eV and 5 eV, the U1 6d states overlap with the O2 and O3 2p states. Fig. 7b illustrates a strikingly similar picture for the AFM clean surface, which is expected given the similar coordination spheres of U1 on these two surfaces.

Fig. 6. PDOS of uranium atoms at the surface (U1) and at the middle of the slab (bulk U) of the (a–b) FM clean surface, (c–d) AFM clean surface, and (e–f) AFM oxidized surface with uranyl groups.

The PDOS of the AFM uranyl-terminated surface atoms is given in Fig. 7c. Orbital mixing between U1 and the O1, O2, and O3 atoms on this surface exhibits bonding patterns comparable to those on the FM and AFM clean surfaces. The O1 and O2 2p orbitals show good overlap with the U 5f orbitals between 4.5 eV and 2 eV

A.M. Chaka et al. / Computational and Theoretical Chemistry 987 (2012) 90–102

with the O3 2p orbitals participating in the lower end of this range. Mixing of the U1 7s, 7p, 6d, and 5f states is also observed between 7 eV and 2 eV below the Fermi level. Covalent interactions between the U1 6d and O2 and O3 2p orbitals occur below 6 eV. Unlike on the FM and AFM clean surfaces, O1 2p orbitals also contribute to states below 6 eV, probably because O1 is nearly coplanar with U1 at the (111) surface and the O1AU1 distance is 0.12 Å shorter on the oxidized surface. The significant differences arising in the U1 PDOS on the uranyl-terminated surface are due to strong covalent interactions between U1 and the uranyl

99

oxygen OUR that results in a short uranyl bond length of 1.81 Å. The U1 5f orbitals exhibit strong mixing with OUR 2p orbitals at higher energies than noted for the covalent interactions on the FM and AFM stoichiometric surfaces. The overlap between these orbitals is apparent in the excellent match in the peaks between 4.5 eV and 2 eV. The uranyl group also gives rise to U 6p and O 2s orbital interactions that are absent on the clean surfaces. The region in the DOS containing these interactions lies between 23 eV and 14 eV below EF (Fig. 8). The clean and oxidized surfaces all show small

Fig. 8. PDOS of the (a) clean FM surface, (b) clean AFM surface, and (c) oxidized AFM surface with uranyl groups showing U p and O s interactions.

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Table 5 Mulliken charge and spin populations and percent of U 5f2 electrons transferred from local U 5f orbitals near EF to overlap with O 2p states from PDOS. Clean surface

U1 U2 U3 U4

Uranyl

P1

P2

P3

Charge

Spin

%f O2p

Charge

Spin

%f O2p

Charge

Spin

%f O2p

Charge

Spin

%f O2p

Charge

Spin

%f O2p

1.69 1.94 1.91 1.91

2.10 1.99 2.00 2.03

37.1 40.7 41.3 41.5

1.75 1.97 1.89 1.89

0.16 1.93 1.98 1.96

93.1 42.1 41.0 39.8

1.77 1.67 1.96 2.01

0.40 1.21 0.88 1.75

90.2 66.9 74.4 49.9

1.73 2.04 1.80 1.87

0.01 1.25 1.35 0.86

99.3 60.6 59.8 76.3

1.79 2.03 1.61 2.07

0.03 0.77 1.47 2.15

92.4 57.6 75.4 56.9

covalent interactions between U 6p and O1, O2, and O3 2s orbitals below 20 eV and above 18 eV below EF (Fig. 8). However, the U1AO bond lengths between U1 and these three oxygen atoms vary between 2.25 Å to 2.39 Å, which prevents strong interactions between the more compact O 2s and the U 6p orbitals. Because the U1AOUR distance is significantly shorter at 1.81 Å, the U1 6p and OUR 2s undergo significant mixing on the uranyl-terminated surface as evidenced by intense peaks at 22.9 eV and 14.2 eV (Fig. 8c). Also mixing with the U1 6p and OUR 2s states at these energies are the O3 2s states. These peaks involve a linear arrangement of atoms perpendicular to the surface (OURAU1AO3) and are therefore attributed to bonding and antibonding orbitals formed from the U1 6pz and OUR and O3 2s orbitals. The U1 6p DOS between these peaks arise from the 6px and 6py orbitals and show only small interactions with the O1 and O2 orbitals due to the fact that O1 and O2 are above and below, respectively, the xy plane containing U1 (Fig. 8c).

3.4. Electronic impact of subsurface oxygen absorption: oxidation and magnetism Quantifying the degree of oxidation of uranium atoms in oxidized UO2 can be done by examination of the amount of charge transfer from uranium to oxygen. Although the charge partitioning methods such as those of Mulliken [103] and Bader [104] do not correspond to formal oxidation states nor are they quantum mechanical observables like the electrostatic potential, they are frequently useful to assess relative trends in oxidation. In the case of uranium oxides, however, this approach is somewhat problematic due to the challenges of describing the shifting localized/delocalized character of the 5f electrons. For example, in bulk UO2 where the two valence 5f electrons are localized on the uranium atoms and the formal oxidation state is +4, the Mulliken charge population for uranium is 1.90. For the uranyl molecular cation (UO2)2+ with a uranium formal oxidation state of +6, the Mulliken charge is lowered by only 0.05 electrons to 1.85. Geng and coworkers utilized Bader population analysis on bulk UO2 to determine if an oxygen interstitial oxidized uranium nearest neighbors, and observed at most a charge transfer of only 0.05 electrons [38]. In our calculations, charge populations for the uranium atoms in the surface models shown in Table 5 range from 1.67 on U2 nearest the P1 interstitial to 2.07 on U4, the most oxidized uranium atom in the bulk between P3 and its inverse interstitial P-3. How these atomic charge populations correspond to formal oxidation states, however, is difficult to assess. Given the limitations of population analysis for uranium oxides and 5f electrons, we turned to the density of states analysis to obtain an alternative picture of oxidation. Veal and Lam performed XPS studies that indicated that the occupation of the localized fband just below the Fermi level in UO2 decreases as the interstitial oxygen content increases through UO2+x and is completely absent in UO3 where uranium is formally oxidized to a +6 state [68]. This decrease in f-band occupation indicates a transfer of localized uranium 5f electrons to the metal oxide band dominated by the 2p character of the oxygen atoms, and is a more direct measure of

the oxidation state of the uranium atom [68,105]. In Table 5 are the results of the density of states analyses that show what percentage of the two 5f electrons have been transferred from their localized position on each uranium atom just below the Fermi level to the band between 3 and 8 eV below the Fermi level that is dominated by O2p character. For the clean stoichiometric slab where all the uranium atoms have a formal +4 oxidation state, approximately 41% of the two 5f electrons are delocalized into the metal-oxide band, and 59% are localized onto the uranium atoms, with a slight enhancement of local character exhibited by the topmost uranium atom U1. Hence uranium atoms that are considered to have a formal oxidation of +4, as evidenced by the stoichiometric slab and U4 5f electron distribution, exhibit approximately 40% of the localized f electrons transferred to the oxygen 2p band. For the surface uranyl moiety, more than 90% of the two U1 f electrons are transferred to the uranyl oxygen, and can be considered to have a +6 formal oxidation state. For the P1, P2, and P3 oxygen interstitials, the results can be interpreted as one electron (or slightly more than one electron) being transferred from one uranium atom (75% 5f states transferred to O2p) to form U+5, and then the second electron from the two remaining subsurface uranium atoms. The oxygen interstitial at P1 causes a redistribution of charge among its oxygen nearest neighbors, resulting in most of the charge transfer coming from U3, which is a surprising 4.64 Å away, rather than the U2 atom that is only 2.34 Å away. A similar situation is observed for P2, where the charge redistribution results in U4 being the most oxidized subsurface uranium atom, although U2 and U3 are closest. For P3 most of the charge is transferred from U3, which is 2.73 Å away, rather than U4 at 2.60 Å.

4. Conclusion DFT and ab initio thermodynamics have been used to determine the structure, degree of oxidation, and thermodynamic thresholds for the initial states of oxidation of the UO2 (1 1 1) surface as a function of temperature and oxygen pressure. The initial oxidation step results in formation of a uranyl group at the topmost uranium atom at the surface, which is so thermodynamically favored with a lO of 2.5 eV that it is expected to form even at negligible p(O2) near 0 K, consistent with experiment. The uranyl group is so strongly bound that temperatures above 800 K and p(O2) below 1021 bar are required to reach the conditions where the clean stoichiometric surface has a lower free energy, and the uranyl oxygen can be driven off. This result is consistent with observations by Ulrich, Giammar and coworkers that the UO2/[UO2]+2 redox potential is so negative that uraninite can reduce water to a very small extent, even under anoxic conditions [106]. Subsurface oxidation is also highly favored, but requires a slightly higher thermodynamic threshold (lO) of 0.5 eV to occur in the presence of a surface saturated with uranyl groups, which corresponds to a p(O2) of 105 mbar at 298 K. These thermodynamic thresholds represent the values for the system to reach saturation for site occupancy, i.e. the chemical potentials for a (1  1) unit cell, when the strongest

A.M. Chaka et al. / Computational and Theoretical Chemistry 987 (2012) 90–102

experimental signal for techniques such as X-ray diffraction would be observed. The highly favorable surface and subsurface oxidation of the UO2 (1 1 1) surface have implications for corrosion, environmental contamination, and techniques for measuring the solubility of UO2. Methods that are used to measure very low levels of dissolved U historically have not been able to distinguish between dissolved U4+ and U6+, and have assumed that all measured U is U4+. Consequently, the presence of U6+ from highly favored surface oxidation will have the effect of artificially escalating the apparent solubility of UO2 by continuously enabling formation of the highly soluble [UO2]+2 species. Indeed, the predicted solubility of UO2 based on enthalpies are very low – less than 1015 M. However, the experimentally observed solubility is almost never below approximately 109 M. The oxidation model presented here provides at least a partial explanation for this behavior. The subsurface oxidation described in this work constitutes the initial steps in the development of thin oxide layers of UO2.33, and the soluble oxides such as UO3 that have been observed in corrosion studies on UO2 and nuclear fuel rods [4,12]. The extent of oxidation of individual uranium atoms have been quantified by the amount of electron transfer from the localized U 5f bands to the bands dominated by the O 2p orbitals. In the 7-layer UO2 slabs, both the top and bottom uranium atoms on the surfaces of the slab were completely oxidized to U6+ by absorption of atomic oxygen and formation of the strongly triple-bound uranyl group. When two subsurface oxygen atoms were placed amongst the remaining five layers, one in the top half of the slab and one in the bottom half, a total of four electrons were transferred from localized U 5f orbitals near the Fermi level to the delocalized bands dominated by the O 2p states. Approximately one electron was transferred to each oxygen interstitial from one uranium atom (either U3 or U4 in the center of the slab, depending on the interstitial) to yield a formal oxidation state of +5. The remaining two transferred electrons, one to each oxygen interstitial, were obtained from a combination of the three remaining U4+ atoms in the slab and resulted in a non-integral oxidation state between +4 and +5. It is possible that this pattern of oxidation would be different for thicker slabs or super cells of larger dimensions. The reserve of localizeds 5f electrons on the subsurface uranium atoms indicate that UO2 has the capacity to absorb an even higher density of oxygen interstitially than was considered in this study. This capability to quantify uranium oxidation by interstitial oxygen atoms coupled with ab initio thermodynamics provide a solid foundation to begin to understand the transformation of UO2 to the higher order oxides observed in oxidative corrosion studies of UO2 and nuclear fuel rods at the atomistic level.

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