ARTICLE pubs.acs.org/JPCB
Oxygen Vacancy Formation and Migration in CexTh1xO2 Solid Solution H. Y. Xiao*,† and W. J. Weber†,‡ † ‡
Department of Materials Science & Engineering, University of Tennessee, Knoxville, Tennessee 37996, United States Materials Science & Technology Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, United States ABSTRACT: A local-density approximation with the Hubbard U correction (LDAþU) method has been employed to investigate oxygen vacancy formation and migration in CexTh1xO2. The addition of CeO2 into ThO2 significantly decreases the oxygen vacancy formation and migration energies. ThO2 containing 50% CeO2 exhibits the lowest calculated formation energy, 3.7 eV, and the lowest calculated migration energy, 0.2 eV, occurs for a CeO2 content of 75%, suggesting that introducing CeO2 into ThO2 promotes the formation of mobile oxygen vacancies. If the ceria content is less than about 35%, the reduced CexTh1xO2 becomes antiferromagnetic (AFM), whereas the ferromagnetic (FM) state dominates for x values above about 35%, which may allow the tailoring of magnetic properties by varying the CeO2 content.
I. INTRODUCTION Thorium dioxide (ThO2), or thoria, is radioactive due to the natural radioactivity of Th isotopes. With the increased interest in nuclear power, the thorium nuclear fuel cycle is receiving renewed interest because of the greater abundance of thorium, superior properties of thoria-based fuels, enhanced proliferation resistance, and reduced production of plutonium and minor actinides. The thorium fuel cycle uses the naturally abundant 232 Th as a fertile isotope, which in an accelerator-driven subcritical system or nuclear reactor is transmuted to the fissile uranium isotope 233U that can be used as fuel to power a nuclear reactor.1 In practice, 232ThO2 and 233UO2 would be mixed together to form a thoria-urania nuclear fuel, in which 233U would be used to sustain a fission chain reaction and 232Th would be used to breed more 233U. Combinations of Th and highly enriched U, or Th and Pu, have been tested as nuclear fuels in both gas- and water-cooled power reactors.2 Investigations of the behavior of ThO2UO2 and ThO2PuO2 fuels under irradiation are important to predicting fuel performance for a thorium fuel cycle. Since U and Pu are controlled radioactive materials, they are not easily studied experimentally.35 However, ThO2, UO2, PuO2, and CeO2 (ceria) have the same cubic fluorite-type crystallographic structure (space group: Fm3m) and similar fundamental radiation-induced defect behavior,6 and the thermodynamic properties of CeO2 are quite similar to those of UO2 and PuO2.3 Thus, CeO2 is often used as a nonradioactive surrogate for UO2 and PuO2 in many laboratories.711 Consequently, studies of ThO2CeO2 will provide fundamental understanding and significant insight into the properties and behavior of ThO2UO2 and ThO2PuO2 nuclear fuels. Because of the existence of two oxidation states (Ce3þ and Ce4þ) and the ability to take and release oxygen under oxidizing r 2011 American Chemical Society
and reducing conditions,5 CeO2 has been widely used in automobile exhaust catalysis, oxygen gas sensors, and fuel cells. Defective ceria containing high vacancy concentrations,1218 along with oxygen vacancy formation and migration in ceria,4,1923 have been studied extensively because the most desirable properties of CeO2 for applications depend strongly on the oxygen vacancies. Despite its importance in the nuclear industry and other applications, such as a solid-state electrolyte, optical component, and laser host, the number of theoretical calculations on ThO2 are limited.5,2430 Calculations have been mainly focused on the structural, elastic, and electronic properties of bulk ThO2, and studies of defect properties in ThO2 are few.31 Likewise, only a few theoretical studies have been performed on the ThO2CeO2 solid solution, and only its redox32 and mechanical and electronic properties5 have been reported. Under irradiation, oxygen vacancies and interstitials are two of the primary defects of interest in oxide and mixed-oxide fuels.33,34 The diffusion of oxygen in these nuclear fuels has been studied extensively, and it has been shown that both oxygen vacancies and interstitials in UO2 and CeO2 contribute almost equally to the diffusion of oxygen because of their comparable migration energies.33,35,36 The high mobility of oxygen vacancies and interstitials can affect defect recovery; however, vacancy diffusion has a greater impact on fission gas diffusion, bubble formation, and restructuring of fuel. In the present work, the focus is on the behavior of the oxygen vacancy, which is more accessible experimentally for validation. A fundamental understanding on Received: November 3, 2010 Revised: April 20, 2011 Published: May 05, 2011 6524
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Figure 1. Schematic view of CexTh1xO2 (x = 0, 0.25, 0.5, 0.75, and 1) structural models.
vacancy properties in CeO2ThO2, as in this study, will provide important insights into the response of ThO2UO2 and ThO2PuO2 fuels under irradiation. Thus far, there is a lack of atomic level understanding on vacancy behavior in the CeO2ThO2 solid solution. In this article, we present a systematic study of oxygen vacancy formation and migration in CexTh1xO2 (0 e x e 1) by employing first-principles calculations based on the density functional theory (DFT). The effects of ceria content on vacancy formation and migration energies, structures, and charge distribution are determined.
II. COMPUTATIONAL DETAILS All of the calculations were performed with the Vienna Ab Initio Simulation Package (VASP) using the projector augmented wave method.37 The exchange-correlation effects were treated using the local-density approximation (LDA) in the CeperlyAlder parametrization, with spin-polarized effects considered. The strong on-site Coulomb repulsion was modified by considering the Hubbard U correction proposed by Dudarev et al.,38 in which EDFTþU = EDFT þ U J/2∑σ[TrFσ Tr(FσFσ)]. Here, Fσ is the density matrix of f states, and U and J are the spherically averaged screened Coulomb energy and the exchange energy, respectively. In this method, only the difference between U and J is significant, and U and J can be treated as a single parameter Ueff = U J. Computations were based on a 2 2 2 supercell (96 atoms) with a 2 2 2 k-point sampling in reciprocal space and a cutoff energy of 450 eV for the plane wave basis set. The CexTh1xO2 (x = 0, 0.25, 0.5, 0.75, and 1) solid solution was modeled by substituting Ce atoms for Th atoms in the supercell. The configurations of these compositions are illustrated in Figure 1. To study oxygen vacancy formation in CexTh1xO2, one oxygen atom was removed from the 2 2 2 supercell, resulting in CexTh1xO2y (95 atoms) with y = 0.03125. The minimum energy pathway for oxygen vacancy migration in solid solution was investigated by the climbing-image nudged elastic band (CI-NEB) method39 and the relaxation method proposed by Gupta et al.36
III. RESULTS AND DISCUSSION A. Structural and Electronic Properties of CexTh1xO2. CeO2 is an insulator with the empty Ce 4f state lying ∼3 eV above the O 2p band.40 Figure 2a shows the density of state (DOS) distribution for CeO2 calculated by the conventional LDA method, in which the energy bands below and above the Fermi level are mainly contributed by O 2p and Ce 4f bands, respectively. The Ce 4f bands are unoccupied, and the O 2p/Ce 4f band gap is predicted to be 1.96 eV, which is smaller than the experimental value of 3.0 eV.40 CeO2y is also an insulator,16 and experimental studies report4143 that the Ce 4f band splits into a localized occupied part and an unoccupied part. The DOS distribution for optimized CeO2y calculated by the conventional LDA method is shown in Figure 2b. Both ferromagnetic (FM) and antiferromagnetic (AFM) states have been considered, and we only present the results for FM ordering here. The relative stability of both states will be discussed in more detail in the next section. As shown in Figure 2b, the Ce 4f band does not split but shows a large peak around the Fermi level that leads to a metallic ground state, which is inconsistent with experimental results.4143 Obviously, the pure LDA calculation without modifying the intra-atomic Coulomb interaction gives an incorrect description for CeO2y. The introduction of the Hubbard U parameter that corrects the intraband Coulomb interaction is necessary for reduced CeO2y. By performing LDAþU calculations for different Ueff values (18 eV), we find complete localization of the Ce 4f electrons is obtained for values of Ueff = 6 eV or larger. The DOS distribution for CeO2y obtained using LDAþU, with Ueff = 6 eV, is shown in Figure 2d. As can be seen, the Ce 4f band is shown to undergo splitting into occupied and unoccupied parts. The occupied part is located in the energy range of 0.38 to 0.13 eV, and the energy gap between the O 2p valence band edge and the occupied f states is 1.2 eV, in good agreement with experimental values of 1.2 1.5 eV.4143 Our calculations are in good agreement with the results reported by Andersson et al.,16 who also proposed a Ueff value of 6 eV for implementation in the LDAþU method for CeO2y (y = 0.03125). Jiang et al.44 suggested a Ueff value of 6525
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Figure 2. Density of state (DOS) distribution for CeO2 and CeO2y (y = 0.03125) obtained by LDA and LDAþU (Ueff = 6.0 eV). EF: Fermi level.
Figure 3. DOS distribution for ThO2 and ThO2y (y = 0.03125) obtained by LDA and LDAþU (Ueff = 4.0 eV).
5.4 eV in the LDAþU for CeO2 and Ce2O3 based on a physical estimate without any fitting. Fabris et al.14 reported a Ueff value of 5.3 eV in the LDAþU for Ce2O3 using a linear-response approach.45 In the present work, the Ce Ueff value of 6 eV is employed 6 0) to be consistent with for CexTh1xO2 and CexTh1xO2y (x ¼ CeO2y. Although the DFTþU method was originally designed for Mott-Hubbard insulators to give the self-energy correction to localized states embedded in delocalized states,4649 this method has also been applied to semiconductors and insulators, such as GaN,50 ZnS,5153 In2O3,54 CeO2,1719,26,30 and ThO25 to improve the
electron localization and the band gap. Figure 2c illustrates the DOS distribution for CeO2 obtained in the LDAþU with Ueff = 6 eV. The main effect of increasing Ueff from 0 to 6 eV is to push the unoccupied f bands toward higher energy levels, resulting in a larger band gap value of 2.64 eV, which is in better agreement with the experimental value, 3.0 eV,40 than the pure LDA result. In the case of ThO2 and ThO2y, both are insulators and their ground states can be described correctly by the pure LDA method, as shown in Figure 3a and b. For ThO2, the minimum conduction bands are mainly contributed by the Th 6d and 5f 6526
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Figure 4. Dependence of the lattice parameter and band gap of CexTh1xO2 (x 6¼ 1) on the Th Ueff parameter.
orbitals. The band gap between the empty bands and the occupied O 2p state is 4.32 eV, significantly smaller than the experimental value of 5.75 eV.55 A deviation from ideal stoichiometry, that is, ThO2y, results in some electrons occupying the Th 6d and 5f orbitals in the energy range of 0.35 to 0.08 eV. The energy gap between the O 2p valence band edge and the occupied Th 6d and 5f states is predicted to be 3.56 eV. In the DFTþU method, the constrained local density approximation5660 and random-phase approximation6163 have been proposed to determine the Hubbard U. In addition, another semiempirical approach, which takes the effective Hubbard U as a variable parameter and fits its value to reproduce certain experimental observables without introduction of nonlocal exchange and its concomitant computational complications,17 has also been employed in several studies.5,12,15,17,64 In the present work, the dependence of the lattice parameters and band gap of CexTh1xO2 (x 6¼ 1) on the effective U parameter for Th has been investigated based on using Ueff = 6.0 eV for Ce, and the results are shown in Figure 4. Recently, (Th,Ce)O2 powder with ceria contents of 25, 50, and 75 mol % have been synthesized by Bukaemskiy et al.,65 and the effect of the addition of ceria on the thermal behavior and crystallization of thoria have been investigated. The lattice parameters were reported to be 5.594, 5.55, 5.505, and 5.45 Å for ThO2, Ce0.25Th0.75O2, Ce0.5Th0.5O2, and Ce0.75Th0.25O2, respectively, which follows Vegard's law for dependence on ceria substitution. The calculated lattice parameters for these compositions agree well with the experimental values,65 as shown in Figure 4a, for Th Ueff values ranging from 4.0 to 5.0 eV. As shown in Figure 4b, the band gap values for ThO2 are underestimated by the LDAþU method over the entire range of Th Ueff values explored, yielding band gaps for Th Ueff values above 4.0 eV that are about 1 eV below the experimental band gap of 5.75 eV,55 but this is a well-known deficiency of the DFT method.17 In the case of ceria substitution into thoria, it appears that the effects of Th Ueff are negligible. This is mainly because the minimum conduction bands of CexTh1xO2 (0 < x < 1) are primarily dominated by Ce 4f orbitals, as demonstrated in the DOS distribution determined by Sevik and C-agın5 employing the LDAþU method. Unfortunately, no experimental values are available, and our results are purely predictive. Since a Th Ueff value of 4 eV gives lattice parameters for CexTh1xO2 (x ¼ 6 1) that are in good agreements with experiments, we employ this value in the subsequent work, which is comparable to the Th Ueff value of 5 eV reported by Sevik and C-agın.5 The DOS distributions for ThO2 and ThO2y obtained in the LDAþU with Ueff = 4 eV are shown in Figure 3 parts c and d, respectively. The main effect of increasing Ueff from 0 to 4 eV is to push the unoccupied orbitals toward higher energy levels, resulting in larger band gap values.
Table 1. Calculated Structural Parameters and Band Gap Values for CexTh1xO2 (x = 0, 0.25, 0.5, 0.75, and 1) Obtained by the LDAþU Method, with Ueff = 4.0 eV for Th and Ueff = 6.0 eV for Cea a0 ThO2
5.58
d< ThO>
d
band gap
(Å)
(Å)
(eV)
2.42
-
4.82 (5.7555)
(5.59465,73,74) Ce0.25Th0.75O2
5.54 (5.5565)
2.41
2.37
2.66
Ce0.5Th0.5O2
5.50 (5.50565)
2.40
2.36
2.48
Ce0.75Th0.25O2
5.45 (5.4565)
2.39
2.35
2.46
CeO2
5.40 (5.417577)
-
2.34
2.64 (3.040)
a
d (M = Th or Ce) is the bonding distance. The values listed in the parentheses are experimental results.
The calculated structural parameters and energy band gap for CexTh1xO2 obtained from our LDAþU calculations are summarized in Table 1. The variation of bond length (d< MO>; M = Th or Ce) with ceria content is small, due to the small difference in d< ThO> of 2.44 Å for x = 0 and d of 2.34 Å for x = 1. On the other hand, the energy band gap value of the doped thoria is reduced significantly, as compared with that of thoria, which is close to that of ceria and is affected slightly by the doping concentration. B. Oxygen Vacancy Formation in CexTh1xO2. The vacancy formation energy was calculated from the expression: Ef = E(CexTh1xO2y) E(CexTh1xO2) þ 1/2E(O2), where E(CexTh1xO2y) is the total energy of the supercell containing one oxygen vacancy, E(CexTh1xO2) is the total energy of the CexTh1xO2, and E(O2) is the total energy of the oxygen molecule. All of the initial configurations for CexTh1xO2y (x g 0.5) models are symmetry-broken structures, in which the Ce ions around the vacancy site are moved outward and two of the Ce ions are moved by shorter distances. If the initial configuration was symmetric, then the final configuration must keep the symmetry. For example, if the initial configuration was symmetric, the two excess electrons in CeO2y would be distributed evenly among the four nearest-neighbor Ce ions around the oxygen vacancy. If the symmetry is broken, the two excess electrons from the oxygen vacancy are transferred to two of four nearest-neighbor Ce ions around the oxygen vacancy, which is consistent with the work of Castleton et al.15 and Iwasawa et al.4 For ThO2 and CeO2, a smaller supercell consisting of 11 atoms was employed for comparison. To study the effects of Ueff on the defect formation energies, we vary the Th Ueff from 3.0 to 5.0 eV and Ce Ueff from 5.0 to 7.0 eV. Table 2 summarizes the calculated formation energies for ThO2 and CeO2 as a function of Ueff and 6527
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system size. The results show that, as a larger supercell containing 95 atoms is employed, the defect formation energies for CeO2 exhibit more dependence on Ueff than those for ThO2. This is mainly because with increasing Ueff values the Ce 4f electrons in CeO2y becomes more localized, whereas the Hubbard U correction in ThO2y has a much smaller effect on its electronic structure, as shown in Figures 2 and 3, respectively. It is also found that the system size has nearly no effect on vacancy formation energies in ThO2, whereas the results for CeO2 obtained from the larger supercell are in better agreement with the experimental value of 4.72 eV.66 Several theoretical studies have been performed on defective ceria,4,12,15,16,19,20,67 and calculated vacancy formation energies range from 2.7 to 6.48 eV, depending on the computational method and parameters. One notable difference in oxygen vacancy formation between ThO2 and CeO2 is that the ground states for the optimized structures are AFM for ThO2y and FM for CeO2y, corresponding to a magnetic moment of S = 0 μB and S = 2.0 μB, respectively. We thus examined the total energies and electronic structures of relaxed ThO2y and CeO2y with the magnetic moment restricted to 0 μB and 2 μB. For ThO2y, the AFM state Table 2. Calculated Oxygen Vacancy Formation Energies (eV) for ThO2 and CeO2 as a Function of Ueff and System Size Ueff (eV) 3.0
4.0
5.0
6.0
7.0
ThO2 (95 atoms)
7.44
7.38
7.32
ThO2 (11 atoms)
7.50
7.43
7.36
CeO2 (95 atoms)
-
4.54
4.42
4.20
CeO2 (11 atoms)
-
5.36
5.41
5.47
-
CeO2 (other calc.)
2.7,4 3.39,19 6.48,19 3.20,20 4.516
CeO2 (exp.)
4.7266
is 0.98 eV more stable than the FM state. As shown in Figure 5a and c, the DOS distribution for FM and AFM ThO2y exhibits remarkably different character. The occupied and localized Th 6d and 5f orbitals are found in the energy range from 0.38 to 0.13 eV for AFM ThO2y, whereas in FM state these orbitals are unoccupied. In addition, the distance between the occupied O 2p states and Fermi level is ∼3.73 eV for AFM ordering, while the occupied O 2p states are located near the Fermi level for FM ordering. For CeO2y, FM ordering is preferred because it is ∼54 meV lower in energy than the AFM ordering. This result is comparable to experiments68 where oxygen vacancy induced ferromagnetism was observed. Theoretically, the energy differences between FM and AFM were found to be
