Abstract
Since the oxygen potential and the oxygen diffusion coefficient of UO2 have a significant impact on fuel performance, many experimental data have been obtained. However, experimental data of the oxygen potential and the oxygen diffusion coefficient in the high temperature region above 1673 K are very limited. In the present study, we aimed to obtain these data and analyze them by defect chemistry. the oxygen potentials and the oxygen chemical diffusion coefficient of UO2 were measured by the gas equilibrium method in the near stoichiometric region at temperatures ranging from 1673 to 1873 K. A data set of oxygen potentials was made together with literature data and analyzed by defect chemistry. The oxygen potential of UO2 was determined as a function of O/U ratio and temperature, and an equation representing the relationship was derived. The oxygen chemical diffusion coefficient values obtained in this study were reasonably close to the literature values. The oxygen partial pressure dependence of the oxygen chemical diffusion coefficients was predicted from the evaluated results of the oxygen potential data, but no clear dependence was observed.
1 Introduction
It is well-known that UO2, which has a fluorite structure, is a non-stoichiometric oxide that is stable in the hyper-stoichiometric composition range. It has also been shown that UO2 can lose oxygen to form a hypo-stoichiometric phase at high temperatures and low oxygen potentials. Many researchers have investigated oxygen potentials to determine the oxygen-to-uranium (O/U) ratio and chemical stability (; ; ; ; ; ; ; Tetenbaum and Hunt 1968; ; Wheeler 1971; ; Wheeler and Jones 1972; ; Ugajin 1983), because its stoichiometry significantly affects thermal properties and fuel performance. Ugajin (1983) investigated the near-stoichiometric region by thermogravimetry in a mixed-gas atmosphere of CO/CO2. Oxygen partial pressure was determined in situ with a stabilized zirconia oxygen sensor. ) and Markin and Bones () determined the oxygen potential for O/U ratios in the range of 2.01 to 2.53 by the electromotive force (EMF) method. The oxygen potential in UO2−x was also measured at temperatures above 1873 K using H2 and CO gases (Wheeler 1971; ), and various methods were employed in the measurements. However, the data were scattered over a range larger than 200 kJ/mol, especially when located in the near-stoichiometric region because of difficulty in determining the O/U ratio and oxygen potential pressure. The relationship between the O/U ratio, the temperature, and the oxygen potential has been represented in previous works. Lindemer and Besmann () derived the relationship from the literature data and the classical thermodynamic theory for a solid solution. Some studies represented the relationship by means of the thermodynamic database (; ).
The diffusion kinetics for the oxygen ions in oxide fuels are closely involved in diffusion-controlled phenomena such as oxidation and reduction, sintering, and irradiation behavior. For this reason, the oxygen diffusion coefficients of UO2 have been measured since the 1960s (; ; ; ; ; ; ; ; ; ; ). The oxidation and reduction of oxide fuels rely on chemical diffusion in thermodynamically non-ideal systems where oxygen ions are the faster species. The oxygen chemical diffusion coefficient, , is generally obtained by measuring weight changes or electrical conductivity changes during redox reactions (; ; ; ) and has been measured over a wide temperature range; but there are very few reports above 1673 K.
In this work, the oxygen potentials of UO2 were obtained in hyper-stoichiometric compositions by the gas equilibrium method, a Brouwer diagram was constructed, and correlations to represent the O/U ratio were derived as functions of temperature and oxygen partial pressure. In addition, the oxygen chemical diffusion coefficients of UO2+x in the temperature range above 1673 K were measured and compared with literature data, and the dependence of oxygen chemical diffusion coefficients on oxygen partial pressure was discussed.
2 Experimental procedures
Samples of UO2 were prepared by powder metallurgy, with UO2 powder made by the ammonium diuranate (ADU) process used as the starting material. The main impurities contained in the raw powder are listed in Table 1. The powder was pressed into a disk-like sample and sintered at 1973 K for 2.5 h in a gas mixture of 4.5% H2–Ar, with added moisture. The amount of moisture was adjusted by passing 4.5% H2–Ar mixed gas through a water bath kept at a constant temperature. The sample weight was 331.91 mg, and the size was 4.253 mm in diameter by 2.275 mm in thickness.
TABLE 1
| Element | Concentration (ppm) |
|---|---|
| Ag | <0.2 |
| Al | <10 |
| B | <0.3 |
| Bi | <5 |
| Ca | <10 |
| Cd | <0.6 |
| Cr | <10 |
| Cu | <1 |
| Fe | 10 |
| Mg | <2 |
| Mn | <6 |
| Mo | <10 |
| Ni | <10 |
| Pb | <10 |
| Si | <10 |
| Sn | <10 |
| Ti | <10 |
| V | <10 |
| Zn | <50 |
Impurities in the UO2 raw powder.
The oxygen potential and the oxygen chemical diffusion coefficient measurements were carried out at 1673 K, 1773 K, and 1873 K by the gas equilibrium method using a thermogravimeter (TG-DTA 2000SA, Bruker AXS). The uncertainty of the thermogravimeter was ±0.01 mg, which corresponds to ±0.0005 in the O/U ratio. In the measurements, it was observed that the sample weight was reduced by 60 μg/h. It was concluded that the high vapor pressure of the UO3 species caused the large weight reduction. Due to the small sample volume and short time to reach equilibrium, the measurement of a data point was carried out in less than 30 min; therefore, the uncertainty in the O/U ratio determination was estimated to be ±0.00015.
The oxygen partial pressure in the atmosphere was controlled by the equilibrium reaction of H2O = H2 + 1/2O2 and determined by oxygen sensors that measured the oxygen partial pressure at the equipment inlet and outlet. The gas phase equilibrium was related to the standard Gibbs free energy of formation of water, (J/mol), by the following equations ()where R is the gas constant (8.3145 J/K/mol) and T is absolute temperature. Eq. 1 represents the value from 298 K to 2500 K. The ratio of was calculated using , which was monitored at 973 K using an oxygen sensor. The of the atmosphere in the thermogravimeter at higher temperature was calculated under the assumption that the ratio had the same value at the oxygen sensor and the thermogravimeter. The was described by the following equation
The uncertainty of was estimated to be ±10 kJ/mol from the difference of between the inlet and outlet gas. In the measurements, the change in specimen weight was measured in response to changes in which were controlled by the ratio of . Equilibrium conditions were obtained in a relatively short time (∼15 min) because of the smallness and thinness of the specimen disk. An effect of vaporization of the specimen on measurement data was not observed.
3 Results
The oxygen potential was measured at temperatures of 1673 K, 1773 K, and 1873 K, and data are shown in Figure 1. The slightly increased with temperature, depending on the O/U ratio. The relationship between and x is plotted in Figure 2. In this figure, the well-known proportionality relationship between and deviation x from stoichiometry was observed:where n is a characteristic number identifying the type of point defect in agreement with literature data (; Wheeler 1971; ; Wheeler and Jones 1972). The figure shows that the present data changed in accordance with the relationship of n = +2. The literature data were also plotted in the figure and analyzed using the relationship of Eq. 4. In the higher region, the relationship was n = +6. In the hypo-stoichiometric region, it was observed to be n = −3, as previously reported (Tetenbaum and Hunt 1968; ).
FIGURE 1
FIGURE 2
Since the specimen used in this work had the shape of a planar sheet, the diffusion equation was set up for planar sheet geometry with a thickness of 2L. If the sheet is initially at a uniform concentration, C1, and the surface condition () is such thatwhere D is the diffusion coefficient, C is the concentration of diffusing substance in the planar sheet, k is the rate constant for surface reaction, Cs is the actual concentration just within the planar sheet, and C0 is the concentration required to maintain equilibrium with the surrounding atmosphere. The obtained solution iswhere the values are the positive roots of
and
is a dimensionless parameter. The total amount of diffusing substance, , entering or leaving the sheet up to time t is expressed as a fraction of , the corresponding quantity after infinite time, by
The measured data were fitted by Eq. 9 using D and k as parameters. The experimental conditions and the fitting results are listed in Table 2, and Figure 3 shows the weight-change curve and the fitted curve at 1673 K. Good agreement can be seen between the experimental data and the fitted curve. The error in the oxygen chemical diffusion coefficient was calculated to be 84%. It is presumed that the periodic noise from the thermogravimeter degraded the fitting accuracy.
TABLE 2
| No. | Temperature °K | O/U ratio | k | ||
|---|---|---|---|---|---|
| Initial | Final | (m2/s) | (m/s) | ||
| 1 | 1673 | 2.116 | 2.082 | 3.73 × 10–8 | 9.52 × 10–7 |
| 2 | 1673 | 2.082 | 2.062 | 1.05 × 10–9 | 2.77 × 10–6 |
| 3 | 1673 | 2.074 | 2.037 | 3.47 × 10–8 | 2.99 × 10–6 |
| 4 | 1673 | 2.020 | 2.004 | 8.36 × 10–9 | 1.03 × 10–5 |
| 5 | 1773 | 2.115 | 2.070 | 8.66 × 10–8 | 2.39 × 10–6 |
| 6 | 1873 | 2.133 | 2.101 | 1.16 × 10–8 | 1.57 × 10–6 |
| 7 | 1873 | 2.101 | 2.080 | 2.38 × 10–7 | 2.45 × 10–6 |
| 8 | 1873 | 2.068 | 2.050 | 6.24 × 10–8 | 3.87 × 10–7 |
| 9 | 1873 | 2.050 | 2.028 | 1.20 × 10–8 | 7.45 × 10–6 |
Experimental conditions, oxygen chemical diffusion coefficient , and surface reaction rate constant, k.
FIGURE 3
4 Discussion
The relationships among n = +6, +2, and −3 are shown in Figure 2. Two types of Brouwer diagram are proposed depending on the kinds of dominant point defects: intrinsic defects and Frenkel defects. The reported electrical conductivity measurements showed that the electronic conduction mechanism was observed, therefore, it is assumed that intrinsic defects were dominant in the stoichiometric composition. Cooper et al. () calculated a Brouwer diagram of UO2 using an ab initio approach in which intrinsic defects were dominant. In the near stoichiometric region, defect equilibria were considered in reactions (10)–(13):
The equilibrium constants in the aforementioned defect reactions can be described by Eqs 14–17, respectively:
In the case where intrinsic defects are dominant, the defect concentrations of and dominate over those of and . Therefore, near the stoichiometric region. The following Eqs 18–20 were obtained from 14–17:
was obtained from experimental and literature data in the near-stoichiometric region as follows:
In the oxidation region where n = +2, the (2:2:2) Willis cluster (Willis 1987) was assumed as follows:
The equilibrium constant in the aforementioned defect reaction can be described by the following equation:
can be written as
In the hypo-stoichiometric region, n = −3 has been reported by previous studies (Tetenbaum and Hunt 1968; ). Kofstad proposed that interstitial uranium ions with two effective charges, , predominated in this region (). The following reaction was assumed:
In the oxidation region where n = +6, more complex defects were expected; however, there have been no reports describing this relationship. Defect reactions were not assumed in this region, and only the relationship of n = +6 was described by the following equation:
The relationships of n = +2 and −2 should be observed in the near-stoichiometric region because intrinsic ionization dominates. The relationships among n = −3, +2 and +6, are shown in Figure 2. The experimental data were fitted by Eqs. 26 and 19–27 assuming that x = , , or , and the equilibrium constants were obtained for each temperature. The equilibrium constant, K, in the defect reactions can be written as
Enthalpy, (J/mol), and entropy, (J/mol/K), for the equilibrium constants were evaluated as follows:
In addition, it was assumed that Eq. 19 equals Eq. 24. The and in each region are shown in Table 3. Eqs 17–27 describe the Brouwer diagram as shown in Figure 4. The figure shows that the Brouwer diagrams at 1673, 1773, and 1873 K represented the experimental data very well. The Brouwer diagram can give the defect concentrations of and . The O/U ratio can be described as Eq. 32, when the main defects are or :
TABLE 3
| UO2 | PuO2 () | |||
|---|---|---|---|---|
| ΔH (kJ/mol) | ΔS (J/mol/K) | ΔH (kJ/mol) | ΔS (J/mol/K) | |
| -130 | -81.0 | - | - | |
| -173.0 | -38.1 | - | - | |
| -60.0 | 5.0 | 159.3 | -4.66 | |
| 464.5 | 32.0 | 282.5 | 54.66 | |
| 1,079.1 | 95.0 | - | - | |
| 300.0 | 85.1 | 325 | 85 | |
| 404.5 | 37.0 | 441.8 | 50 | |
| 240.0 | 90.1 | 484.3 | 80.34 | |
| 764.5 | 117.1 | 607.5 | 134.7 | |
Defect formation energies of UO2 and PuO2.
FIGURE 4
and can be described in Eqs. 33 and 34 using Eqs. 19–27, respectively. The indices −5 and −1/5 are parameters that represent x near the boundary between each line:
Eq. 32 was rewritten as Eq. 35 using Eqs 33 and 34, which can represent the O/U ratio as functions of and T:
Eq. 35 gives the relationships between oxygen potential, temperature, and composition in UO2±x. Figure 5 shows the relationships between x, T, and and literature data (; Wheeler 1971; ; Wheeler and Jones 1972).
FIGURE 5
The and for the equilibrium constants were assessed as shown in Table 3. The formation energies of , , , and in UO2 were -60.0 kJ/mol, 464.5 kJ/mol, 404.5 kJ/mol, and 300.0 kJ/mol, respectively. The Frenkel defect formation energy was compared with literature data (; ; ; ; ; ; ; ; ; ; ; Terentyev 2007; Yun and Kim 2007; ; Tiwary, van de Walle, and Gronbech-Jensen 2009; Yu, Devanathan, and Weber 2009; Staicu et al., 2010; ; ; ; Vathonne et al., 2014), as shown in Figure 6. The present data approximately corresponded to literature data, which were obtained by experiments and calculations. The Frenkel defect formation energies of UO2were compared with those of PuO2 () and they are almost the same (Table 3). The formation energy value for is lower in UO2 than in PuO2, -60.0 kJ/mol and 159.3 kJ/mol, respectively. Conversely, the formation energy value for is lower in PuO2 than in UO2, 282.5 kJ/mol and 464.5 kJ/mol, respectively. These differences are caused by changing from M4+ to U5+ and Pu3+, respectively, in UO2 and PuO2.
FIGURE 6
Figure 7 shows a comparison between the experimental data (; ; ; ; ; ; ; Tetenbaum and Hunt 1968; ; Wheeler 1971; ; Wheeler and Jones 1972; ; Ugajin 1983) and the calculated results of the oxygen potential of UO2. The results of the calculations represent the data within = ±51 kJ/mol. It can be seen that there is no large discrepancy between the calculated values and the literature values in the hyper-stoichiometric composition range, but there is a large discrepancy in the near- and hypo-stoichiometric regions where there are few experimental data (Figure 7). Especially in the near-stoichiometric region, further expansion of experimental data is necessary, but it is greatly affected by impurities (); thus, it is necessary to reduce the impurities in the sample to obtain highly accurate data.
FIGURE 7
Figure 8 shows the comparison between the oxygen chemical diffusion coefficients measured in this study and the literature data (; ; ; ; ; ). The data obtained in this study have larger values than those reported by Bittel et al. and Breitung, but smaller values than those in the near-stoichiometric composition proposed by Berthinier et al. (). The data reported by Bittel et al. are the only experimental data in the temperature range above 1673 K. They evaluated the oxygen chemical diffusion coefficients from the results of the steam oxidation of UO2, but it was pointed out that the U4O9 phase was formed on the sample surface, which caused the evaluated oxygen chemical diffusion coefficients to be lower (). According to the calculation results reported by Berthinier et al., the oxygen chemical diffusion coefficients had maximum values near the stoichiometric composition and decreased with increasing deviation from the stoichiometric composition (). Thus, the oxygen chemical diffusion coefficients measured in this study can be considered reasonable, in general. The dependence of the measured diffusion coefficients on oxygen partial pressure is shown in Figure 9. The oxygen chemical diffusion coefficients and the oxygen self-diffusion coefficients () are related by Darken’s relationship as given by:where the positive and negative signs apply to the hyper- and hypo-stoichiometric ranges, respectively. The oxygen self-diffusion coefficient follows the equation of (; Watanabe, Kato, and Sunaoshi 2020)where is the pre-exponential term for the oxygen vacancy diffusion, is the pre-exponential term for oxygen interstitial diffusion, is the migration energy of the oxygen vacancy, and is the migration energy of the oxygen interstitial. The and in Eq. 37 can be calculated by Eqs 33 and 34. The oxygen self-diffusion coefficient can be calculated by using the pre-exponential terms and the migration energies evaluated by Kato et al. The oxygen chemical diffusion coefficients can be derived from Eqs 36 and 37, and the calculation results are shown in Figure 9. Since the oxygen chemical diffusion coefficients were measured in the regions of n = +2 and n = +6, it is considered that the oxygen diffusion coefficients were dependent on the oxygen partial pressure; however, the oxygen partial pressure dependence was not clearly observed in this study.
FIGURE 8
FIGURE 9
5 Conclusions
The oxygen potentials and oxygen chemical diffusion coefficients of UO2 were measured by the gas equilibrium method. A data set of oxygen potential was made and analyzed based on defect chemistry. The relationships between deviation x from stoichiometric composition and the oxygen partial pressure were investigated. Defect equilibrium constants were evaluated by fitting the experimental data and defect formation energies were determined and used to construct a Brouwer diagram. The correlation with UO2 oxygen potential was then derived. The correlation described the oxygen potential very well even in the near-stoichiometric composition range. The oxygen Frenkel formation energy was estimated to be 404.5 kJ/mol, which was in good agreement with literature values. As a result of comparison with the literature values, it was found that the values of the oxygen chemical diffusion coefficients obtained in this study were generally reasonable. The oxygen partial pressure dependence of the oxygen chemical diffusion coefficient was predicted from the evaluated results of the oxygen potential data, but no clear dependence was observed.
Statements
Data availability statement
The original contributions presented in the study are included in the article/Supplementary Material, further inquiries can be directed to the corresponding author.
Author contributions
MW: investigation, analysis, and writing the original draft; MK: conceptualization, analysis, and reviewing and editing the original draft.
Conflict of interest
The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.
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References
1
AckermannR. J.RauhE. G.ChandrasekharaiahM. S. (1969). 'Thermodynamics study of the urania-uranium system. J. Phys. Chem.73, 762–769. 10.1021/j100724a002
2
AitkenE. A.BrassfieldH. C.FryxellR. E. (1966). “Thermodynamic behaviour of hypostoichiometric UO2,” in Conference: Symposium on thermodynamics with emphasis on nuclear materials and atomic transport in solids (Vienna (Austria), 435–453.
3
AnderssonD. A.UberuagaB. P.NerikarP. V.UnalC.StanekC. R. (2011). U and Xe transport in UO2±x: Density functional theory calculations. Phys. Rev. B84, 054105. 10.1103/physrevb.84.054105
4
AronsonS.BelleJ. (1958). 'Nonstoichiometry in uranium dioxide. J. Chem. Phys.29, 151–158. 10.1063/1.1744415
5
AukrustE.ForlandT.HagemarkK. (1962). “Equilibrium measurements and interpretation of non-stoichiometry in UO2+x,” in Thermodynamics of nuclear materials (Vienna: IAEA), 713–722.
6
AuskernA. B.BelleJ. (1961). 'Oxygen ion self-diffusion in uranium dioxide. J. Nucl. Mater.3, 267–276. 10.1016/0022-3115(61)90194-5
7
BaichiM.ChatillonC.DucrosG.FromentK. (2006). 'Thermodynamics of the O–U system. IV – critical assessment of chemical potentials in the U–UO2.01 composition range. J. Nucl. Mater.349, 17–56. 10.1016/j.jnucmat.2005.09.001
8
BayogluA.LorenzelliR. (1984). 'Oxygen diffusion in fcc fluorite type nonstoichiometric nuclear oxides MO2±x☆', Solid State Ionics, 12, 53–66. 10.1016/0167-2738(84)90130-9
9
BayogluA. S.LorenzelliR. (1979). 'Etude de la diffusion chimique de l'oxygene dans puo2−x par dilatometrie et thermogravimetrie. J. Nucl. Mater.82, 403–410. 10.1016/0022-3115(79)90022-9
10
BelleJ. (1969). 'Oxygen and uranium diffusion in uranium dioxide (a review). J. Nucl. Mater.30, 3–15. 10.1016/0022-3115(69)90163-9
11
BerthinierC.RadoC.ChatillonC.HodajF. (2013). 'Thermodynamic assessment of oxygen diffusion in non-stoichiometric UO2±x from experimental data and Frenkel pair modeling. J. Nucl. Mater.433, 265–286. 10.1016/j.jnucmat.2012.09.011
12
BittelJ. T.SjodahlL. H.WhiteJ. F. (1969). 'Steam oxidation kinetics and oxygen diffusion in UOz at high temperatures. J. Am. Ceram. Soc.52, 446–451. 10.1111/j.1151-2916.1969.tb11976.x
13
BreitungW. (1978). Oxygen self and chemical diffusion coefficients in. J. Nucl. Mater.74, 10–18. 10.1016/0022-3115(78)90527-5
14
CatlowC. R. A. (1977). 'Point-Defect and electronic properties of uranium-dioxide. Proc. R. Soc. Lond. Ser. a-Mathematical Phys. Eng. Sci.353, 533–561.
15
CatlowC. R. A.LidiardA. B. (1974). Symposium on the thermodynamics of nuclear materials, 27-42. Vienna, Austria: IAEA.Theoretical studies of point-defect properties of uranium dioxide.
16
ChiltonG. R.EdwardsJ. (1980). Oxygen potentials of U0.77Pu0.23O2+x in the temperature range 1523-1822 K." 17, United Kingdom Atomic Energy Authority, Northern DivisionIn.
17
ClausenK.HayesW.MacdonaldJ. E.OsbornR.HutchingsM. T. (1984). 'Observation of oxygen Frenkel disorder in uranium-dioxide above 2000-K by use of neutron-scattering techniques. Phys. Rev. Lett.52, 1238–1241. 10.1103/physrevlett.52.1238
18
CooperM. W. D.MurphyS. T.AnderssonD. A. (2018). 'The defect chemistry of UO2±x from atomistic simulations. J. Nucl. Mater.504, 251–260. 10.1016/j.jnucmat.2018.02.034
19
CrankJ. (1979). The mathematics of diffusion. Oxford, United Kingdom, Oxford University Press.
20
CrocombetteJ. P.JolletF.NgaL. N.PetitT. (2001). 'Plane-wave pseudopotential study of point defects in uranium dioxide. Phys. Rev. B64, 104107. 10.1103/physrevb.64.104107
21
FreyssM.DoradoB.BertolusM.JomardG.VathonneE.GarciaP.et al (2012). “First-principles DFT + U study of radiation damage in UO2 : f electron correlations and the local energy minima issue,” in Psi-k newsletter, 35–61.
22
FreyssM.PetitT.CrocombetteJ. P. (2005). 'Point defects in uranium dioxide: Ab initio pseudopotential approach in the generalized gradient approximation. J. Nucl. Mater.347, 44–51. 10.1016/j.jnucmat.2005.07.003
23
GuéneauC.BaichiM.LabrocheD.ChatillonC.SundmanB. (2002). 'Thermodynamic assessment of the uranium–oxygen system. J. Nucl. Mater.304, 161–175. 10.1016/s0022-3115(02)00878-4
24
GuptaF.BrillantG.PasturelA. (2007). 'Correlation effects and energetics of point defects in uranium dioxide: A first principle investigation. Philos. Mag.87, 2561–2569. 10.1080/14786430701235814
25
HagemarkK.BroliM. (1966). 'Equilibrium oxygen pressures over the nonstoicheiometric uranium oxides UO2+x and U3O8-z at higher temperatures. J. Inorg. Nucl. Chem.28, 2837–2850. 10.1016/0022-1902(66)80010-6
26
IwasawaM.ChenY.KanetaY.OhnumaT.GengH. Y.KinoshitaM. (2006). 'First-principles calculation of point defects in uranium dioxide. Mater. Trans.47, 2651–2657. 10.2320/matertrans.47.2651
27
JacksonR. A.MurrayA. D.HardingJ. H.CatlowC. R. A. (1986). The calculation of defect parameters in UO2. Philosophical Mag. a-Physics Condens. Matter Struct. Defects Mech. Prop.53, 27–50. 10.1080/01418618608242805
28
JavedN. A. (1972). 'Thermodynamic study of hypostoichiometric urania. J. Nucl. Mater.43, 219–224. 10.1016/0022-3115(72)90053-0
29
KatoM.NakamuraH.WatanabeM.MatsumotoT.MachidaM. (2017). Defect chemistry and basic properties of non-stoichiometric PuO2. Defect Diffusion Forum375, 57–70. 10.4028/www.scientific.net/ddf.375.57
30
KatoM.WatanabeM.HirookaS.VauchyR. (In press 2023). Oxygen diffusion in flurotite-tyoe oxides, CeO2, ThO2, UO2, PuO2, and (U, Pu)O2. Front. Nucl. Eng.
31
KimK. C.OlanderD. R. (1981). Oxygen diffusion in UO2−x. J. Nucl. Mater.102, 192–199. 10.1016/0022-3115(81)90559-6
32
KofstadP. (1972). Nonstoichiometry, diffusion, and electrical conductivity in binary metal oxides. Hoboken, New Jersey, United States, John Wiley & Sons.
33
KoningsR. J. M.BenesO. (2013). 'The heat capacity of NpO2 at high temperatures: The effect of oxygen Frenkel pair formation. J. Phys. Chem. Solids74, 653–655. 10.1016/j.jpcs.2012.12.018
34
KubaschewskiO.AlcockC. B. (1979). Metallurgical thermochemistry. Pergamon; 5th edition, Pergamon, Turkey.
35
LayK. W. (1970). 'Oxygen chemical diffusion coefficient of uranium dioxide. J. Am. Ceram. Soc.53, 369–373. 10.1111/j.1151-2916.1970.tb12134.x
36
LindemerT. B.BesmannT. M. (1985). Chemical thermodynamic representation of UO2±x. J. Nucl. Mater.130, 473–488. 10.1016/0022-3115(85)90334-4
37
MaillardS.AnderssonD.FreyssM.BrunevalF. (2022). 'Assessment of atomistic data for predicting the phase diagram and defect thermodynamics. The example of non-stoichiometric uranium dioxide. J. Nucl. Mater.569, 153864. 10.1016/j.jnucmat.2022.153864
38
MarinJ. F.ContaminP. (1969). Uranium and oxygen self-diffusion in UO2. J. Nucl. Mater.30, 16–25. 10.1016/0022-3115(69)90164-0
39
MarkinT. L.BonesR. J. (1962a). The determination of changes in free energy for uranium oxides using a high temperature galvanic cell Part 1.
40
MarkinT. L.BonesR. J. (1962b). The determination of some thermodynamic properties of uranium oxides with O/U ratios between 2.00 and 2.03 using a high temperature galvanic cell Part 2.
41
MarkinT. L.WheelerV. J.BonesR. J. (1968). High temperature thermodynamic data for UO2±x. J. Inorg. Nucl. Chem.30, 807–817. 10.1016/0022-1902(68)80441-5
42
MatzkeH. (1987). Atomic transport properties in UO2 and mixed oxides (U, Pu)O2. J. Chem. Soc. Faraday Trans.2, 1243. 10.1039/ft9908601243
43
MurchG. E.BradhurstD. H.De BruinH. J. (1975). Oxygen self-diffusion in non-stoichiometric uranium dioxide. Philosophical Mag. A J. Theor. Exp. Appl. Phys.32, 1141–1150. 10.1080/14786437508228095
44
MurchG. E.CatlowC. R. A. (1987). 'Oxygen diffusion in UO2, ThO2 and PuO2 a review. J. Chem. Society-Faraday Trans. Ii83, 1157–1169. 10.1039/f29878301157
45
MurchG. E.ThornR. J. (1978). 'The mechanism of oxygen diffusion in near stoichiometric uranium dioxide. J. Nucl. Mater.71, 219–226. 10.1016/0022-3115(78)90419-1
46
NerikarP.WatanabeT.TulenkoJ. S.PhillpotS. R.SinnottS. B. (2009). 'Energetics of intrinsic point defects in uranium dioxide from electronic-structure calculations. J. Nucl. Mater.384, 61–69. 10.1016/j.jnucmat.2008.10.003
47
PetitT.LemaignanC.JolletF.BigotB.PasturelA. (1998). 'Point defects in uranium dioxide. Philosophical Mag. B-Physics Condens. Matter Stat. Mech. Electron. Opt. Magnetic Prop.77, 779–786. 10.1080/014186398259176
48
RuelloP.ChirlesanG.Petot-ErvasG.PetotC.DesgrangesL. (2004). 'Chemical diffusion in uranium dioxide – influence of defect interactions. J. Nucl. Mater.325, 202–209. 10.1016/j.jnucmat.2003.12.007
49
StaicuD.WissT.RondinellaV. V.HiernautJ. P.KoningsR. J. M.RonchiC. (2010). 'Impact of auto-irradiation on the thermophysical properties of oxide nuclear reactor fuels. J. Nucl. Mater.397, 8–18. 10.1016/j.jnucmat.2009.11.024
50
TerentyevD. (2007). 'Molecular dynamics study of oxygen transport and thermal properties of mixed oxide fuels. Comput. Mater. Sci.40, 319–326. 10.1016/j.commatsci.2007.01.002
51
TetenbaumM.HuntP. D. (1968). 'High‐Temperature thermodynamic properties of oxygen‐deficient urania. J. Chem. Phys.49, 4739–4744. 10.1063/1.1669953
52
TiwaryP.van de WalleA.Gronbech-JensenN. (2009). 'ab initio construction of interatomic potentials for uranium dioxide across all interatomic distances. Phys. Rev. B80, 174302. 10.1103/physrevb.80.174302
53
UgajinM. (1983). 'Measurements of O/U ratio and oxygen potential for UO2+x (0≤x≲0.1). J. Nucl. Sci. Technol.20, 228–236. 10.1080/18811248.1983.9733384
54
VathonneE.WiktorJ.FreyssM.JomardG.BertolusM. (2014). 'DFT + U investigation of charged point defects and clusters in UO2. J. Phys. Condens Matter26, 325501. 10.1088/0953-8984/26/32/325501
55
WatanabeM.KatoM.SunaoshiT. (2020). Oxygen self-diffusion in near stoichiometric (U, Pu)O2 at high temperatures of 1673-1873 K. J. Nucl. Mater.542, 152472. 10.1016/j.jnucmat.2020.152472
56
WheelerV. J. (1971). High temperature thermodynamic data for UO2−x. J. Nucl. Mater.39, 315–318. 10.1016/0022-3115(71)90151-6
57
WheelerV. J.JonesI. G. (1972). Thermodynamic and composition changes in UO2±x (x< 0.005) at 1950 K. J. Nucl. Mater.42, 117–121. 10.1016/0022-3115(72)90018-9
58
WillisB. T. M. (1987). 'Crystallographic studies of anion-excess uranium-oxides. J. Chem. Society-Faraday Trans. Ii83, 1073–1081. 10.1039/f29878301073
59
YuJ.DevanathanR.WeberW. J. (2009). 'First-principles study of defects and phase transition in UO2. J. Phys. Condens Matter21, 435401. 10.1088/0953-8984/21/43/435401
60
YunY. S.KimW. W. (2007). “First principle studies on electronic and defect structures of UO2, ThO2, and PuO2,” in Proceedings of the KNS spring meeting. Republic of Korea, daejeon, South Korea, (KNS).
Summary
Keywords
oxygen potential, oxygen chemical diffusion, defect chemistry, uranium dioxide, oxygen self-diffusion
Citation
Watanabe M and Kato M (2023) Oxygen potential, oxygen diffusion, and defect equilibria in UO2±x. Front. Nucl. Eng. 1:1082324. doi: 10.3389/fnuen.2022.1082324
Received
28 October 2022
Accepted
13 December 2022
Published
06 January 2023
Volume
1 - 2022
Edited by
Lelio Luzzi, Politecnico di Milano, Italy
Reviewed by
Lionel Desgranges, Commissariat à l'Energie Atomique et aux Energies Alternatives (CEA), France
Jacques Lechelle, Commissariat à l'Energie Atomique et aux Energies Alternatives (CEA), France
Updates
Copyright
© 2023 Watanabe and Kato.
This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.
*Correspondence: Masashi Watanabe, watanabe.masashi81@jaea.go.jp
This article was submitted to Nuclear Materials, a section of the journal Frontiers in Nuclear Engineering
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