Article pubs.acs.org/IC
What Is the Actual Local Crystalline Structure of Uranium Dioxide, UO2? A New Perspective for the Most Used Nuclear Fuel L. Desgranges,*,† Y. Ma,† Ph. Garcia,† G. Baldinozzi,‡,§ D. Siméone,‡,§ and H. E. Fischer∥ †
CEA, DEN, DEC F-13108 Saint Paul lez Durance Cedex, France SPMS, LRC Carmen, CNRS Centrale Supélec, 92295 Châtenay-Malabry, France § CEA, DEN, DMN F-91191 Gif-sur-Yvette Cedex, France ∥ Institut Laue-Langevin, 6 rue Jules Horowitz, B.P. 156, 38042 Grenoble Cedex, France ‡
ABSTRACT: Up to now, uranium dioxide, the most used nuclear fuel, was said to have a Fm3̅m crystalline structure from 30 to 3000 K, and its behavior was modeled under this assumption. However, recently X-ray diffraction experiments provided atomic pair-distribution functions of UO2, in which UO distance was shorter than the expected value for the Fm3̅m space group. Here we show neutron diffraction results that confirm this shorter UO bond, and we also modeled the corresponding pair-distribution function showing that UO2 has a local Pa3̅ symmetry. The existence of a local lower symmetry in UO2 could explain some unexpected properties of UO2 that would justify UO2 modeling to be reassessed. It also deserves more study from an academic point of view because of its good thermoelectric properties that may originate from its particular crystalline structure.
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INTRODUCTION The UO2 crystal structure was first determined by neutron diffraction on a single crystal.1 At high temperature, it was better refined by allowing the oxygen atoms to relax from their regular positions in the Fm3̅m space group.2 This description was further improved by an anharmonic description of oxygen thermal motion.3 Starting from one uranium atom located at the (0, 0, 0) position and one oxygen atom located at the (1/4, 1 /4, 1/4) position, a UO2 crystalline cell can be built by applying symmetries of a Fm3̅m space group (Table 1). Thus, each
tion function (PDF), from which the UO and UU distances were derived. The UO distance was shown to decrease with increasing temperature, while the UU distance increased with increasing temperature from room temperature to the UO2 melting temperature. This discrepancy was explained by the existence of atomic disorder, which may be a satisfactory interpretation at high temperature near the melting point but which is in contradiction with previously published neutron diffraction data for lower temperatures. Three authors (refs 2, 5, and 6) measured the UO2 neutron diffraction pattern at 1300 K, and all agreed on the description of its crystalline structure using the Fm3̅m space group, leading to an increase of the UO distance as a function of the temperature. However, at 1300 K, Skinner et al. already measured a shortening of the UO distance. This discrepancy is difficult to resolve because the UO distance is determined by two different methods even though both are derived from diffraction patterns. In one case, Willis’ approach,2 only the intensity diffracted by crystalline planes is directly modeled in reciprocal space; in the other case, Skinner et al.’s approach,4 the whole diffraction pattern is first Fouriertransformed to get its atomic pair-distribution function PDF(r) and then modeled in real space. In the first case, the distances are derived from the position and intensity of the diffracted peaks, while in the second case, the distances can be read on the PDF(r), which is basically a histogram of the interatomic
Table 1. Atomic Positions in the UO2 Cell with Fm3m ̅ Symmetry Compared to Pa3̅ Symmetry U Fm3̅m U Pa3̅ O Fm3̅m O Pa3̅ O Fm3̅m O Pa3̅
(0, 0, 0) (0, 0, 0) (1/4, 1/4, 1/4) (1/4 + δ, 1/4 + δ, 1/4 + δ) (3/4, 3/4, 3/4) (3/4 − δ, 3/4 − δ, 3/4 − δ)
(1/2, 0, 0) (1/2, 0, 0) (1/4, 3/4, 3/4) (1/4 − δ, 3/4 − δ, 3/4 + δ) (3/4, 1/4, 1/4) (3/4 + δ, 1/4 + δ, 1/4 − δ)
(0, 1/2, 0) (0, 1/2, 0) (3/4, 3/4, 1/4) (3/4 − δ, 3/4 + δ, 1/4 − δ) (1/4, 1/4, 3/4) (1/4+ δ, 1/4 − δ, 3/4 + δ)
(0, 0, 1/2) (0, 0, 1/2) (3/4, 1/4, 3/4) (3/4 + δ, 1/4 − δ, 3/4 − δ) (1/4, 3/4, 1/4) (1/4 − δ, 3/4 + δ, 1/4 + δ)
uranium atom is at the center of a cube, having oxygen atoms at its corners (Figure 1a). With such crystalline symmetry, the UO distance is proportional to the UU distance and also to the cell parameter. In 2014, Skinner et al. published new experimental results that contradict this assumption using synchrotron X-ray diffraction.4 The diffraction pattern was treated by Fourier transformation to get the corresponding atomic pair-distribu© 2016 American Chemical Society
Received: September 15, 2016 Published: December 15, 2016 321
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secondary extinction is needed, in contrast to single crystals). The diffraction patterns were measured up to Qmax =23.5 Å−1, and they were refined using both the Rietveld method and the PDF approach. The diffraction pattern was treated to subtract the intensity due to background and that due to scattering from the silica container, as well as the isotropic scattering coming from incoherent scattering, which is subjected to distortion from inelastic scattering effects (Placzek correction). PDF(r) was then obtained by Fourier transformation of this corrected diffraction pattern. The corrected diffraction pattern was refined in reciprocal space using the Rietveld software JANA9 and the PDF(r) refined in real space using the PDFGUI software.10
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RESULTS The UO2 diffraction pattern at 1273 K, the highest temperature in our data set, and the corresponding PDF(r) are presented on Figure 2. UO2’s PDF(r) was fitted with the Fm3̅m space group at 1273 K. The fit converged reasonably well, on average, but was not able to properly fit the first two peaks corresponding to UO and OO distances (Figure 2a). The measured UO distance was indeed shorter than the calculated one, which is consistent with Skinner et al.’s result. On the other hand, the corresponding diffraction pattern at 1273 K was satisfactorily fitted with the Fm3m ̅ space group using anharmonic thermal motion for oxygen. These two refinement results on the same data set confirmed that UO2’s spatially averaged symmetry was Fm3̅m but evidenced that some local order should exist that could induce both shorter UO distances seen in the PDF(r) and anharmonic oxygen thermal motion refined by the Rietveld method. In order to determine what could be this local disorder, we performed Rietveld refinement in a manner similar to that of Willis’ paper2 using a four-site model for the oxygen atom in the Fm3̅m space group (Table 3). Because Rietveld refinement disregards the diffuse scattering between Bragg peaks, it fits only the spatially averaged structure, and it is not sensitive to local structural distortions. Therefore, a possible local distortion can be detected as a four-site model in the average Fm3̅m space group. The four sites determined by Rietveld refinement should then correspond to sites that are occupied in local symmetry. There are several possibilities for local ordering using these four sites to build a local space group. We chose Pa3̅ for three main reasons. First, it is physically justified to use this space group for describing the UO2 crystalline local structure because Pa3̅ is the crystalline symmetry of UO2 at low temperature11 and because other metal dioxides (SnO2, GeO2, and SiO2) also adopt Pa3̅ 12 and Fm3m ̅ crystalline structures as a function of the pressure. Second, using the Pa3̅ local symmetry gives consistent results with both the PDF and Rietveld refinements. The same 1273 K PDF(r) was refined with the Pa3̅ space group. Pa3̅ symmetry can be obtained starting from Fm3m ̅ symmetry by moving the oxygen atom out of its (1/4, 1/4, 1/4) site along the (1, 1, 1) direction to be settled on the (1/4 + δ, 1/4 + δ, 1/4 + δ) special position, generating a distorted oxygen cube with two longer distances and six shorter distances, as shown in Figure 1b. The refinement was very good for short-range order (up to 6 Å) but bad for longer range order (Figure 2b and Table 2). PDF fitting in Pa3̅ gives two UO peaks, UOs and UOl, in Figure 2b, with a small width, while PDF fitting in Fm3m ̅ gives one peak, in Figure 2a, with a larger width. With all experimental parameters being the same, this difference in width derives from the oxygen displacement parameter, which is small (uO = 0.014 Å) in Pa3̅,
Figure 1. Crystal structures of UO2 in the (a) Fm3m ̅ and (b) Pa3̅ space groups. The two longer distances in Pa3̅ are represented as black lines (see the text for a further explanation).
distances, whose amplitude is proportional to the probability of finding an atom at a distance r from an average atom at the origin. In this study, we performed a neutron diffraction experiment on UO2 and modeled it in both real and reciprocal space.
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EXPERIMENTAL SECTION
The neutron diffraction experiment was performed using a D4 neutron diffractometer7 at the Institute Laue-Langevin in Grenoble, France (http://dx.doi.org/10.5291/ILL-DATA.6-06-453). Two UO2 pellets, 8.3 mm in diameter and 14 mm in height, obtained by sintering at 1970 K under a 5% Ar/H2 atmosphere, were placed in a cylindrical sample container made of silica and sealed under vacuum. The impurity concentration in this polycrystalline sample is about 0.1 mol % (deduced from the electrical measurement of a similar sample in ref 8). The sample container was mounted in a vanadium furnace operated under vacuum. At each temperature, one diffraction pattern of the sample was acquired in its environment. Other diffraction patterns were acquired at a few temperatures in order to accurately measure the various sources of background scattering: first with no sample at all (i.e., an empty furnace) and then with an empty sample container. The stability of the diffraction pattern was checked by comparing data acquired at the same position and at different times. The neutron wavelength was determined by refinement of the diffraction pattern of a standard nickel sample and was found to be 0.4970 Å. Absorption correction was applied by taking into account the cylindrical shape of the sample and its polycrystalline nature (no 322
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Figure 2. Experimental PDF(r) at 1273 K (red) compared to fitted PDF(r) (blue) using the Fm3̅m (a) and Pa3̅ (b) space groups. The difference between the fitted and observed curves is represented as the green curve, and the first three distances, UO (UOs and UOl corresponding to short and long UO distances in Pa3̅), OO, and UU, are indicated by black sticks. (c) Experimental diffraction pattern (in red) compared to the calculated one (in blue). The difference is in green.
corresponding to thermal displacement, and bigger (uO = 0.024 Å) in Fm3m ̅ , corresponding to thermal displacement and local disorder. The consistency between the Rietveld and PDF refinements is demonstrated by looking at the UO distance calculated in each case in Figure 3. The short and long UO distances agree reasonably well in the Pa3̅ PDF refinement and in the split-atom model Rietveld refinement, taking into account not only the error bars given by the refinement programs but also the different biases associated with each method. These results are also in qualitative agreement with Skinner et al.’s paper,4 which evidenced an asymmetric UO distance distribution whose maximum can be associated with UOs, with the asymmetry at a larger distance coming from UOl. However, the UO distance given in Skinner et al.’s paper corresponds to the maximum of the UO distribution and
Table 2. Interatomic Distances (in Å) in the UO2 Cell with Fm3̅m Symmetry Compared to Pa3̅ Symmetrya Fm3̅m UO (first shell) OO (first shell) OO (second shell) UU (first shell) UO (second shell) OO (third shell) UU (second shell) OO (fourth shell)
2.3968 2.7642 3.909 3.909 4.584 4.7878 5.5285 5.5285
Pa3̅ 2.343//6, 2.7642 3.779//6, 3.909 4.438//3, 4.451//1, 5.5285 5.5285
2.561//2 4.054//6 4.558//3, 4.674//6 4.686//3, 4.910//3, 5.125//1
a The number noted as //n corresponds to the number of interatomic distances from one given oxygen atom.
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cannot be directly compared to the fitted UOs value given here because the overlap with UOl is not taken into account in the same manner. Third, the other local structures that can be built using the four oxygen sites may generate eight different OO distances, with Pa3̅ being the only structure in which all OO distances are equal. Local structures different from Pa3̅ would induce longer OO distances compared to the Pa3̅ structure. Because no significant error appears in the OO distance fitting in Pa3,̅ especially for the longer distances, we only considered Pa3̅ as the local symmetry. The Pa3̅ crystalline structure leads to a new interpretation of the uranium coordination polyhedron in UO2. By analogy to the already published crystalline structure of MO2 oxides having Pa3̅ structure, the coordination polyhedron of uranium would include only the oxygen atoms having a short UO bond; i.e., it should be an octahedron instead of a cube, as represented in Figure 2b. Thus, the UO2 crystalline structure can be interpreted as octahedron units that can locally be ordered in domains with Pa3̅ local symmetry having different orientations, which results in the average Fm3m ̅ symmetry. At a small scale within one domain, all atoms obey the Pa3̅ symmetry and PDF(r) is best fitted in Pa3̅ without disorder, while at larger scale, distances between atoms belonging to different domains provide a distribution that is best fitted in Fm3m ̅ with disorder. These domains could be either static or dynamic, which cannot be distinguished by the PDF refinement because PDF(r) constitutes an ensemble average of quasi-instantaneous snapshots of local structures across the sample. The size of these domains can hardly be determined with our data because PDF(r) gives an isotropic distribution of neighboring atoms that is not well suited for characterizing planar or rodlike domains.
Table 3. Fitted Values by the Rietveld and PDF Refinementsa PDF
Rietveld
T (K)
x
a
R
x
a
Rwp
298 323 373 423 473 523 524 573 574 623 624 673 674 723 773 774 823 873 874 973 974 1023 1073 1074 1123 1124 1173 1174 1223 1224 1273
0.2577 0.2586 0.2592 0.2597 0.2613 0.2617 0.2616 0.2622 0.2621 0.2625 0.2624 0.2628 0.2628 0.2634 0.2637 0.2637 0.2642 0.2646 0.2646 0.2653 0.2652 0.2656 0.2660 0.2659 0.2664 0.2664 0.2666 0.2668 0.2670 0.2670 0.2675
5.4677 5.4721 5.4760 5.4797 5.4832 5.4862 5.4868 5.4907 5.4894 5.4919 5.4921 5.4946 5.4948 5.4977 5.5003 5.5004 5.5031 5.5057 5.5052 5.5111 5.5107 5.5136 5.5169 5.5168 5.5194 5.5194 5.5224 5.5221 5.5257 5.5250 5.5285
3.39 6.17 3.07 5.20 6.14 5.19 3.23 3.40 4.50 3.35 4.01 4.47 4.02 5.42 4.84 4.67 4.62 4.68 4.70 4.74 4.34 4.82 5.06 4.61 5.24 4.74 4.57 4.45 4.47 4.62 4.77
0.2582 0.2591 0.2601 0.2608 0.2613 0.2619 0.2616 0.2625 0.2624 0.2640 0.2629 0.2634 0.2642 0.2636 0.2640 0.2640 0.2645 0.2648 0.2648 0.2656 0.2657 0.2660 0.2661 0.2661 0.2665 0.2666 0.2669 0.2668 0.2672 0.2673 0.2677
5.4691 5.4758 5.4799 5.4838 5.4871 5.4910 5.4912 5.4938 5.4926 5.4899 5.4954 5.4991 5.4934 5.58 5.5045 5.5034 5.5063 5.5097 5.5091 5.5150 5.5146 5.5173 5.5203 5.5199 5.5232 5.5222 5.5258 5.5251 5.5282 5.5281 5.5351
3.45 2.55 2.35 2.27 2.22 2.13 2.60 2.10 2.08 2.24 2.03 2.02 2.21 1.95 1.95 1.92 1.88 1.90 1.86 1.86 1.82 1.81 1.80 1.78 1.80 1.79 1.79 1.73 1.75 1.74 1.71
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DISCUSSION AND CONCLUSION It might be surprising to consider a local symmetry of UO2 different from Fm3̅m regarding all literature published about that compound for more than 50 years, yet this statement has to be reassessed considering the progress recently made in PDF analysis. For example, it was previously believed that A2B2O7 compounds in which cations A and B are similar in size (rA/rB < 1.46) should have a disordered Fm3̅m crystalline structure, but
a x represents the position of the oxygen atom at the (x, x, x) crystalline site, and a is the cell parameter (the value of x at 1273 K is consistent with the value of δ = 0.016 given in ref 2 because x = 1/4 + δ). R and Rwp are quality factors for the PDF and Rietveld refinements, respectively.
Figure 3. (a) Different calculated UO distances (error bars are within the symbols): short and long UO distances calculated with the Pa3̅ space group by the PDF refinement and also calculated with a split-atom model by the Rietveld refinement. The regular UO distance in the Fm3̅m space group was calculated from the Rietveld measurement and compared to Ruello’s data.23,26 (b) UO distance as a function of the structural model: (red) with the oxygen atom at its regular position in the Fm3̅m space group; (gray) short UO distance in Pa3̅. The black oxygen atom corresponds to a Pa3̅ configuration, and the black and gray atoms correspond to its average Fm3̅m configuration. 324
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heat capacity of UO2 evidences an unexpected increase from around 1000 K, which becomes nearly twice the expected value by the Dulong and Petit rule. This very unusual behavior was fitted by empirical laws but is still misunderstood. Several attempts by empirical potential modeling showed that no unique potential set was found that can describe satisfactorily both the room temperature and high-temperature behavior of UO2.22 A more phenomenological interpretation attributed the heat capacity increase to the formation of defects, polarons,23 or oxygen Frenkel pairs,24 which required more than 10% defect concentrations at temperatures over 2000 K, a concentration that seems unrealistic. Our study confirmed that the UO distance decreased with increasing temperature, which can be interpreted as a stronger bonding between uranium and oxygen atoms. This could be the reason for the heat capacity increase because this stronger bonding should induce higher phonon frequencies and, hence, higher Cv and Cp. This deserves a thorough interpretation, which is out of the scope of this paper, but justifies further modeling studies that could account for the UO2 local symmetry at high temperature. An equivalent requirement for improved modeling that can account for local order has already been made in ref 13 for isometric pyrochlore and related complex oxides. Another interesting perspective deals with the thermoelectricity. UO2 has electrical properties that would make it a proper thermoelectric material, provided it was not radioactive. UO2 has low thermal conductivity,25 high electrical conductivity, and a significant Seebeck coefficient when nonstoichiometric.26 These characteristics are enhanced with increasing temperature. The existence of a local order, Pa3,̅ different from the average order, Fm3̅m, could explain at least partially this behavior. On the one hand, the existence of domains decreases the propagation of phonons, inducing a decrease of the thermal conductivity. On the other hand, they can also enhance charge migration with fluctuating local environments.
it was recently demonstrated using neutron PDF analysis that HoZrO7, which belongs to this category of compound, has a Ccmm local symmetry.13 Therefore, PDF analysis provides a complementary understanding of the crystalline structures that can be useful in improving the description of crystalline compounds. In the case of UO2, taking into account Pa3̅ local symmetry opens three new directions for further research, which are a new description of a uranium coordination polyhedron, a possible explanation for the UO2 properties that are still not fully understood, and a renewed interpretation of all UO2 properties. First, the crystallography of uranium oxides was intensively studied in the last 10 years focusing mainly on how excess oxygen is incorporated in UO2 either as new crystallographic phases14 or as a local defect structure.15 In these studies, complex environments of uranium have been investigated, considering both oxygen vacancies and interstitials. In our study, a new type of uranium coordination polyhedron has to be considered in the Pa3̅ local symmetry, namely, an octahedral polyhedron. An octahedral coordination polyhedron, which can also be viewed as a square bipyramid, is very common in the structural chemistry of inorganic actinide compounds16 but is usually associated with the 6+ (or 5+) oxidation state. The occurrence of such a polyhedron in UO2 at the 4+ oxidation state can be justified by considering the manner by which these polyhedra are connected one with the other. In δ-UO3,17 one oxygen atom is shared by two uranium octahedral coordination polyhedra, which results in a 6+ formal oxidation state for uranium considering the 2− formal oxidation state for oxygen, while in Pa3̅ UO2, each oxygen atom is shared by three uranium octahedral coordination polyhedra, which results in a 4+ formal oxidation state for uranium. The uranium octahedral coordination polyhedron in Pa3̅ UO2 is distorted compared to this regular polyhedron in δ-UO3. This can be attributed to the lack of strong covalent bonding with U4+; the shape of the polyhedron would then be imposed by the close packing of the oxygen and uranium atoms that would tend toward the Fm3̅m symmetry. Second, UO2 undergoes a magnetic phase transition at 30 K; it has an average Fm3̅m crystalline structure above 30 K and a Pa3̅ crystalline structure below 30 K.11 The local Pa3̅ symmetry can then be seen as domains, all oriented in the same way in the low-temperature phase, that become disoriented in the hightemperature phase. This explanation is consistent with persisting magnetic correlations over the transition temperature, as demonstrated in ref 18; this situation is very similar to the one of MnO, for which atomic and magnetic corefinements support the scenario of a locally monoclinic ground-state atomic structure, despite the average structure being rhombohedral.19 At high temperature, these domains could be aligned under an external stress, which would be consistent with recent anisotropic thermal conduction measurements.20 At temperatures higher that those explored in this study, some oxygen disorder was evidenced by single-crystal neutron diffraction;21 however, no clear interpretation could be given, possibly because the short-range order is mainly visible in the diffuse scattering, which is not measured in single-crystal diffraction. Third, the existence of a local order in UO2 opens the way for a new understanding of its properties. We will focus here on the heat capacity, which is a key parameter in assessing the behavior of UO2 nuclear fuel during an accidental scenario. The
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. ORCID
L. Desgranges: 0000-0002-6327-3482 Notes
The authors declare no competing financial interest.
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REFERENCES
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