The Impact of Coordination Environment on the Thermodynamic

Article Cite This: J. Phys. Chem. C 2019, 123, 15985−15995

pubs.acs.org/JPCC

The Impact of Coordination Environment on the Thermodynamic Stability of Uranium Oxides Ashley E. Shields,*,† Andrew J. Miskowiec,† Ketan Maheshwari,† Marie C. Kirkegaard,†,‡ Daniel J. Staros,§ Jennifer L. Niedziela,† Roger J. Kapsimalis,† and Brian B. Anderson†,‡ †

Oak Ridge National Laboratory, 1 Bethel Valley Road, Oak Ridge, Tennessee 37830, United States Bredesen Center for Interdisciplinary Research and Graduate Education, University of Tennessee, Knoxville, 444 Greve Hall, 821 Volunteer Blvd., Knoxville, Tennessee 37996, United States § Bloomsburg University, 400 E. 2nd Street, Bloomsburg, Pennsylvania 17815, United States Downloaded via UNIV STRASBOURG on August 21, 2019 at 16:48:09 (UTC). See https://pubs.acs.org/sharingguidelines for options on how to legitimately share published articles.

‡

S Supporting Information *

ABSTRACT: Amorphous uranium oxides are known to arise via industrial processes relevant to the nuclear fuel cycle yet evade rigorous structural characterization. A promising approach is to develop statistical relationships between uranium−oxygen coordination environments and thermodynamic stability from which general statements about the likelihood of observing particular U−O arrangements can be made. The number of known crystalline uranium oxides is insufficient to build statistical relationships. We have developed a database of theoretical compounds using genetic algorithms with the density functional theory as a foundation to analyze coordination geometries in the uranium−oxygen phase space. We draw fundamental insights into the nature of uranium−oxygen interactions by correlating total energy with the coordination environment. The most stable configuration of U cations with O anions is in an environment with coordination numbers 5−8 in a cubic configuration. Higher and lower coordination numbers are observed only in metastable phases. General trends are observable in the relationships between the coordination number, density, and uranium fraction in each structure. The new insight into uranium coordination enabled by these analyses is foundational for further studies into the characteristic properties of individual uranium oxide materials and for elucidation of potential oxidation pathways for uranium metal.

1. INTRODUCTION

Here, we attempt to define statistical correlations between the coordination geometry, local order, and material properties. To enable an in-depth statistical study of the uranium oxide phase space, we present an analysis of chemical environments in 3700 uranium oxide structures, representing over 11,000 unique coordination environments for uranium, predicted using genetic algorithms and optimized with the density functional theory (DFT). By building a large sample set of uranium oxide structures of varying composition, common uranium site geometries that recur throughout the UOx phase space can be identified, regardless of whether parent structures are thermodynamically or kinetically stable. This is particularly useful to explore metastable regions of the UOx phase space, including transition states and defect structures. Future studies of transition pathways and defect migration may benefit from leveraging the coordination and energy information in the database of uranium oxides (DUOs). While many of these structures may never be observed in an experimental setting, their free energy may be calculated using DFT, and comparisons between structures and compositions

1.1. Uranium Oxides. Whether as fuel materials or waste forms, uranium oxides are of broad interest in the nuclear fuel cycle. There are several known crystalline phases of UO2, U3O8, and UO3 as well as several uranium oxide mineral forms. However, uranium supports a number of oxidation states and coordination geometries, leading to the ready formation of amorphous uranium oxides and other complex low-symmetry systems such as U2O5, U4O9, and amorphous UO3 in addition to the higher symmetry structures of UO2, U3O8, and δUO3.1−6 Formation of these low-symmetry systems is commonly inferred in industrial processes because many of these complexes can be formed by heating.6,7 Nevertheless, amorphous and low-symmetry systems are difficult to characterize experimentally, and single crystal samples of the intermediate products are difficult or impossible to obtain. Consequently, the development of statistically rigorous structure−property relationships for this important class of materials is hampered by the dearth of robust experimental data, and the known crystalline oxide forms are insufficient to fully explore the uranium oxide phase space. Thus, new tools and approaches are required to better understand this complicated system. © 2019 American Chemical Society

Received: April 8, 2019 Revised: May 28, 2019 Published: June 5, 2019 15985

DOI: 10.1021/acs.jpcc.9b03274 J. Phys. Chem. C 2019, 123, 15985−15995

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The Journal of Physical Chemistry C Scheme 1. Structure Prediction Cycle Using USPEX + VASP

1.3. Coordination Environments in Crystals. The importance of the chemical coordination environment, frequently referred to in terms of the corresponding geometric polyhedron, in understanding the basic chemical and physical properties, including the overall stability, of any compound is well understood and originally described by Pauling’s rules for crystal structures in 1929.22 Pauling’s third rule states that the manner in which these coordination environments are connected (e.g., face-sharing, edge-sharing, or corner-sharing polyhedra) is correlated to structural stability, and face- and edge-sharing structures are typically less stable than cornersharing structures. This observation is generally due to the additional strain of the closer cation−cation distances in faceand edge-sharing structure types. Consequently, a fundamental understanding of common structural building blocks is essential and increasingly accessible as the crystal structure prediction methodology continues to improve and evolve, allowing for a more efficient method of exploring materials that are difficult to access or isolate experimentally. The presence of particular coordination geometries in a material can help facilitate characterization by connecting the coordination geometry to observable chemical or physical properties, which has been shown for transition-metal compounds including oxides and perovskites.23,24 For uranium materials, these relationships have not been so clearly defined although certain structural features can be used to support characterization. For example, the linear uranyl ion (UO22+) has a Raman-active stretching mode between 750 and 900 cm−1, distinguishing it from lower energy oxide modes.25 Similarly, the O−O bond distance in uranium peroxides has been used to identify local coordination in amorphous samples.21 The identification of structure−property relationships in uranium oxides is the long-term aim of the authors. However, first, a robust study must be made of common motifs in the given phase space, which we present herein for uranium oxides. We are not aware of any other efforts to systematically predict crystal structures of uranium oxides and analyze the cation coordination environments.

may be drawn. In this way, we explore the relationship between the coordination geometry and several properties including formation energy, density, and chemical formula of the parent structure. These statistical correlations can guide the investigation of new uranium oxides and provide fundamental information about preferential uranium site geometries. 1.2. Genetic Algorithms for Crystal Structure Prediction. Significant work has been undertaken in the prediction of stable crystal structures, with notable success predicting complex metal-centered compounds such as perovskites and zeolites.8 There are numerous challenges to structure prediction because the phase space is large and starting geometries and other parameters may not be known. Approaches to predicting crystal structures include simulated annealing, topological modeling, and the use of genetic algorithms.9 The utility of genetic algorithms lies in their efficient sampling of the potential energy surface without requiring a reasonable starting geometry or extensive parameterization. Genetic algorithms for crystal structure prediction have been applied successfully to the study of metal oxides and fluorides.10−12 Very recent research into predicting new phases of U2O7, U−Co, and U−Si compounds and uranium polyhydrides with genetic algorithms demonstrates broad interest in identifying new uranium materials for a range of potential applications.13−16 These research efforts to attempt to discover new high-temperature superconductors and new fuel materials have employed the Universal Structure Predictor: Evolutionary Xtallography (USPEX), the same genetic algorithm software package used to build DUOs. USPEX has been used to predict novel crystal phases of materials that have been successfully synthesized and isolated in the laboratory.17,18 Additionally, computational studies have been attempted to identify unknown structures by applying the geometry of analogous nonactinide materials with the same composition or fitting of unknown stoichiometries to known actinide geometries to suggest possible structures for U2O5 and U3O7.19,20 Alternatively, in the absence of identifying long-range crystal order, possible coordination geometries have been evaluated for single formula units.21 While these approaches can be instructive because of the availability of modern crystal structure prediction tools that employ ab initio methods and the ability to easily evaluate a large number of coordination environments, a more thorough study of complex and nonstoichiometric uranium-bearing compounds is needed to characterize this important class of materials.

2. METHODOLOGY 2.1. Genetic Algorithms. To efficiently predict novel crystal structures, USPEX version 9.4.4 was used.26,27 USPEX implements a genetic algorithm search code in MATLAB to search for stable structures and does not require any input geometries or other parameterization. Each search was started from a randomly generated group of 30 structures with the 15986


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The Journal of Physical Chemistry C

Table 1. Guide to Common Coordination Environments and Their Symbols, Using the Notation of Waroquiers et al. in the Pymatgen Chemical Environments Module

hereditary (random slices of parent structures are combined), 10% random, 20% soft mutation (wherein large atomic displacements are generated along the eigenvectors of the softest phonon mode), 10% lattice mutation (strain is induced through changes to the lattice parameters, and then the atomic positions are relaxed), and 10% transmutation. For soft mutation, approximate phonon modes are determined by an approximation of the dynamical matrix based on bond hardness coefficients as described by Lyakhov et al.32 Using the method described above, some structural features of parent structures are retained in subsequent generations, which speeds up the time to solution. For full details about the

composition UxOy. USPEX interfaces with the Vienna ab initio simulation package (VASP) to perform geometry optimizations and calculate the energy of each structure using DFT. 28−31 USPEX reads the results from the VASP calculations to evaluate each structure based on the enthalpy of formation and retains the “best” structures (i.e., those with the lowest enthalpy of formation). These structures then become the “parent” structures of the next generation, and a number of different mutation operators are applied, generating “child” structures, which populate the next generation of 30 new structures, as shown in Scheme 1. The new generations were created by USPEX from the following mutations: 50% 15987


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increasingly dense k spacings in Brillouin zones of 0.13, 0.11, 0.10, and 0.08 Å−1. Results were visualized with the VESTA and CrystalMaker software suites.45 2.3. Chemical Environment Analysis. Analysis of the cation-centered coordination geometries employed the Chemical Environments module of Waroquiers et al. in the Pymatgen Python package.46 Herein, the shorthand symbol notation of Waroquiers et al. is used to refer to the model geometries against which all sites are compared.46 Table 1 contains a list of common polyhedra and their associated shorthand symbol. In this analysis, a Voronoi construction is used to determine nearest neighbors for each site, and using these nearest neighbors as vertices, a polyhedron describing the site geometry is determined. The package uses 65 IUPACapproved model polyhedra for coordination geometries, and the calculated site geometry is compared to and assigned a single coordination environment based on one of these model polyhedra.47 Within each structure, the number of distinct coordination environments may range from one (referred to herein as a single site structure), in which all U atoms share a common coordination environment, up to the number of uranium atoms in the unit cell. Structures where more than one coordination environment exists are referred to herein as multisite structures. In the analysis presented in Sections 3.2 and 3.3, the histogram counts are weighted such that each structure is weighted by 1 , where nc is the number of

USPEX operational mechanism, we refer readers to the works of Oganov and co-workers.26,27,33 Each search was allowed to proceed for 30−50 generations or until the stopping criterion was satisfied. A search was considered to have met this criterion if the best structure remained unchanged through eight generations. The allowable number of atoms per unit cell ranged between 4 and 32 atoms per cell. The computational cost of searching the full uranium oxide phase space with more atoms per cell was found to be prohibitive. Before coordination environment analysis, all of the duplicate structures that USPEX retained as the best structures from previous generations were excluded from the data set. The phase diagram module in the Pymatgen Python package was used to produce a convex hull plot.34,35 2.2. Computational Details. A series of geometry optimizations using VASP were performed on each generation of each structure as part of the USPEX search. The generalized gradient approximation was employed, using the Perdew− Burke−Ernzerhof exchange-correlation functional for solids (PBEsol) with the projector augmented wave (PAW) method to describe the interaction between the core and valence shells.36,37 Integration of the Brillouin zone was performed using the tetrahedron method with Blöchl corrections.38 A cutoff energy of 650 eV was used for the expansion of the plane wave basis set. Convergence tests of the cutoff energy for several UO3 polymorphs and U3O8 indicate that this value is sufficiently high to ensure convergence and avoid Pulay stress in many uranium systems. As the VASP calculations are run in a high-throughput fashion by USPEX, the same setup parameters must be used for each structure, regardless of variations in the composition and structure type. For this same reason, spin−orbit interactions were excluded in these calculations. Wen and co-workers studied the effects of spin−orbit interactions on DFT calculations of nonmetallic uranium materials and determined that spin−orbit interactions do not strongly influence the calculated lattice parameters, electronic properties, or relative energies.39−41 The success of the USPEX + DFT approach in identifying novel stable phases in a number of materials, as discussed previously, indicates that fine-tuning each VASP input parameter for each structure is not necessary. Values for the Hubbard U parameter and k-point mesh in reciprocal space were chosen that are widely used for uranium oxides. To correct for the strong on-site correlation in f elements, the rotationally invariant Hubbard Hamiltonian approach of Dudarev et al. was used EGGA + U = EGGA +

(U − J ) 2

∑ Tr[ρσ σ

nc

structures of a given composition, to correct for oversampling of certain compositions (e.g., UO2 and UO3). Each uranium1 1 centered site is weighted by n × n , where ns represents the c

s

number of sites per structure. One of the key features of the Chemical Environments analysis is the calculation of a continuous symmetry measure (CSM) for each site environment. This value both ensures that each environment is matched to the closest IUPAC polyhedron and quantifies the deviation of the site from the model. CSM values are reported on a scale from 0 to 100 where a CSM value of zero indicates an exact match between the calculated environment and model, and higher CSM values represent a significant deviation from the model shape (i.e., distortion). For a full description of the Chemical Environments module, including a list of all model coordination environments used in the analysis, we refer the reader to the original publication46 and the Pymatgen documentation. In Table 1, common coordination environments are listed with the coordination number, symbol, and a visual representation of the associated polyhedra.

− ρσ ρσ ] (1)

3. RESULTS AND DISCUSSION 3.1. Uranium Oxide Composition Distribution. DUOs were generated using the USPEX + VASP approach described above. It contains 3781 structures with stoichiometries UxOy (x ≥ 0, y ≥ 0). The structures and information in DUOs are available in the Supporting Information. Excluding the pure uranium and oxygen structures, 2975 UOx (x > 0) structures are identified, representing 154 unique compositions (Figure 1). Some compositions are inaccessible in this analysis as a consequence of the number of atoms per cell used in USPEX. Larger systems with more atoms per unit cell would access more possible compositions although at significantly increased computational cost. Owing to the nature of the genetic algorithm, the distribution of these compositions throughout

σ

where ρ is the density matrix. U and J are elements of the spherically averaged matrix of the screened Coulomb interaction, and the difference of which (U − J) can be applied in VASP as a single effective U parameter, Ueff.42 In this work, a value of Ueff of 3 eV was used for all structures. This value for Ueff is similar to those which have been used successfully in DFT + U simulations of a number of uranium oxides, although again it must be emphasized that it is impossible to know at the outset the optimal Ueff value across the full range of U−O solids, and of course, it is unlikely that there is a single optimal value.19,43,44 A Γ-centered k-point mesh was calculated for each structure in each of three relaxations and a fourth and final calculation of the energy with 15988


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coordination geometries, including matches to all model polyhedra with coordination numbers (CN) from 1 to 9, inclusive. Additionally, some of these site geometries in the database are characterized by high CSM values, indicating distortion from the model polyhedron. The mean CSM value for all sites in the UOx database is 4.6. The most common sites (Figure 3), O:6 and C:8, have average CSM values of 4.11 and 0.85, respectively, indicating that where these sites are found, they are typically in an environment more closely matching their corresponding model polyhedron than the average site. As octahedral sites are among the most common coordination geometries found throughout the periodic table, particularly for compounds and molecules with a metal center, it is not surprising that O:6 sites are widely distributed in the database and identified in 104 out of the possible 154 UO x compositions. While it is interesting to note the diversity of site geometries, which are identified with the genetic algorithm + DFT approach, it is also worth noting the geometries that do not occur or that occur in only a handful of cases. The five least common site geometries are all 9- or 10-coordinate sites, with an average CSM value of 6.83, indicating above average distortion from the model polyhedra. These site geometries are identified in five or fewer structures each, and for no more than one uranium site per structure, indicating that these geometries are potentially highly uncommon uranium coordination environments. The nine coordination geometries that were not identified at all in nearly 11,000 uranium sites are all 10-, 11-, or 12-coordinate sites. While several known UOx phases have more atoms per unit cell than were used in these calculations, the repeated identification of the experimental coordination environments by USPEX for UO2, regardless of the unit cell size, indicates that the genetic algorithm approach provides an efficient sampling of cation coordination, independent of the experimental unit cell size of stable compositions. As a large phase space is explored, with many possible compositions that are not known or not well described experimentally, it is impossible to identify a precise range of atoms per unit cell to use in the genetic algorithm searches. Within experimentally identified UO3 polymorphs alone, ß-UO3 has 93 atoms per unit cell, whereas δ-UO3 has only four. Unfortunately, using more than 32 atoms per unit cell for the uranium oxides in our methodology was not feasible because of the additional computation time required to get sufficiently well optimized structures in the larger cells. 3.3. Site Geometry and Material Properties. Analysis in this section is limited to uranium oxides, with pure uranium and pure oxygen structures removed from the data. In Figure 4, we look at the distribution of coordination numbers for each cation site and the overall fraction of uranium atoms (U fraction) in the parent structure to which the site belongs. Here, the fraction of uranium atoms is defined as the number of uranium atoms divided by the total number of atoms in the unit cell. It is notable that CN 4−8 sites are present in compositions throughout the phase space, yet low and high CN sites are concentrated in the uranium-rich portion of the phase diagram, with CN ≤ 3 and CN ≥ 10 almost exclusively in the uranium-rich region. An overall trend is observed in which the number of sites of a given CN and the U fraction increases as both CN and U fraction increase up until CN 8 and a U fraction of 0.3. At this point, there is a distinct reversal in the trend such that as the U fraction increases further, the

Figure 1. Most common compositions in DUOs. Note that percentages do not sum to 100% because only the 11 most common are included.

the structural search space is not even. Certain compositions appear more frequently, particularly those that were most frequently among the lowest energy structures across several generations, resulting in 351 UO and UO3 structures each. Other compositions occur infrequently, such as UO17, for which only a single structure exists in DUOs. Overall, oxygenrich UOx (where x > 1) makes up 74% of the compositions. In crystal structure prediction, thermodynamically stable compositions have a formation energy that lies on the convex hull, with metastable states lying above the convex hull. The convex hull is plotted as a phase diagram (Figure 2a), with the line defining the convex hull calculated such that it defines the smallest convex shape that can be drawn from the data. The lower energy (i.e., closest to the hull) metastable states may represent kinetically stable phases. High energy structures, which are well above the hull, may be analogous to UOx structures that exist in extreme environments, such as high temperature or pressure, or as transition states. Many of the predicted structures may not exist experimentally under any realistic environmental or laboratory conditions though these structures still provide a useful opportunity to explore uranium coordination in oxides. Further sampling of the UOx phase space either through additional genetic algorithm searches or sampling of more complex unit cells may identify more low energy structures, which could change the shape of the convex hull and the prediction of which compositions are thermodynamically stable and this could be explored in future studies. In Figure 2a, compositions that are predicted to be stable include the known phases UO2 and UO3 as well as U2O5 and U7O16. Another known phase, U3O8 lies less than 0.026 eV above the convex hull (within chemical accuracy). The lowest energy predicted structures for these compositions are presented in Figure 2b−f. A low energy U7O2 structure is an outlier in the uranium-rich region of Figure 2a, with an energy above the convex (Ehull) of 0.24 eV. There is also a uranium metal structure, U5, which is significantly lower in energy than the other pure uranium structures predicted by USPEX. 3.2. Analysis of Uranium Coordination Geometries. DUO structures contain almost 11,000 individual uraniumcentered sites in total. The Chemical Environments module compares the geometry of each of these sites against 65 model polyhedra determined by IUPAC. DUOs contain uraniumcentered sites in 56 of the possible 65, highlighting the ability of uranium cations to accept a large range of coordination opportunities. This provides a wide sampling of uranium 15989


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Figure 2. (a) Formation energy of UOx compositions by

U (U + O)

fraction. Stable compositions lie on the convex hull (black line) and metastable

phases lie above the hull. The lowest energy structures identified by USPEX + DFT for (b) UO2, (c) U2O5, (d) U7O16, (e) UO3, and (f) U3O8. Structures are presented as 2 × 2 × 2 supercells to illustrate long-range coordination, except (d), for which the 2 × 1 × 1 is shown.

than a new uranium oxide moiety. Further study of these structures may reveal new insights into the oxidation of uranium metal. The oxygen-rich region of the phase space is dominated by CN 4−8 sites almost exclusively and follows the general trend very strongly. No CN 1, 2, or 13 sites are formed in compositions with a U fraction of 0.2 or lower. While uranium coordination sites in DUOs do span the range of coordination numbers, the strong preference is for U to coordinate 4−8 oxygen atoms, with the notable exception of pure and almost pure uranium metal. Of the four structures that lie on the convex hull, all but one are built from C:8 environments exclusively. The other is UO3,

most common CN value decreases. This trend holds until the fraction of uranium is greater than 0.8. Here, a particular concentration of CN 12 sites is found, observable in Figure 4. These sites are predominantly identified as cuboctahedral units (C:12). The structures in this region of the phase diagram closely resemble pure uranium metal with interstitial oxygen atoms. In U metal structures predicted by USPEX, the uranium atoms can be considered 12-coordinate, and in fact, the Chemical Environments package identifies U metal as being composed of anticuboctahedron (AC:12) sites. This region of the phase space forms an island of metastability, in which these compositions are essentially defective uranium metal rather 15990


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Figure 3. Most common coordination environments in our database, as a percent of the whole. Note that percentages do not sum to 100%, as only the 10 most common are included. The average CSM is listed for each environment.

Figure 4. CN of each uranium vs the fraction of uranium in the parent structure of that site. Each site is weighted to remove oversampling effects. Figure 5. (a) Energy of each structure above the convex hull in electron volts as a function of the CN of its constituent sites, focused on structures lying within 1 eV of the convex hull, (b) energy above the convex hull in electron volts as a function of the density, and (c) density as a function of U fraction. The orange line plots experimental densities of pure oxygen, UO2, γ-UO3, and uranium metal. Each reported value and each structure is weighted to remove oversampling effects.

with one O:6 uranium site. Expanding the analysis to structures lying within 0.041 eV of the convex hull, U2O5 and U3O8 are included, both of which include 7-coordinate uranium-centered sites. Uranium sites with coordination numbers lower than 6 and higher than 8 are not predicted to form in the thermodynamically favored uranium oxide structures although many metastable structures exist outside of this range and may be kinetically stable under certain conditions. This is clearly illustrated in Figure 5a where no very low or very high CN sites have an energy above the convex hull (Ehull) less than 0.1 eV, and each site is weighted as in the previous figure to remove the effects of oversampling. Figure 5a, in which the data has been filtered to include only structures within 1 eV of the convex hull, illustrates a very strong trend in which structures close to the convex hull primarily are composed of uranium sites with coordination numbers between 5 and 8, and the average CN decreases as the Ehull increases. The same island of metastability seen when examining sites by U fraction is again observed at ∼0.8 eV above the convex hull. These represent the same structures as in Figure 4, which are essentially uranium metal with interstitial oxygen atoms. High density structures are concentrated above 0.6 eV above the convex hull (Figure 5b), with the Ehull increasing as density increases above 10 g/ cm3. Below 10 g/cm3, the correlation between Ehull and density is less clear although it is interesting to note that on and very near the convex hull, no extremely high- or low-density structures are observed. Examining the relationship between the density and amount of uranium in the system, the density increases almost linearly with uranium fraction (Figure 5c). In Figure 5c, the experimental densities of O2, UO2, γ-UO3, and uranium metal are plotted in orange, following the general trend. The densest UOx phase in our database (∼17 g/cm3) is

still 2 g/cm3 less than that of pure uranium metal (experimental is 19.1 g/cm3, and our most dense predicted U metal structure is 19.18 g/cm3) due to distortions in the uranium layers created by the presence of oxygen interstitials. Additionally, the generalized gradient approximation employed is well-known to overestimate lattice constants, including those in uranium oxides,48 which can lead to an underestimation of the density. Analysis of interatomic distances in the database finds U−O distances in the first coordination shell (cutoff = 3 Å) mostly lie between 2.2 and 2.6 Å, with an average of 2.32 Å. While there is an overlap between U−O, O−O, and U−U distances beyond ∼1.7 Å, oxygen−oxygen interatomic distances shorter than 1.6 Å, corresponding to a peroxide-type bonding interaction between two oxygen atoms in the structure, are clearly distinguishable from other interactions (Figure 6a) and are only identified in structures with a U fraction less than 0.33 (equivalent to UO2 and higher oxides). Peroxide-containing uranium oxides are known to exist, including the mineral studtite, [(UO2)(O2)(H2O)2](H2O)2, and amorphous U2O7, both of which follow this observed trend wherein peroxidetype bonds are only observed in oxygen-rich phases.21,49 In Figure 6b, the interatomic distances of select compositions illustrate the variation with bonding observed as the composition changes. In general, as the amount of oxygen in 15991


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Figure 6. Histogram of interatomic distances for U−U (blue), U−O (purple), and O−O (red) interactions for (a) all UOx structures up to 4 Å, weighted to remove oversampling effects and (b) select chemistries (unweighted).

Figure 7. Histogram of O−U−O angles for (a) all UOx structures, weighted to remove oversampling effects and (b) select chemistries (unweighted).

the structure increases, the average U−U distance increases, and the average U−O distance is slightly decreased. Recall from Figure 4 that the oxygen-rich phases primarily contain polyhedra with CN 4−8, with the average CN decreasing at high oxygen concentrations. Therefore, the observed trend in U−U distance is likely explainable by the increased presence of bridging oxygen atoms, increasing the U−U distance. The distribution of O−U−O bond angles in all structures (Figure 7a) shows two sharp peaks at ∼70 and 90°. A number of coordination geometries, including O:6, have angles at 90°, whereas 70° is present in C:8 sites. The O−U−O angles were calculated with a cutoff value of 3.3 Å for the nearest neighbors. This yields very few structures that contain bond angles smaller than 30°, and these are exclusively oxygen-rich phases, with no angles less than or equal to 30° occurring in structures with a higher U fraction than 0.33 (equivalent to

UO2). There is a strong overlap between structures with these acute angles and those which contain peroxides; however, this appears to be due to a failure of the cutoff, with 3.3 Å being too large for these structures. The O−U−O angles in peroxide units typically range in value from 34 to 38°. Examining O− U−O angles for selected compositions (Figure 7b), it is clear that UO2, UO3, and U3O8 are distinguishable based on the distribution of bond angles alone. 3.4. Chemical Environments of Stable Phases. While a central motivation of developing the DUO database is to explore uranium oxide structures and compositions that differ from those that have been experimentally characterized, it is nevertheless useful to evaluate how the above methodology can be applied to known phases. Performing the Chemical Environments analysis for experimental structures of the major stable uranium oxides (UO2, UO3, and U3O8) finds that all 15992


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The Journal of Physical Chemistry C three structures are overwhelmingly found in 6-, 7-, and 8coordinate environments. The face-centered cubic (fcc) fluorite structure of UO2 (Figure 8) yields the expected 8-

Figure 8. (a) Experimental crystal lattice of fcc UO2, (b) fcc UO2 structure identified by USPEX, and (c) Chemical Environments in UO2 (notation is from Table 1). Figure 9. Experimentally determined (a) α-, (b) β-, (c) γ-, and (d) δUO3 structures. (e) Chemical Environments in UO3.

coordinate cubic environment (C:8) on each uranium site in the 12-atom unit cell, with a computed CSM value of zero, indicating that there is no deviation from the model cubic polyhedron. In an analysis of UO2 structures in DUOs, the most common uranium site is C:8 with a very low mean CSM value of 0.082 averaged over all C:8 sites. Although the USPEX search does find the 12-atom fluorite structure of experimental UO2 (Figure 8b) slightly above the convex hull, notably, the same C:8 coordination environment is found repeatedly in other UO2 structures on and near the convex hull. There are several known phases of UO3 (Figure 9). For example, α-UO3 is formed of edge-sharing hexagonal bipyramidal (HB:8) cation sites. In γ- and δ-UO3, the uranium-centered coordination sites are distorted octahedral geometries in the γ phase, but δ-UO3 forms in undistorted O:6 sites. β-UO3 forms a complex structure with the 10 uranium ions located in 5 distinct environments in the unit cell, with two ions in each of PB:7, O:6, SS:4, TL:3, and L:2 geometries. In contrast, for our predicted UO3 structures, by far the most common chemical environment found in the database is the 6coordinate octahedral (O:6) geometry, followed by C:8, and ST:7. The lowest energy UO3 structure predicted in DUOs is the δ phase, but under ambient conditions in the environment, γ is expected to be the most common. The difference in the expected structures may be due to the differences in temperature and pressure between calculations and environmental conditions. Experimentally, U3O8 is most commonly found in the pentagonal bipyramidal (PB:7) geometry (Figure 10). In DUOs, the most common cation coordination geometry among the predicted structures is still 7-coordinate, but it is the square-face capped trigonal prism (ST:7), followed by O:6 and C:8 sites. These are also the most common sites for UO3 and UO2 structures in our data set. Likely transition pathways

Figure 10. (a) Experimentally determined U3O8. (b) Chemical Environments in U3O8.

for the oxidation of UO2 to U3O8 and UO3 may proceed via these common coordination polyhedra.

4. CONCLUSIONS An analysis of almost 11,000 uranium-centered sites in solidstate uranium oxides generated using genetic algorithms and DFT identifies preferential geometries, namely, octahedral, cubic, and square-face capped trigonal prismatic, for cationcentered sites in uranium oxides. Equally, given the large number of compositions sampled, certain high-coordination cation geometries are not identified, indicating these are highly 15993


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Postdoctoral Fellowship. The authors would like to thank Ashley Carlson for the 3D rendering.

unfavorable geometries for uranium coordination in the solid state. It is worth noting that O−O peroxide bonds in our database are exclusive to phases with a U fraction of 0.33 or lower. General trends are observable in the relationships between the coordination number (as a proxy of the coordination environment), the energy above the convex hull, density, and the fraction of uranium in each structure. An “island of metastability” is identified composed of uranium-rich structures. Further analysis of these structures may provide insight into the oxidation of uranium metal via the intercalation of oxygen interstitials. A robust understanding of uranium coordination is foundational to further studies into the vibrational or other characteristic properties associated with each of these sites, assisting in the understanding and identification of uranium oxides in an experimental context. This approach is currently being extended to other materials of interest in the nuclear fuel cycle, including uranium fluorides and uranium oxyfluorides. In addition, the vibrational properties of the nearly 3000 predicted uranium oxide structures in DUOs are being calculated to develop structure−property relationships between the phonon modes and the fundamental coordination units.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcc.9b03274.

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REFERENCES

Crystallographic Information Files (CIF) for all predicted structures, with unique ID (ZIP) Spreadsheets with USPEX results and chemical environment analysis for each CIF, organized by ID (ZIP)

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Ashley E. Shields: 0000-0002-1008-5242 Daniel J. Staros: 0000-0002-4317-3599 Brian B. Anderson: 0000-0002-0675-9750 Notes

The authors declare no competing financial interest. Notice: This manuscript has been co-authored by UT-Battelle, LLC, under contract DE-AC05-00OR22725 with the US Department of Energy (DOE). The US government retains and the publisher, by accepting the article for publication, acknowledges that the US government retains a nonexclusive, paid-up, irrevocable, worldwide license to publish or reproduce the published form of this manuscript, or allow others to do so, for US government purposes. DOE will provide public access to these results of federally sponsored research in accordance with the DOE Public Access Plan (http://energy.gov/ downloads/doe-public-access-plan).

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ACKNOWLEDGMENTS This research used resources of the Compute and Data Environment for Science (CADES) at the Oak Ridge National Laboratory, which is supported by the Office of Science of the U.S. Department of Energy under contract no. DE-AC0500OR22725. A.E.S. would like to gratefully acknowledge the United States Department of Homeland Security for the 15994


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