Dependency of f states in fluorite-type XO2 (X = Ce, Th, U) on the stability and electronic state of doped transition metals

Qian Ding, Ruizhi Qiu and Bingyun Ao*
Science and Technology on Surface Physics and Chemistry Laboratory, Mianyang 621908, Sichuan, China. E-mail:

Received 7th August 2019 , Accepted 16th September 2019

First published on 16th September 2019

Fluorite-type XO2 (X = Ce, Th, U) have versatile technological and industrial applications, and the behavior of impurities in the oxides is one of the engaging topics for their application. However, the fundamental behaviors of impurities are still lacking. Herein, we conduct a systematic first-principles DFT+U screening to find the trends of transition metal (TM) behaviors in the three dioxides in terms of energetics and electronic states, with a particular focus on the dependency of f electronic states of the hosts. In order to overcome the long-standing bottleneck of determining the true oxidation state of multivalent TMs, Ce and U, a more rigorous method based on counting orbital occupation numbers of f and d orbitals is performed for clarification. The calculated incorporation energies and formation energies of TMs show that the relative stability of TMs in the three XO2 exhibits similar trends, indicative of the dominant roles played by the host oxides with the same crystal structure and very close lattice parameters. On the other hand, the quantitative differences in the stability and electronic state of doped TMs could be mainly attributed to the differences in the electronic structure of host XO2. The 5f electrons in UO2 are more delocalized than 4f in CeO2, suppressing the formation of high oxidation states of TMs in the former. For ThO2 with the negligible f electrons associated with monovalent Th4+, the doped TMs tend to adopt the oxidation states close to TM4+, achieving the electronically matched states. The appearance of a few unusual oxidation states of TMs sheds light on the flexible delocalization–localization mutual transition of f or d valence electrons.

1. Introduction

Impurity in solid-state materials is no doubt one of the most fundamental and applied research topics, and extensive efforts have been undertaken to understand, eliminate, or make use of impurity effects.1 In terms of the classification of materials, conventional semiconductors are the most outstanding example. Nowadays, the research and development of novel energy and catalytic materials, which are usually semiconductors as well, is largely dependent on the materials’ modification by dopants. Notwithstanding, impurity effects in the actinide oxides, which are also semiconductors from the band structure point of view, have not attracted the likewise extensive attention despite the fact that such oxides have been applied both technologically and industrially.2 So far, UO2 and ThO2 are the two most concerned because the former is the standard nuclear fuel and the latter is the envisioned nuclear fuel for Molten Salt and high temperature gas cooled reactors.3 Owing to the inherent radioactivity and fissionability of U and Th, impurities in oxides are virtually ubiquitous through their lifetime. Generally, impurities in oxides exhibit negative effects; this is particularly true for the incompatible rare gases (RGs) which are undisputedly confirmed to deteriorate the macroscopic properties of the host oxides despite the fact that the underlying microscopic mechanisms remain incompletely understood.4 As for the majority of metallic impurities, no matter whether produced from metallurgy or from fission, the negative effects are noticeable as well. It is nevertheless important to point out that a few metallic impurities are found to be beneficial for improving some specific properties such as radiation resistance and thermal conductivity. Indeed, the modification of oxide-type fuels by doping metals or metal oxides, or by forming ternary compounds, has become the promising strategy for the R&D of novel nuclear fuels.5–7 Notwithstanding, to our knowledge, there is still a great lack of systematic investigations in the open literature regarding impurities in UO2 and ThO2, thereby going against the design of new-type nuclear fuels.8–10

There are similarities and differences between UO2 and ThO2; both crystallize in the very common face-centered cubic (fcc) fluorite-type structure with close lattice parameters (space group: 225/Fm[3 with combining macron]m, lattice parameter: 5.470 Å for UO2 and 5.580 Å for ThO2).2 Knowledge from impurities in solid-state materials reveals that elastic and electron interactions are the two main parts of impurity effects, the former and latter being dependent on the dopant size and valence electron configuration, respectively. In this regard, the structural similarities between UO2 and ThO2 are expected to result in a similar elastic energy effect by the dopant. Indeed, this conclusion was supported, at least partially, by the experimental and theoretical observations of doped oxides apart from the above two oxides.11–15 On the other hand, electron interactions are very complicated as a consequence of multi-factors, among which the electronic structures of hosts might play a decisive role. This particularly holds for UO2 and ThO2 despite the fact that both U and Th are light actinide elements;16–18 however, there is a significant difference in the electronic structure. U and Th are the typical multivalent (U3+–U6+) and monovalent (Th4+) actinide elements, as can be readily derived from the ground-state electron configurations, i.e., U: [Rn]5f36d17s2, Th: [Rn]5f06d27s2. Indeed, the environmentally sensitive bonding features of U 5f electrons give rise to thousands of well-identified solid-state U compounds, and some novel compounds containing unusual U oxidation states (OS) were characterized by tailoring the ligands,19–21 whereas the Th compounds with OS lower than Th4+ could be prepared only under some extreme conditions.22,23 The main outcome from the difference in the electronic structure lies in the aliovalent or non-tetravalent dopants because the charge balance associated with chemical bonding of hosts is abruptly changed, thereby how to compensate charge is the central topic regarding the doped dioxides. Taking the widely concerned trivalent La dopant as an illustration, whether La would result in the formation of oxygen vacancy in ThO2 to compensate charge is one of the research focuses.11 In contrast, for La doped UO2, the challenging task is to rigorously determine whether U4+ would change into U5+ or U6+ because charge compensation by lifting U OS has been rationally demonstrated for such multivalent oxide. Recent element-selective X-ray absorption near edge structure (XANES) spectroscopy in combination with other techniques provided the definitive proof that the substitution of U4+ with La3+ is not accommodated by the creation of oxygen vacancy, and U5+ instead of U6+ ions form.24,25 Naturally, the lower-valent alkali and alkaline-earth metal dopants could induce the formation of U6+; a direct piece of evidence is that there are a rich variety of well identified such ternary compounds with hexavalent U.19 By contrast, the pentavalent and hexavalent metallic dopants definitely suppress the formation of U5+; however, unlike the readily reducible PuO2 and CeO2, it is rather difficult for the formation of the U3+ ion which has really not been detected in pure or doped U–O systems.

By analyzing and summarizing the available literature in doped UO2 and ThO2, we propose that a comprehensive study is much in demand for deeply understanding doping effects, clarifying some long-standing controversial topics, or further, establishing some benchmarks on the fundamental behaviors of dopants or impurities. As such, consideration of all transition metals (TMs) as the probes might be the optimal choice; this is primarily because TMs exhibit regular and interesting variations in atomic properties, physically originated from the periodic valence electron configurations. As aforementioned, the correct determination of electronic states of dopants and host metal ions is one of the most important scientific topics. In this context, CeO2 which is a star material in the field of energy and catalysis26 comes to our attention as well. In fact, tailoring the functionalities of the versatile CeO2 by TM dopants has been the foremost strategy.14,15,27–29 Interestingly, CeO2 and other Ce-based materials have been widely assumed as the ideal analogues for Pu counterparts owing to the similar delocalization/localization dual nature of f electrons.30,31 In fact, in our previous work, we conducted a systematic first-principles calculation to find the general trends of TM behaviors in PuO2 in terms of energetics, atomic properties, OS, and electronic structures, and concluded that the degree of electron match between TMs and Pu plays a decisive role in the phase stability of PuO2.32 Generally, IV-B elements are energetically and electronically favorable in PuO2, suggesting the formation of Pu–TMIV-B–O ternary compounds. In contrast, the remaining TMs tend to destabilize PuO2 and whether phase segregation or transition occurs largely depends on the redox conditions: oxidation condition induces segregation, whereas reduction condition drives the PuO2 → Pu2O3 transition. It is worth pointing out that this is the first theoretical work examining the trends of all TMs in the fluorite-type metal dioxide, which really strengthens our confidence in the further exploration of TM-doped effects and in the establishment of correlation between the fundamental properties of TMs and host dioxides.

Thus, considering the extreme difficulties in the experimental characterization of low-concentration TMs, here we extend the first-principles density functional theory (DFT)+U calculations of TMdoped UO2, ThO2 and CeO2 on the basis of our previous works on PuO2. The goal of the present work can be briefly divided into two parts. First, we provide a complete database of fundamental formation energies of all TMs (3d, 4d and 5d series) and the associated oxygen vacancy formation energies in the three dioxides. The former energies are crucial for the discussion of relative stability of doped TMs while the latter ones are instrumental for clarifying whether TMs can drive the formation of oxygen vacancy associated with charge compensation. Second, owing to the noticeable differences of f electronic states in the three dioxides, we try to establish a universal picture regarding the correlation between f states and TMs’ properties. Such correlations might be very helpful for unraveling the essential differences in the apparently similar trends of TM behaviors in the fluorite-type dioxide family, or even in the wider range of metal oxides. In the meantime we do not intend to focus on the specific applications of the dioxides, yet we still expect that the results might provide a theoretical database for tailoring the specific functionalities of UO2, ThO2 and CeO2.

2. Computational approach

We utilize the 2 × 2 × 2 XO2 supercell, i.e., X32O64, as the parent structure to build the TM doped configurations, which have been demonstrated to be reasonable for the examination of dilute dopants by our previous and other researchers’ studies.32–35 In addition, the metal atom substitutional site has been also proven to be more favorable for the doped TM in comparison to interstitial and lattice O sites; this is mainly due to the fact that the latter two sites are structurally and electronically incompatible with TMs. In order to understand the dependency of TMs on O vacancy formation energy, the crucial parameter for elucidating the microscopic mechanism of charge compensation and scaling the reducibility of metal oxides, we take three O vacancies into consideration: the first nearest-neighboring (1NN), 2NN and 3NN O as shown in Fig. 1, which is expected to be rational because of the negligible long-range interaction beyond 3NN O. Since we focus on the general trends of doped TMs, other complicated defects and various TM concentrations are not considered. In fact, for the dependence of TM concentration on the stability and chemical state, our previous calculation tests demonstrated that TM concentration in the similar fluorite-type PuO2 is not sensitive to the trend of stability and chemical state in the dilution cases;32 therefore, the discussion on the TM effect is mainly focused on the single TM doping.
image file: c9cp04371c-f1.tif
Fig. 1 Calculation model of the fluorite-type 2 × 2 × 2 XO2 (X = Ce, Th, U) supercell containing one substitutional transition metal (TM) atom. The yellow ball represents the doped TM atom, and 1NN (2NN, 3NN) VO represents the first (the second, the third) nearest-neighboring oxygen vacancy.

All density functional theory (DFT) calculations are conducted by using the projector augmented-wave (PAW) method and Perdew–Wang 91 (PW91) exchange–correlation functionals implemented in the Vienna Ab initio Simulation Package (VASP),36 and visualized using visualization for electronic and structural analysis (VESTA).37 The strongly correlated Hubbard model is used to treat 4f/5f electrons within the DFT+U method in the Dudarev formalism.38 The effective Hubbard Ueff (Ueff = UJ, i.e., the difference between Coulomb U and exchange J values, hereafter described as U) values for f electrons of U, Th and Ce are considered as 4, 4 and 5 eV, respectively, consistent with previous works since most of literature values lie around these values.16,26,39 Interestingly, our calculation tests show that the slight variation of the U value has an insignificant influence on the energetics of doped TMs mainly due to the fortunate error cancellation. This holds for the selection of other DFT parameters such as spin–orbit coupling and magnetic order.31–35 A universal U value (U = 4 eV) is selected for all TMs to explore the general trend despite the fact that the literature U values of TMs lie in a wide range (usually 4 ± 2 eV).40 We suggest that the calculation validations on U values of all TMs are not meaningful because one specific U value might just satisfy the reproduction of one specific property of TM, and the electronic states associated with U values of TM as chemical composition and as dopant in oxides might be very different. Indeed, we have conducted the tests on several famous multivalent TMs (Ti, V and Fe) and found that U values varying from 2 to 6 eV have an insignificant influence on the defect energy because of error cancellation, albeit they have some influence on the quantity of d orbital occupation numbers. However, we found that the changes of the quantity of d orbital occupation numbers do not essentially influence the assignment of OS in terms of the critical value for distinguishing occupied and unoccupied orbitals.32 Complete relaxation without symmetry constraints is employed, which is particularly required for the doped systems to reach the energetically and mechanically stable configuration. In fact, we find that the total energies of the relaxed configurations without symmetry constraints are always lower than those of the relaxed configurations with symmetry constraints. Convergence is reached when the total energies converge within 1 × 10−5 eV and the Hellmann–Feynman forces on each ion are lower than 0.02 eV Å−1. A plane-wave kinetic energy cutoff of 500 eV and 3 × 3 × 3 Monkhorst–Pack k point sampling are demonstrated to give accurate energy convergence. For Ce, Th and U, the numbers of f electrons are far smaller than half the numbers of f orbitals; consequently, the spin multiplicity is defined according to Hund's first rule. In fact, our calculation test on XO2 using occupation matrix control confirms that the configuration with the maximum spin multiplicity is energetically most favorable. For the doped system containing a multivalent host ion or dopant, or both, a crucial but still controversial issue is how to unambiguously determine the actual (or physically meaningful) OS of multivalent ions. Notwithstanding, the conventional scheme based on charge transfer or charge balance in the ionic limitation might be viewed as the semi-empirical or educated guess one, or even worse, might point to the wrong answer because there is no direct-proportion relationship between charge transfer and OS.41–43 In this regard, the OS determination method based on orbital (d or f) occupation number allows us to assign the OS of all multivalent ions without much ambiguity, which has been ensured to be very powerful in quantitatively describing the OS population of complicated systems containing open d- or f-shell (or both) metals.44 For clarity, we decide to discard the discussion on the computational details which can be referred to in our previous theoretical works,31,32,45–48 but focus on the main ideal of the methodology. The key of the method is that the occupied Kohn–Sham and the atomic f orbitals can be computed separately. The occupation number (ON) of an orbital is achieved via projecting all occupied orbitals onto the atomic orbitals. Consequently, two 7 × 7 occupation matrices by the projection scenario under spin-polarized calculation can be defined to obtain all ONs of f orbitals. One occupied or unoccupied orbital corresponds to the ON being 1 or 0, respectively. By counting the ONs of orbitals and comparing with valence-electron configuration, OS can be determined without much ambiguity. Taking UO2 as an illustration, the calculated ONs of 5f orbitals of each U ion are 2; consequently, considering that the high-lying itinerant 6d and 7s electrons completely participate in bonding, which holds true for the overwhelming cases, one can assign a robust U4+ irrespective of the potential 5f ↔ 6d valence fluctuation (i.e., U being of 5f3+δ6d1−δ7s2 valence electron configuration with slightly positive or negative δ values). Naturally, the method is suitable for d-block metals and two 5 × 5 occupation matrices are used.

3. Results and discussion

From the theoretical point of view, defect (intrinsic or external) formation energy (Ef) is the foremost parameter for understanding the fundamental behavior of defects. However, there is no universal definition of Ef; for example, whether defect charge state associated with electrostatic interaction is considered might be the greatest divergence. On the whole, considering only the neutral defect has long been the widely accepted scheme for the illustration of general trends of defect behavior,11–15,49,50 which is adopted in the present work as well. In addition, for the single atom doping, incorporation energy (Ei) is another commonly used terminology. Herein, by analogy with our previous definition, Ef and Ei of a single TM atom in the substitutional X site of XO2 (X32O64) are expressed as eqn (1) and (2), respectively:
Ef(TM) ≡ Ef(TM–VX) = Etot(X31TMO64) + Etot(X) − Etot(X32O64) − Etot(TM), (1)
Ei(TM) ≡ Ef(TM) − Ef(VX) = Etot(X31TMO64) − Etot(X31O64) − Etot(TM), (2)
where Etot(X) or Etot(TM) is the total energy per metal X or TM in its room-temperature phases calculated under the same DFT+U frameworks. Clearly, in terms of the definition, the contributions from TM and X vacancy can be examined separately. Ef(TM) is the total energy difference between perfect and TM-containing configurations; in contrast, Ei(TM) is the total energy difference of the configurations before and after incorporating TM. Certainly, Ef does not equal Ei for the case of substitutional TM of our interest because Ef also contains the formation energy of X vacancy Ef(VX). Similarly, the vacancy formation energy of X and O in pure or TM-doped XO2 can be expressed as eqn (3)–(5):
Ef(VX) = Etot(X31O63) + Etot(X) − Etot(X32O64), (3)
Ef(VO) = Etot(X32O63) + Etot(O) − Etot(X32O64), (4)
Ef(VO) = Etot(X31TMO63) + Etot(O) − Etot(X31TMO64), (5)
where the total energy per O atom Etot(O), or exactly 1/2Etot(O2), is calculated via the pure spin-polarized DFT scheme. For the well-known disadvantages of pure DFT in describing molecules, Etot(O2) is obtained from the sum of the energy of free atom O and the well-established dimerization energy, i.e., the reaction energy of 2O = O2. It should be emphasized that Ef(VO) is one of the important indicators for scaling the reducibility of metal oxides,51,52 which is particularly true for most applications of CeO2-based materials. This is mainly due to the fact that the oxidation or reduction process is essentially associated with the annihilation or formation of O vacancy; therefore, we focus on the trends of Ef(VO). In fact, our calculations show that Ef(VX) in pure UO2, ThO2 and CeO2 are high at 10.86, 16.91 and 15.8 eV, respectively, indicative of a low possibility of forming metal vacancy especially for the latter two oxides. The relatively low Ef(VU) is consistent with the electronic structure or 5f states of U: the remaining 5f2 electrons in UO2, characteristic of delocalized behavior, tend to further participate in chemical bonding to form higher U OS, which is evidenced by a wide variety of well identified UO2+x (0 < x ≤ 1) and other multicomponent compounds containing U with OS higher than 4+. However, Th4+ and Ce4+ have long been demonstrated as the highest OS under normal conditions, suggesting the extreme instability of Th1−δO2 and Ce1−δO2 (δ represents the atomic concentration of metal vacancy) with hypothetical higher formal OS of Th and Ce. On the other hand, the calculated Ef(VO) for pure UO2, ThO2 and CeO2 are 7.74, 7.27 and 3.79 eV, respectively, which are basically consistent with the literature values, and the order can be logically understood on the grounds of possible variation of OS. In other words, for the monovalent ThO2, both Th and O vacancies hardly form; O vacancy forms more easily than Ce vacancy in CeO2, and vice versa for UO2. Indeed, under normal conditions there isn't any stable binary U oxide lower than UO2, whereas there are considerable nonstoichiometric Ce oxides between the two borderline oxides CeO2 and Ce2O3, similar to the behavior of the Pu–O system.31,47,53 Physically, the vacancy formation reflects the dominant delocalized 5f electrons of U but localized 4f electrons of Ce, albeit the quantitative ratio of delocalization to localization is still lacking. In this regard, the standard reduction potentials (ER) that are consistent with the Gibbs energies of formation (ΔG, note that ΔG is proportional to −ER in terms of the principle of electrochemistry) might be rational for the scaling. ER related to U, Th and Ce are very different, as listed in the following:2,54
UO22+ + e → UO2+ER = +0.088 V,

UO2+ + e → U4+ER = +0.447 V,

U4+ + e → U3+ER = −0.553 V,

Th4+ + e → Th3+ER = −3.800 V,

Ce4+ + e → Ce3+ER = +1.720 V.

Clearly, the negative ER(Th4+/Th3+) and ER(U4+/U3+) prevent the reduction processes associated with O vacancy formation, particularly for the former ion pair. By contrast, the highly positive ER(Ce4+/Ce3+) suggests the ready formation of O vacancy in CeO2, which might be viewed as the physical origin for its varied applications. Indeed, ER(Ce4+/Ce3+) is even higher than its analogue ER(Pu4+/Pu3+) having +1.047 V, clarifying a slight difference in the f electronic states between CeO2 and PuO2: 4f electrons in the former have a stronger tendency to be localized than 5f electrons in the latter.

Having obtained the fundamental behavior of intrinsic defects associated with f states, we now turn to the discussion of TM-doped XO2. The calculated Ef(TM) and Ei(TM) of a single TM atom are plotted in Fig. 2. Our previous calculations on TM-doped fluorite-type PuO2 unraveled that there is no noticeable dependence of TM concentration (high to four isolated TM atoms in Pu32O64) on Ef(TM) and Ei(TM);32 from this perspective we decide to leave TM concentration out of the discussion but focus on the trend of a single doped TM. Another well-known notorious reason is that the calculation configurations exponentially increase with the increasing numbers of TM atoms, which is computationally insufficient for capturing the general trend of TM behavior. At the first sight of energy profiles in Fig. 2, one can find the overall similarity of Ei(TM) and Ef(TM) in the three dioxides. This is particularly true when we individually compare the energetics of 3d, 4d or 5d-series TMs in the three dioxides; for instance, even the inflection data lie in the same positions. Considering that the three dioxides have an identical crystal structure and very close lattice parameters, we propose that the crystal structures of the host dioxides related to elastic interactions play decisive roles in the general trends of TMs’ energetics, while the electron states of the host dioxides associated with electron interactions quantify the differences in energetics. The greatest difference is that Ei(TM) in CeO2 and ThO2 are wholly more negative than those in UO2, quantitatively consistent with the difference in their Ef(VX). The very high Ef(VX) values indicate the very unstable states of X31O64 and the substitutional TMs favor to stabilize the configurations. Consequently, all Ef(TM–VX) values which are more rational for describing the stability of doped TM fluctuate around Ef(VO). Noticeably, the global energy minima locate at the same TM point for the three systems; however, the global energy maxima locate at VIII (Ni, Pd, Pt) for UO2 while at I-B (Cu, Ag, Au) for CeO2 and ThO2. We consider that the slight difference might result from the difference in f states, or more exactly from the difference in the electronic structures of the hosts, as will be detailed later.

image file: c9cp04371c-f2.tif
Fig. 2 Energies of TMs at the substitutional X sites of XO2 (X = Ce, Th, U). Incorporation energy Ei(TM) and formation energy Ef(TM–VX) or Ef(TM) are marked with open and solid squares, respectively. The shadow area indicates the potential energetically favorable formation of the X–TM–O ternary phase. Ef(VX) and Ef(VO) in the pure XO2 are denoted by the horizontal dotted lines. Note that Ei(Hg) and Ef(Hg) are not calculated because of the liquid ground state of Hg.

As for the specific illustration of TM behavior in dioxides, we concentrate the discussion on TM-doped UO2 for the purpose of clarity and our main interest. As shown in Fig. 2(c), of all TMs Ef(TM) is rather higher than Ei(TM) because the former contains the contribution from very positive Ef(VU), +10.86 eV in the present calculation. According to the thermodynamic equilibrium, in the dilute limit the defect concentration c is determined by the defect formation energy Ef through a Boltzmann expression: c = A[thin space (1/6-em)]exp(−Ef/kBT), where A, kB and T represent the material constant, Boltzmann constant and temperature, respectively. Thus, one can readily conclude that equilibrium c(VU) in UO2 is rather low. Notwithstanding, the preparation process and the radiation damage effect promote the formation of non-equilibrium U vacancies, heightening the likelihood of TM doping. As for the general trend, Ef(TM) basically follows the monotonically upward and then downward tendencies with the turning points of VIII-B (Ni, Pd, Pt) TMs. The slight deviations from the tendencies appear on 4d Zr and 5d Hf having the global energy minima, which might be admitted as the consequences of electron- and size-matched atomic properties with U. Knowledge from material doping has shown that positive formation energy does not always represent the instability of the dopant because a reference defect state is required for the evaluation; in the regard, Ef(VO) in the pure dioxide is frequently used as the scaling parameter.15,32 From this perspective, by comparing the calculated Ef(VO) one can readily find that Ef(TM) of III-B, IV-B and V-B TMs are lower than Ef(VO), suggesting the relative stability or even the likelihood of forming U–TM–O ternary compounds. Indeed, U–TMIV-B–O ternary compounds without the change of U OS and without the significant change of crystal structure have been well identified.55 Certainly, the TMs having much higher Ef(TM) than Ef(VO) might indicate the phase segregations or phase transitions associated with structural reconstructions and OS changes of TM doped UO2. For the chemically inert TMs with very high Ef(TM), elementary TMs instead of their oxides are expected to be more readily segregated to the grain boundary, phase boundary, surface, and much more vacancy-rich extended defects. Taking Cu as an example, Cu even at a very low concentration could degrade, or even worse, destroy the host materials mainly owing to the strong tendency of segregation. On the other hand, for the TMs having Ef(TM) close to Ef(VO) such as Cr, Mn, Fe, Mo, and W, there are really considerable well-identified U–TM–O ternary oxides; however, after carefully checking the ternary oxides we find that the crystal structures and U OS associated with the electronic structure are noticeably deviated from the UO2 host.19 This holds for some reported U–TMIII-B–O and U–TMV-B–O ternary oxides as well albeit with lower Ef(TM) than Ef(VO). Therefore, from the standpoint of tailoring the functionality of UO2, IV-B TMs might be optimal alternatives, which is rationally supported by the R&D of UZrO4 as well as CeZrO4 and PuZrO4 analogues underway.26,39,56

The three fluorite-type stoichiometric dioxides are very stable in a wide range of temperature; however, crystal defects or impurities might accelerate the phase transition or local structure transition. Amongst these, O vacancy formation can be viewed as the rudimentary process for the reduction of dioxides, which is especially important in the realistic applications because high vacuum conditions are commonly required. Indeed, CeO2 is very susceptible to CeO2 → Ce2O3 (or exactly CeO2−x) transition under O-deficiency conditions and the investigations on O vacancy formation associated with reduction almost run through all applications and designs of ceria-based materials despite the fact that the inherent mechanism remains elusive.39,57 As aforementioned, the quantities of Ef(VO) in the three pure XO2 can be well understood in terms of f electron states and reduction potentials; notwithstanding, Ef(VO) in TM doped XO2 is expected to be different from that in pure XO2 due to the structural and bonding alternations around the doped TM. Herein, the 1NN, 2NN and 3NN O vacancies related to the doped TM are taken into consideration and the calculated Ef(VO) are plotted in Fig. 3.

image file: c9cp04371c-f3.tif
Fig. 3 Formation energy of the first, second and third nearest-neighboring (1NN, 2NN and 3NN) O vacancies related to the substitutional TM doped in XO2. Ef(VO) in the pure XO2 are denoted by the horizontal dotted lines.

After a brief survey of Fig. 3, one can find that almost all Ef(VO) in TM doped XO2 are lower than those in pure XO2 with several exceptions appearing for Ef(V3NN-O) in CeO2. This is proposed to be the consequence of bonding and structural changes of the host dioxides after TM doping. By comparing the thermodynamic, bonding-energy, elastic and melting-point parameters, we can conclude that TM–O bonds in many pure TM oxides are stronger than X–O bonds in pure XO2 (especially in CeO2), indicating that Ef(VO) in those pure TM oxides are higher than those in pure CeO2. Yet, the conclusion does not hold for CeO2 with low-concentration TM doping because the CeO2 host still plays a dominant role in the bonding behavior. The TM–O bonds in TM-doped CeO2 cannot reach the optimal bond length and coordination number as those in pure TM oxides, resulting in the weaker or unstable TM–O and Ce–O bonds, thereby lowering Ef(VO). This assumption is basically demonstrated by the higher Ef(V2NN-O) and Ef(V3NN-O) due to the relatively weak perturbation from TM on the farther O atoms. However, most of Ef(V3NN-O) are still lower than those in pure XO2, indicative of the overall bonding change after TM doping. Interestingly, the degree of bonding change is generally associated with the degree of valence-electron-match (or mismatch) between TM and X in XO2. Clearly, IV-B TMs attain the globally maximal Ef(VO), resulting from the well matched electron configurations with X, and the opposite feature is quite evident for the last three TM groups because of the noticeably electron-mismatch configurations. The very low Ef(VO) are indicative of TM doped XO2 being readily reduced, particularly for TM doped CeO2 since some Ef(VO) are slightly negative and the formation of O vacancy could be viewed as a spontaneous process. This is consistent with the extensive experimental observations regarding the easily reducible feature of CeO2. It should be emphasized that the reduction of CeO2 or the formation of O vacancy is suppressed under O-rich conditions because of the increasing O chemical potential. From the perspective of maintaining the essential structures and properties of XO2, the last three TM-group impurities should be avoided in the actual applications. On the other hand, for the purpose of tailoring the functionalities of XO2, IV-B TMs might be the optimal choice for designing ternary oxides, while other TMs might be judiciously selected according to the targeted properties. As aforementioned, the doping effects are the consequences of multi-factors, among which electronic and steric interactions are the two primary ones; certainly, the above discussion on the valence-electron match or mismatch is related to the former. Our previous studies on TM doped PuO2 indicated that electronic interactions prevail over steric ones for both Ef(TM) and Ef(VO);32 this conclusion could hold for the present three XO2 because of the consistent profiles of Ef(TM) and Ef(VO). Several data points significantly deviated from the energy profiles and the more oscillating features in TM doped CeO2 are expected to be the competitive results from the two interactions, which deserve to be carefully studied in the future works.

Since we conclude that electronic interactions associated with bonding features might play a dominant role in the trends of TM behaviors in XO2, we now turn to the exploration of the issue. In principle, electronic band structures and density of states (DOS) are commonly used as an illustration for bonding analysis; however, knowledge from the solid-state materials containing rather low concentration dopants shows that the electron states of defects are very sensitive to the calculation scheme and the underlying mechanisms of impurity effects remain not so clear, or even worse controversial. In this context, OS, which is a combinational parameter associated with the electronic structure and charge transfer, has been assumed as an indicator for evaluating the chemical states of dopants. Indeed, in the domains of material doping, the unambiguous determination of the OS of multivalent dopants and host atoms has long been the foremost, albeit challenging, task; hereby we concentrate on the OS of TM and X in XO2 to capture the dependency of f states on TM behaviors. Notwithstanding, to date, the rigorous determination of OS from first-principles calculations has still been lacking for the solid-state materials; this is mainly due to the fact that the integral OS (or formal OS, OSf, in the standard definition from IUPAC) is physically ill defined in the ionic limit approximation. In order to overcome the bottleneck, recently we have successfully used an orbital ON method under the DFT+U framework to determine the quantum-mechanical OS (OSqm) of 4f- and 5f-block elements even in very complicated solids such as those containing different multivalent elements or containing one multivalent element with different OS. For the details of calculating OSqm, one can refer to ref. 45–48. Here, for simplicity we just take UO2 as an illustrative example for determining U OSqm. The outer valence electron configuration of U is 5f36d17s2 in which the high-lying delocalized d and s electrons completely participate in chemical bonding under normal conditions; therefore, the bonding degree of 5f electrons is crucial for determining OS. The calculated results show that the ONs of two 5f orbitals in UO2 are close to 1, indicative of fully occupied orbitals, while the ONs of the remaining twelve 5f orbitals are close to 0, indicative of fully unoccupied orbitals. Naturally, the OSqm of U in UO2 is assigned to be U4+. It should be emphasized that the ON of an occupied or an unoccupied orbital may deviate from unity 1 or 0 because of the complicated quantum effects of open-shell d or f orbitals; in this regard, we assign a d or f orbital as occupied if the orbital has the ON higher than the critical value 0.8 which has been demonstrated to be reasonable by our and other researchers’ calculations.44–48 The critical value 0.8 represents that the main part of a d or f orbital is occupied. However, in some cases, the occupation numbers are just slightly lower than the critical value, resulting in the ambiguous assignment of OS, as will be detailed later.

The uncertainties in the literature regarding the actual chemical states of dopants mainly appear in the aliovalent doping of multivalent metals, especially in the host with multivalent ions such as U and Ce. Available theoretical works on determining the OS of doped TMs in solid materials were largely based on the educated guesses in a non-quantitative manner. In principle, all TMs can be viewed as multivalent elements; this is due to the fact that even the so-called inert metals such as Cu, Ag, Au and so on might exhibit rich bonding behaviors under specific conditions, which is the inherent origin for their application as catalysts. From the calculated ONs of TMs doped in XO2, we derive their OSqm, as juxtaposed in Fig. 4. At the same time, the OSqm of X in XO2 is assigned as well, and we will consider some specific TM-doped XO2 for the discussion on the OSqm variations of X in XO2. Above all, the ONs of occupied and unoccupied orbitals are well separated for the majority of cases, suggestive of the present assignment of OSqm without much ambiguity. Yet, some unusual OSqm occur, as marked by red rectangles in Fig. 4, in which some ONs adopt the values close to the critical one 0.8, resulting in more or less uncertainty in assigning OSqm. In Table 1, we list the ONs of TMs’ 4d orbitals of some representative XO2 for illustration. Taking Ag doped XO2 as an example with the unusual OSqm behavior, in terms of ONs, Ag adopts Ag3+ in CeO2, Ag4+ in ThO2, and Ag+ in UO2. In the former two cases, the ONs of unoccupied Ag 4d orbitals are higher than 0.7 but lower than 0.8; strictly speaking, it is more reasonable to nominate them as pseudo Ag3+ and Ag4+. Obviously, the neighboring Pd has a stronger tendency to form unusually higher OS because its d electrons are more easily polarized. Notwithstanding, it is clear that the higher OSqm corresponds to the greater possibility of charge transfer, as will be addressed later.

image file: c9cp04371c-f4.tif
Fig. 4 The population of the quantum-mechanical oxidation state (OSqm) of TMs doped into XO2. The unusual OSqm are marked by red rectangles. Note that the definition of OSqm is different from that of formal OS (OSf) and, some unusually high OSqm, or exactly pseudo OSqm such as Pd4+ and Ag4+ in ThO2 just imply their tendency to lose more charge and achieve charge balance, as detailed in the text.
Table 1 Calculated occupation numbers (ONs) of d orbitals and the assigned quantum-mechanical oxidation states (OSqm) of the doped transition metals (TMs) selected particularly with unusual OSqm. The ONs with full occupancy are marked in bold
XO2 TM Valence ONs of TMs’ 4d orbitals OSqm
CeO2 Zr 4d25s2 0.083 0.083 0.083 0.083 0.231 4+
0.231 0.231 0.231 0.231 0.231
ThO2 0.076 0.076 0.076 0.076 0.216 4+
0.216 0.216 0.216 0.216 0.216
UO2 0.080 0.080 0.080 0.080 0.220 4+
0.220 0.224 0.226 0.236 0.236
CeO2 Nb 4d35s2 0.109 0.113 0.113 0.116 0.196 5+
0.196 0.196 0.198 0.215 0.215
ThO2 0.041 0.057 0.068 0.128 0.139 4+
0.139 0.141 0.157 0.157 0.854
UO2 0.044 0.060 0.074 0.131 0.140 4+
0.148 0.148 0.155 0.166 0.844
CeO2 Pd 4d10 0.470 0.470 0.470 0.862 0.862 3+
0.862 0.918 0.918 0.923 0.923
ThO2 0.500 0.512 0.536 0.584 0.920 4+
0.920 0.923 0.923 0.940 0.940
UO2 0.257 0.283 0.906 0.906 0.912 2+
0.912 0.916 0.922 0.940 0.940
CeO2 Ag 4d105s1 0.702 0.702 0.863 0.863 0.935 3+
0.935 0.935 0.935 0.953 0.953
ThO2 0.715 0.715 0.715 0.934 0.934 4+
0.934 0.934 0.952 0.952 0.952
UO2 0.916 0.916 0.917 0.917 0.936 1+
0.936 0.937 0.937 0.937 0.937

In fact, the occurrence of unusually high OSqm of TMs is consistent with the literature on TM doped solids and other material systems.58–60 For the TMs in XO2, the TM–O bond distance and coordinate environment are largely different from those in the ground-state pure TM oxides, thereby the doped TMs being in the extreme bonding condition similar to the high-pressure condition which can readily induce the formation of higher OS with more bonding-state valence electrons. In addition, the judicious tailoring of ligands could yield the unusual OS of relatively inert metals. It is naturally conceivable that those unusual OSqm TMs have higher chemical activities, in favor of some specific chemical or catalytic reactions. Indeed, how to activate those relatively inert metals has long been the focus of designing novel catalysts; in this regard, ThO2 prevails over CeO2 in terms of activation, followed by UO2. The differences in the OSqm population of doped TMs are essentially the outcome of the aforementioned differences in the electronic structures of three XO2. From the fundamental perspective of charge balance, the balance in XO2 is initially destroyed when substituting an X4+ ion by an aliovalent TMn+ ion (n ≠ 4). In order to reach that balance, the charge compensation can be realized by further tuning the OS of either X or TM, which is very straightforward for the solely monovalent ThO2. Taking 4d TMs as an illustration as shown in Fig. 4, almost all TMs in ThO2 tend to be tetravalent with the exception of Y and Cd because the numbers of outer valence electrons of the latter two are lower than 4. For Nb and Mo which can form the stable pentavalent Nb2O5, hexavalent MoO3 and other lower valent oxides under normal conditions, they remain as tetravalent ions in ThO2, achieving the electronically compatible chemical states. The principle that the doped TM inclines to be tetravalent basically holds for CeO2 and UO2 with some exceptions. Owing to the readily reducible property of CeO2, the doped Nb adopts pentavalent Nb5+ associated with the formation of one Ce3+ ion by the reduction of Ce4+, as will be detailed later. Both Pd and Ag doped in CeO2 are activated to be trivalent or pseudo trivalent, basically consistent with the results from Pd or Ag modified CeO2-type catalysts. By contrast, considering the oxidizability of UO2, the OSqm population of TMs in UO2 can be logically understood; for example, Pd and Ag tend to take their ground-state chemical states Pd2+ and Ag+, respectively. Additionally, the OSqm population of 5d TMs is generally in accordance with that of 4d TMs; a few deviations occur on TMs (Re, Pt, Au) doped CeO2. However, in comparison to those of 4d and 5d TMs, the OSqm population of 3d TMs shows a more oscillating feature, similar to the previously discussed energies. We still state that the mechanism behind the more oscillating behavior roots in the larger size mismatch between 3d TMs and X in XO2, and the non-ignorable electronic structure difference among 3d, 4d and 5d TMs. Meanwhile, the detailed discussion of the difference is beyond the scope of the present work and we just take Fe as an instance. Ru and Os can easily form dioxides or beyond (such as RuO4 and OsO4), whereas Fe, in the same group as Ru and Os, might form FeO2 only in some specific conditions similar to Fe doped CeO2 and ThO2.61

We assign the OSqm of all X in TM doped XO2 in terms of calculated ONs of X 5f and 6d orbitals. As expected, Th ions exclusively adopt Th4+ in all TM doped ThO2, and there exist some OS changes of Ce and U in the aliovalent TM doped CeO2 and UO2. The basic rule is that the average OSqm of TM and X tends to be 4+, thereby satisfying the charge balance, which particularly holds for TM doped UO2. We find that each monovalent Sc3+, Y3+ or La3+ ion drives the formation of one U5+ ion while each monovalent Zn2+, Cd2+ or Hg2+ ion yields two U5+ ions. No U6+ ion is observed in the latter cases, consistent with the fundamental principle of structure and bonding of mixed valent U (or other multivalent metal) oxides such as U3O7, U3O8, U4O9, U13O34 and so on. In these mixed oxides, the nominal compositions with adjacent OS, i.e., U4+ + U5+, or U5+ + U6+, are demonstrated to be relatively stable, whereas the compositions with U4+ + U6+ are thermodynamically metastable because of the ultimate auto-reaction between U4+ and U6+. Interestingly, the quantitative assignment of OSqm clarifies the controversies related to the actual chemical states of aliovalent TM (such as widely discussed La) doped UO2, supporting the mechanism of charge compensation instead of O vacancy formation because only slight distortion of lattice O atoms is observed in the doped UO2. For simplicity, here we do not intend to provide all ONs of X in TM doped XO2, but focus on the representative cases listed in Table 1 except for the isovalent Zr4+.

We visualize the spin electron density of the nine TM doped XO2, as shown in Fig. 5; generally, the isosurfaces of spin density pinned on the ions indicate the localized d or f electrons. Taking Nb doping as an illustration, the doped Nb in CeO2 loses all the outer valence electrons associated with the formation of Nb5+; consequently, the surplus one electron localizes at the 1NN Ce ions, inducing the formation of a magnetic Ce3+ ion. This is reminiscent of the extensively studied OS change of CeO2 after the formation of O vacancy associated with the two electrons left; likewise, one O vacancy drives the formation of two 1NN Ce3+ ions. However, for the cases of ThO2 and UO2, the surplus electron localizes at Nb, consistent with the assigned Nb4+. It is worth noting that each U ion in pure UO2 has two surplus electrons, resulting in significant spin electron density on all U ions. The situation becomes more complicated for the relatively inert Pd and Ag. Although we assign Pd and Ag in CeO2 and ThO2 as pseudo Pd3+ and Pd4+, respectively, the ON results show that the unoccupied d orbitals are not completely polarized. As a consequence, more or less localized electrons pin at the 1NN O ions. Notwithstanding, Pd and Ag are activated to a certain degree; much in evidence is the fact that there is clear Pd–O bonding as depicted by the bond length in the Pd doped ThO2: two Pd–O bond lengths are noticeably shorter than others. Pd and Ag in UO2 remain in their ground-state OS, i.e., Pd2+ and Ag+; the electron-deficiency feature promotes the formation of two and three U5+ ions in Pd and Ag doped UO2, respectively. There isn’t any electron delocalized on the doped Ag in UO2, which is consistent with the standard close-shell electron configuration of Ag+, i.e., [Kr]4d10.

image file: c9cp04371c-f5.tif
Fig. 5 Visualization of the spin electron density of the nine representative TM doped XO2 (X = Ce, Th, U) for illustrating the variations of OSqm of TMs and X. Spin up and spin down densities are indicated by the yellow and blue isosurfaces, respectively, at a level of 0.01 electron per Å3. Isosurfaces of spin density pinned on the ions indicate the localized d or f electrons (see the details in the text). The reduced or oxidized X ions (Ce3+ or U5+) are marked in terms of calculated orbital occupation numbers (ONs).

Having determined the stability and chemical state of TM doped XO2, we attempt to find the underlying mechanism to understand the general doping effects since the defect configurations in the realistic conditions might be more complicated than those considered here. In this context, based on the literature and our previous works we state that not any one physical or chemical parameter could be used to scale the trend. Taking the most commonly used atomic radius as an example, it might be effective only in the case that the doped elements have very similar atomic properties.32 This is particularly true for lanthanide (Ln) dopants because their atomic radii vary in a slight range and in most cases Ln3+ ions dominate the Ln chemistry with some exceptions such as Ce4+, Tb4+ and Pr4+/5+.62 However, all TMs show the well-known parabolic-like change in atomic radius with increasing atomic number or d electrons; the first-stage decrease in atomic radius is attributed to the filling of d bonding states, then atomic radii begin to increase as antibonding states are filled. VIII-B group TMs locate at the globally minimal positions in the relationships between atomic number and atomic radius. Obviously, there is no direct correlation with the stability of TMs doped in XO2, as shown in Fig. 2. On the other hand, similar to OSf, the atomic radius in solid state is also ill-defined and physically unobservable because it is very sensitive to the surroundings: the variations of coordinate number and ligand are associated with the flexible changes of atomic radius. As discussed previously, the electronic structure of TM or the degree of electronic match between TM and X in XO2 might be the crucial factor controlling the trends of doped TM; therefore, we present the valence electron configurations and the orbital energy levels of all TMs, along with the Bader charge63 transfer of TMs, as shown in Fig. 6.

image file: c9cp04371c-f6.tif
Fig. 6 (a) Schematic of the atomic orbital energy levels of transition metals (TMs), Ce, Th, U and O. The energy levels are taken from the projector augmented wave (PAW) pseudopotential. (b) Bader charge transfer of TMs. The Bader charge transfer of Ce, Th and U in their pure dioxides is denoted by the horizontal dotted lines.

Apparently, except for d orbital energy levels of II-B TMs (Zn, Cd, Hg), other orbital energy levels of metallic elements are higher than that of the O 2p orbital, indicative of the potential formation of the highest binary oxides when all valence electrons of metallic elements participate in chemical bonding with O. However, in terms of the principles of chemical bonding and quantum effects of d or f orbitals, the possible charge transfer does not always suggest the formation of compounds with strong chemical bonds. Taking VIII-B TMs (Fe, Ru, Os) as an illustration, under normal conditions it is rather difficult for the formation of Fe oxides higher than Fe2O3, whereas solid-state RuO4 and OsO4 are well identified. Herein, the critical charge-transfer point for the formation of chemical bonds is beyond the scope of the present discussion. As mentioned previously, some unusual OSqm such as Fe4+, Ni4+, Pd4+, Ag4+ and so on are named as pseudo OSqm because more d orbitals donate electrons to the hosts, indicative of more or less contributions to chemical bonding. Since all outer valence-electron orbitals of Ce and Th in their dioxides contribute to chemical bonding, here we take 4d TM doped UO2 containing the formal 5f2 configuration into consideration for exploring the trends. Generally, the energy difference between TM 4d and U 5f orbitals calibrates the degree of competition in bonding: the 4d orbitals with a higher energy level suppress the bonding of U 5f orbitals. The 4d15s2 valence states of Sc cannot satisfy the charge balance after substituting a U atom, thereby creating a neighboring U5+. Zr with high-lying 4d orbitals and the completely matched valence electron configuration of U in UO2 are both energetically and electronically favorable, maintaining the U4+. The 4d orbital energies of TMs gradually decrease with atomic number, corresponding to the weaker tendency of donating electrons; thus, the U4+ ion tends to lose an electron to balance charge associated with the creation of U5+. Interestingly, we find that Pd locates at the critical transition point characterized by the close proximity of energies of TM 4d and U 5f, from which U5+ ions begin to form in terms of calculated ONs and OSqm. The results indicate two, three and two U5+ ions in the Pd (Pd2+), Ag (Ag+) and Cd (Cd2+) doped UO2, respectively, satisfying the previously mentioned average OSqm being 4+. The trend of 5d TMs is nearly identical to that of the 4d series; the slight difference lies in the fact that the critical point Pt tends to adopt Pt3+ instead of Pt2+, rationally consistent with the easier formation of higher OS of Pt. Yet, the trend of 3d TMs deviates from those of the 4d and 5d series, similar to the oscillating feature of energetics mentioned above. By analogy, we conclude that the elastically incompatible interactions from the 3d TMs series play a more important role than the 4d and 5d TMs series because of the larger atomic-radii difference between 3d TMs and X in XO2.

Charge transfer is another valuable parameter for interpreting the trend of chemical states of TMs, as shown in Fig. 6(b). It is important to point out that charge and OS are two correlated but essentially different concepts. Generally, for compounds with the same elemental composition but a different atomic ratio such as U–O binary oxides, U OS is basically proportional to charge. However, this scaling does not always hold for the different-composition systems, which is evident in that the charge of TMs adopting the same TM4+ spans a relatively wide range and exhibits a chaotic distribution, as can be found from Fig. 6(b). The difference in atomic electronegativity could be viewed as the main cause. Taking 4d TMs as an illustration, Y has the lowest electronegativity followed by Zr, which accounts for the substantial charge transfer from Y and Zr to the hosts.32 Certainly, the charge transfer of Zr attains the globally maximal value because Zr has one more valence electron than Y. After Zr, the electronegativity increases, thereby suppressing charge transfer despite the increase in valence electrons. As expected, the smallest charge transfer occurs on Ag having the highest electronegativity. This trend is basically consistent with orbital energy levels in Fig. 6(a); that is, the lowering of the orbital energy level weakens the ability of charge transfer. The rather large, or exactly the largest, charge transfer occurring on Ta doped in CeO2 suggests the greatest possibility of being reduced. In addition, the smallest charge transfer occurs on Au because it has the highest electronegativity among all TMs; indeed, Au can adopt negative OS in the active metal aurides.64

4. Conclusions

In summary, we have conducted a systematic first-principles DFT+U investigation on TM (3d, 4d, 5d series) doped fluorite-type XO2 (X: Ce, Th, U) to obtain the general trends of TM behaviors and to unravel the underlying correlations between the trends and the fundamental properties of TMs and XO2. The Hubbard parameter U is used to treat the strongly correlated f and d valence electrons and, a physically more strict method based on calculating orbital occupation numbers of f and d orbitals is utilized for the assignment of the quantum-mechanical oxidation state (OSqm) of the multivalent TMs and X. In terms of the calculated formation energies of TMs and oxygen vacancy, we find that 3d, 4d and 5d TMs show the qualitatively consistent trends of relative stability, suggesting that the properties of three XO2 hosts with an identical crystal structure and very close lattice parameters play a dominant role in the trends. The quantitative differences in the formation energies of TMs and oxygen vacancy are attributed to the differences in the formation energies of X and oxygen vacancy of pure XO2, which is essentially the outcome of differences in f states of X in XO2. The reduction-type CeO2 favors the formation of O vacancy while it is opposite for the oxidation-type UO2, and ThO2 can be viewed as an intermediate one. This standpoint is supported by the calculated OSqm population of TMs, especially aliovalent TMs. Some relatively inert TMs such as VIII-B (Ni, Pd, Pt) and I-B (Cu, Ag, Au) adopt unusually high OSqm in CeO2 and ThO2 owing to the electron-match principle and the localized nature of the Ce 4f electron. In contrast, these unusual OSqm do not occur on TM doped UO2 because the remaining delocalized 5f2 electrons of U in UO2 are able to contribute to balance charge after substituting U by TM. The occurrence of unusual OSqm might be valuable for tailoring the functionalities of the dioxides considered, and the trends of TM behaviors might be extendable to more oxides regarding impurity behavior, material modification and design.

Conflicts of interest

The authors declare no competing financial interests.


The research was supported by the National Natural Science Foundation of China (No. 21771167), the Science Challenge Project of China (No. TZ2016004), and the Foundation of Science and Technology on Surface Physics and Chemistry Laboratory (No. WDZC201802). The computer facilities received from Institute of Computer Applications of China Academy of Engineering Physics and National Supercomputing Center in Shenzhen of China are greatly acknowledged.


  1. C. Freysoldt, B. Grabowski, T. Hickel, J. Neugebauer, G. Kresse, A. Janotti and C. G. Van de Walle, First-principles calculations for point defects in solids, Rev. Mod. Phys., 2014, 86, 253–305 CrossRef.
  2. The Chemistry of the Actinide and Transactinide Elements, ed. L. R. Morss, N. M. Edelstein and J. Fuger, Springer, Berlin, 2006 Search PubMed.
  3. J. Breza, P. Dařílek and V. Nečas, Study of thorium advanced fuel cycle utilization in light water reactor VVER-440, Ann. Nucl. Eng., 2010, 37, 685–690 CrossRef CAS.
  4. S. J. Zinkle and G. S. Was, Materials challenges in nuclear energy, Acta Mater., 2013, 61, 735–758 CrossRef CAS.
  5. R. Parrish and A. Aitkaliyeva, A review of microstructural features in fast reactor mixed oxide fuels, J. Nucl. Mater., 2018, 510, 644–660 CrossRef CAS.
  6. C. Nandi, V. Grover, K. Bhandari, S. Bhattacharya, S. Mishra, J. Banerjee, A. Prakash and A. K. Tyagi, Exploring YSZ/ZrO2–PuO2 systems: candidates for inert matrix fuel, J. Nucl. Mater., 2018, 508, 82–91 CrossRef CAS.
  7. T. Arima, S. Yamasaki, K. Yamahira, K. Idemitsu, Y. Inagaki and C. Degueldre, Evaluation of thermal conductivity of zirconia-based inert matrix fuel by molecular dynamics simulation, J. Nucl. Mater., 2006, 352, 309–317 CrossRef CAS.
  8. X. Y. Liu, D. A. Andersson and B. P. Uberuaga, First-principles DFT modeling of nuclear fuel materials, J. Mater. Sci., 2012, 47, 7367–7384 CrossRef CAS.
  9. Y. Yun, P. M. Oppeneer, H. Kim and K. Park, Defect energetics and Xe diffusion in UO2 and ThO2, Acta Mater., 2009, 57, 1655–1659 CrossRef CAS.
  10. P. S. Ghosh, A. Arya, G. K. Dey, N. Kuganathan and R. W. Grimes, A computational study on the superionic behaviour of ThO2, Phys. Chem. Chem. Phys., 2016, 18, 31494–31504 RSC.
  11. V. Alexandrov, N. Grϕnbech-Jensen, A. Navrotsky and M. Asta, First-principles computational study of defect clustering in solid solutions of ThO2 with trivalent oxides, Phys. Rev. B: Condens. Matter Mater. Phys., 2010, 82, 174115 CrossRef.
  12. D. A. Andersson, S. I. Simak, N. V. Skorodumova, I. A. Abrikosov and B. Johansson, Theoretical study of CeO2 doped with tetravalent ions, Phys. Rev. B: Condens. Matter Mater. Phys., 2007, 76, 174119 CrossRef.
  13. S. C. Hernandez and E. F. Holby, DFT+U study of chemical impurities in PuO2, J. Phys. Chem. C, 2016, 120, 13095–13102 CrossRef CAS.
  14. L. Zhang, J. Meng, F. Yao, W. Zhang, X. Liu, J. Meng and H. Zhang, Insight into the mechanism of the ionic conductivity for Ln-doped ceria (Ln = La, Pr, Nd, Pm, Sm, Gd, Tb, Dy, Ho, Er, and Tm) through first-principles calculation, Inorg. Chem., 2018, 57, 12690–12696 CrossRef CAS PubMed.
  15. D. E. P. Vanpoucke, P. Bultinck, S. Cottenier, V. V. Speybroeck and I. V. Driessche, Aliovalent doping of CeO2: DFT study of oxidation state and vacancy effects, J. Mater. Chem. A, 2014, 2, 13723–13737 RSC.
  16. X. Wen, R. L. Martin, T. M. Henderson and G. E. Scuseria, Density functional theory studies of the electronic structure of solid state actinide oxides, Chem. Rev., 2013, 113, 1063–1096 CrossRef CAS PubMed.
  17. J. T. Pegg, X. Aparicio-Anglès, M. Storr and N. H. de Leeuw, DFT+U study of the structures and properties of the actinide dioxides, J. Nucl. Mater., 2017, 492, 269–278 CrossRef CAS.
  18. C. Mo, Y. Yang, W. Kang and P. Zhang, Electronic and optical properties of (U,Th)O2 compound from screened hybrid density functional studies, Phys. Lett. A, 2016, 380, 1481–1486 CrossRef CAS.
  19. A. J. Lussier, A. K. Lopez and P. C. Burns, A revised and expanded structure hierarchy of natural and synthetic hexavalenr uranium compounds, Can. Mineral., 2016, 54, 177–283 CrossRef CAS.
  20. E. S. Ilton and P. S. Bagus, XPS determination of uranium oxidation states, Surf. Interface Anal., 2011, 43, 1549–1560 CrossRef CAS.
  21. A. E. Shields, A. J. Miskowiec, K. Maheshwari, M. C. Kirkegaard, D. J. Staros, J. L. Niedziela, R. J. Kapsimalis and B. B. Anderson, The impact of coordination environment on the thermodynamic stability of uranium oxides, J. Phys. Chem. C, 2019, 123, 15985–15995 CrossRef CAS.
  22. W. Sun, W. Luo and R. Ahuja, Stability of a new cubic monoxide of thorium under pressure, Sci. Rep., 2015, 5, 13740 CrossRef PubMed.
  23. H. He, J. Majewski, D. D. Allred, P. Wang, X. Wen and K. D. Rector, Formation of solid thorium monoxide at near-ambient conditions as observed by neutron reflectometry and interpreted by screened hybrid functional calculations, J. Nucl. Mater., 2017, 487, 288–296 CrossRef CAS.
  24. L. Zhang, J. M. Solomon, M. Asta and A. Navrotsky, A combined calorimetric and computational study of the energetic of rare earth substituted UO2 systems, Acta Mater., 2015, 97, 191–198 CrossRef CAS.
  25. D. Prieur, L. Martel, J. Vigier, A. C. Scheinost, K. O. Kvashnina, J. Somers and P. M. Martin, Aliovalent cation substitution in UO2: electronic and local structures of U1−yLayOx solid solutions, Inorg. Chem., 2018, 57, 1535–1544 CrossRef CAS PubMed.
  26. T. Montini, M. Melchionna, M. Monai and P. Fornasiero, Fundamentals and catalytic applications of CeO2-based materials, Chem. Rev., 2016, 113, 5987–6041 CrossRef PubMed.
  27. C. Artini, Rare-earth-doped ceria systems and their performance as solid electrolytes: a puzzling tangle of structural issues at the average and local scale, Inorg. Chem., 2018, 57, 13047–13062 CrossRef CAS PubMed.
  28. T. Vinodkumar, B. G. Rao and B. M. Reddy, Influence of isovalent and aliovalent dopants on the reactivity of cerium oxide for catalytic applications, Catal. Today, 2015, 253, 57–64 CrossRef CAS.
  29. J. Koettgen, S. Grieshammer, P. Hein, B. O. H. Grope, M. Nakayma and M. Martin, Understanding the ionic conductivity maximum in doped ceria: trapping and blocking, Phys. Chem. Chem. Phys., 2018, 20, 14291–14321 RSC.
  30. H. S. Kim, C. Y. Joung, B. H. Lee, J. Y. Oh, Y. H. Koo and P. Heimgartner, Applicability of CeO2 as a surrogate for PuO2 in a MOX fuel development, J. Nucl. Mater., 2008, 378, 98–104 CrossRef CAS.
  31. B. Ao and R. Qiu, First-principles explorations of the universal picture of oxide layer structure over metallic plutonium, Corros. Sci., 2019, 153, 236–248 CrossRef CAS.
  32. B. Ao, J. Tang, X. Ye, R. Tao and R. Qiu, Phase segregation, transition, or new phase formation of plutonium dioxide: the roles of transition metals, Inorg. Chem., 2019, 58, 4350–4364 CrossRef CAS PubMed.
  33. B. Ao, R. Qiu, H. Lu and P. Chen, Differences in the existence states of hydrogen in UO2 and PuO2 from DFT+U calculations, J. Phys. Chem. C, 2018, 120, 18445–18451 CrossRef.
  34. B. Ao, R. Qiu, G. Zhang, Z. Pu, X. Wang and P. Shi, Light impurity atoms as the probes for the electronic structures of actinide dioxides, Comput. Mater. Sci., 2018, 142, 25–31 CrossRef CAS.
  35. B. Ao, R. Qiu, H. Lu and P. Chen, First-principles DFT+U calculations on the energetics of Ga in Pu, Pu2O3 and PuO2, Comput. Mater. Sci., 2016, 122, 263–271 CrossRef CAS.
  36. G. Kresse and J. Furthmüller, Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set, Phys. Rev. B: Condens. Matter Mater. Phys., 1996, 54, 11169–11186 CrossRef CAS PubMed.
  37. K. Momma and F. Izumi, VESTA 3 for three-dimensional visualization of crystal, volumetric and morphology data, J. Appl. Crystallogr., 2011, 44, 1272–1276 CrossRef CAS.
  38. S. L. Dudarev, G. A. Botton, S. Y. Savrasov, C. J. Humphreys and A. P. Sutton, Electron-energy-loss spectra and the structural stability of nickel oxide: an LSDA+U study, Phys. Rev. B: Condens. Matter Mater. Phys., 1998, 57, 1505–1509 CrossRef CAS.
  39. J. Paier, C. Penschke and J. Sauer, Oxygen defects and surface chemistry of ceria: quantum chemical studies compared to experiment, Chem. Rev., 2013, 113, 3949–3985 CrossRef CAS PubMed.
  40. Y. Hinuma, H. Hayashi, Y. Kumagai, I. Tanaka and F. Oba, Comparison of approximations in density functional theory calculations: energetics and structure of binary oxides, Phys. Rev. B, 2017, 96, 094102 CrossRef.
  41. A. Walsh, A. A. Sokol, J. Buckeridge, D. O. Scanlon and C. R. A. Catlow, Electron counting in solids: oxidation states, partial charges, and iconicity, J. Phys. Chem. Lett., 2017, 8, 2074–2075 CrossRef CAS PubMed.
  42. S. Riedel and M. Kaupp, The highest oxidation states of the transition metal elements, Coord. Chem. Rev., 2009, 253, 606–624 CrossRef CAS.
  43. A. Walsh, A. A. Sokol, J. Buckeridge, D. O. Scanlon and C. R. A. Catlow, Oxidation states and iconicity, Nat. Mater., 2018, 17, 958–964 CrossRef CAS PubMed.
  44. P. H. L. Sit, R. Car, M. H. Cohen and A. Selloni, Simple, unambiguous theoretical approach to oxidation state determination via first-principles calculations, Inorg. Chem., 2011, 50, 10259–10267 CrossRef CAS PubMed.
  45. B. Ao, H. Lu, Z. Yang, R. Qiu and S. Hu, Unraveling the highest oxidation states of actinides in solid-state compounds with a particular focus on plutonium, Phys. Chem. Chem. Phys., 2019, 21, 4732–4737 RSC.
  46. S. Hu, M. Chen and B. Ao, Theoretical studies on the oxidation states and electronic structures of actinide-borides: AnB12 (An = Th–Cm) clusters, Phys. Chem. Chem. Phys., 2018, 20, 23856–23863 RSC.
  47. B. Ao, R. Qiu and S. Hu, First-principles insights into the oxidation states and electronic structures of ceria-based binary, ternary and quaternary oxides, J. Phys. Chem. C, 2019, 123, 175–184 CrossRef CAS.
  48. B. Ao, R. Qiu and S. Hu, Plutonium oxidation states in complex molecular solids, J. Phys. Chem. C, 2019, 123, 12096–12103 CrossRef CAS.
  49. C. D. Taylor, Periodic trends governing the interactions between impurity atoms [H-Ar] and α-U, Philos. Mag., 2009, 89, 465–487 CrossRef CAS.
  50. S. K. Nayak, C. J. Hung, V. Sharma, S. P. Alpay, A. M. Dongare, W. J. Brindley and R. J. Hebert, Insight into point defects and impurities in titanium from first principles, npj Comput. Mater., 2018, 4, 11 CrossRef.
  51. Z. Helali, A. Jedidi, O. A. Syzgantseva, M. Calatayud and C. Minot, Scaling reducibility of metal oxides, Theor. Chem. Acc., 2017, 136, 100 Search PubMed.
  52. M. V. Ganduglia-Pirovano, A. Hofmann and J. Sauer, Oxygen vacancies in transition metal and rare earth oxides: current state of understanding and remaining challenges, Surf. Sci. Rep., 2007, 62, 219–270 CrossRef CAS.
  53. G. E. Murgida, V. Ferrari, M. V. Ganduglia-Pirovano and A. M. Llois, Ordering of oxygen vacancies and excess charge localization in bulk ceria: a DFT+U study, Phys. Rev. B: Condens. Matter Mater. Phys., 2014, 90, 115120 CrossRef.
  54. J. P. W. Wellington, B. E. Tegner, J. Collard, A. Kerridge and N. Kaltsoyannis, Oxygen vacancy formation and water adsorption on reduced AnO2{111}, {110} and {100} surfaces (An = U, Pu): a computational study, J. Phys. Chem. C, 2018, 122, 7149–7165 CrossRef CAS.
  55. P. Y. Chevalier, E. Fischer and B. Cheynet, Progress in the thermodynamic modeling of the O–U–Zr ternary system, CALPHAD, 2004, 28, 15–40 CrossRef CAS.
  56. T. Wakita and M. Yashima, In situ observation of the tetragonal-cubic phase transition in the CeZrO4 solid solution – a high temperature neutron diffraction study, Acta Crystallogr., 2007, B63, 384–389 Search PubMed.
  57. N. V. Skorodumova, S. I. Simak, B. I. Lundqvist, I. A. Abrikosov and B. Johansson, Quantum origin of the oxygen storage capability of ceria, Phys. Rev. Lett., 2000, 89, 166601 CrossRef PubMed.
  58. J. Gebhardt and A. M. Rappe, Doping of BiFeO3: a comprehensive study on substitutional doping, Phys. Rev. B, 2018, 98, 125202 CrossRef CAS.
  59. M. R. Mian, H. Iguchi, S. Takaishi, H. Murasugi, T. Miyamoto, H. Okamoto, H. Tanaka, S. Kuroda, B. K. Breedlove and M. Yamashita, Multiple hydrogen-bond approach to uncommon Pd(III) oxidation state: a Pd–Br chain with high conductivity and thermal stability, J. Am. Chem. Soc., 2017, 139, 6562–6565 CrossRef CAS PubMed.
  60. J. R. Bour, D. M. Ferguson, E. J. McClain, J. W. Kampf and M. S. Sanford, Connecting organometallic Ni(III) and Ni(IV): reactions of carbon-centered radicals with high-valent organonickel complexes, J. Am. Chem. Soc., 2019, 141, 8914–8920 CrossRef CAS PubMed.
  61. S. Zhu, J. Liu, Q. Hu, W. L. Mao, Y. Meng, D. Zhang, H. Mao and Q. Zhu, Structure-controlled oxygen concentration in Fe2O3 and FeO2, Inorg. Chem., 2019, 58, 5476–5482 CrossRef CAS PubMed.
  62. Z. C. Kang and L. Eyring, A compositional and structural rationalization of the higher oxides of Ce, Pr, and Tb, J. Alloys Compd., 1997, 249, 206–212 CrossRef CAS.
  63. R. F. W. Bader, Atoms in Molecules: A Quantum Theory, Oxford University Press, Oxford, 1990 Search PubMed.
  64. G. Yang, Y. Wang, F. Peng, A. Bergara and Y. Ma, Gold as a 6p-element in dense lithium aurides, J. Am. Chem. Soc., 2016, 138, 4046–4052 CrossRef CAS PubMed.

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