Water on Actinide Dioxide Surfaces: A Review of Recent Progress

Abstract

The fluorite structured actinide dioxides (AnO₂), especially UO₂, are the most common nuclear fuel materials. A comprehensive understanding of their surface chemistry is critical because of its relevance to the safe handling, usage, and storage of nuclear fuels. Because of the ubiquitous nature of water (H₂O), its interaction with AnO₂ has attracted significant attention for its significance in studies of nuclear fuels corrosion and the long-term storage of nuclear wastes. The last few years have seen extensive experimental and theoretical studies on the H₂O–AnO₂ interaction. Herein, we present a brief review of recent advances in this area. We focus on the atomic structures of AnO₂ surfaces, the surface energies, surface oxygen vacancies, their influence on the oxidation states of actinide atoms, and the adsorption and reactions of H₂O on stoichiometric and reduced AnO₂ surfaces. Finally, a summary and outlook of future studies on surface chemistry of AnO₂ are given. We intend for this review to encourage broader interests and further studies on AnO₂ surfaces.

1. Introduction

The fluorite structured actinide dioxides (AnO₂, particularly UO₂) are the most common nuclear fuels currently used in nuclear reactors worldwide. Understanding the surface chemistry of these materials is of both fundamental and technological importance owing to its relevance to many aspects in the nuclear industry from the corrosion of nuclear fuels [1,2], hydrogen gas production, and release from nuclear fuels [3], to the handling and long-term storage of spent fuels. As the interaction of nuclear fuels with environmental species (e.g., water and oxygen) starts at their surfaces, there is a pressing need to study the chemical reactions on AnO₂ surfaces to evaluate the environmental impact of spent nuclear wastes [4]. However, the understanding of the surface chemistry of AnO₂ has been severely limited by the difficulties associated with the handling of radioactive actinides in experiments and the complexity of studying actinide systems using theoretical means.

Specialized laboratory equipment is required to handle actinides in experiments, because all the actinide elements are radioactive and very toxic [5,6]. Early actinides such as thorium and uranium are relatively abundant in nature and their most stable isotopes have long radioactive decay times, making them appropriate for laboratory work, for example, the most stable isotopes ²³²Th and ²³⁸U have half-lives of 1.4 × 10¹⁰ and 4.5 × 10⁹ years, respectively. The transuranics, on the other hand, are not found in nature and have been artificially made; therefore, they are available in small quantities and are highly radioactive. Therefore, most experimental studies of AnO₂ surface chemistry have focused on UO₂, leaving the rest of the AnO₂ essentially unexplored. Theoretical calculations can supplement experimental efforts to understand the surface chemistry of the AnO₂ series and some studies have tried to fill this gap. However, the treatment of actinides using electronic structure calculations remains challenging, in comparison with the lighter elements of the periodic table, owing to a combination of factors: relativistic effects, strongly correlated 5f electrons, and noncollinear magnetism. For example, standard exchange-correlation functional of density functional theory (DFT), such as Local Density Approximation (LDA) and Generalized Gradient Approximation (GGA), yields over-delocalized solutions for 5f electrons, failing to correctly describe their localization behavior [7,8]. Different approaches have been proposed to circumvent this problem. One of the most popular methods is DFT + U, which involves the introduction of an empirical Hubbard U correction term to the Hamiltonian [9,10]. This method has found high appeal because it does not increase the computational cost and can greatly improve the description of the 5f electrons; therefore, it has been widely used to calculate the bulk and surface properties of AnO₂ [7,8,11,12,13,14,15,16]. However, searching of ground state electronic structure in DFT + U calculations presents additional difficulties [17,18,19,20].

Significant experimental and computational efforts have been made to understand the surface chemistry of AnO₂ in the last few years. Herein, we present a brief review of recent progress in the interaction of H₂O with AnO₂ surfaces. We start from the atomic structures of stoichiometric AnO₂ surfaces and their surface energies. Then, the formation of oxygen vacancies and their influence on the oxidation states of actinide atoms are discussed. Finally, we discuss the adsorption and reactions of water on both the stoichiometric and reduced AnO₂ surfaces with oxygen vacancies. This work is not a complete review of all the efforts in the field, but rather we focus on the recent relevant progress in hope that this review can encourage broader interests and further studies on the surface chemistry of AnO₂.

Bulk AnO₂ from the elements Th through Cf has been observed to crystalize in a fluorite structure, as shown in Figure 1 [6]. In this structure, each actinide atom is eight-fold coordinated, and the oxygen atom is four-fold coordinated. Each actinide atom is formally in the +4 oxidation state, and the oxygen atoms are in the −2 state. The properties of actinide materials are closely dependent on the contraction and stabilization of 5f orbitals traversing the actinide series. For example, the lattice constant of bulk AnO₂ shows a monotonic decrease from ThO₂ to CfO₂, however, it deviates from the trend at CmO₂ as a result of orbital mixing and covalency between the metal 5f and the oxygen 2p orbitals. This increased orbital mixing can be tracked down to the proximity in energy between those two orbital manifolds and is now referred to as energy-driven covalency in the literature [21].

The surface properties (surface energy, reconstruction, reactivity, and so on) of AnO₂ are highly dependent on the surface geometry. The top and side views of the low indexed (111), (110), and (100) surfaces of AnO₂ are shown in Figure 2. Along the (111) direction, the surface consists of alternating oxygen and actinide layers with a tri-layer structure (O-An-O). Each tri-layer has a net dipole moment of zero in the direction perpendicular to the surface [22], and the most stable surface is terminated by an oxygen layer. Along the (110) direction, a series of neutral AnO₂ planes are found; therefore, the surface is nonpolar. Along the (100) direction, AnO₂ consists of alternating oxygen and actinide layers with the sequence of -O₂-An-O₂-An-O₂-. Cleaving the crystal perpendicular to the (100) direction yields a polar surface with a net dipole moment, which is inherently unstable. A nonpolar stable surface is achieved by the removal of half of the oxygen atoms from the surface. This reconstruction leads to a slab-type unit cell of the form O-An-O₂-(An-O₂)_n-An-O₂-An-O, as shown in Figure 2. The surface that contains 50% oxygen vacancies on the topmost oxygen layer has been observed for UO₂ (100) [23,24].

Calculated surface energies of AnO₂ have been reported in several papers, particularly for ThO₂, UO₂, and PuO₂.

Table 1. ThO₂ surface energies in units of J/m². DFT, density functional theory.

References	Methods		${\mathbf{\gamma }}_{\left(111\right)}$	${\mathbf{\gamma }}_{\left(110\right)}$	${\mathbf{\gamma }}_{\left(100\right)}$
Rak et al. [37]	DFT	GGA + U (U = 4 eV)	0.79	1.18	-
Alexandrov et al. [38]		GGA	0.8	1.10	1.6
Skomurski et al. [2]		GGA	0.72–0.81	0.98–1.30	1.55–1.75
Shields et al. [39]		GGA	0.50	0.75	1.30
Wang et al. [35]		GGA	0.801	1.202	1.762
Tasker et al. [25]	Classical models	Ionic shell model	1.016	1.451	-
Chatzimichail et al. [26]		Thermodynamic model	0.973	1.297	1.382

,

Table 2. UO₂ surface energies in units of J/m².

References	Methods		${\mathbf{\gamma }}_{\left(111\right)}$	${\mathbf{\gamma }}_{\left(110\right)}$	${\mathbf{\gamma }}_{\left(100\right)}$
Skomurski et al. [2]	DFT	GGA	0.59–0.33	1.01–0.83	1.21–1.07
Rak et al. [37]		GGA + U (U = 4 eV)	0.78	1.05	1.47
Evarestov et al. [40]		Hybrid functional	0.94	-	-
Chaka et al. [41]		GGA	0.888	-	-
Weck et al. [42]		GGA + U (U = 0 to 4 eV)	0.76–0.78	-	-
Bo et al. [22]		GGA + U (U = 4 eV)	0.71	1.08	1.49
Bottin et al. [43]		GGA + U (U = 4 eV)	0.73	1.16	1.46
Rabone et al. [20]		GGA + U (U = 3.96 eV)	0.48	0.77	1.25
Tasker et al. [25]	Classical models	Ionic shell model	1.064	1.561	-
Abramowski et al. [27]		Born model	1.27	2.0	2.72
Tan et al. [29]		Pair potentials	1.29	2.04	2.45
Jelea et al. [30]		Ionic crystal interatomic potentials	1.24	-	2.22
Sattonay et al. [31]		Tight-binding variable-charge model	1.07	1.72	2.03
Benson et al. [32]		Born–Mayer model	1.030	-	-
Chatzimichail et al. [26]		Thermodynamic model	0.95	1.266	1.333
Boyarchenkov et al. [33]		Pair potentials	1.14	-	1.60

and

Table 3. PuO₂ surface energies in units of J/m².

References	Methods		${\mathbf{\gamma }}_{\left(111\right)}$	${\mathbf{\gamma }}_{\left(110\right)}$	${\mathbf{\gamma }}_{\left(100\right)}$
Sun et al. [44]	DFT	LDA/GGA + U (U = 4 eV)	0.72–1.04	1.20–1.44	1.52–1.84
Jomard et al. [28]		GGA + U (U = 3.3 eV)	0.72–0.74	1.10–1.13	1.64–1.69
Rak et al. [37]		GGA + U (U = 4 eV)	0.74	1.15	1.76

summarize the surface energies for the low indexed (111), (110), and (100) surfaces, comparing the different reports that employed DFT and those that relied on other classical models [25,26,27,28,29,30,31,32,33]. It is seen that DFT calculations give rise to smaller surface energies than the classical models for ThO₂, UO₂, and PuO₂ surfaces. A variation in the surface energies is also observed for DFT calculations owing to the use of different level of theory and parameters in the calculations. Despite the variation in the calculated surface energies, all these calculations predict the (111) surface to have the lowest surface energy, hence being the most stable surface for AnO₂. Therefore, nanocrystals of AnO₂ are expected to be mostly terminated by the (111) surface and grow in octahedral shape, according to the Wulff constructions [34]. The relative stability of surfaces can be modified through the selective adsorption of organic ligands on different surfaces, which is key for the controlled synthesis of nanocrystals with different morphologies [35,36].

2. Oxygen Vacancies on AnO₂ Surfaces

The effect of oxygen vacancies is crucial for understanding the reactivity of AnO₂ surfaces as radiation damage can lead to the formation of vacancies on these surfaces. Indeed, studies of the reactivity of H₂O on UO₂ surfaces indicate weak reactivity on stoichiometric UO₂ (111) surface, while dissociative adsorption and hydrogen (H₂) formation upon reduction of the surfaces with oxygen vacancies [45,46]. Similarly, oxygen vacancies have been demonstrated to have a strong impact on the surface chemistry of transition metal and lanthanide oxides, as evidenced by the catalytic properties of CeO₂, a close sibling of AnO₂ sharing the crystal structure and oxidation states [38]. The formation of an oxygen vacancy in CeO₂ leaves two excess electrons in the host material, which localize at two 4f orbitals of Ce sites, reducing them to Ce³⁺ [47]. The formation of Ce³⁺ has been demonstrated to alter the reactivity of CeO₂ (111) surface, such as the activation of the acetaldehyde for coupling reactions [48]. The integrated experimental and theoretical efforts have made great progress in understanding its surface reactivity and reaction mechanism. In this section, we will illustrate the progress for the AnO₂ systems.

2.1. Experimental Work

A thorough experimental study of oxygen vacancies on AnO₂ surfaces has only been performed on UO₂ (111) surface. Artificial oxygen vacancies on UO₂ (111) surfaces were created using Ar⁺ sputtering, and the oxidation states of surface actinide atoms were studied using X-ray photoelectron spectroscopy (XPS) [45]. A comprehensive review of XPS spectra of uranium oxide powder, thin films, and single crystals can be found in the work of [49]. Figure 3 shows the XPS spectra of stoichiometric UO₂ (111) surface (A), the surface after Ar⁺ sputtering at 300 K (B), and after Ar⁺ sputtering at 90 K (C) [45]. The stoichiometric surface has the U4f ^7/2 and U4f ^5/2 peaks at 380.0 and 390.8 eV, and two characteristic satellite peaks S¹ and S² at 386.7 and 397.3 eV [45]. Similar peak positions have been reported in various studies for the U⁴⁺, suggesting that uranium atoms on the stoichiometric surface remain in U⁴⁺ as in the bulk UO₂ [50,51]. After sputtering with Ar⁺ at 300 K, a shoulder on the lower binding energy side of the 4f peaks appears. The broad shoulder has been attributed to uranium atoms in different oxidation states from +4 to 0 (uranium metal) and the slight shift of the U4f ^7/2 and U4f ^5/2 is owing to the formation of an n-type semiconductor upon the creation of oxygen vacancies [45]. The formation of different oxidation states of uranium atoms on the surfaces with oxygen vacancies is evidenced in the fit of XPS spectra, as shown in Figure 4 [49]. An improved fit of the shoulder of U4f ^7/2 peak can be obtained via the inclusion of peaks corresponding to the different oxidation states between +4 and 0, indicating the presence of uranium atoms in the reduced states [49]. However, deriving the structure of an oxygen vacancy at the atomic layer of UO₂ surface and its electronic properties from these XPS data is still not possible without the complementation of DFT simulations. This is because most of the surface analysis techniques such as XPS and Auger electron spectroscopy (AES) have a penetration depth of a few nanometers [52], thus the signal from XPS and AES typically represents an average over a few nanometers of the materials.

2.2. Theoretical Calculations

Several DFT simulations have been reported on the study of oxygen vacancies on the top-surface and the subsurface of AnO₂, providing insights in terms of the electronic structure of the reduced surfaces, the oxidation states of actinide atoms, the formation energies of vacancies, and the electronic structure of excess electrons owing to oxygen vacancies.

Table 4. Formation energies of top-surface and subsurface oxygen vacancy in AnO₂ (111) surfaces.

In Units of eV		ThO2	UO2	PuO2
Wellington et al. [53]	Top	-	6.45	3.35
	Sub	-	6.14	3.40
Bo et al. [54]	Top	-	5.95	-
	Sub	-	6.08	-
Sun et al. [44]	Top	-	-	2.85
	Sub	-	-	2.89
Wang et al. [55]	Top	6.95	5.21	2.81
	Sub	6.58	4.98	2.43

shows the calculated formation energies of oxygen vacancies on (111) surface of ThO₂, UO₂ and PuO₂. The formation energy is defined as $E_v=E_{slab}-\left(E_{v,slab}+\frac{1}{2}{E}_{O_2}\right)$, where $E_{v, slab}$ and $E_{slab}$ are the total energy of the slab with and without oxygen vacancy, respectively. $E_{O_2}$ is the total energy of one isolated O₂ molecule in its ground state. From these calculations, it is seen that the oxygen vacancy formation energies decrease from ThO₂ to PuO₂ [44,53,54,55]. Recent studies found that the oxygen vacancy formation energies are correlated with the reduction potential of An⁴⁺, in accordance with the f-band energy drops as going down the actinide series [53,56]. Interestingly, the fundamental question regarding the relative stability of oxygen vacancy in the top-surface and subsurface is still debatable, although similar DFT + U calculations were used [53,54]. The conclusions for PuO₂ (111) surface are consistent that the oxygen vacancy formation energy is slightly lower in the top-surface than in the subsurface in previous studies [44,53], and the energy difference is within 0.05 eV. However, it has been demonstrated that oxygen vacancy in the subsurface is more stable than in the top-surface on CeO₂ (111) surface, which has an identical structure to AnO₂ [47]. Besides the debate of the relative stability of oxygen vacancy in the top-surface and subsurface of AnO₂, inconsistent results about the distribution of the excess electrons were also reported. On the UO₂ (110) surface, some theoretical calculations based on Perdew-Burke-Ernzerhof (PBE) functional and an effective Hubbard U value of 4.0 eV found that the excess electrons are localized on two uranium atoms, resulting in two U³⁺ next to the vacancy site [54]. Other theoretical studies reported the two electrons to be delocalized over three uranium atoms by natural population analysis for the embedded cluster calculations [53].

The inclusion of a Hubbard-like on-site Coulomb interaction in DFT + U yields a more accurate treatment of the correlated electrons, which overcomes deficiencies of the pure LDA/GGA functionals and has achieved a wide range of successes in treating AnO₂ [7,8]. However, the inclusion of Hubbard term introduces multiple energy local minima, which complicates the search for the ground state [17,18,19,20]. Several methods, such as U-ramping [19] and occupation matrix control (OMC) [17,18], have been proposed to overcome this difficulty presented by DFT + U. These methods have been shown to locate low-energy solutions for a variety of systems containing strongly correlated d and f electrons [17,18,19]. Recently, these approaches have been applied to the study of reduced AnO₂ (111) surfaces [55]. It was found for ThO₂, UO₂, and PuO₂ (111) surfaces that the oxygen formation energy is 0.23–0.38 eV lower for the subsurface vacancy. This is consistent with the calculations for CeO₂ (111) surface, where explicit searching of the low-energy solutions has been carried out by assigning excess electrons to different sites near the vacancy [47,57]. The unexpected lower formation energy for oxygen vacancy energy in the subsurface has been explained in terms of smaller Madelung potential owing to defect-induced lattice relaxation [47]. The excess electrons on the ThO₂ surface stay at the vacancy site, forming a lone electron pair, as shown in Figure 5a,b. On the UO₂ surface, one of the excess electrons stays at the vacancy site, and the other moves to uranium 5f orbitals, reducing it to U³⁺ (Figure 5c,d). On the PuO₂ surface, both excess electrons localize at the Pu 5f orbitals reducing two next-nearest Pu sites (Figure 5e,f). More advanced experimental surface-sensitive characterization will be needed in order to settle the debate and validate these predicted theoretical results.

3. Water on AnO₂ Surfaces

The interaction of water with AnO₂ has attracted numerous works owing to its importance for the storage of nuclear fuels [1,2,4]. In particular, the adsorption, dissociation, and reaction pathways of water on UO₂ and PuO₂ surfaces have been of great interest. For UO₂, the interaction of water with both perfect and reduced single crystalline (111) films and polycrystalline films has been carried out [58,59]. On PuO₂ surfaces, several experimental studies have been performed on polycrystalline films [1,60,61,62,63].

3.1. Experiments

The interaction of H₂O with AnO₂ surfaces initiates with its adsorption and dissociation on the surfaces. It has been shown that the adsorption of H₂O molecules on UO₂ (111) surface is reversible (80%) at 300 K, indicating that H₂O is weakly adsorbed on perfect UO₂ (111) surface [58]. On the contrary, H₂O is strongly adsorbed on surfaces with oxygen vacancies. Figure 6 shows the XPS spectra of reduced surface after exposure to heavy water (D₂O), then followed by annealing at different temperatures [45]. It is clearly seen that the shoulders for the U4f ^7/2 peaks disappear after exposure to D₂O and subsequent annealing. This implies the recovery of uranium atoms to the formal oxidation state of +4. More interestingly, temperature programmed desorption (TPD) experiments for H₂ release upon exposing water to an Ar⁺ sputtered UO₂ surface show that H₂ production can only occur on reduced (111) surface with oxygen vacancies (Figure 7). The amount of H₂ desorption increases with the Ar⁺ sputtering time, namely the concentration of oxygen vacancies on the surfaces [58]. These experiments demonstrate that the interaction of H₂O with AnO₂ surfaces is dependent on the surface oxygen vacancies, and oxygen vacancies prompt the dissociation of H₂O and the production of H₂ on AnO₂ surfaces. The interaction of H₂O with PuO₂ films has been studied using XPS and ultra-violet photoelectron spectroscopies (UPS) [60,61]. It was found that H₂O dissociates and forms a thin hydroxyl (OH^-) layer with small amounts of molecularly adsorbed water at 298 K. While under 80–120 K, H₂O is adsorbed as thick ice multilayers and no significant OH^- is detected. The top surface layer can be reduced to Pu₂O₃ when the ice covered PuO₂ is warmed up under ultraviolet light, while the mechanism of the reduction is still unclear [61]. Another study has reported that H₂O can catalyze the oxidation of PuO₂ surfaces and the formation of stable compounds PuO_2+x (x <= 0.27) containing Pu⁶⁺ [1].

3.2. Theoretical Calculations

Contrary to the lack of experimental data, several theoretical groups have pioneered modeling of H₂O on stoichiometric and reduced AnO₂ surfaces [22,44,53,54,64]. These simulations shed light on the nature of the fundamental interaction between H₂O and AnO₂ surfaces. We will discuss these advances in two main aspects: (i) adsorption and dissociation of water and (ii) mechanism of H₂ production.

3.2.1. Adsorption and dissociation of H₂O on AnO₂ surfaces

The adsorption and dissociation of H₂O on AnO₂ surfaces have been extensively studied in several papers [44,53,54,64,65]. H₂O molecules can adsorb on surfaces in the molecular form or the dissociated form. For the molecular adsorption (Figure 8a,b), the oxygen atom from the H₂O molecule binds via its lone pair with the positive actinide atom on the surface, while, at the same time, one of the hydrogen atoms forms a hydrogen bond with a nearby oxygen atom on the surface. If the H₂O dissociates at the surface into OH^- and H⁺, the hydroxyl group bonds with one surface actinide atom, and the proton bonds with one surface oxygen atom (Figure 8c,d). On the basis of these studies [44,53,54,64], the following general conclusions have been reached on the adsorption and dissociation of H₂O on AnO₂ surfaces:

(i)

A mixture of molecular and dissociated adsorption of H₂O occurs on the (111) surface of AnO₂.

(ii)

Dissociative adsorption of H₂O preferentially occurs on the (110) and (100) surfaces of AnO₂.

(iii)

The adsorption energies of H₂O are correlated with the surface energies; a stronger adsorption energy is expected on the surface with a higher surface energy.

(iv)

The presence of oxygen vacancies on the surface of AnO₂ favors the dissociative adsorption mechanism. The distribution of excess electrons on reduced AnO₂ surfaces is different upon the adsorption of H₂O.

Alexandrov et al. first studied the adsorption configurations of H₂O on ThO₂ surfaces using both accurate calorimetric measurements and first-principle calculations [38]. They observed coverage-dependent adsorption energies and demonstrated a mixture of molecular and dissociative adsorption of H₂O on ThO₂ (111) surface. They also showed that the adsorption energy of water molecules is correlated with the surface energies; a higher surface energy results in a stronger water adsorption on ThO₂ surfaces [38]. Bo et al. [22] found that, for a single water molecule on UO₂ (111) surface, the two adsorption configurations, molecular adsorption and dissociative adsorption, exhibit comparable adsorption energies (0.61 vs. 0.68 eV, as shown in

Table 5. Adsorption energies of one H₂O molecule on perfect UO₂ surfaces. The bold italic numbers correspond to adsorption energies in the dissociative form. The rest are adsorption energies in the molecular form.

In Units of eV	(111)	(110)	(100)
Bo et al. [22,54]	0.61 0.68	0.62 1.27	1.02 1.71
Tegner et al. [67]	0.53 0.50	0.93 1.39	0.97 1.55
Wang et al. [55]	0.62	-	-

). However, the adsorption in the molecular form, on (110) and (100) surfaces, is far less stable than the dissociative adsorption (0.62 vs. 1.27 eV and 1.02 vs 1.71 eV, respectively) [22]. Bo’s results are consistent with those of Wellington et al. [66] and Tegner et al. [67], who also found that the molecular and dissociative adsorptions have similar adsorption energies on UO₂ and PuO₂ (111) surfaces, while there is a clear preference for dissociative adsorption on (110) surfaces. Both groups reported the mixture of molecular and dissociative adsorption to be the most stable adsorption configuration at a higher coverage of H₂O on (111) surfaces [22,66,67]. The calculated adsorption energies of H₂O on UO₂ surfaces increase from (111), (110), to (100) surface, as summarized in Table 5, which is consistent with the observation by Alexandrov et al. that stronger H₂O adsorption energies are expected on ThO₂ surfaces with higher surface energies [38]. Tegner et al. further studied the adsorption of up to five layers of H₂O on PuO₂ and UO₂ surfaces, and found significant variation in the adsorption energies as a result of intra- and interlayer hydrogen bonding network [68].

Ab-initio molecular dynamics (AIMD) simulations have also been carried out to explore the mechanism of adsorption and dissociation of H₂O on AnO₂ surfaces. It was found that the dissociative adsorption of H₂O is feasible for a large range of temperature and water partial pressures on UO₂ (111) surface [69]. The dissociation of H₂O on PuO₂ (110) surface is a two-step hydroxylation process both for single H₂O molecule and H₂O clusters [70]. The dissociation is initiated by the dehydrogenation of water molecules to form a hydroxyl group with surface oxygen atom, followed by successive surface hydroxylation on plutonium with the remaining hydroxide ion of the dissociating molecule. The H₂O molecule dissociates as the consequence of hybridizations between the molecular orbitals of water and the electronic state of the surface with a reaction energy barrier of 0.18 eV. In contrast, the dissociation of H₂O clusters is exothermic by −0.42 eV with no energy barrier [70].

On reduced AnO₂ surfaces with oxygen vacancies, H₂O has much stronger adsorption energies, as shown in

Table 6. Adsorption energies of one H₂O molecule on AnO₂ (111) surface. The bold italic numbers correspond to the dissociative adsorption energies. The rest are the molecular adsorption energies.

In Units of eV	Perfect			Reduced
	ThO2	UO2	PuO2	ThO2	UO2	PuO2
Tegner et al. [67]	-	0.53 0.50	0.40 0.32	-	-	-
Wellington et al. [53]	-	-	-	-	2.23	2.10
Bo et al. [54]	-	0.61 0.68	-	-	2.20	-
Alexandrov et al. [38]	0.57 0.67	-	-	-	-	-
Tian et al. [64]	-	1.08 0.68	-	-	1.88	-
Weck et al. [42]	-	0.85 0.60	-	-	-	-
Wang et al. [55]	0.56	0.62	0.58	2.63	1.90	2.44

. On perfect ThO₂, UO₂, and PuO₂ (111) surfaces, the adsorption energy of water is smaller than 1.1 eV from DFT calculations [38,54,55,64,67], while the adsorption energies are larger than 1.8 eV on surfaces with oxygen vacancies [53,54,55,64]. These DFT calculations are in agreement with experimental results by Senanayake et al. that the adsorption of H₂O on UO₂ (111) surface is weak and reversible (80%) at 300 K [58]. DFT simulations also found that the dissociation of H₂O on reduced AnO₂ surfaces can occur spontaneously at room temperature, as there is a very small energy barrier for the dissociation [54,55]. After H₂O dissociation, the hydroxylate group moves to the oxygen vacancy site, and the proton binds with one surface oxygen atom as shown in Figure 9. The excess electrons are distributed differently on reduced AnO₂ surfaces upon the adsorption of H₂O. On reduced ThO₂ (111) surface, the excess electrons still stay at the vacancy site after H₂O dissociation. One proton from the H₂O molecule is attracted to the vacancy site and forming H^-. However, on both reduced surfaces, UO₂ and PuO₂ (111), the OH^- group from H₂O tends to fill the vacancy site. When OH^- moves to the vacancy site for UO₂ surface, it will push the excess electron to a neighboring uranium site and reduce it to U³⁺.

3.2.2. H₂ production from H₂O splitting

The formation of H₂ owing to the interaction of H₂O with AnO₂ through radiolytic process or chemical reactions can lead to potential pressurization of the containers of nuclear fuels. The formation of H₂ on AnO₂ surfaces owing to chemical reactions with H₂O has rarely been studied in theoretical calculations [54,55]. Bo et al. first systematically investigated the formation and desorption mechanism of H₂ on reduced UO₂ (111) surface [54]. They found that H₂ formation can occur on UO₂ (111) surface with the oxygen vacancies [54]. Figure 10 shows the three possible reaction pathways [54]. The first formation pathway in Figure 10a involves the direct dissociation of H₂O at a vacancy site, forming O-H-H structure on the surface, followed by the desorption of H₂ from the surface and oxygen atom healing the vacancy. This pathway has an energy barrier of 0.56 eV, and the overall reaction is exothermic by 2.62 eV [54]. The second pathway in Figure 10b involves the dissociation of H₂O on the surface, forming hydroxylated surface, and then the combination of the hydrogen atoms from the hydroxyl radicals to form H₂ molecules. This pathway presents a large energy barrier of 1.39 eV and an overall exothermic energy of 2.56 eV. For the third pathway in Figure 10c, there are excess hydroxyl radicals near the vacancy site. The dissociation of H₂O will result in a hydroxyl radical that occupies the vacancy site, and the formation of O-H-H structure. This reaction pathway is also exothermic by 1.98 eV and has an energy barrier of 0.53 eV [54].

A comparative study of H₂ formation on reduced ThO₂, UO₂, and PuO₂ (111) surfaces has been performed to show the difference in the H₂ formation across the AnO₂ series [55]. It is found that the formation of H₂ from catalytic splitting of H₂O is endothermic for all three AnO₂ (111) surfaces evaluated (

Table 7. The reaction energy of H₂O splitting and H₂ formation (H₂O → O* + H₂) on perfect ThO₂, UO₂, and PuO₂ (111) surfaces and corresponding surfaces with oxygen vacancies. A negative/positive value represents the reaction is exothermic/endothermic, respectively.

ΔH (eV)	ThO2	UO2	PuO2
Perfect surface	+1.72	+1.85	+4.11
Oxygen vacancy	−3.55	−3.11	−0.31

). In contrast, H₂O can readily dissociate on the reduced ThO₂, UO₂, and PuO₂ (111) surfaces, while the thermodynamics of H₂ production is significantly different [55]. On reduced ThO₂ (111) and UO₂ (111) surfaces, the H₂O adsorption and H₂ production is exothermic and releases 3.55 eV and 3.11 eV, respectively (Table 7). Although this process releases 0.31 eV on reduced PuO₂ (111) surface, there is a larger energy barrier for the H₂ production. This suggests that the protons of H₂O will stay in the hydroxylated form on PuO₂ (111) surface, instead of forming H₂ molecule [55]. The high reactivity of H₂O with reduced ThO₂ surface is attributed to the lone electron pair at the vacancy site on ThO₂ that can readily participate in the chemical reactions with H₂O. On the contrary, the excess electrons are more tightly bound to the Pu 5f orbitals on reduced PuO₂ surfaces, thus making it harder to participate in the reaction with H₂O molecule.

4. Summary and Outlook

Understanding the surface chemistry of AnO₂ is relevant to many stages in the nuclear industry. Significant efforts have been performed in the community to explore the interaction of H₂O with AnO₂ surfaces. These studies provide significant insights on the adsorption and dissociation of H₂O, the vacancy formation, and the H₂ production on the AnO₂ surfaces owing to chemical reactions with H₂O. There is still important work to be done in this area. (i) AnO₂ surfaces beyond UO₂: Previous experimental studies mostly focus on UO₂ surfaces. The rest of the AnO₂ surfaces have been hardly explored in experiments. Especially, controlled synthesis of high quality AnO₂ films using advanced techniques, such as polymer assisted deposition (PAD), atomic vapor deposition, and crystal truncation rod (CTR), among others, is needed to study the surface chemistry of AnO₂ surfaces beyond UO₂. (ii) AnO₂ surfaces with complicated surface structures: Compared with experiments that mostly focus on UO₂ films, more theoretical simulations have been conducted on AnO₂ surfaces beyond UO₂. However, most of the simulations are on low indexed (111), (110), and (100) surfaces of AnO₂, because the simulation cells are smaller and more accessible to computational methods than the high indexed ones. In fact, other surfaces with higher surface energy are expected to be more reactive, which might be more important for understanding the dissolution, reactivity, and environmental effects of nuclear fuels. Moreover, defected surfaces with only one oxygen vacancy have been investigated in earlier work, while defected surfaces with more complicated structures are yet to be explored both in experiments and in theory. (iii) Chemical reactions on the surfaces and reaction dynamics. Previous theoretical simulations are limited to small systems with a few water molecules on the surfaces and the very early stage of H₂O interaction with the surfaces owing to the computational cost of DFT simulations. To this regard, developing methods that can deal with large systems and perform dynamics on a long time scale, such as density functional tight binding (DFTB) [71], is in urgent need to study the AnO₂ surfaces, chemical reactions and dynamics on the surfaces, and their interactions with the environments.