DFT + U Study of the Adsorption and Dissociation of Water on Clean, Defective, and Oxygen-Covered U3Si2{001}, {110}, and {111} Surfaces.

The interfacial interaction of U3Si2 with water leads to corrosion of nuclear fuels, which affects various processes in the nuclear fuel cycle. However, the mechanism and molecular-level insights into the early oxidation process of U3Si2 surfaces in the presence of water and oxygen are not fully understood. In this work, we present Hubbard-corrected density functional theory (DFT + U) calculations of the adsorption behavior of water on the low Miller indices of the pristine and defective surfaces as well as water dissociation and accompanied H2 formation mechanisms. The adsorption strength decreases in the order U3Si2{001} > U3Si2{110} > U3Si2{111} for both molecular and dissociative H2O adsorption. Consistent with the superior reactivity, dissociative water adsorption is most stable. We also explored the adsorption of H2O on the oxygen-covered U3Si2 surface and showed that the preadsorbed oxygen could activate the OH bond and speed up the dissociation of H2O. Generally, we found that during adsorption on the oxygen-covered, defective surface, multiple water molecules are thermodynamically more stable on the surface than the water monomer on the pristine surface. Mixed molecular and dissociative water adsorption modes are also noted to be stable on the {111} surface, whereas fully dissociative water adsorption is most stable on the {110} and {001} surfaces.

Introduction

There is an increasing interest in the development and use of metallic nuclear fuels such as U3Si2 given the enhanced thermophysical properties compared to traditional uranium dioxide fuel (UO2).[1] However, a key issue to deal with is the ease of oxidation of metallic nuclear fuels in the presence of water, oxygen, or combination of both, which requires the synthesis of U3Si2 in controlled environments. A significant number of earlier experimental works have assessed the behavior of U3Si2 in corrosion-susceptible environments in comparison to other metallic and UO2 fuels. Recently, Nelson et al. investigated the behavior of U3Si2 following exposure to pressurized H2O that is typical in light water reactors (LWRs) at temperatures ranging from 300 to 350 °C. Their results showed that both UN and U3Si5 rapidly pulverize in less than 50 h at 300 °C, while the behavior of U3Si2 was superior but still below the corrosion resistance of UO2 fuel. It is worth mentioning that the mechanism of pulverization of U3Si2 might be due to spallation of UO2 or due to internal hydriding.[2,3] The formation of U3Si2H1.8 with volumetric increase has been shown by experiment and density functional theory (DFT) calculations.[4] In this work, we unraveled the detailed mechanism of the early oxidation of U3Si2 from an atomistic point of view, which is difficult to realize experimentally. Earlier theoretical works have focused on the bulk properties of U3Si2 within the framework of DFT + U formalism and molecular dynamics simulations.[4−10] For instance, Middleburgh et al.[4] investigated the defect evolution in U3Si2 and also proposed a phase diagram capable of predicting fuel behavior during burnup. Furthermore, Wang et al.[7] studied the electronic, structural, and elastic properties showing detailed bonding characteristics of U3Si2 by electron density of states (DOS), charge density, and charge density difference analysis which corroborate the work of Remschnig et al.[11] as regards the metallic nature of U3Si2.

Surface science provides fundamental insight into the chemistry and physics of corrosion in materials, but such experiments are expensive and require dedicated facilities, especially in the study of an actinide containing compound. Hence, theoretical surface science provides an alternative tool for investigating oxidation mechanisms in nuclear fuel materials. Bo et al.[12] modeled the surface properties of the low-index NpO2(111), (110), and (100) surfaces as well as the adsorption and dissociation behaviors of water on these surfaces using DFT + U calculations in combination with ab initio atomistic thermodynamic simulations. Their results showed that water dissociation is enhanced by oxygen vacancy, while coverage of the water molecules plays no significant role during molecular adsorption.[13] More recently, Wellington and co-worker investigated the adsorption and dissociation of water on pristine and reduced UO2 and PuO2 surfaces using the periodic electrostatic-embedded cluster method and Hubbard-corrected periodic conditions implemented in the DFT-based code. Oxygen vacancies were shown to be easily formed on PuO2 compared to UO2, which is due to ease of Pu reduction in comparison to U metal ions. Their results also showed that dissociation is favored over molecular adsorption of water both on defect-free and oxygen deficit surfaces of UO2 and PuO2.

Given the success of first-principles DFT + U calculations in the modeling surfaces, we recently studied the adsorption of molecular and dissociated O2 on stoichiometric U3Si2 lower index surfaces.[14] To further our understanding of the underlying mechanism of oxidation, we have considered the synergetic effect of water and oxygen interaction with U3Si2 perfect surfaces. However, as real surfaces are never perfect but contain defects due to the method of synthesis or service conditions, in the present work, we have explored the effects of U and Si vacancies on the adsorption mechanisms of water and oxygen on the {001}, {110}, and {111} surfaces of U3Si2. Surface vacancies in UN, UO2, PuO2, and CeO2 have been shown in previous studies to affect the oxidation behavior of such surfaces in the presence of oxidizing and hydriding agents.[12,13,15−19] The fundamental aspects of oxygen and water adsorption, including the initial adsorption geometries, adsorption energies, structural parameters, and electronic properties, are presented. Our results reveal a chemical picture of the initial steps involved in the oxidation process of the U3Si2 surfaces in the presence of oxygen and water (considering both molecular and dissociative adsorption).

Computational Methodology

The first-principles calculations were performed within the plane-wave pseudo-potential DFT technique,[20,21] as implemented in the Quantum ESPRESSO code.[22] The exchange–correlation functional potential was described by the generalized gradient approximation (GGA) in the Wu–Cohen (GGA-WC) formulation.[23] All our calculations deployed the norm-conserving Wu–Cohen (WC) pseudopotentials (where these potentials treat 7p06d15f37s1 as valence electrons for U and 3s23p6 as valence electrons for Si). Due to the onsite Coulomb repulsion among the localized U 5f electrons, we used the Hubbard (DFT + U) correction to account for the strong correlation effect.[24] We have used an effective U value of 1.5 eV, which has been shown to give an accurate description of the structural parameters and the electronic properties of U3Si2.[14]

The Fermi surface effects were treated by the smearing technique of Methfessel–Paxton,[25] using a smearing parameter of 0.02 Ry (0.27 eV). An energy threshold defining self-consistency of the electron density was set to 10–8 eV and a β mixing factor of 0.3. The Brillouin zone integration was performed using 7 × 7 × 10 and 5 × 5 × 1 Monkhorst–Pack[22]k-point grids (centered at the Γ point) for the bulk U3Si2 and the surface models, respectively. Structural relaxation was carried out to minimize the energy using the conjugate gradient method within the Broyden–Fletcher–Goldfarb–Shanno algorithm,[26] until the magnitude of the residual Hell–Feynman force on each relaxed atom reached 0.01 eV Å–1. Visualization and analysis of the structures were performed using the VESTA program.[27,28]

The {001}, {110}, and {111} surfaces were considered for the oxygen and water adsorption calculations as they are the dominant growth facets of U3Si2. The different surface structures were created from the fully optimized bulk tetragonal U3Si2 structure (Figure ) to eliminate the presence of fictitious forces during surface relaxation using the METADISE code,[29] which ensures the creation of surfaces with a zero dipole moment perpendicular to the surface plane. A vacuum of 15 Å was introduced to the surface models in the z direction, which is large enough to avoid any spurious interactions between periodic slabs. Bader population analysis was carried out on all adsorbate–substrate systems to quantify any charge transfer between the U3Si2 surface and O2/H2O species.[30]

Figure 1

Unit cell of ordered uranium silicide containing two formula units of U3Si2 (10 atoms) (color scheme: U = gray and Si = blue).

Results and Discussion

Defective Surface Models

Surface Defect Energies and Stability

Defective surfaces (vacancies) were created by removing one Si/U atom at a time from either the first or second layer (Figure ) to access their energetics or stability.

Figure 2

Optimized surface geometry of (a) U3Si2{001}, (b) U3Si2{110}, and (c) U3Si2{111} with Si and U1 surface vacancy represented by a rectangular red box in the second and third rows respectively (color scheme: U = gray and Si = blue).

The silicon vacancies are denoted as VSi, whereas the two considered uranium vacancy sites are denoted as VU1 and VU2, respectively, on the surface. The method of Wellington et al.[19] was employed in the creation of vacancy such that the uranium and silicon atoms removed from the supercell, both from the surface and subsurface layers, are fully coordinated by other quantum mechanically treated atoms and lie close to the center of the supercell to avoid problems that may occur in forming a defect at the edge.[19] The vacancy formation energy was calculated using eq where Esurface+X is the energy of the relaxed slab with X = Si or U vacancy, Esurface is the energy of the relaxed stoichiometric slab of the same type, and EX is the reference energy for X = Si and U as the energy per atom in its fundamental face-centered cubic and orthorhombic structure, respectively. Presented in Table are the calculated vacancy formation energies on the {001}, {110}, and {111} U3Si2 surfaces. We found higher Si vacancy formation for the {110} surface (2.62 eV) than for the {001} surface (0.16 eV) and {111} surface (1.54 eV), and a similar trend is observed in the subsurface Si vacancies formation. Clearly, Si vacancy on the {110} subsurface (2.62 eV) is close to 2.48 eV, calculated for bulk U3Si2 by Andersson et al.[31] This is not surprising, given that the {110} surface has the lowest surface energy and similar neighboring atom coordination. There are two U sites denoted here as U1 and U2 with vacancy defect formation energies of 1.64 and 2.65 eV, respectively, for the bulk. The first and second layer U vacancy energies were calculated as presented in Table . Generally, it is easier to form a vacancy in the surface layer compared to the subsurface, which is due to the difference in the nearest neighbor atoms and the coordination numbers.

Table 1

Uranium and Silicon Vacancy Formation Energies (eV) of the {001}, {110}, and {111} Surfaces of U3Si2

	first layer			second layer
surface	VSi	VU1	VU2	VSi	VU1	VU2
{001}	0.16	1.72	1.87	1.74	2.13	2.88
{110}	2.62	3.18	2.41	1.62	2.03	2.61
{111}	1.54	3.81	3.70	2.44	1.46	3.10

The formation of Si and U vacancies resulted in a nonstoichiometric surface, which allows variation in the surface energies as the chemical potential, μ, of Si and U changes. The thermodynamic stability of a given surface, in general, depends on the specific chemical environment. To determine the stability of the surfaces due to vacancies, we calculate the surface energy, γ, as a function of the Si and U chemical potential, respectively. At zero temperature the surface energy of a crystal may be derived from a N-layer slab using eq In this equation, Esurf is the slab energy with all atomic coordinates relaxed unconstrainedly; NEbulk is the energy of an equal number, N of bulk U3Si2 atoms; A is the area of the slab surface; and the factor of 2 reflects the fact that there are two surfaces for each slab. Due to the surface vacancy defects, the surface energy depends on the specific thermodynamic conditions, i.e., the reservoir with which the atoms of the compound are exchanged in a structural transition. Therefore, the chemical potential of the constituents enters the surface energy. The most stable surface structure is determined by the minimum of the free energy which at zero temperature is given by eq In the case of U3Si2, eq can be expressed by eq to account for the chemical potential μ of U and Si atomsThe μU and μSi are bounded by a set of conditions. Assuming U and Si are in thermal equilibrium with the U3Si2 crystal, it would imply thatFurthermore, since there is no precipitation of U and Si on the U3Si2 surface, the following conditions must also be fulfilledAlso, the heat of formation of bulk U3Si2, ΔHf (eV f.u.–1), is defined asCombining eqs , 6a,b, and 7, we obtain a range for possible values of the Si chemical potentialCombining eqs and 5, gives the surface energy as a function of μSiSimilar to eq , the surface energy can also be expressed as a function μUAt ambient temperature and pressure, Esurf can be taken as the total energy from DFT calculation neglecting contributions from configurational or vibrational entropies. In Figure , we show the results of the calculated surface energies of the {001}, {110}, and {111} surfaces of U3Si2 as functions of the change in silicon chemical potential μSi, ranging from Si4 (−7.46 eV) to that of an isolated Si atom (0 eV), which denotes lower and upper limit of the Si environment, data from NIST database.[32] The lower limit, which is the Si-poor environment, is defined by the decomposition of the silicide into U and Si. Meanwhile, the upper limit is the Si-rich state that corresponds to a situation where the gas phase is so rich in silicon that they condensed on the substrate. In the case of stoichiometric surfaces considered in this work, the surface free energy is independent of μSi as expected, since the coefficient of eq a,b containing μSi vanishes. For the nonstoichiometric cases, the surface free energy is a linear function of μSi according to eq . It can be seen from Figure that the equilibrium surface stoichiometry of the U3Si2 surfaces can be tuned by changing μSi through the use of different U3Si2 growth (Si vacancy is considered here) and annealing environments. It is clear from the increase in surface energies that the stoichiometric surfaces are found to be more stable than the silicon deficient (silicon vacancy) surfaces. This implies that surface adsorption of an oxidizing adsorbate is more stable on the defective surface in comparison to the stoichiometric surface.

Figure 3

Calculated surface energies of the {001}, {110}, and {111} surfaces of U3Si2 as functions of the change in silicon chemical potential μSi.

Adsorption of Water Molecule

The adsorption of the water molecule on the U3Si2 surfaces is an important starting step toward understanding its early oxidation mechanisms. The first interest of this study is therefore to determine the lowest-energy adsorption structures and modes of water on the low-index U3Si2{001}, {110}, and {111} surfaces, and to characterize the strength of their interaction and the extent of O–H bond activation during the dissociation process. Different H2O initial adsorption possibilities, including Hw and Ow head-on configurations, have been subjected to geometry optimization until the residual forces on all atoms were ≤0.03 eV Å–1. Prior to adsorption, we have calculated the reference energies, bond length, bond angle, and vibrational frequencies of one free H2O molecule and compared them with earlier theoretical results and available experimental data. The values of the O–H bond and the H–O–H angle of water are determined to be 0.970 Å and 104.5°, respectively, which are in good agreement with the previous experimental and theoretical values.[33,34] The calculated scissoring bend, asymmetric and symmetric stretching vibrational frequencies are calculated to be 1555, 3523, and 3635 cm–1, which agree well with the experimental results (1596, 3652, and 3756 cm–1),[35] thus making our calculation method reliable.

The adsorption energy (Eads), which characterizes the strength of water adsorption has been defined as the mean adsorption energy per molecule of H2O–U3Si2 interaction using eq where Esurface+ is the total energy of the substrate–adsorbate system in the equilibrium state, Esurface and nEH are the total energies for the surface and free molecules, respectively, and n is the number of water molecules in the cell. By this definition, a negative value of Eads indicates an exothermic and stable adsorption, whereas a positive value indicates an endothermic and unstable adsorption.

Water Adsorption and Dissociation on Clean U3Si2{001}

For the adsorption of molecular water on the U3Si2{001} surface, different adsorption sites and configurations were explored to determine the lowest-energy adsorption structures, as presented in Figure . The calculated adsorption energies and the optimized interatomic bond distances are summarized in Table . The calculated lowest-energy water adsorption structure is presented in Figure a, wherein the water molecule adsorbs through the O atom at the U site (U–O = 2.56 Å), releasing an adsorption energy of −3.70 eV. The adsorption of water at the Si site (O–Si = 2.376 Å) released an adsorption energy of −3.11 eV. When the water molecule is adsorbed with the hydrogen atoms pointing toward the surface Si site (Figure b), it moved away perpendicularly from the surface during energy minimization until the closest H–Si distance was 3.044 Å. The adsorption energy of this configuration was calculated to be −1.97 eV, while the α(H–O–H) bond angle and O–H bonds are obtained at 102.32° and 0.965/0.967 Å, respectively. Compared to the lowest-energy water adsorption on U3Si2{001}, Bo et al. calculated the adsorption energies of −2.07 and −1.27 eV for the lowest-energy adsorption structures of the water monomer on UN(001) and UO2(110), respectively, which suggest that U3Si2{001} is more reactive toward water adsorption than both UN(001) and UO2(110).[36,37] In all three adsorption modes, the O–H bond lengths were slightly elongated and the α(H–O–H) bonds bond angle was larger compared to the gas-phase free H2O molecule in a vacuum, suggesting that the O–H bonds are activated to some extent when water is adsorbed on U3Si2{001}. In the lowest-energy O–U structure (Figure a), the two O–H bonds are calculated at 0.975 and 0.996 Å compared to the gas-phase molecule at 0.970 Å and this is consistent with O–H bond stretching vibrational frequencies presented in Table , whereas the α(H–O–H) bonds bond angle is obtained at 107.6° compared to the gas-phase value of 104.5°, which is supported by the red and blue shifts in the bending vibrational frequencies as shown in Table . The stretched O–H bond lengths are indicative of weaker O–H bonds, resulting from the π-antibonding occupation. The activated O–H bonds suggest that these molecular adsorption states are likely precursors for H2O dissociation.

Figure 4

Top and side views of the relaxed adsorption structures of molecular H2O adsorbed at: (a) O–U, (b) H–Si, and (c) O–Si (color scheme: U = gray, Si = blue, H = white, and O = red).

Table 2

Calculated Adsorption Energy (Eads), Relevant Bond Distance (d), Vibrational Frequencies, and Variation of the Total Bader Charge of Molecular (H2O) and Dissociated (OH + H) Adsorbed on the {001}, {110}, and {111} Surfaces of U3Si2

surface	adsorbate	config.	Eads. (eV)	d(O–H1) (Å)	d(O–H2) (Å)	d(Si–O) (Å)	d(U–O) (Å)	d(U–H) (Å)	d(Si–H) (Å)	α(HOH) (deg)	νb (cm–1)	νs (cm–1)	νas (cm–1)	Δq (e–)
		H2O		0.970	0.970					104.490	1555	3523	3635
{001}	H2O	O–U	–3.70	0.975	0.996		2.622			107.642	1534	3390	3661	0.08
		O–Si	–3.11	0.994	0.976	2.376	2.562			105.399	1543	3553	3675	0.09
		H–Si	–1.97	0.975	0.977					102.323	1540	3767	3862	0.05
	OH + H	OH–Si: H on adj. U	–6.81	0.983			2.598		1.551					2.13
		OH–Si: H on Si	–5.43	0.971		1.741	2.618		1.501					1.21
		OH–Si: H on U	–3.61	0.965		1.644		2.119						1.17
{110}	H2O	O–Si	–2.46	0.996	0.978	2.120				107.343	1532	3418	3673	0.15
		O–U	–0.60	0.985	1.005					104.041	1600	3326	3590	0.16
		H–Si	0.55	0.971	0.970					103.232	1601	3425	3571	0.05
	OH + H	OH–Si: H on U	–3.24	0.979		1.676		2.396	1.583					0.44
		OH–U: H on Si	–2.27	0.974			2.200		1.510					0.17
{111}	H2O	O–U	–1.40	0.977	0.995		2.548			105.454	1543	3432	3690	0.19
		H–Si	–0.20	0.957	0.977					99.181	1575	3677	3948	0.05
		O–Si	1.02	0.977	0.982					102.205	1622	3584	3691	0.01
	OH + H	OH–U: H on Si	–3.30	0.971			2.194		1.697					2.18
		OH–Si: H on U	–1.21	0.969		1.702		2.181						0.34

Dissociative adsorption of H2O on the clean U3Si2{001} surface is found to be highly exothermic with adsorption energies of −6.81, −5.43, and −3.61 eV, respectively, for the different configurations presented in Figure and Table . Consistent with their stronger adsorption, the collective amount of charge transfer gained by the dissociated H2O species is larger than those of the molecular adsorbed water systems. Due to its metallic nature, the U ions donate more electrons than Si ions during bond formation. The preference for dissociative over molecular adsorption of water can be attributed to the fact that the energy required to break an O–H bond requires less energy compared to the energy released in the formation of the Si–H and U–OH bonds on the U3Si2{001} surface. In like manner, on several metals and oxide surfaces, the dissociative state of H2O is thermodynamically more stable than the molecularly adsorbed state, for example, on Cu and Al2O3, because the breaking of an O–H bond is effectively balanced by the formation of a metal–O and another O–H bond with a surface oxygen.[38,39]

Figure 5

Top and side views of the relaxed adsorption structures of dissociated water configuration with (a) OH–Si: H on adj. U, (b) OH–Si: H on Si, and (c) OH–Si: H on U, on the U3Si2{001}-Si terminated surface (color scheme: U = gray, Si = blue, H = white, and O = red).

Water Adsorption and Dissociation on Clean U3Si2{110}

As on the U3Si2{001} surface, we have also explored different adsorption configurations of H2O on the {110} surface, including O adsorbed laterally at U or Si sites or H placed head-on Si sites. The optimized adsorption structures are shown in Figure , whereas the energies of adsorption, geometric parameters, and Bader charge transfer analysis are presented in Table . The lowest-energy water adsorption configuration at U3Si2{110} was calculated to be the O–Si structure (Figure a), wherein the water molecule is adsorbed at the Si site through the oxygen atom (O–Si = 2.120 Å), releasing an energy of −2.46 eV. In this structure, we observed elongation of the O–H bond calculated at 0.996 and 0.978 Å, and broadening of the α(H–O–H) bond angle (107.3°). The next stable configuration is the O–U structure (Figure b), which released an adsorption energy of −0.60 eV. The interacting O–U distance is calculated at 2.805 Å, and O–H bonds and α(H–O–H) bond angle are calculated at 0.985/1.005 Å and 104.0°, respectively. When the H atoms placed head-on Si (Figure c), the adsorption process is found to be endothermic by 0.55 eV and an average O–H bond length is 0.971 Å and there is a preferential Si–O bond formation with an interatomic distance of 1.932 Å after energy minimization. From Bader populations analysis, we found that the adsorption process is characterized by charge transfer from the surface to the water molecule, with the water molecule gaining a charge of 0.15e–, 0.16e–, and 0.05e– in the O–Si, O–U, and H–Si configurations, respectively. We also observed that the change in the vibrational modes and bond strengths is related to the Bader charge transfer between the surface and the adsorbed water molecule (Table ).

Figure 6

Top and side views of the relaxed adsorption structures of molecular oxygen adsorbed at (a) O–Si, (b) O–U, and (c) H–Si on the U3Si2{110} surface (color scheme: U = gray, Si = blue, H = white, and O = red).

Compared to the molecular adsorption, dissociative water adsorption is found to have average adsorption energies of −3.24 and −2.27 eV for OOH placed head-on Si and head-on U, respectively. For dissociative adsorption through the HOH, we initially placed an HOH above the Si surface. After optimization, a Si–O bond was formed through the OOH atom, which means that dissociative adsorption through the HOH is unstable. The dissociative adsorption structures are characterized by more electrons being transferred from the surface to the dissociating species as evident by the calculated Bader charges of 0.44e– and 0.17e–. The charge transfer from the U3Si2 surface to the OH group is a necessary condition for water to bind to the surface, which is consistent with water dissociation on metal surfaces.[40] Furthermore, the above energetics results indicate that the dissociative adsorption of water is notably stronger than the molecular adsorption on the U3Si2{110} surface. We also observed the formation of U–H with bond lengths of 2.396 and 2.275 Å in the dissociative configurations, which is required for the H+ to achieve stability. In comparison to previous work, the U–H distances are 2.30–2.32 Å in α and β-UH3 configurations.[41] The schematic representations of adsorption structures of dissociated water on the clean U3Si2{110} surface are shown in Figure .

Figure 7

Top and side views of the relaxed adsorption structures of dissociated H2O at (a) OH–Si: H on U and (b) OH–U: H on Si on the U3Si2{110} surface (color scheme: U = gray, Si = blue, H = white, and O = red).

Water Adsorption and Dissociation on Clean U3Si2{111}

The geometries of the lowest-energy adsorption structures obtained on the U3Si2{111} surface are shown in Figure a–c. Compared to the {001} and {110} surfaces, the water molecules are adsorbed least strongly on the {111} surface. The lowest-energy adsorption structure on the U3Si2{111} surface is calculated to be the O–U configuration (Figure a), which released an adsorption energy of −1.40 eV. In this structure, the water molecule binds via the O atom lying laterally above the U atom at an O–U distance of 2.548 Å, with the α(H–O–H) bond angle that slightly increased to 105.5° compared to the gas-phase value of 104.5°. When the H2O molecule is adsorbed with the H atoms pointing toward the surface Si atoms (Figure b), an adsorption energy of −0.20 eV was released. The closest distance between H and Si/U sites is calculated to be 2.632/2.942 Å ruling out the formation of silane and uranium hydrides. The O–H bond lengths are elongated within the range of 0.977–0.995 Å while the α(HOH) bond angle increased slightly by 0.964° as presented in Table . The adsorption of H2O through Ow is unstable with an endothermic energy of 1.20 eV and tends to move further away from Si after optimization as shown in Figure c.

Figure 8

Top and side views of the relaxed adsorption structures of molecular H2O adsorbed at (a) the O–U site, (b) the H–Si site, and (c) the O–Si site on the U3Si2{111} surface (color scheme: U = gray, Si = blue, H = white, and O = red).

For dissociative adsorption of water on U3Si2{111}, the OH radical and one H atom are placed on the surface with two different adsorption modes as shown in Figure a,b. In Figure a, the OH– forms a bond with a surface U atom while the H atom bonded to a neighboring Si atom. The formed U–O, Si–O, and Si–H bond lengths are 2.655, 1.722, and 1.610 Å, respectively. The calculated adsorption energy for this configuration is −0.76 eV, whereas the adsorption of OOH on U leads to the formation of U–O (2.194 Å) and Si–H (1.697 Å) bonds after optimization requiring an energy of −3.30 eV. The larger adsorption energies suggest a preference for dissociative water adsorption over molecular adsorption on the U3Si2{111} surface, which is consistent with previous studies of uranium-bearing systems.[37,42,43]

Figure 9

Top and side views of the relaxed adsorption structures dissociated water configuration with (a) O–U: H and (b) O–Si: H, on the U3Si2{111}-Si terminated surface (color scheme: U = gray, Si = blue, H = white, and O = red).

Effects of Surface Coverage, O-Covered, and Surface Vacancy on Adsorption of Water

Water Adsorption at Higher Coverage

The effect of coverage on the adsorption properties of water on the U3Si2 surfaces was investigated by adsorbing up to four water molecules in a molecular, mixed, and partially dissociative modes. The optimized structures of the most stable adsorption modes are shown in Figure , whereas the adsorption energies are reported in Table . We found no clear trends in the adsorption energies with an increasing number of water molecules on the U3Si2 surfaces. At the {001} surface, the adsorption energies of one, two, three, and four water molecules representing a coverage of 0.25, 0.50, 0.75, and 1.00 monolayers (ML) are −3.70, −2.83, −3.02, and −3.10 eV, respectively. At the {110} surface, the adsorption energy increased from −2.46 eV for one water molecule to −3.23, −3.06, and −2.58 eV for two, three, and four water molecules, respectively. A decrease in the adsorption energy is observed at the {111} surface with an increasing number of water molecules; −3.30 for one water molecule compared to −1.42, −2.01, and −2.53 eV for the two, three, and four water molecules, respectively.

Figure 10

Top and side view of the relaxed adsorption structures of mixed (dissociative to molecular) 3:1 adsorption of H2O on (a) {001} and fully dissociative adsorption of H2O on (b) the {110} and (c) {111} U3Si2 surface (color scheme: U = gray, Si = blue, H= white, and O = red).

Table 3

Adsorption Energies (eV) per Water Molecule, Mixed Molecular and Dissociated Water on U3Si2 Surfacesa

adsorbate	{001}	{110}	{111}
1M	–3.70	–2.46	–3.30
2M	–2.83	–3.23	–1.42
3M	–3.02	–3.06	–2.01
4M	–3.10	–2.58	–2.53
1D + 3M	–3.25	–2.68	–2.69
2D + 2M	–3.26	–2.69	–2.65
3D + 1M	–4.12	–2.72	–2.48
4D	–3.54	–3.68	–3.45

Where M = H2O and D = OH + H.

Apart from the molecularly adsorbed water molecules, we have also explored mixed adsorption modes, wherein some of the water molecules are dissociated and some remained molecularly adsorbed, and investigated the case of fully dissociated modes in which all of the water molecules are dissociated at full coverage. The optimized structures of the most stable adsorption states are shown in Figure , and the adsorption energies are reported in Table . The mixed adsorption modes of molecular and dissociative water results in the formation different oxides, hydroxides, and oxygen molecules on the U3Si2 surface depending on the ratio of dissociative to molecularly adsorbed water as shown in Figure for the most stable adsorption energies. The remaining structures are given in the Supporting Information (Figures S1–S3). For instance, on the {001} surface, in the case of 75/25 mix adsorption, the oxygen molecule was formed with a bond length of 0.99 Å directly on the surface Si with a bond distance of 1.70 Å typical of SiO2 formation. The strongest and most stable adsorption modes at the {001} surface are predicted for 3D + 1M, which released an adsorption energy of −4.12 eV, compared to the 4D structures on the {110} and {111} surfaces, which released adsorption energies of −3.68 and −3.45 eV, respectively. Even though U3Si2 is a metallic fuel, it is important to draw a comparison between the silicide and urania, which is the standard fuel for LWRs. Hence, it is interesting to note that studies by Bo et al.[37] on UO2 and recent work by Tegner et al.[44] predicted the mixed 50/50 molecular/dissociative adsorption modes as the most stable adsorption configurations. The differences in the results can be attributed to differences in the crystallographic arrangement of the two systems and their electronic structures, UO2 is a semiconductor with an experimental band gap of 2.1 eV,[45,46] whereas U3Si2 is metallic. Note, however, that the energy difference between the fully dissociative case and the fully molecular case is −0.44, −1.10, and −0.92 eV on the {001}, {110}, and {111} surfaces, respectively. The increase in adsorption energies in the dissociative configuration is due to the formation of stronger intramolecular hydrogen bonds on the crowded surfaces compared to the purely molecular mode.

We also carried out a detailed analysis of the bond lengths for molecular and dissociative adsorption of multiple water molecules on the surfaces as shown in Table . We observed a shorter hydrogen bond length for the Si–H compared to U–H on the U3Si2{001}, {110}, and {111} surfaces, which suggest stronger hydrogen bonding in Si–H when it is formed on the surface. There is also strong adsorption of molecular H2O on the surface forming U–H2O and Si–H2O complexes with the exception of the {111} surface where the formation of Si–H2O is not observed.

Table 4

Selected Interatomic Distances (Å) for Molecular and Dissociative Water on the U3Si2{001}, {110}, and {111} Surfaces at Coverages from 0.5 to 1.0 Monolayers (ML)

bond type	{001} 0.5–1.0 ML (Å)	{110} 0.5–1.0 ML (Å)	{111} 0.5–1.0 ML (Å)
Si–O	1.70	N/A	N/A
Si–H	1.50–1.71	1.57–1.60	N/A
Si–OH	1.66–1.68	1.67–1.68	1.62–1.70
Si–H2O	1.89–2.11	2.02–2.06	N/A
U–O	2.13	N/A	N/A
U–H	2.17–2.34	2.34–2.45	2.16–2.35
U–OH	N/A	2.31–2.78	2.48–2.71
U–H2O	2.51–2.67	2.35–2.65	2.64–2.69

Water Adsorption and Dissociation on O-Covered U3Si2{100}, {110} and {111} Surfaces

Preadsorbed oxygen atoms play an important role in the activation of the O–H bond and further increase the rate of surface oxidation due to rapid water dissociation.[47,48] Hence, it is important to investigate the adsorption behavior of H2O on oxygen-covered U3Si2{001}, {110}, and {111} surfaces. Prior to investigating the adsorption of H2O on oxygen-covered U3Si2{001}, {110}, and {111} surfaces, we have systematically characterized the adsorption of atomic oxygen on different U3Si2 surfaces to elucidate their surface oxide formation. In our previous study,[14] we have provided comprehensive information regarding the mechanism of oxide layer formation on the U3Si2 surface by adsorbed O2 molecule. The adsorption of atomic O is found to be energetically more favorable at U sites than Si sites on the {001}, {110}, and {111} U3Si2 surfaces (Table S4 and Figure S5). The adsorption energies at the U and Si sites were calculated to be −2.44 and −0.67 eV on the {001} surface, −2.71 and −0.77 eV on the {110} surface, and −2.85 and −0.81 eV on the {111} surface. Similar results were predicted for molecular O2 at the different U3Si2 surfaces, which implies that the formation of UO2 on pristine U3Si2 is favored over SiO2.[14]

For the adsorption of water on the O-covered U3Si2 surfaces, various coadsorption structures were explored with the water adsorbed at the neighbor or distant sites from the preadsorbed O atoms. The coadsorption energies between the H2O and O on the U3Si2 surface is calculated as followswhere EH, EO, Esurface, and Esurface+(H are the total energy for the free molecule of water, molecular oxygen, the clean U3Si2 surface, and the coadsorbed (H2O + O) + U3Si2 surface systems, respectively. In most cases at the {001} surface, we found that the water molecule coadsorbed with oxygen dissociate to form OH ions due to the attractive force between the hydrogen atoms and preadsorbed O atoms. The most favorable coadsorption mode on the {001} surface is predicted for the configuration in which the water molecule is adsorbed at the U site near the O atom that is preadsorbed at the Si site. Due to the strong attractive force between the two adsorbates, the H2O molecule spontaneously dissociate to form two hydroxyl species, releasing an adsorption energy of −5.47 eV (Table ), which is consistent with water dissociation on oxygen-covered metal surfaces.[34,49] The U–OH and Si–OH interaction bond lengths are calculated to be 2.339 and 1.641 Å, respectively. Consistent with the strong adsorption, the two OH species draws a combined charge of 1.95e– from the interacting surface species. When the water molecule remained molecularly adsorbed at a Si site near a preadsorbed O atom (Figure b), an adsorption energy of −3.54 eV is released.

Table 5

Calculated Adsorption Energy (Eads) and Relevant Bond Distances for H2O Coadsorbed with Atomic Oxygen on U3Si2{001}, U3Si2{110}, and U3Si2{111} Surfaces

surface	adsorbate	config.	Eads (eV)	d(Ow–H1) (Å)	d(Ow–H2) (Å)	d(O–H2) (Å)	d(Si–O) (Å)	d(Si–OH) (Å)	d(U–O) (Å)	d(U–OH) (Å)	α(HOH) (deg)	Δq (e–)
{001}	H2O + O	Hw–U: O on U	–5.47	0.977		1.026		1.641		2.339		1.95
		Ow–Si: O on Si	–3.54	0.970	0.988		1.729		2.525		106.760	1.83
		Ow–Si: O on U	–3.49	0.975		0.953		1.680		2.525		1.79
		Ow–U: O on Si	–2.87	0.973		1.099	1.675					1.75
{110}	H2O + O	Ow–U: O on U bridge	–7.41	0.975	0.975		2.763		2.268		105.523	1.21
		Ow–Si: O on U	–4.13	0.982					2.236			0.92
		Hw–Si: O on U	–3.67	0.978		1.154				1.80
{111}	H2O + O	Ow–Si: O on U	–1.39	0.979		1.006		1.710		2.145		1.67
		Ow–U: O on Si	–0.81	0.977	0.974		1.695		2.567		109.975	1.87
		Hw–Si: O on U	–0.27	0.974					2.021

Figure 11

Top and side views of the relaxed adsorption structures of molecular H2O (a) H–U: O on U, (b) Ow–Si: O on Si, (c) Ow–Si: O on U, and (d) Ow–U: O on Si U3Si2{001} surface (color scheme: U = gray, Si = blue, H = white, and O = red).

We have also investigated the adsorption and dissociation of water on the U3Si2{110} surface in the presence of preadsorbed atomic oxygen. Three coadsorption modes have been explored with the H2O and O coadsorbed at the neighboring surface U and U bridge sites. The optimized adsorption geometries are shown in Figure a–c, while the coadsorption energies and the relevant optimized geometric parameters are summarized in Table . When water is adsorbed with the Ow head-on Si and the preadsorbed O atom at the nearest neighbor U–U bridge, the coadsorption energy is −7.41 eV, which is more negative than the sum of the separate adsorption energies (−3.23 eV), suggesting a strong interaction evident by the stretching of the OH bonds and significant transfer of electrons (1.21e–) from Si to the water molecule. It is clear that the oxygen atom has a stronger affinity for the uranium forming a U–O–U complex with a bond angle of 97.65°. Hence, the water molecule preferred to bond with the surface Si atom rather than deprotonate to form hydroxyl ions as was observed on iron sulfide surfaces.[34] When water is coadsorbed with the Ow head-on a neighboring U site, the coadsorption energy is calculated to be −4.13 eV, which is also more negative than the sum of the separate adsorption energies (−3.31 eV), suggesting that the oxygen atom promotes the dissociation of water due to deprotonation resulting in the formation of silane (Si–H), uranium oxide (U–O), and hydroxyl (O–H) species (Figure b). In this case, where Hw is placed on the Si atom, we observed a repulsion between H and Si while the nearest O atom forms a bond with one of the Hw leading to the formation of hydroxyl ions as shown in Figure c releasing an energy of −2.67 eV.

Figure 12

Top and side views of the relaxed adsorption structures of molecular H2O (a) Ow–Si: O on the U bridge, (b) Ow–Si: O on U, and (c) Hw–Si: O on U on the U3Si2{110} surface (color scheme: U = gray, Si = blue, H = white, and O = red).

The most favorable coadsorbed configuration of the (H2O + O)/U3Si2 system on the {111} surface is found to be the structure with the water molecule adsorbed on Si while one of the hydrogen atoms pointing toward the preadsorbed O atom on the top-U site (Figure a) releasing an energy of −1.39 eV, which is more negative than the sum of the separate adsorption energies of 0.39 eV. This is indicative of attraction between the two species on the U3Si2{111} surface for this configuration. This accounts for the dissociation of the water molecule leading to the formation of two Si–OH and U–OH. Although in the adsorption of the O atom on the Si site (Figure b) leads to the O atom, preferentially forming a trihedral network with U and Si atoms, this is facilitated by drawing electrons from a metal surface that is easy compared to a Si atom while there is stretching of the OH bonds (0.977 and 0.974 Å) with the Ow forming bond with the surface U atom.

Figure 13

Top and side views of the relaxed adsorption structures of molecular H2O (a) Ow–U: O and (b) Ow–Si: O on the U3Si2{111} surface (color scheme: U = gray, Si = blue, H = white, and O = red).

Water Adsorption on Defective (Nonstoichiometric) Surfaces

Considering that real surfaces are never perfect under reaction conditions and chemical processes often occur at defect sites, we have also investigated water adsorption at the defective surfaces containing one Si or U vacancies at the {001}, {110}, and {111} surfaces. The optimized structure of defective U3Si2 with H2O is shown in Figure and the calculated adsorption energies and optimized geometry parameters are listed in Table . At the defective {001}, {110}, and {111} surfaces containing one Si vacancy site (Si-1), the adsorption energies of the water monomer in the molecular state is calculated to be −7.52, −3.18, and −7.0 eV, respectively. In {001} and {110} adsorption structures, there is a complete dissociation of the water molecule which is consistent with the chemisorbed nature of water[16] while the OH bonds on the {111} surface stretch to 1.245 and 0.980 Å, respectively, suggesting the instability of the water molecule on the nonstoichiometric surface. The computed bond distance of U–O (2.163–2.321 Å) and Si–O (1.536–1.892 Å) suggest the formation of UO2 and SiO2.

Figure 14

Top and side views of the relaxed adsorption structures of Si and U vacancy-assisted molecular H2O adsorption (a) H2O–U3Si2– {001}, (b) H2O–U3Si2– {110}, (c) H2O–U3Si2– {111}, (d) H2O–U3–Si2{001}, (e) H2O–U3–Si2{110}, and (f) H2O–U3–Si2{111} surface (color scheme: U = gray, Si = blue, H = white, and O = red).

Table 6

Adsorption Energies (eV) of the Water Molecule on Nonstoichiometric U3Si2{001}, {110}, and {111} Surfaces

adsorption site	{001}	{110}	{111}
Si vacancy	–3.43	–3.18	–2.92
U1 vacancy	–4.85	–4.35	–2.17
U2 vacancy	–5.84	–4.22	–3.54

At the surfaces containing one U vacancy site (U-1), the dissociative adsorption of H2O on the defective U3–Si2{110} is found to be highly exothermic (Eads = −5.84 eV), which suggests that the defective U3–Si2{001} favors dissociative H2O adsorption rather than molecular adsorption, similar to the findings on the defective U3–Si2{001} and {111} surfaces. Bader population analysis reveals that a significant amount of charge (∼1.32e–) was transferred to dissociated water species from the interacting surface species. This is not surprising since vacancies result in the formation of dangling bonds (reactive sites) due to the availability of electrons for transfer to water molecules on the surface.

Electronic Structure and Bonding Mechanism

Fundamental understanding of the nature of interactions between the H2O molecule and the U3Si2 surfaces and any adsorption-induced changes in the electronic structures of U3Si2 were gained through projected density of states (PDOS) analysis (Figure ). The empty (filled) electronic states near the Fermi level can accept (donate) more electrons to enhance the reduction (oxidation) reactions. We observed various degrees of shifts in the PDOS, indicative of a change in the electronic structure due to electron transfer from U and Si ions to the water molecules leading to OH bond elongation; a step before deprotonation of the water molecule. The charge gained by the H2O molecule in different adsorption complexes is calculated to be in the range of 0.05–0.11e– at the water–U3Si2{001} surface, 0.04–0.05e– at the water–U3Si2{111} surface, and 0.15–0.25e– at the water–U3Si2{110} surface (Table ).

Figure 15

(Right) PDOS for the interacting surface U f-states before and after the adsorption of H2O at the (a) water–U3Si2{001} and (b) for interacting surface Si p-states at the water–U3Si2{110} interface, and for the interacting surface U f-states before and after the adsorption of H2O at the (c) water–U3Si2{111} interface. (Left) the corresponding optimized water–U3Si2 interfaces with U–O and Si–O bond lengths.

There is a possibility of surface oxide formation as shown by the U–O bond lengths of 2.620 and 2.555 Å and Si–O bond length of 2.120 Å on the {001}, {111}, and {110} surfaces, respectively. This suggests that water–U3Si2 oxidation would proceed by any of the following chemical reactions[50,51]The reaction energy of the different possible reaction pathways is found to be highly exothermic, which suggest that they are thermodynamically favorable and feasible reactions.

We further analyzed the PDOS of the isolated water molecule in the adsorbed state at the various surfaces and compared to the gas-phase molecule (Figure ). The DOS for the gas-phase H2O molecule is shown in Figure a where the molecular orbitals (MOs) are labeled as 2a1, 1b2, 3a1, and 1b1, respectively, while those for the lowest-energy adsorption configurations at the water–U3Si2{001}, {110}, and {111} interfaces are shown in Figure b–d, respectively. Due to the strong water–U3Si2 hybridization, electron transfer from the interacting surface U f-states, we observed a shift or disappearance of the 3a1 and 1b1 MOs around the Fermi level of water adsorbed at the {001} and {111} surfaces. At the water–U3Si2{110} interface, we observe a splitting of the 1b1 MO, coupled with a shift toward lower energy levels (Figure d), which signifies stabilization of the water molecule via physisorption. The reactivity of the surface is influenced largely by the ease of electron transfer between the surface and the adsorbate. Previous, work by Li et al. showed that the electronic states of the valence band of the surface play a key role during the surface–adsorbate interaction due to the hybridization energy between the bonding and antibonding adsorbate states and the metal valence-bands.[52]

Figure 16

DOS for H2O in the (a) free state and adsorbed in the lowest-energy geometry at the water–U3Si2 interfaces (b–d).

As the preadsorbed oxygen species enhance the O–H bond activation to dissociate, a necessary step for the formation of surface oxides, we have also characterized the electronic structures of the O-covered U3Si2 surfaces and showed that the U atoms to which atomic oxygen is bound become more positive (1.12e–, 1.20e–, and 1.61e– on the {001}, {110}, and {111} surfaces, respectively) compared to the clean surface U charge of +0.98e– {001}, 0.96e– {110}, and 1.01e– {111}, which, from the qU4+/qU6+ ratio, is enough to suggest that they have been oxidized from U4+ to U6+ (see Table S4 and Figure S5, for full details of O–U3Si2 in terms of bond lengths and charge transfer). We further investigated the nature of the interaction of the bonding between surface U and atomic oxygen by analyzing the projected density of states (PDOS) of the interacting surface U f-states and O p-state, as shown in Figure . We observed strong hybridization between the interacting U f-states and O p-state, which is due to the charge transfer from surface U ions into the adsorbed oxygen π orbital, in good agreement with previous studies of oxygen adsorption on metal surfaces[53]

Figure 17

Partial DOS projected on the interacting surface U f-states and O p-states for adsorbed atomic oxygen on the top-U site on (a) {001}, (b) {110}, and (c) {111} surfaces.

The work function gives a picture of the nature of such electronic interactions; hence, we have calculated the work function of the clean and adsorbate containing U3Si2 surfaces to characterize the level of difficulty for an electron transferring from the surface to the vacuum. The work function is the minimum energy needed to remove an electron from the bulk of a material through a surface to a point outside the material and can be written asThe potential in the vacuum region (Vvacuum) and the Fermi energy (EFermi) were derived from the same calculation. In practice, this is the energy required at 0 K to remove an electron from the Fermi level of the material to the vacuum potential. We determined the work function of the clean surface and further probed the effect of oxygen on the electronic states of the surface and oxygen-assisted dissociation of H2O.

The work function depends on the crystallographic direction as shown by the results in Table . The anisotropic nature of the work function comes from the crystallographic arrangement of the surface planes, which determines the spreading of the electronic charge into the vacuum.[54] Furthermore, the adsorption acts to smoothen the surface electric charge distribution that lowers the work function. The work function is such that Φ(H < Φ(H) < Φdry due to the partial transfer of electron charge from the substrate to the adsorbate and the resulting adsorption-induced surface dipoles (Table ).[55]

Table 7

Calculated Work Functions of the Dry (Φdry), Hydrated (ΦH), and Coadsorbed H2O + O (ΦH) U3Si2 Surfaces

surface	Φdry (eV)	ΦH2O (eV)	ΦH2O+O (eV)
{001}	3.09	3.05	2.86
{110}	1.89	1.48	1.21
{111}	2.86	2.30	1.96

Summary and Conclusions

We have investigated the adsorption and dissociation reactions of H2O on clean, oxygen-covered and defective U3Si2{001}, {110}, and {100} surfaces using density functional theory calculations. The adsorption energetics and characteristics of molecular water adsorption were compared with full dissociative and mixed (molecular and dissociative) adsorption modes on the U3Si2 surfaces. We showed from our calculations that the major interactions between the adsorbing water molecules and the U3Si2 surfaces occur through oxygen and the surface U or Si site. Compared to the clean surfaces, preadsorbed O atoms are shown to enhance the activation of the O–H bonds of water and their subsequent dissociation reactions to form surface hydroxyl species, which are driven by significant charge transfer from the surface to the adsorbing species. We demonstrated that surface vacancy defects enhance the adsorption and dissociation of H2O compared to a stoichiometric defect-free surfaces. The molecular-level insights derived from this work provide a fundamental understanding of the adsorption processes and mechanisms of the early stage of oxidation of U3Si2 in the presence of oxygen and water and might open new avenues for the rational design of oxidation resistance of metallic fuels for nuclear reactors.