First-principles study of nitrogen adsorption and dissociation on α-uranium (001) surface

Abstract

The adsorption and dissociation of nitrogen on the α-uranium (001) surface have been studied with a first-principles density functional theory (DFT) approach. The effects of strong 5f electron–electron correlation and spin–orbit coupling on the adsorption of nitrogen on the uranium (001) surface are also discussed. Different coverages of nitrogen atoms and different initial configurations of nitrogen molecules are considered on the uranium surface. The structural parameters and electronic states of nitrogen on the uranium surface are obtained. The calculated results indicate that nitrogen atoms are energetically favorable at the hollow1 sites. The nitrogen molecules adsorbed horizontally on the long-bridge site are found to dissociate completely, and the corresponding adsorption energies are about −4 eV. The electron structure of the most preferred adsorption configuration is investigated, and it is found that the adsorbed nitrogen atoms only seize electrons from the top-most uranium layer. Based on ab initio atomistic thermodynamics, the surface phase diagram for nitrogen adsorption on the α-uranium (001) surface is obtained and the initial stages of nitridation for the uranium surface are discussed.

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1. Introduction

Uranium (U) is one of the heaviest elements in nature. Until now no other element has such a formidable reputation as that of uranium in the Periodic Table for its applications in nuclear power and its potential applications for uranium catalysts.^1,2 As early as 1909, it was found that uranium was one of the most efficient catalysts used for the synthesis of ammonia during the Haber–Bosch process.³ In recent decades, numerous reactions were shown to proceed efficiently with the participation of uranium-containing catalysts.^4,5 In the last few years the non-aqueous chemistry of uranium has been an active area and there is an increased interest in uranium compounds containing metal–nitrogen multiple bonding.^6–9

Dinitrogen is a diatomic molecule with a very strong bond (945.33 ± 0.59 kJ mol⁻¹) that dominates its chemical properties and makes it difficult to dissociate. However, small molecules such as nitrogen, carbon monoxide and carbon dioxide can be activated by uranium coordination complexes, which are ascribed to the role of f orbitals for binding ligands. Such catalytic advantages of uranium over conventional, transition-metal catalysts have attracted much attention.¹⁰ In addition, much theoretical effort has been devoted to studying the activation of the nitrogen molecule (N₂). Rochana et al.¹¹ investigated the nitrogen adsorption, dissociation, and subsurface diffusion on the V(110) surface, and found a dissociation energy of 0.4 eV. Yeo et al.¹² performed first-principles calculations to investigate the full nitridation mechanism for the N₂ molecule on and in bcc Fe, and found that dissociation of the N₂ molecule occurred at the place of strongest adsorption in the hollow site. Using ab initio techniques and thermodynamic considerations, Soon et al.¹³ investigated the interaction between the nitrogen atom (N) and the Cu(111) surface, and the surface nitride formation was discussed. Zheng et al.¹⁴ studied the adsorption of N₂ on the UO(100) surface within the DFT framework, and they predicted that the lowest energy barrier for the dissociation reaction was 266.9 kJ mol⁻¹. Wang et al.¹⁵ found that the N₂ molecule is moderately activated when adsorbed onto the IrO₂(110) surface, which indicated that the IrO₂(110) surface might be applied in the catalytic reaction of N₂ fixation.

The electronic structure of uranium is mainly determined by 5f electron states, which form bands that are very narrow and hybridize with the U 6d and 7s electronic states. This behavior determines the uranium exotic geometric structure, characterized by atoms bonded in complex and distorted ways.¹⁶ Due to its chemical reactivity, uranium metal will be easily eroded by oxidation reactions with O₂, CO or H₂O in the atmosphere.¹⁷ Therefore, protection of the uranium surface against air-corrosion is a great challenge in the field of nuclear engineering. Surface modification is a corrosion-resistant treatment for metallic uranium, and nitridation is a typical surface treatment that can lead to good anticorrosion properties by producing thin nitride surface layers on the metal surface. A uranium sesquinitride (α-U₂N₃) layer would be formed on a uranium surface at low substrate temperatures of 230–250 °C during the R. F. plasma nitriding process, and it would provide considerable protection against corrosion by other reactive gases, e.g. H₂ and H₂O.¹⁸ Arkush et al.¹⁹ used N₂⁺ ion implantation to form thin surface layers with gradual gradients of α-U₂N₃ compounds, which provided near absolute protection against air corrosion. This study is similar to that of Liu et al.,^20,21 who used all-direction ion implantation technology to form a modified nitride layer (α-U₂N₃) on the uranium surface. Corrosion tests indicated that the nitride layer was effective in preventing the matrix from corrosive erosion. Zhang et al.²² reported that a nitride layer, mainly composed of UN and U₂N₃, was formed on a uranium surface by excimer laser irradiation, which also showed good anticorrosion properties.

Many researchers have theoretically investigated the interactions between U and some gases in the atmosphere, such as O₂, H₂, CO, CO₂ and H₂O.^23–29 However, no theoretical work has been done about the interactions between the uranium surface and nitrogen. Recently we have carefully discussed the interaction of one single N atom with α-U.³⁰ In that paper, we systematically studied N adsorption/absorption on U surfaces, N penetration/diffusion in the bulk U, and vacancy trapping for a single N atom in a bulk environment. Continuing that work, in the present paper the adsorption and dissociation behaviors of N₂ molecules onto the α-U(001) surfaces are investigated carefully with first-principles DFT calculations. With ab initio atomistic thermodynamics, N/U(001) surface diagrams are also obtained to bridge the energetic information of such stable configurations to the situations of finite temperature and finite pressure, which will shed light on some experimental observations.

2. Computational details

All the calculations in the present work were performed using the Vienna ab initio simulation package (VASP)^31,32 based on the DFT framework.^33,34 The projector augmented wave (PAW) method^35,36 was used to describe electron–ion interaction. The electron exchange–correlation was performed within the generalized gradient approximation (GGA) using the Perdew–Burke–Ernzerhof (PBE) functional.³⁷ Based on the convergence test, the plane-wave cutoff energy was set to be 380 eV, and the structural relaxations were performed until the residual forces on each atom were less than 0.02 eV Å⁻¹. When the relaxed calculations were performed, a broadening approach proposed by Methfessel and Paxton³⁸ was used with N = 2 and sigma = 0.2 eV to determine the partial occupancies of each wave function.

The strong correlation effects related to 5f electrons have been reported to be important in actinides.³⁹ However, because of uranium’s threshold level of f-electron location, the corresponding effects of strong 5f electron–electron correlation are weak and many of them can only be observed at low temperature.^40–42 Several studies have analyzed the strong correlation problem in uranium recently and found that such effects appear to be less crucial. Chantis et al.⁴³ used the quasiparticle self-consistent GW method to study the moderate f-electron correlation effects in α-U and found that most of them only appear in the excited-state spectra in the unoccupied f states. They concluded that the ground-state properties and the occupied band structure around the Fermi energy were not significantly affected because of the relatively small f-electron occupation number in U. Opeil et al.^44,45 performed photoemission spectroscopy on high quality uranium single crystals and compared the measured results with first-principles GGA band structure calculations. The favorable agreement between their experimental and theoretical results suggested that strong 5f electron–electron correlations effects were not very large in α-U, thus it was reasonable to consider it as a not highly correlated system. Additionally, another challenge for self-consistent electronic structure calculations of heavy elements such as U is the relativistic effect of spin–orbit coupling (SOC). However, previous studies found that this effect was mainly predominant in the unoccupied states and the effect of SOC on the calculated properties was not obvious. Söderlind⁴⁶ studied the elastic and structural properties of uranium metal with a DFT-GGA framework, and it was found that the SOC effect on the equilibrium volume, bulk modulus and total energy of α-U was very small. Similar results were also found by Richard et al.⁴⁷ during their plane-wave pseudopotential study of the light actinides. They suggested that a more careful treatment of the relativistic effects of SOC should be necessary from neptunium on. Taylor⁴⁸ performed first-principles calculations based on PAW formalism to investigate the materials properties of bulk α-U and its (001) surface. Their full spin–orbit and scalar relativistic calculations were shown to give results with similar levels of accuracy compared to experiment.

Nonetheless, we need to validate the strong 5f electron–electron correlation effect and the relativistic effect of SOC in the N/U(001) systems, especially on the adsorption energies. Though the standard DFT-GGA mode in its GGA formulation does include exchange and correlation energy, it has limits in dealing with the strong 5f electron–electron correlation. The conventional so-called DFT + U method⁴⁹ was applied here to deal with the strong correlation effects, in which an additional Hubbard-type term was introduced to address the effective on-site Coulomb interactions among the localized 5f orbitals. The rotationally invariant form introduced by Dudarev et al.⁵⁰ was used; thus the parameters U and J did not enter separately, and only the difference (U_eff = U − J) was meaningful. As Xie at al.⁵¹ have systematically investigated the strong correction effects in U metal and finally found a statistical optimal value of 1.24 can improve all the calculated properties. Here we followed their suggestion and took U_eff = 1.24 to verify the influence of correlation effects on our research system. In a standard DFT mode with PAW calculations, a fully relativistic effect is restricted to the core electrons, and the valence electrons are treated with a scalar relativistic approximation;^52,53 thus the relativistic effects were considered at least at the scalar relativistic level in our N/U(001) system. The GGA + SOC method was applied in some cases to validate the relativistic effect of SOC in the LS-coupling limit.

The structure of the uranium crystal depends on the temperature at ambient pressure. The crystal structure of bulk α-U, stably existing from 43 K to 940 K, is face-centered orthorhombic (as shown in Fig. 1(a)), which belongs to the CmCm space group.⁵⁴ Using the 14 × 7 × 8 Monkhorst–Pack⁵⁵ grid for the primitive bulk cell, the shape and volume of the conventional cell were optimized first to verify the strong 5f electron–electron correlation and the relativistic SOC effects on the structural properties of bulk α-U. As shown in Table 1, our GGA results compared well with Beeler’s⁵⁶ and Taylor’s⁴⁸ results. These calculated values also matched well with the experimental results measured at 40 K.⁵⁷ When the strong 5f electron–electron correlation effects were considered by the GGA + U method, we reproduced Xie’s results⁵¹ with U_eff = 1.24. It was found that the GGA + U results were somewhat improved to be closer to the experimental results compared with the GGA results. The relativistic effect of SOC was proved to have a small impact on the structural parameters of α-U, as also shown in Table 1. However, as we mainly cared about the N adsorption on the α-U(001) surface in the present paper, the strong 5f electron–electron correlation and the relativistic SOC effects on the adsorption results would be further discussed in the next section.

Fig. 1 Schematic views of the (a) bulk α-U and (b) slab model for α-U(001) surface.

Table 1 Structural parameters for ground state α-U. Results calculated with different ab initio approaches and the experimental observation at 40 K are listed in the table. a, b and c are the lattice constants and y is the internal parameter; V represents the volume per atom

Approach		a (Å)	b/a	c/a	y	V (Å^3)
GGA	PBE (this work)	2.796	2.091	1.752	0.098	20.04
	PBE (Beeler^56)	2.793	2.094	1.752	0.098	19.99
	PW91 (Taylor^48)	2.800	2.106	1.748	0.097	20.19
GGA + U (1.24)	PBE (This work)	2.849	2.060	1.742	0.100	20.74
	PBE (Xie^51)	2.840	2.074	1.747	0.100	20.75
GGA + SOC	PBE (this work)	2.795	2.094	1.755	0.099	20.06
	PW91 (Taylor^48)	2.797	2.098	1.749	0.098	20.07
Experiment^57		2.836	2.068	1.740	0.102	20.52

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The adsorption of nitrogen atom and molecule onto the α-U(001) surface was primarily calculated using a C(3 × 2) surface unit cell. N atom adsorption on a larger C(4 × 2) surface unit cell was also studied in such a way that more stable N/U(001) adsorption configurations with different coverages would be considered. These two different surface unit cells were both modelled as periodically repeating slabs with five atomic layers (Fig. 1(b)), of which the upper two metallic layers were relaxed and the bottom three layers were fixed in their bulk-like positions. A vacuum layer of 12 Å between two successive slabs was thick enough for all the relevant calculations. The nitrogen atom or molecule was placed on one side of the slab where the induced dipole moment was considered by applying a dipole correction.⁵⁸ The Brillouin zone was sampled using 4 × 4 × 1 and 3 × 3 × 1 k-meshes for the C(3 × 2) and C(4 × 2) surface unit cells, respectively. The computational expense of these simulations was quite substantial as more than two hundred kinds of structures were considered.

The adsorption energies (E_ads) of nitrogen on U surfaces are defined as

where E(U/N_m) and E(U) are the total energy of the U slabs with and without nitrogen adsorption, respectively. E(N_2(g)) is the energy of an isolated N₂ molecule and it can be obtained by putting one N₂ molecule in a cubic box with side-length 20 Å and carrying out a gamma-point calculation. The plane-wave energy cutoff for the N₂ molecule calculation was increased to 600 eV to achieve greater numerical accuracy. The value of m is one or two when a nitrogen atom or molecule is used in the calculation. The calculated bond length, vibrational frequency and binding energy of the N₂ molecule were 1.11 Å, 2422 cm⁻¹ and 10.39 eV, respectively, which agreed well with the reported experimental values⁵⁹ of 1.10 Å, 2359 cm⁻¹ and 9.76 eV.

To study the diffusion kinetics of nitrogen, the Climbing Image Nudged Elastic Band (CI-NEB) Method⁶⁰ was employed to find the minimum energy paths (MEPs) and the transition states. In this method, a chain of linear interpolation images (seven in the present calculations) along an initial pathway between the given initial and final states of a reaction would be relaxed to determine the MEP and its corresponding saddle point. The images were relaxed until the maximum residual forces on each atom are less than 0.02 eV Å⁻¹.

3. Results and discussion

3.1. Nitrogen atom adsorption on α-U(001) surface and the effect of coverage

The adsorption of a single N atom on the clean α-U(001) surface was systematically discussed in our previous paper.³⁰ As shown in Fig. 2, five possible high-symmetry adsorption sites on the α-U(001) surface (denoted as top, hollow1, hollow2, long-bridge and short-bridge, respectively) were considered. Previous results proved that only two stable quasi-trigonal sites (hollow1 and hollow2) were preferred for the adsorption of one N atom on the α-U (001) surface and the hollow1 site was slightly more energetically stable for N atom adsorption than the hollow2 one. Here we would focus on the strong 5f electron–electron correlation and the relativistic SOC effects on the N adsorption. Taking the C(3 × 2) α-U(001) surface as an example, we calculated the adsorption energies, stable structural parameters and Bader charge⁶¹ with three different approaches, i.e. GGA, GGA + U and GGA + SOC. As shown in Table 2, when the strong 5f electron–electron correlation or relativistic SOC effect was introduced, the largest changes of adsorption energy, N–U bond length and N-surface height were ∼4%, ∼2% and ∼5%, respectively, when compared with the GGA results. Furthermore, when compared with the GGA results, the Bader charges of the adsorbed N atom by GGA + U or GGA + SOC calculations only changed by 0.01–0.03|e|. Generally speaking, the adsorptions of nitrogen on a α-U (001) surface were not significantly affected by the strong 5f electron–electron correlation and the relativistic SOC effects. Thus all the calculations in the following were performed with the standard DFT-GGA calculations, which we think could give reasonable results for the adsorption properties of nitrogen on the α-U (001) surface and save a great amount of computational resources.

Fig. 2 Schematic illustrations of the α-U(001) surface cells and adsorption sites, where H1 = hollow1 site, H2 = hollow2 site, LB = long-bridge site, SB = short-bridge site, and T = top site. Blue and green spheres denote the first and second layer of the uranium slab, respectively.

Table 2 Energetic, structural parameters and Bader charge for N atoms adsorbed on a α-U(001) C(3 × 2) surface. E_ads denotes the adsorption energy according to eqn (1); d_N–U represents the shortest binding length between N and U atoms; d_N-surf is the average binding height from the N atom to the first layer; the Bader charge represents the average charge states of the absorbed N atom

Approach	Stable N site	Eads (eV)	dN–U (Å)	dN-surf (Å)	Bader charge (|e|)
GGA	Hollow1	−2.09	2.176	1.110	1.42
	Hollow2	−2.03	2.092	1.149	1.39
GGA + U	Hollow1	−2.18	2.175	1.069	1.43
	Hollow2	−2.10	2.108	1.091	1.41
GGA + SOC	Hollow1	−2.17	2.141	1.069	1.44
	Hollow2	−2.12	2.085	1.093	1.42

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To understand the properties of the uranium surface adsorbed with more N atoms, we tested the effect of N coverage on the adsorption features. The average adsorption energy (adsorption energy per N atom) is estimated by the following formula

where E(U/N) is the total energy of the N adsorption configuration, N_N denotes the number of adsorbed N atoms. In this section, we took the C(3 × 2) surface unit cell for example to elaborate the adsorption behaviors of N atoms at various degree of coverage. As listed in Table 3, eight degrees of coverage were considered, ranging from 1/12 monolayer (ML) to 1 ML. Moreover, various combinations of N atoms occupying different adsorption sites were studied at a certain coverage. Finally, the most stable structure of the corresponding coverage was selected to obtain the average adsorption energy and the corresponding configuration parameters.

Table 3 The average adsorption energies and structural parameters for various coverages of N atoms on the α-U(001) C(3 × 2) surface. ΔZ represents the degree of surface wrinkle, which indicates the maximum perpendicular distance between two surface U atoms

C(3 × 2)	Coverage (ML)
	1/12	1/6	1/4	1/3	1/2	3/4	5/6	1
Eads (eV)	−2.09	−2.17	−2.18	−2.20	−2.17	−2.05	−1.89	−1.24
dN-surf (Å)	1.110	1.101	1.093	1.093	—	—	—	1.133
ΔZ (Å)	0.153	0.305	0.240	0.479	1.438	1.264	2.397	0
Bader charge (|e|)	1.42	1.38	1.37	1.37	1.46	1.42	1.37	1.17

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We first investigated how the structures change with increasing number of absorbed N atoms (as shown in Fig. 3). One N adatom preferred to occupy the hollow1 site on the α-U(001) surface (Fig. 3(a)), as described above. Finally two N adatoms were located at the two next-nearest neighboring hollow1 sites (Fig. 3(b)), producing the most stable structure under the corresponding coverage. Further increasing the coverage to three absorbed N atoms, the added N atom sequentially resided at another next-nearest neighboring hollow1 site. The neighboring distances between the adsorbed N atoms were about 3.3 Å, and they finally relaxed to a similar structure of linear nitrine (Fig. 3 (c)). It was interesting to see that, for a coverage of 1/3 ML, the four N adatoms eventually formed a periodic zigzag structure on the uranium surface, which consisted of two dinitrogen structures (with a distance of 3.29 Å) and showed the same bond length (about 2.10 Å) to the surrounding U atoms (Fig. 3(d)). As summarized in Table 3, the four low-nitrogen-coverage structures analyzed above demonstrated almost the same d_N-surf and underwent a low degree of surface reconstruction. However, the surface U atoms would suffer significant reconstruction on increasing the N coverage, just as depicted in Fig. 3(e)–(g). The U atoms of the topmost layer shifted a lot, especially along the vertical direction, which led to the severe surface wrinkle. When the N coverage was added to 1 ML, all the attached N atoms equally resided the hollow1 sites, thus the relaxed surface would not reconstruct any more. Rochana et al.¹¹ found the reconstruction of V(110) surface when 0.25 ML atomic N was adsorbed at the LB site, and more apparent surface reconstruction was observed upon 0.5 ML atomic N adsorption in the β state. Mortensen et al.⁶² suggested that at higher N coverage, the islands consisting of C(2 × 2)-N/Fe(100) reconstructed overlayer structures would form on the (111) and (110) surfaces. Kaghazchi et al.⁶³ also reported the similar N-induced surface reconstruction that the hcp(112̄1) surfaces of Ru, Os, and Re would break up to form facets of atomically-rough hcp(134̄2).

Fig. 3 Top and side views of the most stable configurations for different nitrogen coverages on α-U(001) C(3 × 2) surface: (a) 1 N (1/12 ML); (b) 2 N (1/6 ML); (c) 3 N (1/4 ML); (d) 4 N (1/3 ML); (e) 6 N (1/2 ML); (f) 9 N (3/4 ML); (g) 10 N (5/6 ML); (h) 12 N (1 ML).

To further study the change of the average adsorption energy as a function of nitrogen coverage, we also analyzed the variation of average Bader charge for the corresponding stable structures. As summarized in Table 3, it was found that the average adsorption energy did not change too much at low coverages (Θ ≤ 1/3 ML), mirroring the trend of the corresponding d_N-surf and average Bader state.

Interestingly, obvious surface reconstruction occurred with the increase in N coverage to a critical point of 1/2 ML, and the average Bader charge of the structure unexpectedly rose to a peak value, which can be attributed to the surface wrinkle that provides more bonding U atoms to the absorbed N atoms. Moreover, as the coverage increased to 5/6 ML, the average adsorption energy increased a lot, which agreed well with the decreasing trend of average Bader charge. Additionally, when the surface hollow1 sites were all adsorbed by N atoms, they would be negatively charged because of the strong N–U bonding. The dense charges produced significant lateral coulomb repulsion, which brought about the lowest average absorption energy. Stampfl et al. observed a similar phenomenon when O atoms were adsorbed on the Ru(0001)^64,65 and Ag(111)⁶⁵ surfaces. Jiang et al.⁶⁶ found lateral repulsions between H atoms on the Fe(110) and Fe(100) surfaces, which led to significant destabilization of the adsorbate at higher coverages. Rochana et al.¹¹ also reported the lateral interaction between neighboring N atoms on the LB–Top–LB and the TF–TF sites of the V(110) surface, which led to weaker adsorption energies than those on the same sites with 0.25 ML coverage.

For the ensuing computations, we also investigated the N adsorption behaviors on a larger C(4 × 2) surface. With similar analysis methods, a wide range of N coverages were considered to obtain the stable adsorption phases on the U surface. Nine varying N coverages of 1/16, 1/8, 1/4, 3/8, 1/2, 5/8, 3/4, 7/8 and 1 ML were selected to find the stable configurations. Finally, the most probable geometries of an N atom adsorbed on a C(4 × 2) surface unit cell at certain coverages were listed in Fig. 4. It was interesting to note that adsorbed N atoms on such a surface showed a similar structural trend to that of the C(3 × 2) surface unit cell with increasing coverages: the hollow1 site was clearly the preferential adsorption site, and periodic zigzag nitrogen configurations occupied the U surface on increasing the coverage to 1/4 ML. More intriguingly, two reversed zigzag nitrogen structures existed as the coverage increased to 1/2 ML. On the other hand, a large distortion to the surface structure occurred under coverages ranging from 3/8 ML to 3/4 ML. Additionally, the variation of average adsorption energies relative to the N coverage was also investigated, just as plotted in Fig. 5. We compared this tendency for the two surface unit cells, and found similar results, in that the average adsorption energies changed little under the coverage of 3/4 ML, but increased a lot with coverage up to 1 ML. What’s more, the energy differences between the two surfaces at the same coverages were also compared. As shown in the inset of Fig. 5, the differences at coverages of 1/4, 1/2, 3/4 and 1 ML were all so modest that we found the largest disparity to be only ∼0.05 eV, which indicated that the geometric factor (the size of the cell) contributed little to the average adsorption characters in such cases.

Fig. 4 Top and side views of the most stable configurations for different degrees of nitrogen coverage on the C(4 × 2) surface: (a) 1 N (1/16 ML); (b) 2 N (1/8 ML); (c) 4 N (1/4 ML); (d) 6 N (3/8 ML); (e) 8 N (1/2 ML); (f) 10 N (5/8 ML); (g) 12 N (3/4 ML); (h) 14 N (7/8 ML); (i) 16 N (1 ML).

Fig. 5 Average adsorption energy vs. nitrogen coverage of the C(3 × 2) and C(4 × 2) surface unit cells. Inset: the average adsorption energy differences between the C(4 × 2) and C(3 × 2) surfaces at the same four degrees of coverage.

3.2. Adsorption and dissociation of the nitrogen molecule

Dissociative chemisorption is a key step in most surface chemistry, especially for some industrially important catalytic systems. Moreover, prior to the nitriding process of the uranium substrate, pure nitrogen gas should be fed to the clean surface. Thus, to study the catalytic properties and nitridation mechanism of the uranium surface, the adsorption and dissociation properties of N₂ molecules should be examined in detail. Here adsorption of one N₂ molecule on the C(3 × 2) surface unit cell was studied. As mentioned above, five possible symmetrically distinguishable on-surface sites were taken into account. For each adsorption site, three approaches of the adsorption configurations were obtained, based on the orientations of the diatomic molecule. Taking the N₂ molecule located at the hollow1 site for example, it was denoted as ‘Hor1’ or ‘Hor2’ when the molecule was horizontally placed on the α-U(001) surface and its orientation was parallel to the x-axis or y-axis of the coordinate system, respectively; and it was denoted as ‘Ver’ when the molecule was perpendicular to the surface, as illustrated in Fig. 6.

Fig. 6 Horizontal and vertical adsorption configuration for N₂ on the hollow1 site: (a) top view of the Hor1 configuration, (b) top view of the Hor2 configuration, (c) top view of the Ver configuration, (d) side view of the Ver configuration.

The N₂ molecule is difficult to dissociate because of its strong triple-bond. Even so, the strength of the bond is weakened when it is adsorbed onto the α-U(001) surface. The adsorption energies and optimized adsorption parameters obtained with DFT calculations were listed in Table 4. It was found that there were three kinds of adsorption situations (see Fig. 7) for the interactions between the N₂ molecule and the U surface. The first one (type-I) was that the N₂ molecule was physically adsorbed onto the α-U(001) surface, where the N–N bond was slightly lengthened by about 0.02 Å compared to that of the free N₂ molecule, and the adsorption energies were −0.20 to −0.60 eV. The second one (type-II) was that the adsorption energies of the stable configurations range from −1.10 to −2.32 eV, with N–N bond lengths of about 1.4 Å, which indicated dissociative behavior of the N₂ molecule. The third one (type-III) was the configuration with the largest adsorption energy, where the N₂ molecule dissociated completely and the two dissociative N atoms were separated remarkably to a distance greater than 4.5 Å. In a word, the fate of the N₂ molecule depended strongly on the adsorption sites and orientations, which will be elaborated further in the following.

Table 4 Adsorption energies and geometric parameters of the N₂ molecule adsorbed on α-U(001) surface calculated for different sites and approaches. d_N–N represents the nitrogen-to-nitrogen distance upon adsorption; d_N–U represents the shortest binding length between the N and U atoms; β represents the angle between the N–N bond and the surface level; FS represents the final structure

Approach	Initial N2 site	Eads (eV)	dN–N (Å)	dN–U (Å)	dN-surf (Å)	β (°)	FS
Ver	Hollow1	−2.02	1.406	2.139	1.438	11.03	II-4
	Hollow2	−1.83	1.409	2.177	1.438	8.93	II-3
	Long-bridge	−2.02	1.406	2.141	1.438	10.96	II-4
	Short-bridge	−0.20	1.149	2.607	2.779	85.24	I-1
	Top	−0.56	1.143	2.411	2.975	87.75	I-2
Hor1	Hollow1	−1.10	1.376	2.206	1.482	0	II-1
	Hollow2	−2.32	1.370	2.297	1.344	0	II-5
	Long-bridge	−3.93	4.547	2.049	1.159	0	III-1
	Short-bridge	−1.16	1.384	2.222	1.413	0	II-2
	Top	−2.32	1.371	2.295	1.344	0	II-5
Hor2	Hollow1	−2.02	1.406	2.141	1.438	11.11	II-4
	Hollow2	−1.83	1.410	2.178	1.438	9.01	II-3
	Long-bridge	−4.20	4.777	2.066	1.161	0.97	III-2
	Short-bridge	−2.02	1.407	2.141	1.438	11.08	II-4
	Top	−0.56	1.143	2.410	2.975	87.54	I-2

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Fig. 7 Top and side views of the optimized structures of N₂ adsorption onto the α-U(001) surface.

There were two configurations for the physical adsorption of a N₂ molecule onto the α-U(001) surface. After being relaxed, the N₂ molecule initially placed at the short-bridge site with vertical orientation (Ver approach) remained perpendicular to the surface (denoted as I-1) and the adsorption energy was as low as −0.20 eV, which indicated a weak interaction between the N₂ molecule and the U surface. There existed another physical adsorption configuration when the N₂ molecule was initially placed at the top site of the U surface with a Ver approach. Although the N₂ molecule was tilted to the surface with an angle of 2.25°, it almost stayed at the original top site (denoted as I-2). The N₂ molecule experienced a stronger interaction with the U surface and the adsorption energy was −0.56 eV, which was attributed to the shorter N–U bond length between the N atom and its nearest neighboring U atom. The final Hor2 configuration on the top site was nearly degenerate with the final I-2 configuration, because both had similar structural parameters after relaxation.

Several configurations of N₂ molecules on the α-U(001) surface involved in chemical dissociative adsorptions were investigated and they have been detailed below according to the descending order of E_ads. For the relaxed Hor1 configuration at the hollow1 site (here denoted as II-1), the adsorption energy was −1.10 eV and the two dissociated N atoms finally diffused to the nearby long-bridge sites. The bond length of N–N was elongated to 1.376 Å. The d_N-surf was 1.482 Å, which was significantly shorter than that of the physisorption configuration. The N₂ molecule initially placed at short-bridge with Hor1 orientation finally moved to the hollow2 site, with two N atoms dissociated to the nearest long-bridge sites (denoted as II-2). The structural parameters were similar to those of the II-1 configuration analyzed above, but it had a slightly lower adsorption energy of −1.16 eV. For the N₂ molecules initially located at the hollow2 site, both the Ver and Hor2 approaches reached the same final configuration (denoted as II-3) with very similar parameters, and the two dissociative N atoms with larger bond distances of about 1.41 Å stayed close to the surface. The d_N–U was determined to be 2.178 Å, which contributed to the stronger adsorption energy (−1.83 eV). The axis of the diatom was somewhat tilted, with an angle of about 9° relative to the surface level. It was worth pointing out that the four initial configurations, i.e. Ver configurations on hollow1 and long-bridge sites, and Hor2 configurations on hollow1 and short-bridge sites, all relaxed to a similar structure (denoted as II-4), with almost the same parameters. One dissociative N atom finally occupied the hollow1 site and the other was located close to the nearby short-bridge site, and the distance between the neighboring N atoms was 1.406 Å. The adsorption energies, d_N–U and d_N-surf were −2.02 eV, 2.141 Å and 1.438 Å, respectively, which indicated that the configuration was more energetically stable than those studied above. For the Hor1 approach, the N₂ molecule initially placed at the hollow2 or top site was shifted to the long-bridge one; then it dissociated and the two dissociative N atoms were finally located at the nearest neighboring hollow1 and hollow2 sites (see II-5 structure), which were 1.370 Å apart. The average binding height d_N-surf with respect to the surface was 1.344 Å, which was lower than those of all the structures elaborated above and led to the stronger adsorption energy of −2.32 eV.

Then we focused on two horizontal structures on the long-bridge site, which existed for complete N₂ molecule dissociative adsorption and reached the lowest adsorption energy (approximately −4.0 eV). When the N₂ molecule was placed initially at the long-bridge site with the Hor1 approach, two dissociative N atoms were dragged to the hollow1 and hollow2 sites (denoted as III-1), respectively, whose distance was 4.547 Å. The structural parameters d_N–U and d_N-surf were 2.049 Å and 1.159 Å, respectively, which were shorter than those of the five dissociative configurations analyzed above (II-1 to II-5 configurations); this contributed to its lower adsorption energy of −3.93 eV. The N₂ molecule initially located at the long-bridge site with Hor2 orientation finally dissociated to the most stable structure of III-2, where the two N atoms severally diffused to the hollow1 and hollow2 sites. Though the d_N–U and d_N-surf of III-2 configuration were similar to those of the III-1 one, the greater distance of 4.777 Å between the two N atoms indicated a more complete dissociative adsorption with the lowest adsorption energy of −4.20 eV. However, for H₂ adsorption on the α-U (001) surface at the coverages of 0.25 and 0.5 ML, both the horizontal configurations on the long-bridge site were found to be unstable.²⁵ As for the Fe(100) and Fe(110) surfaces, the N₂ molecules were found to have strong adsorption energies on the hollow sites in both their horizontal and vertical configurations.¹² Furthermore, the N₂ molecule preferred to bind strongly to the V(110) surface on the LB and SB sites in a parallel orientation, corresponding to the adsorption energies of −2.82 and −2.27 eV.¹¹

In the previous section, we proved that two isolated N atoms would stably reside in the next-nearest neighboring hollow1 sites, producing the most energetically favored configuration under the corresponding coverage. However, the most stable III-2 structure with the completely dissociated N₂ molecule had not relaxed to the above-mentioned state, thus it was supposed that there exists an energy barrier between these two states, so we calculated the MEP for this reaction. As is shown in Fig. 8, the energy profile manifested a very low energy barrier of 0.09 eV, indicating that the two dissociative N atoms could easily diffuse to the more stable adjacent hollow1 sites, even at low temperature. However, Wang et al.⁶⁷ studied the dissociation of N₂ molecule on Cu(111) and Au(111), and obtained the energy barriers of more than 3.75 eV. Yeo et al.¹² investigated the dissociation of one N₂ molecule, and calculated an energy barrier of 1.15 eV on Fe(100) and 1.18 eV on Fe(110). Rochana et al.¹¹ calculated the dissociation path of the N₂ molecule on V(110) and found a dissociation barrier of 0.4 eV.

Fig. 8 The MEP between the most completely N₂ dissociative adsorption structure and the more stable structure with two nitrogen atoms adsorbed.

To get information on the N–U bonding, we performed a detailed study on the electronic structure of the III-2 configuration. By using Bader charge analysis,⁶¹ we quantitatively calculated the charge transfer between the dissociative N atoms and the uranium substrate. As listed in Table 5, two N adatoms accepted nearly the same net charge of 1.38|e|, which were almost transferred from their nearby surface U atoms; whereas the U atoms in the 2nd and 3rd layers contributed little to the charge transfer. Therefore, we concluded that there existed obvious ionic bonds between the N atoms and their nearby surface U atoms, which could be attributed to the significant electronegativity difference between N (K = 3.04) and U (K = 1.38).

Table 5 Bader charges of two dissociative nitrogen adatoms and the uranium atoms in the three surface layers. A negative charge value indicates gain of electrons, whereas a positive value indicates loss of electrons

Net charge of each atom
2 N	1.38				1.38
1^st_U	−0.45	−0.32	−0.54	−0.39	−0.49	−0.41	−0.03	−0.01	−0.01	−0.03	−0.11	−0.04
2^nd_U	0	−0.01	0	0.02	0.02	0.02	0	0.01	0	0	0.01	0
3^rd_U	0	0	0	0	0	0	0	0	0	0	0	0

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Unlike the transition metals, uranium has three f electrons, which enable it to catalyze some reactions that are impossible with conventional transition-metal catalysts, especially in non-aqueous chemistry.¹ To further investigate the orbital contributions to the N–U interaction, we calculated the projected density of states (PDOSs) of an adsorbed N atom and its nearest U atom in the III-2 configuration, and the PDOSs of the isolated N atom and the U atom on a clean U surface were also calculated for comparison. The contribution of the d electron to N–U bonding was validated with the d-band model,⁶⁸ and that of the f-band was also dealt in a the similar way. As shown in Fig. 9, the 2p state of the isolated N atom was marked at ∼−5 eV by aligning the vacuum level with that of the clean U(001) surface,^69,70 and the Fermi levels for others were aligned to 0 eV. From the PDOS of the U atom on a clean surface, it was observed that the U 5f state was dominated at the Fermi level and located from −3 eV to 1.2 eV, while the U 6d state was relatively broad and located at the lower energies (−4.5 eV to 1.2 eV). This was further confirmed by band-center analysis, which revealed the f-band and d-band centers were at −0.2 eV and −2.10 eV, respectively. It was clear from the PDOSs of the clean surface U atoms that the 5f and 6d states at the Fermi level were distinctly reduced due to the N–U bonding, with the d-band and f-band centers shifting from −2.10 eV and −0.20 eV down to −3.17 and −0.60 eV, respectively. It finally exhibited some degree of overlapping and mixing between N 2p and U 5f/6d orbits within the range −4.5 eV to −3 eV, which indicated that there also existed some covalent interaction for N–U bonding. As the d-band center of the U atom on the clean U surface was closer to the 2p states of the isolated N atom than that of the f-band center, a stronger mixing between the N 2p and U 6d states was expected than that between the N 2p and U 5f states. This was clearly seen on the PDOSs of the adsorbed N atom and the U atom upon adsorption, in which the overlapping between N 2p and U 6d states, localized in the range −4.5 eV to −3 eV, was much more obvious than that between N 2p and U 5f. This was consistent with general trends developed from d-electron elements, i.e. delocalized sp states (relative delocalized d states in the present case) usually contributed the largest part of the bonding and involved considerable hybridization and charge transfer, while localized d states (more localized f states in the present case) characterize bonding.⁷¹

Fig. 9 PDOS of an adsorbed N atom and its nearest U atom. PDOS of the corresponding U atom on the bare surface is superimposed for comparison, and the green arrow denotes the 2p state of the isolated N atom by aligning the vacuum level with that of the bare U surface (dashed lines: before adsorption, solid lines: after adsorption).

The ionic part of U–O bonding and the covalent part due to U 5f/6d and O2p mixing similarly appeared in the dissociative adsorption of O₂ on the α-U (001) surface.^24,72 Rochana et al.¹¹ described the interaction between N₂ and V(110) with the d-band model, and expected stronger adsorption energy as the d-band shifts up in energy. Using the GGA approach, Mei et al.⁷³ analyzed the bonding behavior in UN, and found a similar result that the 2p orbitals of N atoms mixed with the 6d orbitals of U to some extent below the Fermi level. Moreover, Weck et al.⁷⁴ investigated the DOS of UN₂, and discovered some degree of 2p–5f mixing appears at the top of the valence band, which agreed well with the HSE DOS result reported by Wen et al.⁷⁵

3.3. Surface N/U phase diagram with ab initio atomistic thermodynamics

Even though the most stable N/U(001) configurations at different coverages were studied systematically, the present DFT calculations were merely based on the zero-temperature and non-pressure technique, which introduced a temperature and pressure gap between the theoretical and actual conditions. In this section, we tried to combine the DFT calculations with the thermodynamic formalism, i.e. ab initio atomistic thermodynamics,^64,76–78 aiming to obtain the surface phase diagram for equilibrium nitrogen adsorption on the α-U(001) surface.

Here we considered the uranium surface to be surrounded by a nitrogen environment, which was described by a nitrogen pressure p and temperature T, and the surface under such realistic conditions would exchange atoms with the chemical reservoirs. Therefore, the surface free energy (γ) of a slab at temperature T and partial pressure p can be calculated as

where G (T, p, N_U, N_N) is the Gibbs free energy of the system and N_U and N_N are the numbers of U and N atoms in the system, respectively. A is the surface area and μ_U and μ_N are the relevant chemical potentials for uranium and nitrogen atoms, respectively. The Gibbs free energy of the system is given by

G(T, p, N_U, N_N) = E(N_U, N_N) + F^vib − TS^conf + pV, (4)

where F^vib, pV and TS^conf terms can be safely neglected for typical pressure and temperature,^78,79 and E(N_U, N_N) is the total energy of the system calculated by the first-principles approach. Thus, we get a simplified form of the Gibbs free energy of adsorption with respect to the clean surface, which can be expressed as

To calculate the values of the chemical potential for nitrogen atom, we use

whereHere p⁰ corresponds to standard atmospheric pressure and (T, p⁰) can be obtained from thermochemical tables.⁸⁰ By incorporating eqn (2) and (6) into eqn (5), we can getwhich determines the most stable structure under a specified temperature and partial pressure of nitrogen.

As shown in Fig. 10, the energetically preferred structures at every considered coverage were depicted in the phase diagram; and three typical temperatures (300, 600 and 900 K) were selected to correlate the nitrogen chemical potential with the pressure. A natural starting point to analyze the surface phase diagram was the leftmost part, which represented the vanishing concentrations of the N/U(001) surface phase species and indicated that the clean α-U(001) surface would be the most stable system state under the corresponding Δμ_N of −2.20 eV. For a slightly higher Δμ_N, ranging from −2.20 eV to −2.14 eV, the structure of C(3 × 2)-1/3 ML emerged to be more stable, and the C(4 × 2)-6/16 ML configuration exhibited a higher ΔG when Δμ_N was increased to a higher range of −2.14 eV to −2.10 eV, resulting in a more favorable phase. Despite having the same number of adsorbed N atoms, the C(3 × 2)-1/2 ML configuration showed a steeper slope with higher coverage, which made it more stable for Δμ_N > −2.10 eV. By further increasing the nitrogen concentration, i.e. moving the red vertical line to a larger value of −1.83 eV in the surface phase diagram, the structure of C(3 × 2)-3/4 ML would gradually become more populated, which occupied a large domain in the phase diagram. Apart from these on-surface phases discussed above, we also investigated an ensuing state with 1 ML nitrogen atoms adsorbed on the surface and another 1 ML atoms diffused into the sub-surface interstitial sites. What’s more, by further increasing the Δμ_N to a larger value of −1.17 eV, we would intriguingly find a direct phase transition to C(4 × 2)-2 ML state without undergoing the corresponding C(4 × 2)-1 ML surface structure, which indicated that the 1 ML on-surface configuration never corresponds to a thermodynamically stable phase.

Fig. 10 The calculated Gibbs energy of adsorption energy ΔG for surface structures versus the nitrogen chemical potential Δμ_N: all unfavorable adsorption phases are indicated in grey, while colored think lines indicate thermodynamically stable phases.

4. Conclusion

In the present work, we systematically investigated the adsorption of nitrogen atoms and the dissociation of nitrogen molecules on the α-U(001) surface, as well as the surface phase diagram for the adsorption of nitrogen onto the α-U(001) surface through DFT calculations. The strong 5f electron–electron correlation and the relativistic SOC effects on the adsorption of nitrogen onto the C(3 × 2) α-U(001) surface were tested and it was found that the adsorption energies, structural parameters and Bader charge were not significantly affected.

The effect of N-coverage (ranging from 1/12 ML to 1 ML) on the adsorption features was investigated. For low coverage (Θ ≤ 1/3 ML), the nitrogen adatoms continuously located the next-nearest neighboring hollow1 sites, and composed a periodic zigzag chain at the coverage of 1/3 ML. The U surface reconstructed severely at higher N coverages, and this phenomenon disappeared until the N atoms fully covered the surface, with each adsorbate equally residing in the hollow1 sites and leading to the weakest average absorption energy, which was attributed to the significant lateral coulomb repulsion among the adatoms.

The dissociative adsorption of the N₂ molecule was also investigated with three different orientations at five adsorption sites. It was found that two horizontal structures on the long-bridge site existed for completely N₂ dissociative adsorption with adsorption energies of about 4 eV, and it was easy to overcome the low energy barrier of 0.09 eV to reach the most stable configuration where two N atoms stably resided in the next-nearest neighboring hollow1 sites. Two dissociative N atoms accepted the same net charge of 1.38|e| from their nearby surface U atoms, and the electronic structures exhibited some degree of overlapping and mixing between the N 2p and U 5f/6d states within the range −4.5 eV to −3 eV.

Finally, the surface phase diagram for equilibrium nitrogen adsorption on the α-U(001) surface was obtained by ab initio atomistic thermodynamics. It was found that the clean U(001) surface would be the most stable system state under the corresponding Δμ_N of −2.20 eV, and with increasing value of Δμ_N several structures of C(3 × 2)-1/3 ML, C(4 × 2)-3/8 ML, C(3 × 2)-1/2 ML and C(3 × 2)-3/4 ML gradually became the favorable phase. It was interesting to find a direct phase transition from the C(3 × 2)-3/4 ML to the C(4 × 2)-2 ML state when the Δμ_N was larger than −1.17 eV.

Acknowledgements

We gratefully acknowledge many helpful discussions with Dr Zhenhua Zeng (Purdue University). This work was financially supported by the National Natural Science Foundation of China (NSFC-NSAF 10976009, NSFC 51371080). The work was carried out at National Supercomputer Centers in Changsha and Tianjin, and the calculations were performed on TianHe-1(A).

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