Computational analysis of the early stage of cuprous oxide sulphidation: a top-down process

ABSTRACT

The initial steps of Cu₂O sulphidation to Cu₂S have been studied using plane-wave density functional theory at the PBE-D3+U level of sophistication. Surface adsorption and dissociation of H₂S and H₂O, as well as the replacement reaction of lattice oxygen with sulphur, have been investigated for the most stable (111) and (100) surface facets under oxygen-lean conditions. We find that the (100) surface is more susceptible to sulphidation than the (111) surface, promoting both H₂S adsorption, dissociation and the continued oxygen–sulphur replacement. The results presented in this proceeding bridge previous results from high-vacuum experiments on ideal surface to more realistic corrosion conditions and set the grounds for future mechanistic studies. Potential implications on the long-term final disposal of spent nuclear fuel are discussed.

This paper is part of a supplement on the 6th International Workshop on Long-Term Prediction of Corrosion Damage in Nuclear Waste Systems.

GRAPHICAL ABSTRACT

KEYWORDS:

• Density functional theory
• sulphidation
• cuprite (Cu₂O)
• corrosion
• water (H₂O)
• hydrogen sulphide (H₂S)
• nuclear waste disposal
• chalcocite (Cu₂S)

Introduction

Regardless of the choice of concept, the safe disposal of spent nuclear fuel resides on a number of critical premises. In the KBS-3 model for final disposal under Swedish bedrock conditions, one such premise is the slow and uniform, sulphide-controlled corrosion of the copper waste canister [1,2]. This type of behaviour is believed to dominate during the main part of the repository life-time. The corrosion is assumed to be uniform since the sulphide film (mainly chalcocite, Cu₂S) is active under the predicted steady-state conditions [3–6]. However, in the initial phase of the disposal, the canister’s surface will be covered by passivating (hydr)oxide films, predominantly in the form of cuprite (Cu₂O) and other corrosion products, owing to surface oxidation during the prehandling process and residual O₂ trapped in the bore holes.

While the above could potentially pose a problem in the nuclear waste disposal, numerous studies have shown that the sulphidation process(1) ${\text{H}}_2\text{S}\left(\text{g}\right)+{\text{Cu}}_2\text{O}\left(\text{s}\right)\to {\text{H}}_2\text{O}\left(\text{l}\right)+{\text{Cu}}_2\text{S}\left(\text{s}\right)(\mathrm{\Delta }G{}^{\circ }=-144\text{kJ}\text{mo}{\text{l}}^{-1})$(1) occurs readily in aqueous environments and that the initial oxide film will be converted to the sulphide chalcocite (Cu₂S) [7–9]. The mechanism for this conversion, which is an important part in the understanding of sulphur-assisted degradation of passive films [10], is, nevertheless, not as well understood as the corrosion process. A correct description of the mechanism is necessary in order to obtain a comprehensive picture of the performance of the copper canister and to rule out the possibility of the formation of a passive film that may result in localised corrosion. It should be noted here that the present study assumes a somewhat simplified picture of the canister film composition: for instance are chloride-containing Cu(II) hydroxides, such as para-atacamite, also expected to form under early repository conditions.

Herein, we present results on the initial stage of the cuprite sulphidation process from density functional theory (DFT) calculations on the Cu₂O(111) and (100) low-index crystal surfaces. Computational chemistry has previously been successful in modelling similar problems [11,12] and allows for the study at the necessary atomic resolution. The current study should be seen as a first attempt to model the complex mechanism of Cu₂O sulphidation, setting the grounds for continued studies. We, therefore, include a perspective over the route ahead by describing the required future steps for understanding the sulphidation mechanism under different conditions. We also highlight the complementary roles of experiments and theoretical computations, where computational methods reinforce experiments by their ability to provide an atomic scale rationale to experimental results and by offering the possibility to make elaborate estimations into areas yet to be explored experimentally. Although our results are discussed in the perspective of the nuclear waste disposal, we also anticipate them to be of broader relevance, e.g. in heterogeneous catalysis, corrosion in the petroleum and chemical industry as well as for the corrosion of electronic materials [13].

Results and discussion

DFT calculations at the PBE-D3+U level of theory [14–17] were conducted on periodic slab models for (111) and (100) surfaces of Cu₂O as described in the computational methods section of the supplemental material. Both surface facets were represented by their most stable terminations under oxygen-lean conditions: the non-polar, stoichiometric O-terminated (111) surface and the Cu-terminated (100) surface, as shown in Figure 1 [18–21]. In the present study, we investigate the early stages of sulphidation of cuprous oxide under vacuum conditions. This is a necessary first step to understand the atomistic mechanism of sulphidation and ultimately provides us with $p{\text{H}}_2\text{O - }p{\text{H}}_2\text{S}$ phase diagrams for the surface sulphidation on the (111) and (100) low-index surface facets. By the use of thermodynamic relations and complementary experimental and computational data, these diagrams can be extended to cover also wet conditions, the effect of pH, sulphide concentration and impurities, to mention a few examples. Figures of all the optimised structures considered herein are included in the supplemental material.

Figure 1. Atomic models showing the top and side views of the ideal p(1×1) (111) and the copper terminated and c(2×2) ridge-dimer reconstructed (100) surface facet of Cu₂O. CS(CUS) = coordinatively (un)saturated atom.

Surface adsorption and reactions

Figure 2 shows the very initial stage of H₂S sulphidation of cuprite: the adsorption and dissociation of H₂S onto and at the surface. The equivalent processes are also shown for H₂O. These processes are experimentally relatively well studied by e.g. photoelectron spectroscopy and surface tunnelling microscopy on the Cu₂O(111) low-index surface under ultra-high vacuum conditions for both H₂O [22,23] and H₂S [24]. Although no quantitative adsorption data are available, Lin et al. [24] have shown that, at low coverage, H₂S completely dissociates on the Cu₂O(111) surface to form S²⁻ _ad and 2H_ad, where the latter are adsorbed on the surface O atoms. Water adsorbs molecularly on the ideal (111) surface [23,25–27], but as the mixture of H₂O_ad and OH_ad + H_ad on the oxygen vacant surface [22,26,27]. As can be seen in Figure 2, experimental and computational data are in qualitative agreement: DFT shows that H₂S adsorbs stronger than H₂O and its dissociation is more thermodynamically favourable than that of H₂O on the cuprite (111) surface (assuming identical H₂S and H₂O partial pressures). Where available, the computed DFT adsorption energies are in line with previous DFT calculations, see the supplemental material [23,25–30]. Note also that the relations of Figure 2 can be converted to arbitrary pressures via ΔG = −RTlnK.

Figure 2. Gibbs free energy surfaces for H₂X (X = O,S) adsorption and dissociation to H_ad + XH_ad and 2H_ad + X_ad on the (111) and (100) surfaces of Cu₂O at 298.15 K, p_H2O = p_H2S = 1 bar and p_H2 = 531 nbar (i.e. tropospheric annual mean [34]).

The (111) surface is the most stable [19,20] low-index surface of cuprite under various conditions and is accordingly the most common surface facet. However, many surface-related properties will be controlled by other, more reactive, surface facets. Therefore, we have also studied the less stable [19,20] low-index Cu₂O(100) surface. H₂O adsorption and dissociation have been studied both experimentally and computationally on the (100) surface [30–32]. In contrast, no data are available for H₂S interactions on the same surface.

Figure 2 also includes computed data for H₂O and H₂S on the (100) surface. We find similar trends as for the (111) surface, namely that H₂S adsorbs stronger and dissociates further than H₂O. In comparison to (111), it is evident that the (100) surface generally disfavours molecular adsorption but significantly promotes adsorbate dissociation. For the sulphidation process, the formation of S²⁻ _ad is likely a key step and the fact that it is more exothermic on the (100) surface than on the (111) surface is a strong indicator with regard to at which surface the oxide-to-sulphide conversion process is expected to dominate.

Sulphide-oxide replacement

The full sulphidation process is anticipated to pass through numerous elementary steps, with the possibility of different competing mechanistic routes [7]. The comprehensive investigation of all of these steps and mechanisms is beyond the scope of the present study. This will, however, be the topic of future studies. Nevertheless, the most fundamental knowledge is, arguably, understanding of the overall process leading from nH₂S to nH₂O with n lattice O²⁻ replaced by n S²⁻. This is studied in the following and will provide us the thermodynamic driving force for the surface sulphidation reaction.

Table 1 summarises our results for the H₂S_ad + Cu₂O_surf → H₂O_ad + Cu₂S_surf reaction at low degrees of sulphidation. Sulphidation leading to S²⁻ at different lattice positions, including the first subsurface layers, was considered. We find from this that sulphidation of the top layer is beneficial over sulphidation of the subsurface layer for both the (111) and (100) surface facets. The result is reasonable since Cu₂O and Cu₂S have dissimilar crystal structures and thus placing the larger S²⁻ ion in a subsurface layer will add residual strain to the structure. The result is also reasonable since the sulphidation energy is expected to converge towards that of the bulk reaction for subsurface replacement. From our study, we can, furthermore, conclude that the (100) surface is more easily sulphidised than the (111) surface, which may most conveniently be explained by the fact that the (100) surface atoms have a lower degree of saturation (i.e. lower coordination number) than the (111) surface atoms. Additionally, the results show that the adsorbed H₂O molecule formed during the replacement process has a stabilising effect on adjacent S²⁻, and more so on the surface exchange than for subsurface exchange. For the (100) surface, the water stabilisation has the effect of retaining the sulphur atom inside the lattice, whereas without the (H₂O)_ad the sulphur atom instead prefers to migrate to a site on top of the surface.

Table 1. Relative electronic energies, ΔE_sulph, in kJ mol⁻¹ for the low degree (25%) surface and subsurface Cu₂O sulphidation process defined by: H₂S_ad + Cu₂O_surf/sub → H₂O_ad + Cu₂S_surf/sub.

Index	Layer	Site^a	ΔEsulph
(111)	Surf.	${\text{O}}_{\mathrm{CUS}}$^b	−178.5
(111)	Surf.	${\text{O}}_{\mathrm{CS}}$^b	−149.2
(111)	Sub.	${\text{O}}_{\mathrm{Sub}/{\mathrm{O}}_{\mathrm{CUS}}}^{\mathrm{W}}$	−93.4
(111)	Sub.	${\text{O}}_{\mathrm{Sub}/{\mathrm{O}}_{\mathrm{CUS}}}$	−89.2
(111)	Sub.	${\text{O}}_{\mathrm{Sub}/\mathrm{C}{\mathrm{u}}_{\mathrm{CUS}}}^{\mathrm{W}}$	−118.6
(111)	Sub.	${\text{O}}_{\mathrm{Sub}/\mathrm{C}{\mathrm{u}}_{\mathrm{CUS}}}$	−114.1
(100)	Surf.	${\text{O}}_{\mathrm{Surf}}^{\mathrm{W}}$	−142.3
(100)	Surf.	${\text{O}}_{\mathrm{Surf}}$	−281.5
(100)	Sub.	${\text{O}}_{\mathrm{Sub}}^{\mathrm{W}}$	−119.7
(100)	Sub.	${\text{O}}_{\mathrm{Sub}}$	−108.4

^aSuperscript W indicates site adjacent to/underneath H₂O_ad.

^bCS(CUS) = coordinatively (un)saturated, see Figure 1 for depiction.

Larger degrees of sulphidation were also studied via the reaction nH₂S(g) + nCu₂O_surf → nH₂O(g) + nCu₂S_surf. Based on the conclusions from the low degree of sulphidation, we assumed that the process would first proceed to a full top layer of Cu₂S before the subsurface layer is sulphidised. Thus only top layer surface replacement is considered in the following. We also conclude that, although the H₂O adsorbent does have a stabilising effect on the replacement, the effects are small compared to other aspects and the overall trends can be recovered by considering H₂O (and H₂S) in gas phase. All unique combinations of replacement to surface layer site(s) were considered, where the lowest energy structures for each degree of sulphidation were used in the analysis below. The full results are reported in the supplemental material.

Figure 3 shows the free energy profile for the successive sulphidation of the (111) and (100) surfaces at 298.15 K, assuming standard pressures of 1 bar for all species. At these conditions, full sulphidation of the top layer is beneficial for both the surface facets. By converting the free energies to arbitrary pressures of H₂O and H₂S at 298.15 K, we obtain the phase diagrams (Figure S5) in the supplemental information. These pinpoint that the stability region for the sulphidised surface is large on both surfaces: a fully Cu₂S terminated Cu₂O surface is beneficial under essentially all realistic, oxygen-lean, conditions for both the (111) and (100) surfaces, in agreement with experimental findings [24,33]. We again find that the (100) surface is more readily sulphidised than the (111) surface. Note that at high pressures, cooperative adsorbate effects may alter the relative stabilities of the sulphidised surfaces.

Figure 3. Standard Gibbs free energy profile for step-wise (0, 25, 50, 75 and 100%) surface sulphidation of the (111) and (100) Cu₂O surface facets at 298.15 K.

Conclusion

The results presented herein on the initial sulphidation process of the Cu₂O(111) and Cu₂O(100) surfaces aim to bridge our knowledge from experimental ultra-high vacuum conditions to realistic conditions applicable to the predicted conditions in nuclear waste repository vaults. H₂O and H₂S adsorption and dissociation have been studied by DFT, indicating that H₂S adsorption and dissociation are more beneficial than the corresponding processes for H₂O on the (111) surface, in line with experimental results. We find the same trends for the (100) surface, where H₂S interactions have not yet been studied experimentally. We have also established that the (100) surface adsorbs both H₂O and H₂S stronger than the (111) surface and that adsorption is molecular for H₂O onto (111) and dissociative to OH⁻ _ad on (100). H₂S_ad dissociates to S²⁻ _ad on both surface with the dissociation being more exothermic on (100).

By the study of O²⁻ à S²⁻ lattice replacement reaction, we have found that the (100) surface is more readily sulphidised than the (111) surface. Furthermore, it is more beneficial to sulphidise the surface top layer in comparison to the subsurface layer at low degrees of sulphidation for both surface facets. From an extended analysis at larger degrees of sulphidation, we conclude that complete sulphidation of the top layer is favourable under realistic Swedish nuclear waste repository conditions. In future studies, we intend to investigate the sulphidation mechanism, in further detail, on ideal as well as defective surfaces. We also intend to analyse a wider range of conditions, including the effects of aqueous and oxygen-rich environments.

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

J. H. Stenlid http://orcid.org/0000-0003-3832-2331

A. J. Johansson http://orcid.org/0000-0001-7686-7776

C. Leygraf http://orcid.org/0000-0002-9453-1333

T. Brinck http://orcid.org/0000-0003-2673-075X

Additional information

Funding

This work was supported by the Swedish Nuclear Fuel and Waste Management Company (SKB) and by the excellence stipend of the School of Chemical Science and Engineering at KTH (to JHS). The computations were carried out at recourses provided by the Swedish National Infrastructure for Computing (SNIC) at the National Supercomputer Centre in Linköping University NSC.