Identification of an AgS2 Complex on Ag(110)

Adsorbed sulfur has been investigated on the Ag(110) surface at two different coverages, 0.02 and 0.25 monolayers. At the lower coverage, only sulfur adatoms are present. At the higher coverage, there are additional bright features which we identify as linear, independent AgS2 complexes. This identification is based upon density functional theory (DFT) and its comparison with experimental observations including bias dependence and separation between complexes. DFT also predicts the absence of AgS2 complexes at low coverage, and the development of AgS2 complexes around a coverage of 0.25 monolayers of sulfur, as is experimentally observed. To our knowledge, this is the first example of an isolated linear sulfur-metal-sulfur complex.

Silver is an important industrial catalyst that plays a role in reactions such as epoxidation of ethylene [1][2][3][4] , dehydrogenation of methanol [5][6][7][8] , and oxidation of CO [9][10][11] . Because of this, the interactions of oxygen with silver substrates or supported silver nanoparticles have been studied extensively [12][13][14][15][16][17][18][19] . While sulfur has not received as much attention as oxygen, many studies have examined sulfur-containing molecules on silver surfaces due to the widely known tarnishing of silver by sulfur containing vapors in the atmosphere [20][21][22] . Also, sulfur is a known poisoning agent for many metal catalysts 23,24 , so it is important to understand the effects that adsorbed sulfur can have on metal nanoparticles.
Sulfur is also known as an important adsorbate in terms of affecting the stability of nanoparticles, i.e. increasing their susceptibility to coarsening. Previous coarsening studies of adsorbed sulfur on coinage metal surfaces have shown that even trace amounts of sulfur lead to a dramatic destabilization of metal nanoislands on the surface [25][26][27] . There is mounting evidence that supports the reason for the accelerated destabilization of the metal islands as being the formation of mobile surface mass carriers 28,29 . The mass carriers are proposed to be metal sulfur complexes. For the coinage metal surfaces, metal-sulfur complexes were observed with low-temperature STM on Cu(111) 28 , Ag(111) 29 , and Au(100) 30 , with structures proposed for each of the complexes. A common motif observed in these metal-sulfur complex structures is a linear sulfur-metal-sulfur unit, although that unit does not exist-or at least, has not been observed-independently from the larger complexes. In this paper, we will show for the first time (to our knowledge) that it can be isolated and observed directly, when sulfur is adsorbed on the Ag(110) surface.
A related system, sulfur on Cu(110), has been studied at sub-monolayer sulfur coverages. It was found that S adatoms coexist with possible Cu x S y clusters 31 . No detailed structures of these clusters have been proposed and the clusters were imaged at 77 K, leading to the clusters appearing streaky or fuzzy in STM images due to the clusters being semi-mobile on the surface. In another related system, it has been demonstrated using low-temperature STM, that oxygen on Ag(110) can produce a variety of features 32,33 . Two of these features contain a linear O-Ag-O structure. One feature is a zigzag chain of -O-Ag-O-Ag-O-aligned along the [1 −1 0] direction 32 . The zigzag chain is composed of silver atoms within a row of the substrate being partially displaced vertically and the oxygen occupying three-fold hollow sites along the substrate rows. The chain can be regarded as oxygen atoms densely decorating a pre-existing row of Ag atoms. The second feature is an isolated, linear O-Ag-O unit, where the central Ag atom is embedded in (but slightly displaced from) a pre-existing row of Ag atoms 33 . It was proposed that the embedded complex can detach from its lateral surroundings and become "free, " hence aiding in the creation of surface vacancies. These "free" AgO 2 complexes may serve as the building blocks of the Ag(110)-O-(2 × 1) added row reconstruction 33 . However, they were not observed directly. In this paper we will show that there are some similarities but also major differences between AgO 2 complexes and AgS 2 complexes on this surface. This paper is organized as follows. Section 2 describes the experimental and computational methods. Section 3 presents the results, and Section 4 is a discussion. Auxiliary information is given in the Supplemental Information.
www.nature.com/scientificreports www.nature.com/scientificreports/ Methods Experimental details. More detailed description of experimental conditions are provided elsewhere 34 . To summarize, a single Ag(110) crystal was cleaned via Ar + sputtering and annealing cycles. S 2 (gas) was generated with the sample held at room temperature by an electrochemical evaporator that has been described in previous studies 28,30,[34][35][36] . Sulfur coverage (θ S ), in units of monolayers, was determined by counting protrusions in STM images in a given area (individual S adatoms associated with small protrusions and the brighter and larger protrusions with 2 S), and taking the ratio of S atoms to the number of Ag atoms in the Ag(110) surface plane.
The primary experimental technique was low temperature STM, imaging at 5 K. The XY (in-plane) piezoelectrics were calibrated against the p(1 × 1) of the clean Ag(110) substrate; consequently, lengths measured along the [1 −1 0] direction were multiplied by a factor of 1.1. There was no significant distortion in the [1 0 0] direction. All dimensions are reported accordingly, though the STM images themselves remain unadjusted. The Z (vertical) calibration was checked using step heights, and agreement with the expected bulk value was within 1.4%. All tunneling voltages, V S , are given as sample bias.
Computational details. Energetics. Energetics were assessed by methods similar to those employed in earlier work 30,[37][38][39] . Briefly, DFT calculations were performed using the plane-wave based VASP code 40 with standard PAW potentials 41 optimized for the PBE method 42,43 that were distributed with versions 5.2 and higher. The energy cutoff was 280 eV. Gamma centered k-point grids that correspond approximately to (24 × 17 × 1) for primitive (1 × 1) cells were used. All atoms in a slab were allowed to relax except the bottom layer. Energies were averaged over values for slabs in a range of thicknesses, L = 7 to 12 (in layers), to mitigate quantum size effects 44 which are strong on Ag(110) 45 . Error bars in graphs, and parentheses in numerical values, show estimated uncertainties due to different slab thicknesses unless otherwise stated.
The relative stability of species that (potentially) incorporate both S and Ag, such as complexes and reconstructions, must reflect the energetic cost of providing both. The chemical potential per S atom, µ S , serves this purpose, where µ S is defined as: here E is energy, while µ Ag is the chemical potential of Ag in the bulk metal (at 0 K), which equals the bulk cohesive energy and serves as the energy reference point for the metal. If bulk and surface are equilibrated, µ Ag also equals the binding energy of a Ag atom at a kink site 46 . The energy of the triplet state of the gas-phase dimer, E(S 2,g ), serves as the energy reference point for S. Choosing gas-phase S 2 reduces the significant ambiguity and error that would arise in the calculation of the self-energy of an atom using DFT. Since a positive µ S thus defined means the system is unstable towards associative desorption of S 2 , it is also more physically relevant. The integers m and n are the number of Ag and S atoms in the complex, respectively. When m = 0, µ S is simply the adsorption energy of the S adatom.
Simulating STM images. Elsewhere 34 , we have described the modified Tersoff-Hamann method 47,48 used to generate simulated STM images using DFT. For purposes of comparison with experimental data, two main parameters are the tunneling current I, and the bias voltage V S , which together fix the gap between tip and sample. In the simulations, I can only be expressed in arbitrary units, but a low current of I = 1 × 10 −3 a.u. corresponds to a realistic gap of 0.5-0.8 nm, whereas larger I correspond to smaller, less realistic gaps. In turn, achieving low I places certain demands on the calculations. The vacuum between slabs must be large and the energy cutoff must be high, to ensure appropriate exponential decay of electron density into vacuum. In this work we use 600 eV and 2.1 nm for image simulation, respectively. For image simulation, we also average over various values of L = 7 to 12.

Experimental and Computational Results
Sulfur adatoms at very low coverage. At low sulfur coverage, only sulfur adatoms are observed. They are illustrated in Fig. 1 for θ S = 0.02 ML, where each bright spot surrounded by a dark ring (sombrero) corresponds to a sulfur atom. The full-width at half-maximum (FWHM) of the central protrusion, at negative V S , is 0.31 ± 0.04 nm, which compares favorably with sizes of single sulfur adatoms measured under comparable conditions on Ag(100) 34 , Cu(100) 35 , and Au(111) 36 , where the FWHM ranges from 0.34 to 0.38 nm. Furthermore, as has been reported previously 34 , the central protrusion in these features disappears with increasing V S , leaving only a dark depression at sufficiently positive V S . The reason for this was clarified from DFT 34 ; in short, the change in appearance is caused by different rates of change in through-surface and through-adsorbate conductances 49 as V S increases. This transition from protrusion to depression with increasing V S is thus expected for sulfur adatoms on Ag(110), from DFT. Finally, the preferred adsorption site of the sulfur adatom is the two-fold hollow site, in the trough, as illustrated in Fig. 2a. DFT shows that this is favored over other high-symmetry sites, based upon the values of chemical potential μ S given in Fig. 2. Sulfur is known to occupy this site on other structurally-similar surfaces: Cu(110) 50 , Ni(110) 51,52 , and Rh(110) 53 . Later, we will show that DFT also predicts that sulfur adatoms are more stable than sulfur complexes at low coverages θ S  0.25 ML, hence reinforcing the conclusion that these sombreros are sulfur adatoms. www.nature.com/scientificreports www.nature.com/scientificreports/ sombreros but with a reduction in height [ Fig. 3b]. This is consistent with the prediction from DFT and previous observations with STM, showing that the bias-dependence weakens as θ S increases 34 .

Coexisting bright features and
Sulfur adatoms exhibit local ordering at θ S = 0.25 ML. Approximately half the S adatoms exist in small chains that are 2-5 S atoms long in the [1 −1 0] direction [ Fig. 4a, ovals]. The spacing between S adatoms in a chain is 0.44 ± 0.02 nm, which is 2a 1 (2x larger than the experimental unit cell length in the [1 −1 0] direction, a 1 is 0.22 nm experimentally). In some regions local p(2 × 2) order emerges, as in Fig. 4b (ovals).
The second feature existing at this coverage is brighter and larger than a S adatom. Two examples are encircled in Fig. 4c. It is common to find these features grouped into chains, 2-7 units long, along the [1 −1 0] direction. Their bias dependence clearly distinguishes these features from S adatoms. As shown in Fig. 3c, the height of the bright features does not change with V S , remaining constant at 0.025 ± 0.003 nm, in contrast to the behavior of the S adatom features shown in Fig. 3b. The bright features do show a more subtle bias dependence, such that as the sign of V S is switched, the shape changes from being oval-shaped, elongated in the [1 −1 0] direction, to being more circular. This can be seen in In addition, the bright features exhibit different short-range order. The separation within the bright chains is 0.66 ± 0.03 nm, which is 3a 1 , rather than the 2a 1 spacing that is common between S adatoms.
Finally, the bright chains are often collinear with chains of S adatoms. This indicates that the bright features are centered above the troughs, like the S adatoms in Fig. 2a.
To summarize, the bright features differ from S adatoms in three major respects: Size, response to V S , and spacing within chains. Based on the following information, these bright features are identified as AgS 2 complexes.
Identification of AgS 2 complexes from DFT. All DFT calculations described below were done with the PBE functional unless noted otherwise.
We have calculated the chemical potential of sulfur, μ S , for many configurations of S and Ag atoms on the Ag(110) surface. It is convenient to show the results as μ S vs. 1/θ S , as in Fig. 6. With this choice of axes, we connect selected phases of the system by linear segments to form a convex hull of chemisorbed phases. More detail about the construction of the convex hull is given in the SI. This μ S vs. 1/θ S construction allows the chemisorbed phase composition at any coverage to be predicted from the well-known lever rule of thermodynamics, i.e. the solid lines can be treated as tie-lines. The main phases at θ S ≤ 0.5 are the c(2 × 2) with θ S = 0.5, and the p(2 × 2)  www.nature.com/scientificreports www.nature.com/scientificreports/ with θ S = 0.25. It can be seen that the coverage dependence of the adsorption energy is very small (<0.02 eV), for θ S ≤ 0.25. The stability of the p(2 × 2) phase is consistent with the STM observations above.
DFT also reveals the nature of the bright features. Among the complexes and reconstructions considered, the best fit to the experimental data is given by AgS 2 complexes, where each complex is linear and aligned with the [1 −1 0] direction. The most stable configuration of such a complex has the Ag atom in each AgS 2 unit above a two-fold hollow site and separated by 3a 1 from its neighbor, as shown in Fig. 7a,b. The separation of 3a 1 agrees exactly with experiment. Furthermore, the most stable phases have the AgS 2 complexes arranged in simple rectangular patterns, rather than staggered. This also fits the experimental observation. The chemical potentials of such simple AgS 2 phases are shown by the red circles in Fig. 6, relative to the baseline of chemisorbed phases. At low coverage, the AgS 2 phase is slightly less stable than the S adatom phase, but close to θ S = 0.25, it crosses  www.nature.com/scientificreports www.nature.com/scientificreports/ over and becomes more stable than the S adatom phase. This is due mainly to variation in μ S for the S adatom phases, since values for AgS 2 phases are nearly constant. This crossover also agrees very well with experiment, which shows coexistence of these two phases at θ S = 0.25. At higher coverage, µ S of both AgS 2 and chemisorbed phases rises sharply, but the value for AgS 2 remains below the chemisorbed baseline, predicting that AgS 2 complexes should be observed. We caution, however, that reconstructions may also become competitive at higher coverages.
Further evidence comes from examining the bias dependence using DFT. Results are shown in Fig. 8 for different values of I and V S . As noted in Sec. 2, a value of I ≅ 0.001 a.u. should correspond to realistic experimental conditions. Two conclusions can be drawn from Fig. 8. First, the AgS 2 complex appears as a protrusion under all conditions, consistent with experimental data (Fig. 3c). The apparent height of the complex ranges from 0.077 to 0.055 nm as V S increases from −1.5 to 2.0 V. Second, the shape is elongated at negative voltage, but becomes rounder as bias voltage increases. This also agrees with experimental data (Fig. 3a and Fig. 5b,c).
In summary, the stability, periodicity, and bias dependence in STM images all confirm that the bright features are AgS 2 complexes. It is noteworthy that these are discrete complexes, i.e. they do not share Ag or S atoms. Their discreteness is also demonstrated by the fact that individual complexes exist that are not part of a chain, as in the circles of Fig. 4c.   Fig. 9a,b. These are fundamentally different than the linear rows of AgS 2 complexes shown in Fig. 7, since in the former case the AgS 2 complexes are independent, whereas in the latter case the zigzag chains consist of concatenated AgS 2 units, i.e. AgS 2 units sharing S atoms. Many more zigzag configurations have been considered. Illustrations and details of these DFT calculations are given in Table SI-3. The two structures in Fig. 9a,b are similar except that in Fig. 9a, top rows of Ag atoms are in two-fold hollow sites, i.e. bulk-terminated  www.nature.com/scientificreports www.nature.com/scientificreports/ sites. Consequently, S adatoms are in quasi-three-fold hollow sites. In Fig. 9b, top rows of Ag atoms occupy long bridge sites, which puts S adatoms in quasi-four-fold hollow sites. Despite the less-favorable coordination of the Ag atom, µ S is much lower for the latter configuration than the former. This must be due to the more favorable bonding of S at a four-fold hollow site, which is well-known 54,55 . The most stable zigzag phases all have Ag atoms in long bridge sites and S adatoms in quasi-four-fold hollow sites. Values of μ S for the most stable zigzag phases are shown as black squares in Fig. 6. They are significantly more stable than the adatom phases or the AgS 2 complex phases. However, they all have periodicity 2a 1 , which precludes them from consideration based on the experimental data.
Zigzag chains with a periodicity of 3a 1 are also considered because that is the periodicity seen in the experimental data. Schematics are shown as insets in Fig. 10 (Larger schematics are shown as Fig. VI and Fig. VII in SI). These zigzag structures of Fig. 10a,b are significantly less stable than the discrete AgS 2 complex phase (by 0.13 eV and 0.08 eV respectively, at fixed coverage of 0.33 ML using PBE). The zigzag structure of Fig. 10b is metastable and reconstructs at a larger slab thickness. The factor that mainly excludes these zigzag chains is the DFT simulated STM images (Fig. 10). The DFT simulated STM images of these zigzag chains do not match the shape and bias dependence of the bright features observed in experiments.

Consideration of the functional in DFT.
The absence of zigzag chains in experiment, yet their significantly higher stability in DFT (relative to the observed species, discrete AgS 2 complexes), poses a quandary. On one hand, one might argue that the DFT predicts equilibrium phases, and perhaps the surface is not equilibrated in experiment. In particular, phases which incorporate extra Ag adatoms (as do the zigzag phases) might be blocked by energetic barriers. We reject this argument, however, on the basis that the discrete AgS 2 species also involves incorporation of extra Ag, and this species is clearly observed. The other possibility is that the DFT is flawed. To examine this more carefully we perform additional DFT calculations using other functionals: RPBE, 56 optB88-vdW 57,58 , meta-GGA SCAN 59 , and SCAN + rVV10 60 functionals [ Table 1]. Since all three structures-p(2 × 2) of S adatoms, AgS 2 complexes, zigzag Ag-S chains-are compared at the same sulfur coverage of 0.25 ML S in Table 1, we can directly compare their relative stabilities using the difference in chemical potential (∆µ S ) relative to the (2 × 2) phase. For discrete AgS 2 complexes, all functionals predict a positive ∆µ S , ranging from 0.01 to 0.05 eV. There is much wider variation in ∆µ S for the zigzag chains, where it ranges from −0.2 to +0.02 eV (although in no case is the zigzag chain predicted to be less stable than AgS 2 complexes, i.e. no functional gives a result that is compatible with experiment). This wider variation in ∆µ S indicates that there are relatively large errors in DFT at the GGA level for the prediction of zigzag structure stability, which could explain the absence of zigzag structures in experimental observations.

Discussion
In this paper we have reported experimental and theoretical evidence of a discrete AgS 2 complex on Ag(110). These complexes coexist with atomic sulfur at 0.25 monolayers, but they are very distinctive from atomic sulfur.
It is interesting to compare these observations with others introduced in Sec. 1. First, as noted there, we have previously identified sulfur-metal complexes on surfaces of Ag(111), Cu(111), and Au(100), at extremely low sulfur coverages (<0.01 ML). The present observation is distinctive in the sense that it is the first observation of the independent MS 2 complex. In the previous studies, the MS 2 subunit was identified as a component of the larger complex, but it was not observed independently.
Second, O/Ag(110) and S/Ag(110) systems show some similarities but also differences. The obvious similarity is the report of AgO 2 and AgS 2 complexes. However, a major difference is in the source of the Ag atoms. In AgO 2 , the source is the Ag atoms in the Ag rows, and formation of the complex leads to vacancies in the rows. In the present work, the Ag rows are unperturbed and the Ag atoms in the AgS 2 complex must come from the two-dimensional Ag adatom gas (and, ultimately, from the Ag step edges). Another difference is in the experimental ability to isolate the discrete complex (unattached to other complexes or embedded in Ag rows). The discrete AgO 2 complex was not observed directly (though its existence was inferred from the observation of Ag vacancies and the development of the added-row reconstruction.) Instead, the complex was only observed directly in its embedded form, wherein it can be regarded as two chemisorbed oxygen atoms adjacent to a somewhat-displaced Ag atom within a Ag row. In the present work, the AgS 2 complex can be isolated and observed. The AgS 2 complex is not embedded but resides above the surface plane within the troughs of the substrate (Fig. 7). A final point of comparison arises from the zig-zag chains. These are clearly observed in the O/Ag(110) system, again embedded within the surface, where they can be regarded as oxygen atoms densely decorating the sides of pre-existing Ag rows. We do not observe such features in the S/Ag(110) system. Despite these differences, the common evidence that AgO 2 and AgS 2 complexes can form on the Ag(110) surface is very interesting, and may have broader ramifications, especially for interpreting mass transport. Specifically, it has been observed that both oxygen and sulfur can strongly accelerate coarsening on many coinage metal surfaces [26][27][28][29][30][31] . While M 3 S 3 is a strong candidate on the (111) surfaces, MS 2 and MO 2 are reasonable candidates for (110) and (100) surfaces. Indeed, AgS 2 was implicated (but never observed directly) in enhanced coarsening on Ag(100) 25 . The present work, in which AgS 2 is observed directly, lends credence to its existence on other surfaces.
Finally, it is interesting to comment on the strengths and weaknesses of the PBE functional in DFT as revealed by the present analysis. Considering only the discrete AgS 2 complex phase and the chemisorbed phases, DFT does remarkably well. It predicts that the chemisorbed phase alone will be observed with increasing coverage until 0.25 ML, and then the complex phase will emerge. This is exactly what is observed in the experiment. However, DFT with PBE breaks down when considering the relative stability of the concatenated zigzag phases; it predicts that these should be observed in experiment even at very low coverages (Fig. 6)-displacing the chemisorbed phases-but the zigzag structure is not observed at all. The relative stability of the zigzag phases is more sensitive to the functional than is the relative stability of the discrete complex phase, suggesting that DFT does not treat the zigzag phases accurately at the level of PBE. The reasons for this are not fully understood but may be related to underestimation of the Ag bulk cohesive energy in PBE.  www.nature.com/scientificreports www.nature.com/scientificreports/

Conclusion
In summary, adsorbed sulfur has been explored on Ag(110) surface at two different coverages, 0.02 and 0.25 ML. At 0.02 ML S, only sulfur adatoms are present. At 0.25 ML S, there is coexistence of sulfur adatoms and bright features. Sulfur adatoms exhibit local ordering in the form of short chains with sulfur adatoms separated by 2a 1 , or small local p(2 × 2). The bright features also form short chains but are separated by 3a 1 . These bright features are determined to be linear AgS 2 complexes from DFT. Experimental observations, such as bias dependence and separation of complexes, agree well with DFT prediction. DFT also predicts the absence of AgS 2 complexes at 0.02 ML, and the coexistence of S adatoms and AgS 2 complexes at 0.25 ML of sulfur, which is experimentally observed. Other phases are determined to be more stable than S adatoms and AgS 2 complexes, mainly zigzag Ag-S chains with a periodicity of 2a 1 , but are not considered to be the bright features due to periodicity mismatch. To our knowledge, this is the first example of an isolated linear MS 2 complex.