Theoretical study of Sn adsorbed on the Au(1 1 1) surface

Computational Materials Science 127 (2017) 48–59

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Theoretical study of Sn adsorbed on the Au(1 1 1) surface Lorena A. Meier, Norberto J. Castellani ⇑ IFISUR, Universidad Nacional del Sur, CONICET, Departamento de Física - UNS, Av. L. N. Alem 1253, B8000CPB Bahía Blanca, Argentina

a r t i c l e

i n f o

a b s t r a c t

Article history: Received 29 March 2016 Received in revised form 3 October 2016 Accepted 10 October 2016 Available online 31 October 2016

In the present work, the adsorption of Sn atoms on the Au(1 1 1) surface was theoretically studied in the framework of density functional theory with a slab model. The results show that the most likely site for the adsorption of Sn is the FCC hollow site at low Sn coverage while at full monolayer degeneracy is produced for the four possible adsorption sites. The energy barrier for Sn surface diffusion is of near 0.1 eV at low coverage and negligible at high coverage. The magnitude of the Sn adsorption energy, Eads, decreases as the overlayer grows. For high coverage values the Sn-Sn interaction has a predominant contribution to Eads. It was observed that for 1/2 ML coverage the adsorbed Sn atoms and the Au atoms of the first and second layers of the substrate can suffer a reordering, resulting in an important surface reconstruction, giving a surface alloy superstructure. An electronic transfer from tin to gold takes place, which is significant at low Sn coverage. The binding of Sn to Au was analyzed in terms of the electronic structure of the Sn/Au(1 1 1) system at different values of coverage. Ó 2016 Elsevier B.V. All rights reserved.

Keywords: Tin Au(1 1 1) Adsorption DFT

1. Introduction The interaction of a s-p metal as Sn with d-band metals was investigated in the past as a way to improve the catalytic and electrocatalytic properties of the pure d-band metal surfaces. The reaction pathways for the hydrogenation of butadiene on Pt/Sn alloys undergo important modifications when both metals are exposed [1]. Tin exerts a role of ligand that weakens the molecular adsorption and allows the coordination of double bonds prior to the hydrogenation, which decreases the energy barriers for the selective pathway to butene. The spontaneous Sn deposition on a Pt surface shows a superior activity toward adsorbed CO oxidation in comparison with pure Pt [2]. Recently, the spontaneous adsorption of Sn on Au(1 1 1) was studied with Scanning Tunneling Microscopy in relation to the electrocatalytic properties of this surface [3]. Only a few results using ultrahigh vacuum techniques on such system have been published in the past [4,5]. On the other hand, the Au-Sn interface was particularly studied regarding the diffusion process taking place in Au-Sn intermetallics [6] and Au/Sn junctions in nanowires and nanoparticles [7]. Regarding the previous theoretical works on the Sn/Au system, an atomistic simulation of Sn growth on Au(1 1 1) was performed with the Bozzolo-Ferrante-Smith method [8] for low Sn coverage (0.1–0.5 ML). Within this approach, Monte Carlo simulations at ⇑ Corresponding author. E-mail addresses: (N.J. Castellani).

[email protected]

(L.A.

http://dx.doi.org/10.1016/j.commatsci.2016.10.017 0927-0256/Ó 2016 Elsevier B.V. All rights reserved.

Meier),

[email protected]

room temperature show a close competition between surface alloying and layer-by-layer growth. Besides, in a recent work, Density Functional Theory (DFT) calculations with periodic conditions were applied to study the adsorption of atoms and dimers of group IV elements on Au(1 1 1) [9]. The corresponding results show that the interaction with the Au substrate decreases in the order C > Si > Ge > Sn. The electronic structure of a graphene-like Snsheet adsorbed on Au(1 1 1) was studied in another work because the adsorbate structure resembles the sp2-hybridized form of tin, commonly referred as stanene [10]. The adsorption of d- (Pd, Pt, Cu, Au) and p-metals (Sn, Pb, Bi) on Pt(1 1 1) was studied [11] and the electronic properties of Pt-Me surface alloys (Me: Au, Bi, In, Pb, Pd, Sn, Cu) was addressed [12], showing different behavior the p-metal counterpart of Pt in comparison with the d-metal counterpart. In the present approach the adsorption of Sn atoms on the (1 1 1) face of Au was theoretically investigated within the framework of DFT, representing the substrate with a slab model. Different Sn/Au(1 1 1) structures for increasing Sn coverage were studied, analyzing the corresponding electronic structure and the physical interactions involved between Sn and substrate atoms. 2. Theoretical details The results reported in this work are based on the DFT formalism and were implemented by means of the Vienna Ab-initio Simulation Program (VASP) [13,14]. In this code, the Kohn-Sham equations are solved employing a plane-wave basis and periodic

L.A. Meier, N.J. Castellani / Computational Materials Science 127 (2017) 48–59

boundary conditions. The valence electrons are treated within the scalar-relativistic approximation. Electron exchange and correlation effects are described by the generalized gradient approximation using the functional due to Perdew-Burke-Ernzerhof [15]. The electron–ion interactions are taken into account by the projector-augmented wave (PAW) potentials. The PAW method is a frozen core all-electron method that uses the exact shape of the valence wavefunctions instead of pseudo-wavefunctions [16,17]. The fixed convergence of the plane-wave expansion was obtained with a cut-off energy of 415 eV. The Au(1 1 1) system was represented by a slab model with a hexagonal surface cell of variable size according to Sn coverage. The repeated slab representing the Au(1 1 1) surface contains five layers of atoms and a vacuum gap in the normal direction. The width of this gap (12 Å) was optimized to minimize the interaction between slabs. Spurious effects due to image charges were eliminated by the dipolar correction for cells as implemented in VASP. The adsorption of Sn atoms were studied on the sites of high symmetry of the Au (1 1 1) surface: top, bridge, HCP hollow and FCC hollow sites, as schematized in Fig. 1. Four values of Sn coverage (h) were considered, h = 1/9 ML, 1/4 ML, 1/2 ML and 1 ML, using for that purpose the following primitive supercells of Sn adatoms: p(3
3), p (2
2), p(1
2) and p(1
1), respectively, as schematized in Fig. 2. Integrations in the first Brillouin zone were made using Monkhorst [18] grids of 3
3
1, 5
5
1, 9
7
1 and 9
9
1 k-points, respectively. The coordinates of tin and gold atoms of the four first layers of each Sn/Au(1 1 1) system were allowed to relax until the residual Hellmann-Feynman forces were below 0.02 eV/Å, while the Au atoms of the last two layers of the slab were frozen in their bulklike positions, with an equilibrium lattice constant of 4.17 Å, obtained by optimization of a bulk FCC Au structure, in good agreement with the experimental value [19] and other calculations [20]. In this work the unit vectors of supercell were maintained as fixed. This is an usual procedure in calculations to obtain the equilibrium geometry of adsorbed species on crystalline solid surfaces because the slab as model for a surface must satisfy the geometrical constraints coming from the bulk of substrate, particularly along the directions parallel to the exposed face of solid (see Refs. [21–23]). On the other hand, the cell of bulk FCC Au structure was optimized to attain the corresponding lattice parameter. The interaction energy between Sn atoms and Au(1 1 1) surface was calculated in terms of the adsorption energy per Sn atom defined as:

Eads ¼

1 ðEAu-Sn  EAu  NESn Þ N

ð1Þ

In this expression EAu-Sn is the total energy of Au-Sn system, EAu is the total energy of the clean Au substrate slab, ESn is the energy of the isolated Sn atom, and N is the number of adsorbed Sn atoms per cell. In this way, negative values for Eads correspond to exothermic processes. The vibrational frequencies of the adsorbed Sn atom

Fig. 1. Schematic view of the adsorption sites.

49

Fig. 2. Schematic view of the supercells for Sn/Au(1 1 1) system. Sn atoms: gray spheres, Au atoms: yellow spheres. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

were calculated by diagonalizing the Hessian matrix as implemented in VASP, considering a finite difference approach with a step size of 0.024 Å for the displacement of the adsorbed atom along each Cartesian coordinate. The electronic structure was analyzed by computing the projected density of electronic states (PDOS) of selected atomic states of Sn and Au atoms. For that purpose a grid of 15
15
1 k-points was used. Atomic net charges were calculated according to the Bader atoms-in-molecules method [24]. Moreover, the work function of the Sn/Au(1 1 1) system, /, was obtained for the different values of Sn coverage by the following expression:

/ ¼ Vð1Þ  EF

ð2Þ

where V(1) is the electrostatic potential in the vacuum at a distance from the surface where the microscopic potential has reached its asymptotic value and EF is the Fermi energy of the metallic slab [25]. All calculations were primarily performed at the non-spin polarized level. Several tests at different values of coverage performed at the spin polarized level show no difference with the non-spin polarized results. The inclusion of dispersive interactions according to the method of Grimme [26] produces negligible changes on the Eads values at low Sn coverage and an increase of only 3% in their magnitude at full monolayer, maintaining the relative stability of adsorption sites. Therefore all the results presented in the following section remain essentially unchanged if dispersive interactions were included. In addition, taking into account that both Sn and Au are heavy metals and that previously it was established that for stanene, spin-orbit coupling (SOC) effects are important in relation to the electronic structure of this system [10,27] a particular study was realized considering this term of the relativistic electron Hamiltonian. For that purpose

50

L.A. Meier, N.J. Castellani / Computational Materials Science 127 (2017) 48–59

[11], showing a change of 1.55 eV when h increases from 1/4 to 1 ML, with a value at h = 1/2, 4.21 eV, which is 0.23 eV more stable than that obtained here for Sn on Au(1 1 1) at the same level of coverage. With the purpose to study the effect of Sn coverage on adsorption energies, another procedure was accomplished where a (3
3) supercell with an increasing number of Sn atoms in the basis was used, each of them adsorbed on a FCC hollow site. The corresponding Eads results are plotted in Fig. 3 as a function of Sn coverage, showing a weakening of Sn-Au interaction as h increases. Notice that a linear relationship Eads vs. h could be established with a slop of dEads/dh = 0.780 eV/ML. This result can be compared with the values of 1.12 eV/ML, 2.47 eV/ML, 1.29 eV/ML, 1.88 eV/ML and 2.49 eV/ML for the S/Ag(1 1 1) [29], S/Co(0 0 0 1) [30], O/Pd(1 1 1) [31], N/Pd(1 1 1) [31] and C/Pd(1 1 1) [31] systems, respectively. They constitute other adsorbate/d-metal systems where the adsorbate has also s-p valence electrons. The case of h = 2/3 ML corresponds to the same Sn coverage where a graphene-like Sn-sheet was reported by Nigam et al. [10]. The adsorption energy obtained here with the (3
3) supercell for h = 2/3 ML is of 3.89 eV, compared the value of 3.30 eV of Ref. [10]. At h = 7/9 ML a decrease is produced of near 0.25 eV, followed by an increase of similar magnitude at h = 8/9 ML. The total electronic energies involved in the Eads values reported in Fig. 3 can be analyzed regarding the concept of differential adsorption energy, (DE)ads, to adsorb an atom of tin when there are present N  1 atoms previously adsorbed, defined as

self-consistent calculations with geometry optimization were performed with the SOC version of VASP. Recently, the SOC effects on cohesive and structural properties of heavy metals were considered employing this code [28].

3. Results and discussion In order to study the adsorption of Sn atoms on the Au(1 1 1) surface the four adsorption sites of high symmetry of the Au (1 1 1) surface were considered (see Fig. 1). The corresponding values of Eads and main geometrical parameters are summarized in Table 1. Notice that the FCC hollow is the most favored site for Sn coverage lower than a monolayer, followed by the HCP hollow site. Particularly, for h = 1/9 ML and 1/4 ML, the last site is 0.07 eV less favored. For full monolayer coverage the four sites have nearly the same adsorption energy, the top site being very slightly favored (by nearly 0.02–0.03 eV). Considering the hollow sites, the variation of the Eads as a function of coverage shows a monotonous increasing behavior between h = 1/9 and 1/2 ML. More specifically, for the FCC hollow site, the adsorption energy changes from 4.53 eV to 3.98 eV; after that, the Eads values increase slightly, arriving to 3.72 eV for h = 1 ML. In a previous theoretical work for the Sn/Au(1 1 1) system, performed with a slab of four Au layers, it was reported a Eads value of 4.82 eV [9] for Sn adsorbed on the FCC hollow site with a coverage of 1/16 ML. This value is particularly in good agreement with our result of 4.53 eV for h = 1/9 ML taking into account the above comment about the monotonous increasing behavior of Eads as a function of Sn coverage. Besides, in a recent work due to Nigam et al. [10], a study of Sn adsorption on Au(1 1 1) was performed also with a slab model of four Au layers, considering Sn coverage values of 1/25 ML and 2/3 ML, the last case corresponding to a graphene-like hexagonal arrange. Their results indicate that the FCC and HCP hollow sites are the most favored, in agreement with our calculations. Moreover, they found as here, that for the lowest Sn coverage (1/25 ML) the Sn atoms adsorbed on the less coordinated sites eventually move to the FCC sites. The adsorption energy values per Sn atom obtained from their reported Sn binding energies for the FCC site are very similar for both values of Sn coverage, i.e., 3.35 eV and 3.30 eV, for h = 1/25 and 2/3, respectively. In our calculations for the same site we have a variation of 0.55 eV in the range of h between 1/9 and 1/2 ML and a variation of 0.81 eV in the range of h between 1/9 and 1 ML (see Table 1). Interestingly, in other previous work, the adsorption of Sn on Pt(1 1 1) was theoretically evaluated for different values of Sn coverage

ðDEÞads ¼ EAu-Sn ðNÞ  EAu-Sn ðN  1Þ  ESn

ð3Þ

In this expression EAu-Sn(N) is the total energy of Au-Sn system with N atoms of tin in the unit cell, EAu-Sn(N  1) is the total energy of AuSn system with N  1 atoms of tin in the unit cell and ESn is the energy of the isolated Sn atom. The corresponding results of (DE)ads are plotted in Fig. 4 as a function of Sn coverage. We notice that the formation of a Sn layer is always an exothermic process, up to the level of coverage evaluated here. Nevertheless, we can outline that, with the exception of the relative large energy delivery for h = 8/9, this process becomes more difficult as h increases. From Table 1 we can observe that the Sn-Au distance for the hollow sites does not change between h = 1/9 ML and h = 1/4 ML, with a value of 2.72 Å, but it undergoes a non negligible stretching of 0.13 Å for h = 1/2 ML and a more significant one of 0.40 Å in the case of full monolayer coverage. Moreover, and according to Table 2, for Sn adsorbed on these sites the mean interplanar distance z12 between the first and second Au layers undergoes a stretching that increases with h, in the interval 0.02–0.05 Å, in

Table 1 Adsorption energy and geometrical parameters for Sn/Au(1 1 1) system. Site

(3
3)Sn h = 1/9 ML Eads (eV)

hSn-Au (Å)b a

dSn-Au (Å)

Top

a

3.67

2.54 2.13a

2.54

Bridge

4.42a

2.08a 1.87a

FCC hollow

4.53

HCP hollow

4.46

Reconstructed a

(2
2)Sn h = 1/4 ML

a

Eads (eV) a

2.66a

2.02 2.08 2.04 2.12

(1
2)Sn h = 1/2 ML hSn-Au (Å)b

dSn-Au (Å)

Eads (eV)

2.55 1.93a

a

2.55

3.78

4.06a

2.16a 2.16a

2.67a

2.72

4.17

2.01 2.07

2.72

4.10

2.02 2.08

3.42

a

a

(1
1)Sn h = 1 ML hSn-Au (Å)b a

dSn-Au (Å) a

Eads (eV)

hSn-Au (Å)b

dSn-Au (Å)

3.75

2.76 2.76

2.76

2.58 2.76a

2.76

3.94

2.24 2.24

2.77

3.73

2.60 2.60

2.99

2.72

3.98

2.24 2.24

2.85

3.72

2.59 2.59

3.12

2.72

3.97

2.25 2.25

2.86

3.73

2.57 2.57

3.10

3.86

2.60 1.03

2.77 2.83

Obtained by constraining the geometry of Au atom on the (1 1 1) plane (with fixed x and y coordinates). The first value corresponds to the normal distance to the plane intersecting the nearest Au atom/atoms underneath the Sn atom, the second value to the normal distance to the plane intersecting the next nearest Au atoms. b

L.A. Meier, N.J. Castellani / Computational Materials Science 127 (2017) 48–59

Fig. 3. Eads calculated with a (3
3) supercell for the FCC hollow site as a function of Sn coverage.

Fig. 4. (DE)ads calculated with a (3
3) supercell for the FCC hollow site as a function of Sn coverage.

comparison with the bare Au(1 1 1) value of 2.44 Å. In particular, the Au atoms of the first layer most affected are the first near neighbors of Sn atoms, for which the vertical distance with respect to the second Au layer undergo a stretching of 0.05–0.06 Å, for all values of Sn coverage (see Table 2). On the other hand, the mean interplanar distance z23 between the second and third Au layers shows only a minor stretching of about 0.01 Å (bare Au(1 1 1) value: 2.40 Å). Regarding the geometry for full monolayer coverage it is interesting to note that in the case of hollow sites the trigonal symmetry becomes slightly distorted: the Sn-Au distance is smaller by 0.30 Å for one of the three Au atoms of the adsorption site as it is schematized in Fig. 5. For the lowest values of Sn coverage here considered, h = 1/9 and 1/4 ML, it was observed that the top and bridge sites are unstable sites of the Potential Energy Surface (PES). In order to analyze the topography of PES, the minimal total energy was obtained by

Table 2 Variation of interplanar z12 and z23 distances for the FCC hollow site of Sn/Au(1 1 1) system with respect pure Au(1 1 1) surface.a

Dz12 (Å)b Dz23 (Å) a

(3
3)Sn h = 1/9 ML

(2
2)Sn h = 1/4 ML

(1
2)Sn h = 1/2 ML

(1
1)Sn h = 1 ML

0.02/0.06 0.01

0.03/0.05 0.00

0.04/0.06 0.01

0.05/0.05 0.01

For pure Au(1 1 1) surface, z12 = 2.44 Å and z23 = 2.40 Å. The first value is a mean for the unit cell, the second corresponds to the change undergone by the first near neighbors of Sn atoms. b

51

Fig. 5. Schematic top view of distortion of FCC hollow site for h = 1 ML. Atom graphics as in Fig. 2.

constraining the geometry of the Sn atom on the (1 1 1) plane, keeping fixed its ‘‘x” and ‘‘y” coordinates and relaxing its ‘‘z” coordinate and all the coordinates of Au atoms of first three layers. It was observed that using this procedure the symmetry of the site (C6v for the top site and C2v for the bridge site) is not changed. In the case of h = 1/9 ML the Eads value for the constrained bridge site is 0.11 eV smaller in magnitude than that for the hollow sites, and the Eads value for the constrained top site is even smaller, 0.86 eV. When h = 1/4 ML we have a similar instability, with the magnitude of Eads being 0.11 eV and 0.75 eV smaller for the bridge and top sites, respectively. For h = 1/9 ML a distortion of the Au surface is produced underneath the adsorbed tin atom. In the case of the hollow sites the three nearest Au atoms of Sn rise by 0.06–0.08 Å with respect to the plane intersecting the next nearest Au atoms, as it can be observed examining the corresponding heights in Table 1. This very local effect produces a non negligible stretching of 0.02 Å for the mean interplanar distance z12, as it was commented above. Conversely, for the constrained top site the Au atom underneath the adsorbed Sn undergoes a drop of 0.41 Å with respect to the next Au atoms. This distortion is smaller (=0.22 Å) for the constrained bridge site but of the same sign. In Fig. 6 are depicted these two opposite behaviors. These distortions are likely related to the respective adsorption energy values: the constrained top site, which is the less stable, shows a larger Sn-Au distance in comparison with the hollow sites. A similar situation can be observed in the case of h = 1/4 ML. The adsorption energy values summarized in Table 1 can be viewed as stationary points of the PES for the Sn/Au(1 1 1) system. Their specific character, minima or saddle points, was studied by making a vibrational frequency analysis. In Table 3 the corresponding vibrational frequency values are reported. Looking at the results for low Sn coverage values (h = 1/9 and 1/4 ML) we notice that the top sites are second order points (with two imaginary frequencies for vibrations coplanar to the Au(1 1 1) surface) and that the bridge sites are first order points or transition states of the PES (with only one imaginary frequency for coplanar vibrations). The diffusion energy barrier of Sn atoms between FCC hollow sites on Au(1 1 1) can be obtained, giving a value of 0.11 eV for both Sn coverage values. When Sn atoms are constrained to be adsorbed on top sites for a greater Sn coverage of 1/2 ML, the first Au layer rearranges completely, giving a geometrical configuration that does not retain the top C6v symmetry. The Sn atoms remain aligned only with the Au atoms of the third substrate layer. As it can be verified from the vibrational frequencies of Table 3, these ‘‘quasi-top” sites constitute transition states of PES. On the other hand, from Table 3 we note also that the bridge sites are minima of PES. Since the Eads difference between a FCC hollow and a bridge site is of 0.04 eV it results that the diffusion is a much more easy process at h = 1/2 ML.

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L.A. Meier, N.J. Castellani / Computational Materials Science 127 (2017) 48–59

(a)

Δh=0.06 Å

(b)

Δh=-0.41 Å

Fig. 6. Schematic lateral view of distortions of FCC hollow (a) and constrained top (b) sites for h = 1/9 ML. Atom graphics as in Fig. 2.

Once the constraints for the Sn coordinates that are coplanar to the Au(1 1 1) face are liberated, the surface of Sn/Au(1 1 1) at h = 1/2 ML reconstructs, giving a new superstructure. The corresponding p(1
2) supercell has one Sn atom and two Au atoms placed at three different planes within the supercell, as depicted in Fig. 6. Notice that half of the atoms of the first bare Au(1 1 1) surface become displaced to form a plane in between the outermost Sn plane and the other inner Au plane. The atoms of the supercell basis have the following internal coordinates: for the first Au atom, 0 a + 0 b + 0 c, for the second Au atom, 0.569 a + 0.069 b + 0.605 c and for the Sn atom, 0.134 a + 0.134 b + 1 c, where a, b and c are the unit vectors whose lengths are 5.90 Å, 2.95 Å and 2.58 Å, respectively (see Fig. 7). The first Au atom of each supercell is placed near a FCC hollow site of the unreconstructed Au underlayer, but displaced by 0.99 Å along one of the medians of the site. In order to verify that this reconstruction is not an effect created by the supercell, the superstructure was tested with a (2
2) supercell. We arrived to an optimized geometry which is very similar to that obtained with the (1
2) supercell. The interplanar distances between the Sn layer and the first and second Au layers are slightly longer, by 1% and 0.8%, respectively. It is important to note that the magnitude of Sn adsorption energy on different adsorption sites, including those that are saddle points of PES follows, excepting the reconstructed site, the same top < bridge < HCP hollow < FCC hollow sequence for h = 1/9 ML, 1/4 ML and 1/2 ML. Moreover, we can observe that increasing the Sn coverage from h = 1/9 ML and h = 1/4 ML to h = 1/2 ML the top and bridge geometries changes from being second order points and transition states of the PES to transition states and local minimum, respectively. Therefore, the surface for h = 1/2 ML exhibits more stability considering the PES topography. For the last value of Sn coverage, the reconstructed site appears as an alternative structure from the energetic point of view, following the top < reconstructed site < bridge < HCP hollow < FCC hollow sequence. It can be argued that the reconstructed site satisfies the role of the top geometry when

we change from low Sn coverage to h = 1/2 ML. The last observation is in agreement with the fact that the reconstructed site is obtained relaxing the on-top configuration. This bimetallic superstructure, which can be considered as a surface alloy, corresponds to a minimum of PES that is only 0.12 eV less stable than the Sn/Au (1 1 1) surface h = 1/2 ML but with Sn occupying FCC hollow sites (see Tables 1 and 3). This result indicates that an increase of the substrate temperature is advisable to attain the production of a surface Sn-Au alloy, such as in previous experimental observations for low temperature coatings of Sn over Au(1 1 1) [4]. Recently it was reported that after the deposition of Sn [32] or Ge [33] on Ag(1 1 1) a stable surface alloy is produced for h = 1/3 ML according p p to a p( 3
3)R30° superstructure. As a complementary test on the energetic conditions that allow the formation of a surface SnAu bimetallic alloy, the energy involved in the exchange between an adsorbed Sn atom and a substrate Au atom, Eexchange, was evaluated. More specifically, the Eexchange energy was calculated according to the following equation:

Eexchange ¼ EAu=AuðSnÞ  ESn=AuðAuÞ

ð4Þ

where ESn/Au(Au) is the energy of Sn/Au(1 1 1) system with the Sn atom adsorbed on a HCP hollow site and EAu/Au(Sn) is the energy of the system for which the adsorbed Sn atom and the Au atom of the second subsurface layer were exchanged. A positive value for this energy implies an endothermic process. The obtained Eexchange values for h = 1/9 ML, 1/4 ML, 1/2 ML and 1 ML are 1.07 eV, 0.86 eV, 0.78 eV and 0.24 eV, respectively. These results show that in general the formation of a Sn-Au surface alloy would be an endothermic process, this condition being more exigent for low values of Sn coverage. Looking at Table 3 the frequencies corresponding to the PES minima at FCC or HCP hollow sites we can notice that they have similar values for h = 1/9 and 1/4 ML. The corresponding modes become softer as the Sn coverage increases: the perpendicular fz mode of the FCC hollow site, in particular, decreases from 139.19 cm1 for h = 1/9 to 76.80 cm1 for h = 1 ML, in agreement with the idea that at a larger Sn coverage the PES has little topographic structure and that the diffusion process is largely facilitated. In relation to the negative effect of coverage on the adsorption energy of Sn atoms on Au(1 1 1) an open question about the dominant factor governing this effect would be: it is due to a larger interaction between the Sn atoms or to a weakening of the Sn-Au interaction itself? In order to quantify the relevance of the Sn-Sn interaction in comparison with the Sn-Au interaction, a partitioning of the Eads energy per Sn atom into different contributions was performed, accordingly to the following methodology:

Eads ¼ Eads ¼

 1
EAu=Sn  EAu  NESn N

ð5Þ

 1
EAu=Sn  EAu  NESn þ ESn;layer  ESn;layer þ EAu;relax  EAu;relax N ð6Þ

Table 3 Vibrational frequencies for Sn/Au(1 1 1) system. Sitea

Top Bridge FCC hollow HCP hollow Reconstructed a

(3
3)Sn h = 1/9 ML

(2
2)Sn h = 1/4 ML

(1
2)Sn h = 1/2 ML

(1
1)Sn h = 1 ML

fz (cm1)

fx (cm1)

fy (cm1)

fz (cm1)

fx (cm1)

fy (cm1)

fz (cm1)

fx (cm1)

fy (cm1)

fz (cm1)

fx (cm1)

fy (cm1)

158.11 139.36 139.19 139.45

53.14 i 92.55 73.05 69.02

53.82 i 23.39 i 72.62 68.37

157.79 143.54 144.51 142.22

57.31 i 86.93 69.79 64.54

58.37 i 29.24 i 69.11 64.04

118.10 114.48 112.48 114.82 99.7

22.99 54.97 53.13 52.86 85.56

21.94 i 34.59 33.94 33.54 38.65

97.06 79.99 76.80 79.46

15.74 14.98 12.36 9.96

13.73 9.12 9.29 7.94

The corresponding geometrical parameters are those summarized in Table 1.

L.A. Meier, N.J. Castellani / Computational Materials Science 127 (2017) 48–59

Fig. 7. P(1
2)-Sn reconstructed superstructure for h = 1/2 ML. (a) Upper panel: lateral view. (b) Medium panel: top view, with unit cell. (c) Lower panel: perspective view. Sn atoms: gray spheres, Au1 atoms: yellow spheres with crossed motive, Au2 atoms: yellow spheres with border motive, Au atoms of substrate: yellow spheres. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

¼

 1
 1
EAu=Sn  EAu;relax  ESn;layer þ ESn;layer  NESn N N  1
EAu;relax  EAu þ N

ð7Þ

¼ E0ads þ ESn-Sn þ EAu;distor

ð8Þ 0

In this way the Eads energy has three contributions, E ads, the interaction energy of the Sn layer with the Au(1 1 1) surface, expressed per Sn atom, with both fragments (the Sn layer and the Au(1 1 1) surface) with the geometry identical to that present in the Sn/Au(1 1 1) system at equilibrium, ESn-Sn, the interaction energy between N Sn atoms to form a layer with the geometry of the Sn/Au(1 1 1) system, expressed per Sn atom, and EAu,distor, the distortion energy of Au(1 1 1) due to the relaxation of that surface to accommodate the Sn layer, expressed also per Sn atom. In order to calculate ESn-Sn it is necessary to compute ESn,layer, the total energy of the Sn layer with the geometry present in the adsorbed state, and to calculate EAu,distor, it is necessary to compute EAu,relax, the total energy of Au(1 1 1) relaxed to the geometry of the Sn/Au (1 1 1) system. The corresponding values of these energies have been summarized in Table 4 in the case of the FCC hollow sites with increasing Sn coverage and for the reconstructed surface at h = 1/2 ML. Considering the FCC hollow sites, we can notice that for Sn coverage values lower than 1/2 ML the stabilizing E0 ads contribution is largely predominant on Eads, while for h larger or equal to 1/2 ML the stabilizing ESn-Sn contribution is more relevant. The SnSn interaction represents only the 10% of the adsorption energy when h = 1/4 ML, while it reaches to 83% when h = 1 ML. The result

53

for low Sn coverage is reasonable because the Sn atoms are far away, while the relevance of the Sn-Sn contribution to the formation of Sn adlayer at high Sn coverage values can be related to the fact that the Sn-Sn distance for h = 1 ML, 2.95 Å, is near to the sum of atomic covalent radii of Sn atoms, 2.78 Å. The destabilizing contribution coming from distortion of the Au(1 1 1) surface generally is not a significant contribution at any Sn coverage. It can be noticed that whereas the EAu,distor energy decreases as the Sn coverage increases (with a value of 0.07 eV for h = 1/9 ML and being negligible for h = 1 ML), the local distortion measured by the z12 stretching is practically uniform (about 0.05–0.06 Å). This observation can be rationalized considering that the energy demanded to distort the z coordinate of each of the three Au atoms of a quasiisolated FCC hollow site (for low values of h) must be shared with the other vicinal hollow sites for a full monolayer coverage, resulting that the energy required for the same distortion in the last case (h = 1 ML) is about (or less) one third the value of the EAu,distor energy for low Sn coverage values. Regarding the reconstructed surface at h = 1/2 ML, both E0 ads and ESn-Sn contributions are of the same magnitude and the distortion is significant, reaching to 37% of the any of the other stabilizing energies. Interestingly, in the work due to Pašti and Mentus [11], the adsorption energy of Sn on Pt(1 1 1) was analyzed for different values of Sn coverage taking into account a analogous partitioning as here. More specifically, regarding the two stabilizing contributions E0 ads and ESn-Sn, they obtained that the ESn-Sn contribution represents about 0%, 40% and 57% the of sum of E0 ads and ESn-Sn for h = 1/4 ML, 1/2 ML and 1 ML, respectively, whereas in our calculations for the Sn/Au (1 1 1) it represents about 10%, 62% and 80%, respectively. We can infer that the ESn-Sn contribution is relatively much important for Sn/Au(1 1 1), compared to Sn/Pt(1 1 1). In particular, in Ref. [11] it was outlined that the magnitude of ESn-Sn has a maximum at a specific coverage degree, an observation that cannot be noted in our calculations. In Table 5 the net Bader atomic charges of Sn and its neighboring first and second Au atoms for Sn adsorbed on the FCC hollow and reconstructed sites are summarized. We notice that for the lower values of Sn coverage a significant electron charge transfer of nearly 2 e per Sn atom from the Sn atoms to the Au substrate is produced. For a full Sn layer this charge has decreased to 0.026 e per Sn atom. In Fig. 8 the distribution of net Bader atomic across the layers of the slabs for h = 1/2 ML has been schematized. Notice that the charge transferred by Sn atoms is gained mainly by the Au atoms of the first layer. Moreover we can observe that the reconstructed site implies a somewhat larger electron charge transfer of nearly 0.2 e than the FCC hollow site. This electron charge can be related to the larger electronegativity of atomic Au compared with atomic Sn, 2.54 vs. 1.96, respectively. The present results are in agreement with earlier DFT calculations performed on AunSn clusters [34]. Otherwise, in the recent DFT study on Sn adsorbed on Au(1 1 1) due to Nigam et al. [10], a positive net Bader atomic of 2.06 as reported for a Sn coverage of 1/25 ML, whereas each Sn atom donates 0.37 e and each Au atom tends to gain 0.07 e in the case of the graphene-like Sn-sheet (h = 2/3). Both results indicate, as here, a significant electron transfer at low coverage degree and a decreasing transfer for large coverage degree. Furthermore, when the charge distribution was analyzed on the Pt/Au(1 1 1) system with the Löwdin population analysis in Ref. [11], it showed a pronounced charge transfer from the adatoms to Pt(1 1 1). In order to have a more descriptive analysis of the electronic charge redistribution of the charge transfer between Sn and Au atoms, a charge density difference analysis was performed for the case of h = 1/2 ML. The charge density difference, Dq, can be expressed as

Dq ¼ qAu-Sn  qAu  qSn

ð9Þ

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L.A. Meier, N.J. Castellani / Computational Materials Science 127 (2017) 48–59

Table 4 Partitioning of Eads into E0 ads, ESn-Sn and EAu,distor contributions for Sn/Au(1 1 1) system. (3
3)Sn h = 1/9 ML

E0 ads (eV) ESn-Sn (eV) EAu,distor (eV) Eads (eV)

(2
2)Sn h = 1/4 ML

(1
2)Sn h = 1/2 ML

(1
1)Sn h = 1 ML

FCC hollow

FCC hollow

FCC hollow

Reconstructed

FCC hollow

4.58 0.02 0.07 4.53

3.83 0.43 0.09 4.17

1.53 2.47 0.01 3.98

2.25 2.46 0.85 3.86

0.63 3.09 0.00 3.72

Table 5 Electronic structure parameters for Sn/Au(1 1 1) system. Site

FCC hollow

(3
3)Sn h = 1/9 ML

(2
2)Sn h = 1/4 ML

(1
2)Sn h = 1/2 ML

QSn (e)a QAu1 (e)b QAu2 (e)c

ed (eV)d wd (eV)e ndf

/ (eV)g

QSn (e)a QAu1 (e)b QAu2 (e)c

ed (eV)d wd (eV)e ndf

/ (eV)g

QSn (e)a QAu1 (e)b QAu2 (e)c

ed (eV)d wd (eV)e ndf

/ (eV)g

QSn (e)a QAu1 (e)b QAu2 (e)c

ed (eV)d wd (eV)e ndf

/ (eV)g

2.07 0.66 0.04

3.48 4.04 0.94

5.10

1.99 0.64 0.05

3.59 4.09 0.94

5.04

0.98 0.53 0.31

3.59 4.04 0.93

4.81

0.26 0.25 0.25

3.74 4.23 0.95

3.98

1.02 0.6 0.57

3.55 3.85 0.96

4.69

Reconstructed

a b c d e f g

(1
1)Sn h = 1/2 ML

QSn = net atomic Bader charge for Sn atom. Second value: Au atom, first near neighbor of Sn atom. Third value: Au atom, second near neighbor of Sn atom. QAu1 = net atomic Bader charge for Au atom, first near neighbor of Sn atom. QAu2 = net atomic Bader charge for Au atom, second near neighbor of Sn atom. ed, d-band center obtained from PDOS of d-atomic orbitals for Au atom first near neighbor of Sn atom, measured from the Fermi level. For bare Au(1 1 1), ed = 3.01 eV. wd, d-band width obtained from PDOS of d-atomic orbitals for Au atom first near neighbor of Sn atom, measured from the Fermi level. For bare Au(1 1 1), wd = 3.49 eV. nd, d-band filling obtained from PDOS of d-atomic orbitals for Au atom first near neighbor of Sn atom, measured from the Fermi level. For bare Au(1 1 1), nd = 0.95. U, work function. For bare Au(1 1 1), / = 5.26 eV.

where qAu-Sn in the charge density of the total Sn/Au(1 1 1) system, qAu the charge density of the Au(1 1 1) substrate and qSn the density of the Sn monolayer, the last two charge densities calculated as isolated fragments but with the same geometry as for Sn/Au(1 1 1) with h = 1/2 ML. Fig. 9 shows the contours of the Dq iso-surfaces calculated for planes cutting the Sn layer and the Au layer underneath obtained with the code VESTA3 [35]. The red and blue colors represent the maximum and minimum electron densities, respectively, following a rainbow pallet. We can notice the large concentration of electron charge around the Au atoms and the large deficit around the Sn atoms, verifying the results obtained with the net atomic Bader charges. Furthermore, the electronic structure of Sn/Au(1 1 1) system was evaluated through the calculation of the PDOS considering the atomic orbitals of Sn atom and of its nearest Au atom. In Figs. 10 and 11 the results corresponding to the FCC hollow site for different degrees of coverage are shown. In Fig. 10 the Au dstates are included and in Fig. 11, the Au sp-states, respectively. The PDOS for a surface atom of bare Au(1 1 1) has also been plotted for the sake of comparison in both figures. Considering the results for h = 1/9 ML, from Fig. 10 we observe that the Au dstates extend from about 8 eV to at least 2 eV above the Fermi level, presenting a large and localized band, mainly between 6 eV and 1.5 eV. On the other hand, the Au sp-states form a broad and flat band superimposed to Au d-states in the same interval of energies, as is it evident comparing with the PDOS of Fig. 11. The Sn p-states form two bands in the higher part of the energy spectrum. They mainly couple with Au d-states in two regions with bonding (between 2.5 eV and 5 eV) and antibonding (between 1 eV and 2 eV) character (Fig. 10). The presence of two resonances in the PDOS of Sn p-states can be rationalized in terms of the arguments of Hammer and Nörskov [36]. According to the latter, the sharp atomic states of the gas phase are firstly broadened into resonances due to the interaction

with the metal sp-states and, subsequently, these modified states interact with the d-band of noble metal, forming covalent bonding and antibonding states below and above the initial states of adsorbate and substrate. On the other hand, the Sn s-states are developed in the lower part of the energy spectrum, forming a band from 9 eV to around 1 eV. The states at 8 eV are largely localized, indicating a much smaller coupling with Au d-states (Fig. 10). Nevertheless, the Sn s-states also have an extended queue at higher energies superimposed to the Au-d band. Since the last states, which have antibonding character, are below the Fermi level they do not contribute to the binding of Sn atom. Looking at the PDOS of Au sp-states and Sn p-states (Fig. 11) we can observe that Au sp-states make some contribution to the two bands identified in the coupling with the Au d-states. The Au sp-states are coupled also with Sn s-states in the energy interval from 9 eV to 2 eV. As the degree of coverage increases we can notice that the Sn presonances are less pronounced and more nearer between them. It is noticeably the observation of a progressive decrease of the amount of Sn p-states above the Fermi level and the increase of them below EF (Figs. 10 and 11). The Sn s-states are more extended in energy, showing particularly a broader feature in the bottom of the s-band (Figs. 10 and 11). In the case of a full Sn monolayer, we can observe the developing of extended and large delocalized bands of Sn p- and s-states. In Fig. 12 the PDOS results corresponding to the FCC hollow and reconstructed sites for h = 1/2 ML are shown together for the sake of comparison. Comparing the PDOS for d-states, we can observe that the Au d-band is narrower in the reconstructed site. This result can be rationalized recognizing that in the latter case, as a consequence of the reordering, the first Au layer divides in two sublayers. The overlapping between the atomic orbitals of surface Au atoms decreases and hence the d-band becomes narrower than that for the unreconstructed surface.

L.A. Meier, N.J. Castellani / Computational Materials Science 127 (2017) 48–59

55

Fig. 9. Charge density difference analysis for h = 1/2 ML. (a) Dq iso-surfaces plotted in a plane cutting the Sn atoms. (b) Dq iso-surfaces plotted in a plane cutting the Au atoms underneath. At left, the rainbow pallet used, from the maximum value of Dq (red) to the minimum value of Dq (blue). The iso-surface value is 0.0015 e bohr3. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

Fig. 8. Atomic distribution of net atomic Bader charges for h = 1/2 ML. (a) FCC hollow site. (b) Reconstructed site. Atom graphics as in Fig. 2.

In Table 5 the position of the d-band center in the energy spectrum, ed, the d-band width, wd, and the d-band filling, nd, for Sn adsorbed on the FCC hollow and reconstructed sites are summarized. They were calculated according to the following expressions:

R1

ed ¼ R1 1

eLDOSd ðeÞde ; LDOSd ðeÞde

ð10Þ

1

R1 2 e LDOSd ðeÞde w2d ¼ R1 ; 1 LDOSd ðeÞde 1 R EF nd ¼ R1 1 1

LDOSd ðeÞde ; LDOSd ðeÞde

ð11Þ

ð12Þ

respectively, and where the energies were referred with respect to the Fermi level.

From Table 5 we can observe that value of ed decreases by 0.45 eV while the value of wd increases by 0.55 eV if the results for Sn/Au(1 1 1) h = 1/9 ML are compared with that of bare Au (1 1 1). Similar results have been reported for Sn/Pt(1 1 1) for low Sn coverage [11]. The position of the d-band center also decreases as the Sn coverage is increased, but this effect is much less relevant: when the Sn coverage is increased from h = 1/9 to 1 ML, the value of ed decreases by 0.26 eV while the value of wd increases by 0.19 eV. On the other hand, the d-band filling shows negligible modifications at all Sn coverage values (nd = 0.94–0.95). This dband shift to lower energies could be explained in Ref. [35] by considering a simple rectangular band with constant area which must adjust its position with respect to EF accordingly to the variations of the band width. In Fig. 13 the relationship between the Sn adsorption energy for the FCC hollow site and the position of the Au d-band center was plotted. Notice that, as a general trend, it could be said that the Eads value increases (i.e., we have a weaker Sn-Au bond) as the value of ed decreases. However, this relationship is not monotonous, showing a step between h = 1/4 ML and h = 1/2 ML, and an important change of Eads (0.45 eV) within a relative narrow interval of ed (0.15 eV) for Sn coverage values greater than 1/4 ML. This behavior is more outstanding if we look at the relationship between E0 ads and ed (see the insert in Fig. 13). Noticeably, below h = 1/4 ML, the E0 ads contribution predominates in Eads, while the ESn-Sn contribution is much relevant for larger h values. Previously, a linear decreasing relationship was established between the adsorption energy and ed for atomic oxygen adsorbed on Au(1 1 1) [37]. This behavior was explained considering that due the lowering of dband center, the antibonding resonance of O p-states also lowers, becoming more occupied and, therefore, the binding of O to the

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L.A. Meier, N.J. Castellani / Computational Materials Science 127 (2017) 48–59

Fig. 10. Electronic PDOS of Sn/Au(1 1 1) for the FCC hollow site. Sn-s, Sn-p and Au-d states.

Fig. 11. Electronic PDOS of Sn/Au(1 1 1) for the FCC hollow site. Sn-s, Sn-p and Ausp states.

Au surface is disfavored. This argument could be employed for the lowest degrees of coverage of Sn/Au(1 1 1), where the bonding and antibonding resonances of Sn p-states can be distinguished in the PDOS curves. On the other hand, we notice that the amount of occupied Sn p-states is more relevant as h increases. This observation is in agreement with the presence of Sn atoms less positive charged, giving a weaken attractive coulombic interaction between adatoms and substrate, as well as with the formation of stronger

covalent bonds between Sn atoms, as shown by the significant increase of ESn-Sn. In Table 5, the values of the work function, /, of the Sn/Au(1 1 1) system for Sn adsorbed on the FCC hollow and reconstructed sites have been summarized. Looking at Table 5 we notice that / is a decreasing function of the Sn coverage. The modification undergone by the work function is usually taken as an evidence of the change of the adsorbate charge. When an electropositive species

L.A. Meier, N.J. Castellani / Computational Materials Science 127 (2017) 48–59

57

Fig. 14. Work function of Sn/Au(1 1 1) versus Sn coverage.

Fig. 12. Electronic PDOS of Sn/Au(1 1 1) for h = 1/2 ML. Sn-s, Sn-p and Au-d states for FCC hollow site and reconstructed site.

is adsorbed the resulting dipole layer that is directed positive above the surface should result in a lowering of the work function [38]. This is just what was obtained in our case, in agreement with the results corresponding to the net atomic Bader charges of Sn and Au atoms (see above). In Fig. 14 the variation of / as a function of h has been plotted, beginning with the value for bare Au(1 1 1). Notice that the change of / with respect to h = 0 ML shows two regimes, one corresponding to low Sn coverage and another for larger h values. A reasonable approximation for the changes at low coverage is that they would be proportional to the change in the

surface dipole induced by a single adsorbate and to the surface density of the adsorbate [39]. This simple rule, particularly followed by the alkaline metals, is approximately followed by Sn taking into account that the net atomic Bader charges of Sn decreases only by 0.1 e between h = 1/9 and 1/4 ML. Nevertheless, for higher coverage values the charge transfer from Sn to Au is largely diminished and the surface dipole would also diminish significantly, specially for h = 1 ML. Hence, it would be expected a less pronounced decrease of / than that predicted by a linear relationship between / and h. This behavior could be related to fact that in this range of the coverage the Sn overlayer shows a predominant interaction between Sn atoms and a much less relevant Au-Sn interaction, as it was commented above. Interestingly, in Ref. [11], the variation of / of the Sn/Au(1 1 1) system was studied for different values of Sn coverage. The general profile of relationship between / and h is similar to that obtained here. Moreover, the value of / reported for a full Sn monolayer is very close to that calculated here, i.e., 4.1 eV vs. 3.98 eV. Finally, the influence of SOC effects on the Sn/Au(1 1 1) system was studied for Sn adsorbed on the highest coordinated sites, FCC hollow and HPC hollow, at different h values and for the reconstructed structure at 1/2 ML. The values of the adsorption energy obtained with SOC, ESO ads, and the main geometrical parameters are summarized in Table 6. If we compare these results with the values of Eads in Table 1 we observe a general decrease of the

Fig. 13. Adsorption energy of Sn, Eads, versus d-band center position, ed, of Au. In the insert: E0 ads versus ed of Au.

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Table 6 Adsorption energies including spin-orbit coupling for Sn/Au(1 1 1) system. (3
3)Sn h = 1/9 MLa

FCC hollow HCP hollow Reconstructed a b c

(2
2)Sn h = 1/4 ML

(1
2)Sn h = 1/2 ML

(1
1)Sn h = 1 ML

Eads (eV)

hSn-Au (Å)b

dSn-Au (Å)

Eads (eV)

hSn-Au (Å)b

dSn-Au (Å)

Eads (eV)

hSn-Au (Å)b

dSn-Au (Å)

Eads (eV)

hSn-Au (Å)b

dSn-Au (Å)

3.60 3.61

2.15 2.14

2.73 2.72

3.35 3.35

2.14 2.14

2.72 2.73

3.33 3.32 3.30

2.26 2.26 2.60 1.07c

2.87 2.87 2.77 2.85

2.95 2.95

2.61 2.61

3.12 3.12

In this case a (3
3) supercell with 3 Au layers was considered. The value corresponds to the normal distance to the plane intersecting the nearest Au atom/atoms underneath the Sn atom. This value corresponds to the normal distance to the plane intersecting the next nearest Au atoms.

magnitude of adsorption energies. More specifically, for h = 1/9 ML, 1/4 ML and 1 ML, they diminished by 18–21%. For h = 1/2 ML a decrease of 14–16% was obtained. Therefore, the consideration of SOC produces an non-negligible destabilizing effect on adsorption energies; nevertheless, the relative stability of adsorption sites is maintained. It is noteworthy that spin-orbit effects substantially lower the cohesive energy for solid lead (by 34%) but less remarkably for solid tin (by 6%) [28]. Regarding in Table 6 the normal distances to the plane intersecting the nearest Au atoms underneath the Sn atom, hSn-Au, they show a small stretching in comparison with the results without SOC: for h = 1/9 ML and 1/4 ML, they decreased by 5–6%, while for h = 1/2 ML and 1 ML, a decrease of less than 2% was obtained. On the other hand, the interatomic Sn-Au distances show a negligible stretching because the optimized cell parameter for Au bulk considering SOC is 1% smaller, and therefore there is a compensation between the stretching undergone by hSn-Au and the shortening of Au-Au distances. With respect to the reconstructed structure at 1/2 ML, it shows the same symmetry than that obtained without SOC. The most affected Au atoms are those of the second layer where the normal distance to the plane containing the Sn atoms decreases by 4%. We notice that recently it was reported that the geometrical parameters obtained considering SOC effects in heavy metals exhibited a difference of only 3% or less, compared to the results calculated without SOC [28]. Furthermore, we investigated the influence of SOC on the PDOS. The results (not shown) performed for the FCC site and h = 1/2 ML indicate that the PDOS profiles are similar to those obtained without SOC, with the exception of an PDOS increase for the Au d-states evaluated below the Fermi level. 4. Conclusions The main conclusions regarding the bonding and geometry of the Sn/Au(1 1 1) system are the following: The most likely site for the adsorption of Sn is the FCC hollow site at low Sn coverage values while at full monolayer there is degeneracy for the four possible adsorption sites. It was able to identify the character of the different sites in the PES and to define the route for the surface diffusion of Sn. The energy barrier for Sn surface diffusion is of near 0.1 eV at low Sn coverage and negligible for high Sn coverage. The value of the adsorption energy, for Sn atoms increases as the Sn coverage increases, from 4.43 eV at h = 1/9 ML to 3.72 eV at h = 1 ML for the FCC hollow site. This binding weakening can be related, for the lowest Sn coverage values, to a shift of the dband center of Au to lower energies, whereas for h values larger than 1/4 ML, to an increase of Sn p-states below the Fermi level and concomitantly to the fact that the contribution of the Sn-Sn interaction to Eads is predominant. At h = 1/9 ML the Au atoms underneath the Sn rise with respect to other Au atoms. For at h = 1/2 ML the adsorbed Sn atoms and the Au atoms of the first and second layers of the substrate can suffer a

reordering, resulting in an important surface reconstruction phenomenon, giving a surface alloy superstructure. Half of the atoms of the first bare Au(1 1 1) surface become displaced to form a plane in between the outermost Sn plane and the other inner Au plane. An electronic transfer from tin to gold takes place. It is significant at low Sn coverage values, involving mainly the first Au layer. This charge transfer can be related to the observed work function decrease, particularly for the lower Sn coverage values. The inclusion of spin-orbit effects produces an non-negligible destabilizing effect on adsorption energies; nevertheless, the relative stability of adsorption sites obtained without this relativistic effect is maintained.

Acknowledgments The authors want acknowledge the financial support of these Argentine institutions: Consejo Nacional de Investigaciones Científicas y Técnicas, Agencia Nacional de Promoción Científica y Tecnológica and Universidad Nacional del Sur, under Grants PIP N°112-200801-02286, PICT-2010-0830 and PGI 24/F063, respectively.

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