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DFT study of the formation of Cd–Ag surface alloys on Ag surfaces
Computational Materials Science 118 (2016) 316–324
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DFT study of the formation of Cd–Ag surface alloys on Ag surfaces Rubén E. Ambrusi a, Silvana G. García b, María E. Pronsato a,⇑ a b
Departamento de Física, Universidad Nacional del Sur & IFISUR (UNS-CONICET), Av. Alem 1253, 8000 Bahía Blanca, Argentina Departamento de Ingeniería Química, Universidad Nacional del Sur e Instituto de Ing. Electroquímica y Corrosión (INIEC), Av. Alem 1253, 8000 Bahía Blanca, Argentina
a r t i c l e
i n f o
Article history: Received 26 January 2016 Received in revised form 13 March 2016 Accepted 15 March 2016
Keywords: Adsorption energies Cadmium Silver Surface alloy Density functional calculations Underpotential deposition
a b s t r a c t We investigate the feasibility of forming a surface alloy between Ag and Cd on Ag surfaces, employing Density Functional Theory calculations. Six layers slabs are used to model surface alloy systems. Adsorption energies for Cd atoms and a monolayer on Ag(1 1 1) and Ag(1 0 0) surfaces are calculated, and compared with surface alloy formation energies, verifying the energetic preference of Ag and Cd to stay in alloyed form on the surface, as found in different electrochemical experiences for this system. This means that there is an electronic effect which favors this type of phenomenon. An analysis of the charge densities and projected densities of states for the different structures proposed is also performed. Ó 2016 Elsevier B.V. All rights reserved.
1. Introduction Underpotential deposition (UPD) of metals is of great importance for the chemistry and physics of solid/liquid interfaces, electrocrystallization, electrocatalysis, and electrodeposition of alloys and heterostructured ultrathin films [1]. Early metal UPD electrochemical experiments on metal single crystals faces by different authors [2–6], showed evidence of the formation of ordered bidimensional overlayers onto the monocrystals surface. Later, the monocrystalline substrate and the bidimensional overlayers structures formed by UPD were investigated on an atomic level, combining electrochemical measurements with in situ scanning probe techniques such as scanning tunneling microscopy (STM) and atomic force microscopy (AFM) [7–12]. The UPD process occurs when the interaction between the adsorbed and substrate atoms is stronger than the adsorbed atoms interaction between themselves; then it is feasible, in principle, that a site exchange between the adsorbate and substrate atoms occurs after adsorption, resulting in the formation of surface alloys [1]. The Cd/Ag system has been extensively studied experimentally by electrochemical techniques and by in-situ STM, analyzing the Cd UPD on Ag(1 1 1), Ag(1 0 0) and polycrystalline silver [13–16]. Cd UPD deposition on Ag(1 1 1) and Ag(1 0 0) occurs epitaxially, starting with the deposition of expanded monolayers, which then leads to compact monolayers by a first order phase transition ⇑ Corresponding author. Tel./fax: +54 291 4595142. E-mail address: [email protected] (M.E. Pronsato). http://dx.doi.org/10.1016/j.commatsci.2016.03.025 0927-0256/Ó 2016 Elsevier B.V. All rights reserved.
[1,15,17]. Different electrochemical measurements suggest that the formed Cd monolayers are in some conditions unstable resulting in the formation of Cd–Ag surface alloys on Ag(1 0 0) and Ag (1 1 1) [13–15,18]. The phenomenon of surface alloys is also supported by previous studies that show the formation of surface alloy between Ag and Cd during the Cd UPD onto Ag irregular and polycrystalline substrates [19,20]. Cd UPD on Ag surfaces has become an important method for ultrathin Cd/Ag films formation onto Au (1 1 1) substrates [21]. The Cd–Ag system and the formation of surface alloy between these two metals, are interesting also due to the potential catalytic effect for the electroreduction of the nitrate ion which Ag and Cd have shown individually [22–25], and is a process of great significance in effluents detection and treatment. The Cd–Ag system has also been studied theoretically. Density functional theory (DFT) calculations on Cd–Ag bulk alloys have been performed by Curtarolo et al. [26], to establish the most stable structures at different Cd and Ag compositions. Additionally, Chouhan et al. [27] have calculated electronic, elastic and mechanical properties of bulk Ag–Cd alloy at the ground state. However, even though extensive theoretical studies have been carried out on surface binary alloys [28,29] including Bi, Pt, Pd and Sb deposition on Ag(1 1 1) [30–33], Cd–Ag surface alloys have not been analyzed by first principles calculations. In addition, most of these works on surface alloys were based on experimental works that include vapor deposition technique [30,34–36] but not the electrochemical UPD method. In this work, we employ DFT calculations to make a first attempt to evaluate the interaction between Cd and Ag in surface
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alloys onto Ag(1 1 1) and Ag(1 0 0) surfaces and the mechanisms that intervene in their formation. There is evidence that the formation process of the surface alloy between these two metals, starts on the substrate surface defects at low coverage or high underpotentials while in the case of high coverage or low underpotentials, alloy formation is independent of the inhomogeneities on the surface, like the density of monoatomic steps [1]. Therefore, the study of the feasibility of formation of surface alloy was performed using a model that does not contain inhomogeneities on the surface and in principle represents the situation at low underpotentials. 2. Computational method DFT calculations were performed using the Viena Ab-initio Simulation Package (VASP) [37–40], which employs a plane-wave basis set and a periodic supercell method. The generalized gradient corrected approximation (GGA) Perdew, Burke, and Ernzerhof (PBE) functional was used [41]. The Kohn–Sham equations were solved variationally using the projector-augmented-wave (PAW) method [42,43]. Spin polarization was considered in all calculations, observing no magnetization for the different systems analyzed. For bulk calculations, DFT parameters such as kinetic cutoff energy value (Ecut), k-points set and smearing function, were optimized. This task was carried out using the Methfessel-Paxton first order smearing approach, for the partial occupancies for the electronic states near the Fermi level. For all calculations, a smearing width of 0.2 eV was used. Analysis of the system energy shows that the use of a 13 13 13 Monkhorst–Pack k-point grid to sample the Brillouin Zone and Ecut = 400 eV, is enough for the total energy to converge within 10 meV. Geometry optimizations were obtained by minimizing the total energy of the unit cell using a conjugated gradient algorithm to relax ions [44]. Slab models were employed for surface calculations. Surface energy was calculated for slabs with increasing number of layers in order to determine the number of layers necessary for our model. During calculations, DFT parameters previously obtained from bulk optimization and a 13 13 1 k-points grid were used, concluding that five layers are enough to ensure surface energy convergence (see Table 1). Eq. (1) was used for calculating the surface energy (r), where Eslab is the total energy of the slab, nAg is the number of silver atoms in the slab model and Ebulk is the energy per atom for silver bulk.
r¼
ðEslab nAg Ebulk Þ 2
ð1Þ
Details on the slab model will be given in the following sections. The surface energies calculated, shown in Table 1, were obtained for a 1 1 slab. The values of the surface energies calculated are in agreement with values obtain from literature [45]. Eqs. (2a) and (2b), were used to calculate the adsorption energy for an adatom (Eadadat ) and a monolayer of unitary coverage (Eadmon ), where ESurfAg is the energy of the clean silver surface (Ag(1 1 1) or
Ag(1 0 0)), ECd is the energy of an isolated Cd atom and nCd is the number of Cd atoms adsorbed.
Eadadat ¼
ECdadat =SurfAg ESurfAg ECd nCd
ð2aÞ
Eadmon ¼
ECdmon =SurfAg ESurfAg nCd ECd nCd
ð2bÞ
With this definition a negative adsorption energy corresponds to a stable adsorption on the surface. To evaluate the surface alloy formation between Ag and Cd, two mechanisms were considered. One where Cd atoms replace Ag atoms from the surface, and another where Ag atoms replace Cd atoms from a Cd monolayer formed on the Ag surface. These two mechanisms are shown schematically in Fig. 1. SAgsCd indicates the substitution of Ag surface atoms by Cd atoms (Fig. 1a)), while SCdmAg represents the substitution of Cd atoms of a preformed Cd monolayer (Fig. 1b)), by Ag atoms. To calculate the formation energy of the surface alloy, both mechanisms were considered using Eqs. (3a) and (3b) for SAgsCd and SCdmAg respectively, based on equations of previous theoretical studies on the subject [30,46,47].
Efa1 ¼
Efa2 ¼
ðEAgCdalloy EsurfAg þ nAg EbulkAg nCd ECd Þ
ð3aÞ
nCd ðEAgCdalloy ECdmon=surfAg þ nCd EbulkCd nAg EAg Þ nAg
ð3bÞ
EAgCdalloy is the energy of the alloy slab, with the substitution of Ag surface atoms by Cd atoms in Eq. (3a); and Cd atoms from the monolayer by Ag atoms in Eq. (3b). Regarding the other terms; ECdmon=surfAg , is the energy of the Ag surface with a Cd monolayer adsorbed, EAg and ECd are the energies of Ag and Cd isolated atom, respectively, EbulkAg and EbulkCd , are the energies of Ag and Cd atom in the bulk respectively. Finally, in Eq. (3a) nAg and nCd represent the number of Ag atoms removed from the surface and the number of Cd solute atoms respectively, whereas in Eq. (3b), nAg and nCd represent the number of Ag solute atoms and the number of Cd atoms removed respectively. EAg and ECd in Eqs. (3a) and (3b) respectively, have a dual function. First, subtracting the energy contribution from the system solute atoms, in order to obtain the bond contribution between solvent and solute. They also are reference values with respect to which the alloy formation energies are calculated. Using the EbulkAg or
(a)
SAgsCd
(b)
SCdmAg
Table 1 Surface energy for Ag surfaces (1 1 1) and (1 0 0). Number of layers
3 4 5 6 7
Surface energy/eV Ag(1 1 1)
Ag(1 0 0)
0.314 0.339 0.327 0.331 0.331
0.436 0.426 0.423 0.422 0.423
Cd
Ag
Fig. 1. Schematic representation for the alloy formation through a substitution mechanism. (a) Surface Ag atoms are substituted by Cd atoms. (b) Cd atoms from a monolayer adsorbed onto Ag surface are substituted by Ag atoms.
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EbulkCd instead of EAg or ECd , would lead to results for Efa1 and Efa2 that could not be compared. In this way we are substracting the energy contribution of Ag or Cd atoms from the energy gain due to the Ag–Cd interaction, isolating the effective Ag–Cd binding energy. The formation energy for the surface alloy was calculated for different structures of bidimensional Ag–Cd alloy. Structures pffiffiffi pffiffiffi pffiffiffiffiffiffi pffiffiffiffiffiffi 2 1, ð 3 3ÞR30 , 2 2, ð 19 19ÞR19 and 3 3 were used, where the length of the surface alloy unit cell lattice vectors, with respect to the Ag(1 1 1) primitive cell lattice vectors, are indicated. The bidimensional alloy lattice vectors point towards the Cd atoms in the case of the Ag surface or the Ag atoms in the case of the Cd adsorbed monolayer. In the case of rotated structures, the letter R is added followed by the magnitude of the rotated angle, which represents the angle between the surface lattice vectors and that of the alloy structure. The Cd monolayer was adsorbed on Top and Hollow-hcp sites, which are represented in our nomenclature by the letters T or Hhcp added to the right of SCdmonAg. Each structure corresponds to different Cd surface concentrations (CCd), defined as (Cd atoms on the surface)/(Cd + Ag atoms on the surface). Following the same procedure, a 2D alloy was obtained for the Ag(1 0 0) surface, considering the structures pffiffiffi pffiffiffi ð 2 2ÞR45 , 2 2 and 3 3 for the unit cell, in which the unit cell lattice vectors are referred to the primitive cell for Ag(1 0 0) surface. The surface alloys were obtained by substituting Ag surface atoms by Cd atoms, and Cd by Ag in the Cd monolayer adsorbed on Top and Hollow. A scheme of the structures obtained for some of the different cases are shown in Fig. 2. Six layers slabs were used to perform the calculations of the surface alloy, with a vacuum space of approximately 12 Å. The size of the slab in the direction parallel to the surface was varied
according to the structure studied. In each case a k-points optimization was made to obtain converged results. In all cases, the first four layers were allowed to relax, leaving the two bottom layers fixed at their bulk positions. In order to analyze the electronic structure, the electronic charges on atoms were computed using Bader analysis [48] and the atom projected density of states (PDOS) was obtained by projection of the one-electron wave functions onto atomic Bader volumes [49]. 3. Results 3.1. Bulk and surface structures optimization In order to test the reliability of our calculations some properties were calculated and compared with experimental data from literature. A geometry optimization was performed to determine silver fcc and cadmium hcp lattice parameters. Ion positions, cell volume and cell shape were allowed to simultaneously relax. The calculated lattice parameter is a = 4.154 Å for silver, which overestimates 1.6% the experimental value of 4.09 Å [50]. In the case of cadmium the calculated lattice parameters are a = 3.018 Å and c = 5.845 Å, in good agreement with the experimental values (a = 2.98 Å, c = 5.62 Å) [50]. For the case of bulk Cd, an Ecut = 500 eV and a 15 15 15 gamma centered k-point grid were used. The Ag(1 1 1) and Ag(1 0 0) surfaces were modeled with a slab consisting of five silver layers within a 3 3 unit cell and a vacuum spacing between slabs of about 10 Å. The size of the supercell is large enough to allow further study of Cd adsorption and the
Alloy structures in Ag(111) surface a1 a1
a1
a2 a1
a2
a2
SAgsCd-2x1
a2
Ag second layer
SCdmAg-Hhcp-
Ag surface
Cd surface
Alloy structures in Ag(100) surface
a1 a2
a1 a2
a2 a1
a2
a1
SAgsCd-2x2
SCdmAg-H-
Fig. 2. Scheme of some structures of surface alloy formed on Ag(1 1 1) and Ag(1 0 0), by substitution of the Ag surface atoms or by substitution of Cd atoms of the adsorbed monolayer.
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vacuum spacing ensures no interaction between slabs. The k-points were reduced to 11 11 1, in this case. Silver atoms on the surface were allowed to relax in all directions for the top three layers, keeping the bottom two layers fixed. No change in the positions of silver atoms in the direction parallel to the surface was found as expected for a symmetric surface, presenting no reconstruction. Only some surface relaxation for both surfaces occurs. The Ag(1 1 1) surface evidences an expansion of the first interlayer of approximately 0.018 Å, then the second and third interlayer changes with respect to the bulk ideal interlayer distance are negligible. Regarding the Ag(1 0 0) surface, it shows a little contraction in the first interlayer distance of approximately 0.031 Å and an expansion of the second interlayer of approximately 0.014 Å, with no noticeable change in the third interlayer.
Table 2 Adsorption energies for an adatom and a Cd monolayer on Ag(1 1 1) and Ag(1 0 0). System
Eadmon (eV/at.)
Ag(1 1 1)
Top Bridge Hollow-fcc Hollow-hcp
0.478 0.649 0.688 0.687
0.854 0.955 0.971 0.975
Ag(1 0 0)
Top Bridge Hollow
0.444 0.562 0.759
0.699 0.806 0.925
Table 3 Theoretical and experimental binding energies and equilibrium distances of dimmers.
3.2. Cd adsorption on Ag(1 1 1) and Ag(1 0 0)
Dimmer
The Cd adsorption energy on Ag(1 0 0) and Ag(1 1 1) surfaces, whether for an adatom or a complete monolayer, was evaluated on different sites in order to elucidate the factors involved in these processes in vacuum. For calculating the absolute adsorption energy for a Cd adatom and a monolayer on the Ag surface, Eqs. (2a) and (2b) were used respectively. The different adsorption sites used for the calculations are shown schematically in Fig. 3, and Table 2 summarizes the adsorption energies calculated in each case. These results show that adsorption energies are noticeably lower for the monolayer formation, which evidences an energetic gain due to the electronic interaction with the neighboring atoms which favor its formation. This stabilization explains why the difference between the adsorption energy for an adatom and for the monolayer is greater for the Ag(1 1 1) than the Ag(1 0 0) surface. Due to the difference in their structures, the Cd atoms on Ag (1 1 1) have a higher coordination number. It can also be observed that the adsorption energy for a Cd adatom in Hollow-fcc site on Ag (1 1 1) is less negative than for a Cd adatom in a Hollow site on Ag (1 0 0). We presume that this is, again, due to the different structure of the surfaces. In this case the Ag(1 1 1) have an hexagonal structure which gives a coordination number of three for a Cd adatom on Hollow site, while Ag(1 0 0) have a square structure with coordination number four, giving a more stable adsorption on Hollow site for Ag(1 0 0). Based on these results, and taking into account that the Cd–Cd binding energy (see Table 3) is smaller than the Cd–Ag surface interaction (Table 2), we can predict that Cd will prefer to form ordered structures in an epitaxial way on the Ag surface, as was
Eadadat (eV/at.)
Ag Cd Ag–Cd
Theoretical calculation
Experimental
Ebinding/eV
Equilibrium distance/Å
Ebinding/eV
Equilibrium distance/Å
1.75 0.014 0.339
2.58 3.49 2.76
1.65 [51] 0.03 [51] –
2.53 [52] 3.02 [51] –
observed by García et al. [15], during the Cd UPD deposition on Ag(1 1 1) surface. The most stable site was found to be Hollow for the Ag(1 0 0) surface for both cases; the formation of the monolayer and for an adatom, while for the Ag(1 1 1) surface the hollow-hcp is slightly the most stable position for the formation of the monolayer and the Hollow-hcp and fcc hollow-sites are also the most stable sites for an adatom.
3.3. Cd–Ag surface alloy formation on Ag(1 1 1) and Ag(1 0 0) surfaces The surface alloy formation energy for both mechanism, and different Cd concentrations, on Ag(1 1 1) and Ag(1 0 0) is plotted in Fig. 4a and b respectively. To interpret the SAgsCd mechanism results, it should be noted that there is an energy cost when Ag atoms from the surface are replaced by Cd atoms. This is because the Ag–Cd binding energy is lower than the Ag–Ag binding energy (see Table 3), therefore, the interaction energy with the Ag–Cd does not exceed the energy required to generate a surface vacancy. However, the Ag atoms removed from the surface to form the alloy, were considered to remain in an adjacent pure Ag surface, using
Ag (111)
Ag (100)
a1
a1
a2
a2
Ag second layer
Ag surface
Fig. 3. Scheme of the adsorption sites on Ag(1 1 1) and Ag(1 0 0) surface.
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(a)
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0,0
Efa(eV/atom)
-0,5 -1,0 -1,5
Monolayer SAgsCd SCdmAg-T
-2,0
SCdmAg-Hhcp
-2,5 -3,0
0,0
0,1
0,2
0,3
0,4
0,5
0,6
0,7
0,8
0,9
1,0
0,6
0,7
0,8
0,9
1,0
CCd
(b)
0,0
Efa(eV/atom)
-0,5 -1,0 -1,5
Monolayer SAgsCd SCdmAg-T
-2,0
SCdmAg-H
-2,5 -3,0
0,0
0,1
0,2
0,3
0,4
0,5
CCd Fig. 4. Surface alloy formation energy by substitution mechanisms for: (a) Ag(1 1 1) surface, (b) Ag(1 0 0) surface, corresponding to different structures (different concentrations). Also the corresponding formation energy for a Cd monolayer in the most stable position is plotted.
the silver bulk energy in Eq. (3a), because at low temperatures, considering the equilibrium between atoms on surface and in bulk positions is valid. Considering that the Ag atoms, are not carried to the infinity, it is consistent with the fact that experimentally, the
alloy formed by the electrochemistry method between Ag and Cd uses potentials at which no Ag dissolution is observed because Ag is more noble than Cd [15]. Comparing these results with the adsorption energy of a Cd monolayer on the most stable site (Hollow-hcp), it can be observed that the alloy formation by substitution of substrate atoms is more stable for the different concentration of Cd. However, experimentally it is observed that the Cd monolayer forms first with high recovery and after long polarization times the formation of the alloy occurs [1]. Fig. 4a also shows the alloying energy calculations at different concentrations by the SCdmAg mechanism, that is, by the introduction of Ag atoms in vacancies formed in the Cd monolayer on the Ag(1 1 1) surface, with the monolayer on Hollow and Top sites. Based on these results, it is observed in the tested concentration range, that the alloying energy by this mechanism is vastly more favorable than the formation of a monolayer on the surface in the most stable position and alloying by substitutions of the atoms from the Ag surface by Cd atoms. This would indicate the possibility of alloy formation at different Cd concentrations, by inserting Ag atoms in the Cd monolayer through vacancies created in it. The effect that makes this mechanism much more favorable, is the fact that the substitution of Cd atoms in the monolayer by Ag atoms, is exothermic and therefore spontaneous from a thermodynamic point of view (this last affirmation strictly at 0 K and vacuum). The increased stability is given by the formation of Ag–Cd bonds stronger than Cd–Cd bonds, when Cd is replaced by Ag. Contrasting the results in Fig. 4a and b, no significant changes were observed in the calculated energies, however the alloys on Ag (1 1 1) surface have a slightly higher stability. Through the analysis made in this section, it can be suggested that the bimetal alloy between Ag and Cd occurs first with the formation of the monolayer of Cd and then with the introduction of Ag atoms in it, through vacancies. A similar mechanism was proposed by other authors [13], as a model for the Ag–Cd surface alloy formation, based on experimental results obtained during the UPD deposition of Cd on Ag(1 0 0) and Ag(1 1 1) at long polarization times. In this model, the formation of a Cd monolayer in which Ag diffuses from the surface to the monolayer vacancies is proposed. It should be clarified that being rigorous, the theoretical treatment used in this section does not apply exactly to this case because it is assumed that the Ag does not belong to the substrate. Nevertheless, the results obtained here allow us to demonstrate quantitatively the Cd preference to alloy with Ag on a Cd monolayer adsorbed on the metal and not directly on the substrate. This type of mechanism is also applicable in the case of both atoms, Ag and Cd, are present in the solution used to obtain Ag–Cd structures,
Table 4 Bader charges for Ag and Cd in the surface alloy. System
Surface alloy of Ag(1 1 1)
Electronic gain or loss of the solute atom
Substrate substitution Substitution in the Cd monolayer
Surface alloy of Ag(1 0 0)
Substrate substitution Substitution in the Cd monolayer
2 1 (CCd = 0.50) 3 3 (CCd = 0.11) 2 1 T (CCd = 0.50) 3 3 T (CCd = 0.89) 2 1 Hhcp (CCd = 0.50) 3 3 Hhcp (CCd = 0.89) pffiffiffi pffiffiffi 2 2 R45° (CCd = 0.50) 3 3 (CCd = 0.11) pffiffiffi pffiffiffi 2 2 R45° T (CCd = 0.50) 3 3 T (CCd = 0.89) pffiffiffi pffiffiffi 2 2 R45° H (CCd = 0.50) 3 3 H (CCd = 0.89)
Ag
Cd
– – 0.1289 0.1951 0.1332 0.1856
0.1888 0.2622 – – – –
–
0.2148
– 0.1809
0.2913 –
0.1051 0.1566
– –
0.1334
–
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to 0.26 e- for Ag(1 1 1) surface and 0.21–0.29 e for the Ag(1 0 0) surface. These electronic transfers far exceed those found in the adsorption of Cd on Ag surfaces, suggesting a stronger interaction between Ag and Cd atoms when these metals are alloyed. In order to study the origin of the increase in the charge transfer in alloyed structures, projected density of states (PDOS) on Bader volumes was calculated for selected atoms in the structures studied. The states calculated in all cases are normalized, so the graphs heights are not comparable and the only objective is to establish the energy range for the interaction between orbitals. Fig. 5 shows the PDOS obtained for 2 1 and 3 3 structures, in the case of the alloy formed by the replacement of Cd atoms in a monolayer in Top position on Ag(1 1 1) surface by Ag atoms. A high degree of overlap between Cd and Ag s bands is observed on the surface, at the CCd = 0.89. For a CCd = 0.5, the degree of overlap between the s bands is smaller, and it is possibly, more influenced by the interaction between the Ag d band with the Ag and Cd s bands. Furthermore, there is a small overlap between the Ag d and Cd d bands, because of the peaks appearing at lower energies to 7.5 eV, although the d bands practically do not overlap with each other. The fact that s bands overlap more than d bands, can be understood on the basis that; the s bands are partially filled bands, because both the valence band and the conduction band contain states
as was found in the Ag–Cd electrochemical system by del Barrio et al. [53]. These authors established the formation of alloy between these metals, which not only can occur by solid state diffusion of the metal atoms, but also by the effect of the co-deposition of Ag while the UPD deposition of Cd is occurring. 3.4. Electronic structure analysis Initially Bader analysis was performed for the different systems studied in this work. The net charges in the case of the Cd monolayer adsorption on Ag surfaces show that Cd loses 0.07 to 0.09 e while Ag atoms in the surface receives e approximately in the same amount. The values of charge transfer are quite small, justifying the low Cd adsorption energy on the Ag surface. In Table 4, the gain or loss of electrons are specified, for the atom in low proportion (solute) forming the alloy for the different surface alloy structures corresponding to extremes of Cd surface concentration. For the different configurations, alloys formed by replacement of atoms in the Cd monolayer, present electronic transfers between 0.13 to 0.20 e- for the Ag(1 1 1) surface, and 0.10–0.18 e for the Ag(1 0 0) surface. In the case of substitution of Ag atoms of the surface by Cd atoms, Cd presents electronic losses from 0.19
2x1 T CCd=0.5
1,0
(a) 0,8
PDOS (arb.units)
(b)
sAg sCd
0,6
dAg dCd
0,4
0,2
0,0 -10
-5
0
5
10
-10
-5
5
10
3x3 T CCd=0.89
1,0
(d)
(c) 0,8
PDOS (arb.units)
0
E-E Fermi
E-E Fermi
sAg
dAg
sCd
dCd
0,6
0,4
0,2
0,0 -10
-5
0
E-E Fermi
5
10
-10
-5
0
5
10
E-E Fermi
Fig. 5. PDOS on Cd and Ag atoms from the surface for two different structures of the surface alloy, corresponding to a CCd of 0.5 and 0.89. These alloys were obtained by substitution, in certain positions, for Ag atoms the atoms of a Cd monolayer, on Top site, adsorbed on Ag(1 1 1) surface.
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2x1 Hhcp CCd=0.5
1,0
(a) 0,8
PDOS (arb.units)
(b)
sAg sCd
0,6
dAg dCd
0,4
0,2
0,0 -10
-5
0
5
10
-10
-5
5
10
3x3 Hhcp CCd=0.89
1,0
(c)
(d) sAg
0,8
PDOS (arb.units)
0
E-E Fermi
E-E Fermi
sCd
dAg dCd
0,6
0,4
0,2
0,0 -10
-5
0
5
E-E Fermi
10
-10
-5
0
5
10
E-E Fermi
Fig. 6. PDOS on Cd and Ag atoms from the surface for two different structures of the surface alloy, corresponding to a CCd of 0.5 and 0.89. These alloys were obtained by substitution, in certain positions, for Ag atoms the atoms of a Cd monolayer, on Hhcp site, adsorbed on Ag(1 1 1) surface.
(Fig. 5a and c) while d bands are practically filled because they exhibit a density of states negligible above EF (Fig. 5b and d). This leads to greater interaction between the Cd s and Ag s bands. This behavior is expected because of the electronic configuration of these elements, [Kr] 5s1 4d10 and [Kr] 5s2 4d10 for Ag and Cd respectively; that have 4d atomic orbital filled. The same behavior for high and medium Cd concentrations in surface alloys formed by replacing Cd atoms of the monolayer adsorbed on Hollow-hcp, is shown in Fig. 6. In this case, there is an the overlap between the Ag d and Cd d bands between 7.5 and 10 eV for both concentrations, and not only for high concentrations of Cd. Again, the observed gap between certain peaks of the s bands (Fig. 6a and c) may be due to the overlap between Ag d band and Ag and Cd s bands that spread over a wide range of energy. Despite this fact, the overlapping of the Ag s and Cd s bands from 7.5 eV to 0 eV seems to be the main source of contribution to the bond between the Ag and Cd, existing also a greater degree of overlap at CCd = 0.89. For Ag–Cd surface alloys formed by replacing the Ag substrate atoms by Cd atoms at CCd = 0.5, the behavior is similar to that observed when the formation mechanism is the creation of vacancies in a monolayer of Cd. This is consistent with the fact that the obtained structure is the same. This behavior can be seen in Fig. 7. An interesting effect is observed at CCd = 0.11, in which not only the
overlap of the Ag s and Cd s bands is observed, but also Ag d and Cd d bands throughout the valence band. This effect is probably responsible for a higher charge transfer to the structure 3 3 with respect to 2 1 (see Table 4). A large amount of Ag atoms with 5 s unpaired atomic orbital, allow the promotion of electrons of the Ag d and Cd d bands to the Ag s band, resulting in partially filled Ag d and Cd d bands, as observed in the plot of Fig. 7d, which have a higher density of unoccupied states. At the same time, probably there are interactions between s and d bands, because they are in the same energy range, and there is some shift between the peaks of the Cd s and Ag s bands, and between Ag d and Cd d bands. Similar results to those observed for the Ag(1 1 1) surface alloys were also obtained for Ag(1 0 0) surface alloys, despite having different structure. Therefore, the behavior of the electronic structure is more dependent on the composition or Ag–Cd ratio of the structure formed. To conclude this section, it can be seen that in most of the analyzed structures, the interaction between Ag and Cd atoms occurs mainly through s bands overlap. This behavior leads to bond formation with angles of approximately 180° due to the radial symmetry of the orbital s, which is reflected in the geometric structure of the analyzed systems after atomic relaxation, since they do not present reconstructions, neither appreciable variation in their structures.
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2x1 CCd=0.5
1,0
(a) 0,8
PDOS (arb.units)
(b)
sAg
dAg
sCd
dCd
0,6
0,4
0,2
0,0 -10
-5
0
5
10 -10
-5
E-E Fermi
5
10
E-E Fermi
3x3 CCd=0.11
1,0
(c)
(d)
sAg
0,8
PDOS (arb.units)
0
dAg dCd
sCd
0,6
0,4
0,2
0,0 -10
-5
0
5
10 -10
-5
0
5
10
E-E Fermi
E-E Fermi
Fig. 7. PDOS on Cd and Ag atoms from the surface for two different structures of the surface alloy, corresponding to a CCd of 0.5 and 0.11. These alloys were obtained by substitution for Cd atoms, in certain positions, the Ag atoms from the Ag(1 1 1) surface.
4. Conclusions
Acknowledgments
Adsorption of Cd atoms and a Cd monolayer on silver surface was studied by DFT calculations. Hollow sites were found to be the most stables sites for Cd adsorption for both, adatoms and a monolayer either for (1 1 1) or (1 0 0) orientations. The adsorption energy increases for a complete monolayer adsorption, showing the tendency of Cd to adsorbed in an epitaxial compact way. Comparison of these results with those obtained for the formation of surface alloy on the analyzed surfaces, allow us to predict more stable structures when the Ag and Cd are alloyed, for two different mechanism of substitution. These results are in consonance with electrochemical results that support the formation of surface alloy for the Cd–Ag system, allowing us to infer that the alloy formation process is favored by an electronic influence besides other interactions like the solvent and adsorption of anions. PDOS analysis shows that the interaction of Ag and Cd occurs predominately by the overlap of the s bands of these atoms on the surface. Only at low concentrations of Cd, the interaction occurs via the overlap of d bands, explaining the larger electron transfer of Cd to Ag in this case, obtained by the Bader method. Also by this technique, we can infer that the bond of Ag and Cd atoms is stronger when these metals are alloyed, due to a considerable higher charge transfer obtained for this case.
The authors are grateful for the financial support from PICT 1770, SGCyT-UNS PGI 24/F048 and PGI 24/F128. R.E. Ambrusi and M.E. Pronsato are members of CONICET. References [1] E. Budevski, G. Staikov, W.J. Lorenz, Electrochemical Phase Formation and Growth: An Introduction to the initial Stages of Metal Deposition, VCH, Weinheim, 1996. [2] H. Bort, K. Jüttner, W.J. Lorenz, E. Schmidt, J. Electroanal. Chem. 90 (1978) 413– 424. [3] W.J. Lorenz, H.D. Herrmann, N. Wüthrich, F. Hilbert, J. Electrochem. Soc. 121 (1974) 1167–1177. [4] T. Vitanov, A. Popov, G. Staikov, E. Budevski, W.J. Lorenz, E. Schmidt, Electrochim. Acta 31 (1986) 981–989. [5] A. Bewick, B. Thomas, J. Electroanal. Chem. 65 (1975) 911–931. [6] K. Takayanagi, D.M. Kolb, K. Kambe, G. Lehmpfuhl, Surf. Sci. 100 (1980) 407– 422. [7] S.G. Garcia, D. Salinas, C. Mayer, J.R. Vilche, H.-J. Pauling, S. Vinzelberg, G. Staikov, W.J. Lorenz, Surf. Sci. 316 (1994) 143–156. [8] W.J. Lorenz, G. Staikov, Surf. Sci. 335 (1995) 32–43. [9] S. Manne, P.K. Hansma, J. Massie, B.V. Elings, A.A. Gewirth, Science 251 (1991) 183–186. [10] W. Obretenov, U. Schmidt, W.J. Lorenz, G. Staikov, E. Budevski, D. Carnal, U. Miiller, H. Siegenthaler, E. Schmidt, Faraday Disc. 94 (1992) 107–116. [11] G. Staikov, K. Jüttner, W.J. Lorenz, E. Budevski, Electrochim. Acta 39 (1994) 1019–1029.
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Computational Materials Science journal homepage: www.elsevier.com/locate/commatsci
DFT study of the formation of Cd–Ag surface alloys on Ag surfaces Rubén E. Ambrusi a, Silvana G. García b, María E. Pronsato a,⇑ a b
Departamento de Física, Universidad Nacional del Sur & IFISUR (UNS-CONICET), Av. Alem 1253, 8000 Bahía Blanca, Argentina Departamento de Ingeniería Química, Universidad Nacional del Sur e Instituto de Ing. Electroquímica y Corrosión (INIEC), Av. Alem 1253, 8000 Bahía Blanca, Argentina
a r t i c l e
i n f o
Article history: Received 26 January 2016 Received in revised form 13 March 2016 Accepted 15 March 2016
Keywords: Adsorption energies Cadmium Silver Surface alloy Density functional calculations Underpotential deposition
a b s t r a c t We investigate the feasibility of forming a surface alloy between Ag and Cd on Ag surfaces, employing Density Functional Theory calculations. Six layers slabs are used to model surface alloy systems. Adsorption energies for Cd atoms and a monolayer on Ag(1 1 1) and Ag(1 0 0) surfaces are calculated, and compared with surface alloy formation energies, verifying the energetic preference of Ag and Cd to stay in alloyed form on the surface, as found in different electrochemical experiences for this system. This means that there is an electronic effect which favors this type of phenomenon. An analysis of the charge densities and projected densities of states for the different structures proposed is also performed. Ó 2016 Elsevier B.V. All rights reserved.
1. Introduction Underpotential deposition (UPD) of metals is of great importance for the chemistry and physics of solid/liquid interfaces, electrocrystallization, electrocatalysis, and electrodeposition of alloys and heterostructured ultrathin films [1]. Early metal UPD electrochemical experiments on metal single crystals faces by different authors [2–6], showed evidence of the formation of ordered bidimensional overlayers onto the monocrystals surface. Later, the monocrystalline substrate and the bidimensional overlayers structures formed by UPD were investigated on an atomic level, combining electrochemical measurements with in situ scanning probe techniques such as scanning tunneling microscopy (STM) and atomic force microscopy (AFM) [7–12]. The UPD process occurs when the interaction between the adsorbed and substrate atoms is stronger than the adsorbed atoms interaction between themselves; then it is feasible, in principle, that a site exchange between the adsorbate and substrate atoms occurs after adsorption, resulting in the formation of surface alloys [1]. The Cd/Ag system has been extensively studied experimentally by electrochemical techniques and by in-situ STM, analyzing the Cd UPD on Ag(1 1 1), Ag(1 0 0) and polycrystalline silver [13–16]. Cd UPD deposition on Ag(1 1 1) and Ag(1 0 0) occurs epitaxially, starting with the deposition of expanded monolayers, which then leads to compact monolayers by a first order phase transition ⇑ Corresponding author. Tel./fax: +54 291 4595142. E-mail address: [email protected] (M.E. Pronsato). http://dx.doi.org/10.1016/j.commatsci.2016.03.025 0927-0256/Ó 2016 Elsevier B.V. All rights reserved.
[1,15,17]. Different electrochemical measurements suggest that the formed Cd monolayers are in some conditions unstable resulting in the formation of Cd–Ag surface alloys on Ag(1 0 0) and Ag (1 1 1) [13–15,18]. The phenomenon of surface alloys is also supported by previous studies that show the formation of surface alloy between Ag and Cd during the Cd UPD onto Ag irregular and polycrystalline substrates [19,20]. Cd UPD on Ag surfaces has become an important method for ultrathin Cd/Ag films formation onto Au (1 1 1) substrates [21]. The Cd–Ag system and the formation of surface alloy between these two metals, are interesting also due to the potential catalytic effect for the electroreduction of the nitrate ion which Ag and Cd have shown individually [22–25], and is a process of great significance in effluents detection and treatment. The Cd–Ag system has also been studied theoretically. Density functional theory (DFT) calculations on Cd–Ag bulk alloys have been performed by Curtarolo et al. [26], to establish the most stable structures at different Cd and Ag compositions. Additionally, Chouhan et al. [27] have calculated electronic, elastic and mechanical properties of bulk Ag–Cd alloy at the ground state. However, even though extensive theoretical studies have been carried out on surface binary alloys [28,29] including Bi, Pt, Pd and Sb deposition on Ag(1 1 1) [30–33], Cd–Ag surface alloys have not been analyzed by first principles calculations. In addition, most of these works on surface alloys were based on experimental works that include vapor deposition technique [30,34–36] but not the electrochemical UPD method. In this work, we employ DFT calculations to make a first attempt to evaluate the interaction between Cd and Ag in surface
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alloys onto Ag(1 1 1) and Ag(1 0 0) surfaces and the mechanisms that intervene in their formation. There is evidence that the formation process of the surface alloy between these two metals, starts on the substrate surface defects at low coverage or high underpotentials while in the case of high coverage or low underpotentials, alloy formation is independent of the inhomogeneities on the surface, like the density of monoatomic steps [1]. Therefore, the study of the feasibility of formation of surface alloy was performed using a model that does not contain inhomogeneities on the surface and in principle represents the situation at low underpotentials. 2. Computational method DFT calculations were performed using the Viena Ab-initio Simulation Package (VASP) [37–40], which employs a plane-wave basis set and a periodic supercell method. The generalized gradient corrected approximation (GGA) Perdew, Burke, and Ernzerhof (PBE) functional was used [41]. The Kohn–Sham equations were solved variationally using the projector-augmented-wave (PAW) method [42,43]. Spin polarization was considered in all calculations, observing no magnetization for the different systems analyzed. For bulk calculations, DFT parameters such as kinetic cutoff energy value (Ecut), k-points set and smearing function, were optimized. This task was carried out using the Methfessel-Paxton first order smearing approach, for the partial occupancies for the electronic states near the Fermi level. For all calculations, a smearing width of 0.2 eV was used. Analysis of the system energy shows that the use of a 13 13 13 Monkhorst–Pack k-point grid to sample the Brillouin Zone and Ecut = 400 eV, is enough for the total energy to converge within 10 meV. Geometry optimizations were obtained by minimizing the total energy of the unit cell using a conjugated gradient algorithm to relax ions [44]. Slab models were employed for surface calculations. Surface energy was calculated for slabs with increasing number of layers in order to determine the number of layers necessary for our model. During calculations, DFT parameters previously obtained from bulk optimization and a 13 13 1 k-points grid were used, concluding that five layers are enough to ensure surface energy convergence (see Table 1). Eq. (1) was used for calculating the surface energy (r), where Eslab is the total energy of the slab, nAg is the number of silver atoms in the slab model and Ebulk is the energy per atom for silver bulk.
r¼
ðEslab nAg Ebulk Þ 2
ð1Þ
Details on the slab model will be given in the following sections. The surface energies calculated, shown in Table 1, were obtained for a 1 1 slab. The values of the surface energies calculated are in agreement with values obtain from literature [45]. Eqs. (2a) and (2b), were used to calculate the adsorption energy for an adatom (Eadadat ) and a monolayer of unitary coverage (Eadmon ), where ESurfAg is the energy of the clean silver surface (Ag(1 1 1) or
Ag(1 0 0)), ECd is the energy of an isolated Cd atom and nCd is the number of Cd atoms adsorbed.
Eadadat ¼
ECdadat =SurfAg ESurfAg ECd nCd
ð2aÞ
Eadmon ¼
ECdmon =SurfAg ESurfAg nCd ECd nCd
ð2bÞ
With this definition a negative adsorption energy corresponds to a stable adsorption on the surface. To evaluate the surface alloy formation between Ag and Cd, two mechanisms were considered. One where Cd atoms replace Ag atoms from the surface, and another where Ag atoms replace Cd atoms from a Cd monolayer formed on the Ag surface. These two mechanisms are shown schematically in Fig. 1. SAgsCd indicates the substitution of Ag surface atoms by Cd atoms (Fig. 1a)), while SCdmAg represents the substitution of Cd atoms of a preformed Cd monolayer (Fig. 1b)), by Ag atoms. To calculate the formation energy of the surface alloy, both mechanisms were considered using Eqs. (3a) and (3b) for SAgsCd and SCdmAg respectively, based on equations of previous theoretical studies on the subject [30,46,47].
Efa1 ¼
Efa2 ¼
ðEAgCdalloy EsurfAg þ nAg EbulkAg nCd ECd Þ
ð3aÞ
nCd ðEAgCdalloy ECdmon=surfAg þ nCd EbulkCd nAg EAg Þ nAg
ð3bÞ
EAgCdalloy is the energy of the alloy slab, with the substitution of Ag surface atoms by Cd atoms in Eq. (3a); and Cd atoms from the monolayer by Ag atoms in Eq. (3b). Regarding the other terms; ECdmon=surfAg , is the energy of the Ag surface with a Cd monolayer adsorbed, EAg and ECd are the energies of Ag and Cd isolated atom, respectively, EbulkAg and EbulkCd , are the energies of Ag and Cd atom in the bulk respectively. Finally, in Eq. (3a) nAg and nCd represent the number of Ag atoms removed from the surface and the number of Cd solute atoms respectively, whereas in Eq. (3b), nAg and nCd represent the number of Ag solute atoms and the number of Cd atoms removed respectively. EAg and ECd in Eqs. (3a) and (3b) respectively, have a dual function. First, subtracting the energy contribution from the system solute atoms, in order to obtain the bond contribution between solvent and solute. They also are reference values with respect to which the alloy formation energies are calculated. Using the EbulkAg or
(a)
SAgsCd
(b)
SCdmAg
Table 1 Surface energy for Ag surfaces (1 1 1) and (1 0 0). Number of layers
3 4 5 6 7
Surface energy/eV Ag(1 1 1)
Ag(1 0 0)
0.314 0.339 0.327 0.331 0.331
0.436 0.426 0.423 0.422 0.423
Cd
Ag
Fig. 1. Schematic representation for the alloy formation through a substitution mechanism. (a) Surface Ag atoms are substituted by Cd atoms. (b) Cd atoms from a monolayer adsorbed onto Ag surface are substituted by Ag atoms.
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EbulkCd instead of EAg or ECd , would lead to results for Efa1 and Efa2 that could not be compared. In this way we are substracting the energy contribution of Ag or Cd atoms from the energy gain due to the Ag–Cd interaction, isolating the effective Ag–Cd binding energy. The formation energy for the surface alloy was calculated for different structures of bidimensional Ag–Cd alloy. Structures pffiffiffi pffiffiffi pffiffiffiffiffiffi pffiffiffiffiffiffi 2 1, ð 3 3ÞR30 , 2 2, ð 19 19ÞR19 and 3 3 were used, where the length of the surface alloy unit cell lattice vectors, with respect to the Ag(1 1 1) primitive cell lattice vectors, are indicated. The bidimensional alloy lattice vectors point towards the Cd atoms in the case of the Ag surface or the Ag atoms in the case of the Cd adsorbed monolayer. In the case of rotated structures, the letter R is added followed by the magnitude of the rotated angle, which represents the angle between the surface lattice vectors and that of the alloy structure. The Cd monolayer was adsorbed on Top and Hollow-hcp sites, which are represented in our nomenclature by the letters T or Hhcp added to the right of SCdmonAg. Each structure corresponds to different Cd surface concentrations (CCd), defined as (Cd atoms on the surface)/(Cd + Ag atoms on the surface). Following the same procedure, a 2D alloy was obtained for the Ag(1 0 0) surface, considering the structures pffiffiffi pffiffiffi ð 2 2ÞR45 , 2 2 and 3 3 for the unit cell, in which the unit cell lattice vectors are referred to the primitive cell for Ag(1 0 0) surface. The surface alloys were obtained by substituting Ag surface atoms by Cd atoms, and Cd by Ag in the Cd monolayer adsorbed on Top and Hollow. A scheme of the structures obtained for some of the different cases are shown in Fig. 2. Six layers slabs were used to perform the calculations of the surface alloy, with a vacuum space of approximately 12 Å. The size of the slab in the direction parallel to the surface was varied
according to the structure studied. In each case a k-points optimization was made to obtain converged results. In all cases, the first four layers were allowed to relax, leaving the two bottom layers fixed at their bulk positions. In order to analyze the electronic structure, the electronic charges on atoms were computed using Bader analysis [48] and the atom projected density of states (PDOS) was obtained by projection of the one-electron wave functions onto atomic Bader volumes [49]. 3. Results 3.1. Bulk and surface structures optimization In order to test the reliability of our calculations some properties were calculated and compared with experimental data from literature. A geometry optimization was performed to determine silver fcc and cadmium hcp lattice parameters. Ion positions, cell volume and cell shape were allowed to simultaneously relax. The calculated lattice parameter is a = 4.154 Å for silver, which overestimates 1.6% the experimental value of 4.09 Å [50]. In the case of cadmium the calculated lattice parameters are a = 3.018 Å and c = 5.845 Å, in good agreement with the experimental values (a = 2.98 Å, c = 5.62 Å) [50]. For the case of bulk Cd, an Ecut = 500 eV and a 15 15 15 gamma centered k-point grid were used. The Ag(1 1 1) and Ag(1 0 0) surfaces were modeled with a slab consisting of five silver layers within a 3 3 unit cell and a vacuum spacing between slabs of about 10 Å. The size of the supercell is large enough to allow further study of Cd adsorption and the
Alloy structures in Ag(111) surface a1 a1
a1
a2 a1
a2
a2
SAgsCd-2x1
a2
Ag second layer
SCdmAg-Hhcp-
Ag surface
Cd surface
Alloy structures in Ag(100) surface
a1 a2
a1 a2
a2 a1
a2
a1
SAgsCd-2x2
SCdmAg-H-
Fig. 2. Scheme of some structures of surface alloy formed on Ag(1 1 1) and Ag(1 0 0), by substitution of the Ag surface atoms or by substitution of Cd atoms of the adsorbed monolayer.
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vacuum spacing ensures no interaction between slabs. The k-points were reduced to 11 11 1, in this case. Silver atoms on the surface were allowed to relax in all directions for the top three layers, keeping the bottom two layers fixed. No change in the positions of silver atoms in the direction parallel to the surface was found as expected for a symmetric surface, presenting no reconstruction. Only some surface relaxation for both surfaces occurs. The Ag(1 1 1) surface evidences an expansion of the first interlayer of approximately 0.018 Å, then the second and third interlayer changes with respect to the bulk ideal interlayer distance are negligible. Regarding the Ag(1 0 0) surface, it shows a little contraction in the first interlayer distance of approximately 0.031 Å and an expansion of the second interlayer of approximately 0.014 Å, with no noticeable change in the third interlayer.
Table 2 Adsorption energies for an adatom and a Cd monolayer on Ag(1 1 1) and Ag(1 0 0). System
Eadmon (eV/at.)
Ag(1 1 1)
Top Bridge Hollow-fcc Hollow-hcp
0.478 0.649 0.688 0.687
0.854 0.955 0.971 0.975
Ag(1 0 0)
Top Bridge Hollow
0.444 0.562 0.759
0.699 0.806 0.925
Table 3 Theoretical and experimental binding energies and equilibrium distances of dimmers.
3.2. Cd adsorption on Ag(1 1 1) and Ag(1 0 0)
Dimmer
The Cd adsorption energy on Ag(1 0 0) and Ag(1 1 1) surfaces, whether for an adatom or a complete monolayer, was evaluated on different sites in order to elucidate the factors involved in these processes in vacuum. For calculating the absolute adsorption energy for a Cd adatom and a monolayer on the Ag surface, Eqs. (2a) and (2b) were used respectively. The different adsorption sites used for the calculations are shown schematically in Fig. 3, and Table 2 summarizes the adsorption energies calculated in each case. These results show that adsorption energies are noticeably lower for the monolayer formation, which evidences an energetic gain due to the electronic interaction with the neighboring atoms which favor its formation. This stabilization explains why the difference between the adsorption energy for an adatom and for the monolayer is greater for the Ag(1 1 1) than the Ag(1 0 0) surface. Due to the difference in their structures, the Cd atoms on Ag (1 1 1) have a higher coordination number. It can also be observed that the adsorption energy for a Cd adatom in Hollow-fcc site on Ag (1 1 1) is less negative than for a Cd adatom in a Hollow site on Ag (1 0 0). We presume that this is, again, due to the different structure of the surfaces. In this case the Ag(1 1 1) have an hexagonal structure which gives a coordination number of three for a Cd adatom on Hollow site, while Ag(1 0 0) have a square structure with coordination number four, giving a more stable adsorption on Hollow site for Ag(1 0 0). Based on these results, and taking into account that the Cd–Cd binding energy (see Table 3) is smaller than the Cd–Ag surface interaction (Table 2), we can predict that Cd will prefer to form ordered structures in an epitaxial way on the Ag surface, as was
Eadadat (eV/at.)
Ag Cd Ag–Cd
Theoretical calculation
Experimental
Ebinding/eV
Equilibrium distance/Å
Ebinding/eV
Equilibrium distance/Å
1.75 0.014 0.339
2.58 3.49 2.76
1.65 [51] 0.03 [51] –
2.53 [52] 3.02 [51] –
observed by García et al. [15], during the Cd UPD deposition on Ag(1 1 1) surface. The most stable site was found to be Hollow for the Ag(1 0 0) surface for both cases; the formation of the monolayer and for an adatom, while for the Ag(1 1 1) surface the hollow-hcp is slightly the most stable position for the formation of the monolayer and the Hollow-hcp and fcc hollow-sites are also the most stable sites for an adatom.
3.3. Cd–Ag surface alloy formation on Ag(1 1 1) and Ag(1 0 0) surfaces The surface alloy formation energy for both mechanism, and different Cd concentrations, on Ag(1 1 1) and Ag(1 0 0) is plotted in Fig. 4a and b respectively. To interpret the SAgsCd mechanism results, it should be noted that there is an energy cost when Ag atoms from the surface are replaced by Cd atoms. This is because the Ag–Cd binding energy is lower than the Ag–Ag binding energy (see Table 3), therefore, the interaction energy with the Ag–Cd does not exceed the energy required to generate a surface vacancy. However, the Ag atoms removed from the surface to form the alloy, were considered to remain in an adjacent pure Ag surface, using
Ag (111)
Ag (100)
a1
a1
a2
a2
Ag second layer
Ag surface
Fig. 3. Scheme of the adsorption sites on Ag(1 1 1) and Ag(1 0 0) surface.
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(a)
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0,0
Efa(eV/atom)
-0,5 -1,0 -1,5
Monolayer SAgsCd SCdmAg-T
-2,0
SCdmAg-Hhcp
-2,5 -3,0
0,0
0,1
0,2
0,3
0,4
0,5
0,6
0,7
0,8
0,9
1,0
0,6
0,7
0,8
0,9
1,0
CCd
(b)
0,0
Efa(eV/atom)
-0,5 -1,0 -1,5
Monolayer SAgsCd SCdmAg-T
-2,0
SCdmAg-H
-2,5 -3,0
0,0
0,1
0,2
0,3
0,4
0,5
CCd Fig. 4. Surface alloy formation energy by substitution mechanisms for: (a) Ag(1 1 1) surface, (b) Ag(1 0 0) surface, corresponding to different structures (different concentrations). Also the corresponding formation energy for a Cd monolayer in the most stable position is plotted.
the silver bulk energy in Eq. (3a), because at low temperatures, considering the equilibrium between atoms on surface and in bulk positions is valid. Considering that the Ag atoms, are not carried to the infinity, it is consistent with the fact that experimentally, the
alloy formed by the electrochemistry method between Ag and Cd uses potentials at which no Ag dissolution is observed because Ag is more noble than Cd [15]. Comparing these results with the adsorption energy of a Cd monolayer on the most stable site (Hollow-hcp), it can be observed that the alloy formation by substitution of substrate atoms is more stable for the different concentration of Cd. However, experimentally it is observed that the Cd monolayer forms first with high recovery and after long polarization times the formation of the alloy occurs [1]. Fig. 4a also shows the alloying energy calculations at different concentrations by the SCdmAg mechanism, that is, by the introduction of Ag atoms in vacancies formed in the Cd monolayer on the Ag(1 1 1) surface, with the monolayer on Hollow and Top sites. Based on these results, it is observed in the tested concentration range, that the alloying energy by this mechanism is vastly more favorable than the formation of a monolayer on the surface in the most stable position and alloying by substitutions of the atoms from the Ag surface by Cd atoms. This would indicate the possibility of alloy formation at different Cd concentrations, by inserting Ag atoms in the Cd monolayer through vacancies created in it. The effect that makes this mechanism much more favorable, is the fact that the substitution of Cd atoms in the monolayer by Ag atoms, is exothermic and therefore spontaneous from a thermodynamic point of view (this last affirmation strictly at 0 K and vacuum). The increased stability is given by the formation of Ag–Cd bonds stronger than Cd–Cd bonds, when Cd is replaced by Ag. Contrasting the results in Fig. 4a and b, no significant changes were observed in the calculated energies, however the alloys on Ag (1 1 1) surface have a slightly higher stability. Through the analysis made in this section, it can be suggested that the bimetal alloy between Ag and Cd occurs first with the formation of the monolayer of Cd and then with the introduction of Ag atoms in it, through vacancies. A similar mechanism was proposed by other authors [13], as a model for the Ag–Cd surface alloy formation, based on experimental results obtained during the UPD deposition of Cd on Ag(1 0 0) and Ag(1 1 1) at long polarization times. In this model, the formation of a Cd monolayer in which Ag diffuses from the surface to the monolayer vacancies is proposed. It should be clarified that being rigorous, the theoretical treatment used in this section does not apply exactly to this case because it is assumed that the Ag does not belong to the substrate. Nevertheless, the results obtained here allow us to demonstrate quantitatively the Cd preference to alloy with Ag on a Cd monolayer adsorbed on the metal and not directly on the substrate. This type of mechanism is also applicable in the case of both atoms, Ag and Cd, are present in the solution used to obtain Ag–Cd structures,
Table 4 Bader charges for Ag and Cd in the surface alloy. System
Surface alloy of Ag(1 1 1)
Electronic gain or loss of the solute atom
Substrate substitution Substitution in the Cd monolayer
Surface alloy of Ag(1 0 0)
Substrate substitution Substitution in the Cd monolayer
2 1 (CCd = 0.50) 3 3 (CCd = 0.11) 2 1 T (CCd = 0.50) 3 3 T (CCd = 0.89) 2 1 Hhcp (CCd = 0.50) 3 3 Hhcp (CCd = 0.89) pffiffiffi pffiffiffi 2 2 R45° (CCd = 0.50) 3 3 (CCd = 0.11) pffiffiffi pffiffiffi 2 2 R45° T (CCd = 0.50) 3 3 T (CCd = 0.89) pffiffiffi pffiffiffi 2 2 R45° H (CCd = 0.50) 3 3 H (CCd = 0.89)
Ag
Cd
– – 0.1289 0.1951 0.1332 0.1856
0.1888 0.2622 – – – –
–
0.2148
– 0.1809
0.2913 –
0.1051 0.1566
– –
0.1334
–
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to 0.26 e- for Ag(1 1 1) surface and 0.21–0.29 e for the Ag(1 0 0) surface. These electronic transfers far exceed those found in the adsorption of Cd on Ag surfaces, suggesting a stronger interaction between Ag and Cd atoms when these metals are alloyed. In order to study the origin of the increase in the charge transfer in alloyed structures, projected density of states (PDOS) on Bader volumes was calculated for selected atoms in the structures studied. The states calculated in all cases are normalized, so the graphs heights are not comparable and the only objective is to establish the energy range for the interaction between orbitals. Fig. 5 shows the PDOS obtained for 2 1 and 3 3 structures, in the case of the alloy formed by the replacement of Cd atoms in a monolayer in Top position on Ag(1 1 1) surface by Ag atoms. A high degree of overlap between Cd and Ag s bands is observed on the surface, at the CCd = 0.89. For a CCd = 0.5, the degree of overlap between the s bands is smaller, and it is possibly, more influenced by the interaction between the Ag d band with the Ag and Cd s bands. Furthermore, there is a small overlap between the Ag d and Cd d bands, because of the peaks appearing at lower energies to 7.5 eV, although the d bands practically do not overlap with each other. The fact that s bands overlap more than d bands, can be understood on the basis that; the s bands are partially filled bands, because both the valence band and the conduction band contain states
as was found in the Ag–Cd electrochemical system by del Barrio et al. [53]. These authors established the formation of alloy between these metals, which not only can occur by solid state diffusion of the metal atoms, but also by the effect of the co-deposition of Ag while the UPD deposition of Cd is occurring. 3.4. Electronic structure analysis Initially Bader analysis was performed for the different systems studied in this work. The net charges in the case of the Cd monolayer adsorption on Ag surfaces show that Cd loses 0.07 to 0.09 e while Ag atoms in the surface receives e approximately in the same amount. The values of charge transfer are quite small, justifying the low Cd adsorption energy on the Ag surface. In Table 4, the gain or loss of electrons are specified, for the atom in low proportion (solute) forming the alloy for the different surface alloy structures corresponding to extremes of Cd surface concentration. For the different configurations, alloys formed by replacement of atoms in the Cd monolayer, present electronic transfers between 0.13 to 0.20 e- for the Ag(1 1 1) surface, and 0.10–0.18 e for the Ag(1 0 0) surface. In the case of substitution of Ag atoms of the surface by Cd atoms, Cd presents electronic losses from 0.19
2x1 T CCd=0.5
1,0
(a) 0,8
PDOS (arb.units)
(b)
sAg sCd
0,6
dAg dCd
0,4
0,2
0,0 -10
-5
0
5
10
-10
-5
5
10
3x3 T CCd=0.89
1,0
(d)
(c) 0,8
PDOS (arb.units)
0
E-E Fermi
E-E Fermi
sAg
dAg
sCd
dCd
0,6
0,4
0,2
0,0 -10
-5
0
E-E Fermi
5
10
-10
-5
0
5
10
E-E Fermi
Fig. 5. PDOS on Cd and Ag atoms from the surface for two different structures of the surface alloy, corresponding to a CCd of 0.5 and 0.89. These alloys were obtained by substitution, in certain positions, for Ag atoms the atoms of a Cd monolayer, on Top site, adsorbed on Ag(1 1 1) surface.
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2x1 Hhcp CCd=0.5
1,0
(a) 0,8
PDOS (arb.units)
(b)
sAg sCd
0,6
dAg dCd
0,4
0,2
0,0 -10
-5
0
5
10
-10
-5
5
10
3x3 Hhcp CCd=0.89
1,0
(c)
(d) sAg
0,8
PDOS (arb.units)
0
E-E Fermi
E-E Fermi
sCd
dAg dCd
0,6
0,4
0,2
0,0 -10
-5
0
5
E-E Fermi
10
-10
-5
0
5
10
E-E Fermi
Fig. 6. PDOS on Cd and Ag atoms from the surface for two different structures of the surface alloy, corresponding to a CCd of 0.5 and 0.89. These alloys were obtained by substitution, in certain positions, for Ag atoms the atoms of a Cd monolayer, on Hhcp site, adsorbed on Ag(1 1 1) surface.
(Fig. 5a and c) while d bands are practically filled because they exhibit a density of states negligible above EF (Fig. 5b and d). This leads to greater interaction between the Cd s and Ag s bands. This behavior is expected because of the electronic configuration of these elements, [Kr] 5s1 4d10 and [Kr] 5s2 4d10 for Ag and Cd respectively; that have 4d atomic orbital filled. The same behavior for high and medium Cd concentrations in surface alloys formed by replacing Cd atoms of the monolayer adsorbed on Hollow-hcp, is shown in Fig. 6. In this case, there is an the overlap between the Ag d and Cd d bands between 7.5 and 10 eV for both concentrations, and not only for high concentrations of Cd. Again, the observed gap between certain peaks of the s bands (Fig. 6a and c) may be due to the overlap between Ag d band and Ag and Cd s bands that spread over a wide range of energy. Despite this fact, the overlapping of the Ag s and Cd s bands from 7.5 eV to 0 eV seems to be the main source of contribution to the bond between the Ag and Cd, existing also a greater degree of overlap at CCd = 0.89. For Ag–Cd surface alloys formed by replacing the Ag substrate atoms by Cd atoms at CCd = 0.5, the behavior is similar to that observed when the formation mechanism is the creation of vacancies in a monolayer of Cd. This is consistent with the fact that the obtained structure is the same. This behavior can be seen in Fig. 7. An interesting effect is observed at CCd = 0.11, in which not only the
overlap of the Ag s and Cd s bands is observed, but also Ag d and Cd d bands throughout the valence band. This effect is probably responsible for a higher charge transfer to the structure 3 3 with respect to 2 1 (see Table 4). A large amount of Ag atoms with 5 s unpaired atomic orbital, allow the promotion of electrons of the Ag d and Cd d bands to the Ag s band, resulting in partially filled Ag d and Cd d bands, as observed in the plot of Fig. 7d, which have a higher density of unoccupied states. At the same time, probably there are interactions between s and d bands, because they are in the same energy range, and there is some shift between the peaks of the Cd s and Ag s bands, and between Ag d and Cd d bands. Similar results to those observed for the Ag(1 1 1) surface alloys were also obtained for Ag(1 0 0) surface alloys, despite having different structure. Therefore, the behavior of the electronic structure is more dependent on the composition or Ag–Cd ratio of the structure formed. To conclude this section, it can be seen that in most of the analyzed structures, the interaction between Ag and Cd atoms occurs mainly through s bands overlap. This behavior leads to bond formation with angles of approximately 180° due to the radial symmetry of the orbital s, which is reflected in the geometric structure of the analyzed systems after atomic relaxation, since they do not present reconstructions, neither appreciable variation in their structures.
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2x1 CCd=0.5
1,0
(a) 0,8
PDOS (arb.units)
(b)
sAg
dAg
sCd
dCd
0,6
0,4
0,2
0,0 -10
-5
0
5
10 -10
-5
E-E Fermi
5
10
E-E Fermi
3x3 CCd=0.11
1,0
(c)
(d)
sAg
0,8
PDOS (arb.units)
0
dAg dCd
sCd
0,6
0,4
0,2
0,0 -10
-5
0
5
10 -10
-5
0
5
10
E-E Fermi
E-E Fermi
Fig. 7. PDOS on Cd and Ag atoms from the surface for two different structures of the surface alloy, corresponding to a CCd of 0.5 and 0.11. These alloys were obtained by substitution for Cd atoms, in certain positions, the Ag atoms from the Ag(1 1 1) surface.
4. Conclusions
Acknowledgments
Adsorption of Cd atoms and a Cd monolayer on silver surface was studied by DFT calculations. Hollow sites were found to be the most stables sites for Cd adsorption for both, adatoms and a monolayer either for (1 1 1) or (1 0 0) orientations. The adsorption energy increases for a complete monolayer adsorption, showing the tendency of Cd to adsorbed in an epitaxial compact way. Comparison of these results with those obtained for the formation of surface alloy on the analyzed surfaces, allow us to predict more stable structures when the Ag and Cd are alloyed, for two different mechanism of substitution. These results are in consonance with electrochemical results that support the formation of surface alloy for the Cd–Ag system, allowing us to infer that the alloy formation process is favored by an electronic influence besides other interactions like the solvent and adsorption of anions. PDOS analysis shows that the interaction of Ag and Cd occurs predominately by the overlap of the s bands of these atoms on the surface. Only at low concentrations of Cd, the interaction occurs via the overlap of d bands, explaining the larger electron transfer of Cd to Ag in this case, obtained by the Bader method. Also by this technique, we can infer that the bond of Ag and Cd atoms is stronger when these metals are alloyed, due to a considerable higher charge transfer obtained for this case.
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