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Surface relaxation and surface stress of Au(1 1 1)
Surface Science 513 (2002) 263–271 www.elsevier.com/locate/susc
Surface relaxation and surface stress of Au(1 1 1) R.J. Nichols
a,*
, T. Nouar b, C.A. Lucas b, W. Haiss a, W.A. Hofer
c
a
Department of Chemistry, University of Liverpool, Liverpool L69 7ZE, UK Oliver Lodge Laboratory, Department of Physics, University of Liverpool, Liverpool L69 7ZE, UK Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT, UK b
c
Received 1 November 2001; accepted for publication 27 February 2002
Abstract Changes in surface stress and in the top-layer expansion of Au(1 1 1) electrodes in sulfuric acid have been measured as a function of electrode potential by combining surface stress and X-ray diffraction measurements. Both are linear functions of interfacial charge in the electrode potential range of changing anion coverage. Over this range the surface stress changes by 0.5 N m1 (compressive direction), while the outward top-layer relaxation decreases from þ1.5% to þ0.2%. The surface stress changes can be rationalized in terms of a jellium model, while ab initio simulations are needed to explain the top-layer expansion. These simulations yield þ1.3% relaxation for the uncharged gold surface, in good agreement with the X-ray diffraction measurements. They also demonstrate that the outward relaxation of the surface is curbed in the presence of an electron withdrawing adsorbate (Cl), which mimics the effects of positive surface charging. Ó 2002 Elsevier Science B.V. All rights reserved. Keywords: Surface stress; Surface relaxation and reconstruction; X-ray scattering, diffraction, and reflection; Density functional calculations; Gold
1. Introduction The bonding and electronic structure of substrate surfaces can be affected by molecular chemisorption. The bonding in the outmost substrate layers can have significant effects on surface structure and dynamics, leading to phenomena such as surface reconstruction or enhanced substrate mobility [1]. Electrochemists have the unique ability to affect the bond strengths of the substrate surface, by tuning the electrode potential and consequently altering the surface electronic
*
Corresponding author.
structure. These changes in surface bond strengths are not at present directly measurable, but they result in changes in the surface energy, surface stress, top-layer surface relaxation and in extreme cases surface reconstruction; all of which can now be monitored in situ [2–5]. In this paper in situ measurements of surface stress and outward surface relaxation are presented and compared. Surface stress has been measured previously at the metal–electrolyte interface using a number of mechanical methods to monitor strain changes in the electrode [4,6–13]. Although some of the results on polycrystalline samples were ambiguous, the more recent experiments for single crystals show that the tensile surface stress decreases linearly with increasing
0039-6028/02/$ - see front matter Ó 2002 Elsevier Science B.V. All rights reserved. PII: S 0 0 3 9 - 6 0 2 8 ( 0 2 ) 0 1 5 1 0 - 8
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electrode potential [14]. Both the natural tensile stress of metals and the increase in surface stress upon positively charging the surface can be explained by a simple qualitative model of the surface bonds, which is described in a review by Ibach [15]. This ‘‘simple bonding model’’ considers that upon cleaving a surface, the bond charge in the missing bonds that are broken by the surface termination is relocated between the surface atoms and their backbonds. The resulting increase in charge density between the surface atoms can be used to explain the tensile stress of metal surfaces [15]. The adsorption of electronegative atoms or positive surface charging removes charge from the surface bonds, effectively weakening them and causing the tensile stress to decrease (compressive stress change). This qualitative bonding model, is described later in this paper in terms of a jellium model for the surface, which is used to quantify the stress changes with surface charging. It is described how this model predicts the correct sign and magnitude of the stress change. The qualitative bonding model described by Ibach also predicts a contraction of the distance between the first and second layers (top-layer relaxation), which should be lessened by positive surface charging [15]. Top layer relaxation is measured by an X-ray diffraction technique to monitor the interlayer spacing at the surface [16,17]. X-ray diffraction has been employed for some years to monitor surface and adsorbate structures in the electrochemical environment although it has not yet been widely used to monitor top-layer relaxation of singlecrystal surfaces. In ultra-high-vacuum (UHV) surface relaxation has been monitored by means of low energy electron diffraction (LEED) I–V analysis and a significant database now exists [16, 17]. Although the outermost atomic layer on most metal surfaces in UHV shows an inward relaxation, tantamount to a reduction of the interlayer spacing between the first two layers, a number of metals exhibit outward relaxation [18]. These include Pd(0 0 1) and Rh(0 0 1) surfaces, with an outward relaxation of (3:0 1:5)% and (0:5 2)%, respectively [19,20]. Attempts to establish trends in surface relaxation effects by state-of-the-art theoretical calculations have highlighted discrepancies
both in the theoretical results and the experimental studies [21]. The Au(1 1 1) surface in aqueous surface acid provides a good model system for studying the effects of electrode potential on the top-layer relaxation and surface stress of Au(1 1 1) electrodes. The surface electrochemistry of Au(1 1 1) in aqueous surface acid is relatively well understood. pffiffiffi Sulfate adsorption assists in lifting the 22 3 surface reconstruction and at very positive potentials, close to the onset of gold surface oxidation, the sulfate ions form an ordered pffiffiffi adsorbed pffiffiffi ð 3 7Þ structure [22,23]. In between the potential at which the surface reconstruction is lifted and that at which the ordered anion overlayer is formed, there exists a defined potential region in which the coverage of the adsorbed anion varies with electrode potential on the unreconstructed (1 1) gold surface. As the potential is increased in this region the coverage of the adsorbate anion increases creating a positive image charge in the Au surface that leads to changes in the band structure at the metal surface. These changes leads to the observed changes in surface stress and in the top-layer expansion of Au(1 1 1) electrodes. It is important to note that surface reconstruction can also lead to changes in surface stress and in the top-layer expansion, but the electrochemical environment allows measurements to be made for Au(1 1 1) in the absence of the reconstructed surface. Experimentally, we were at first puzzled by an unexpected trend in surface stress and layer relaxations, when we analyzed the changes in the atomic structure of a unreconstructed Au(1 1 1) surface in sulfuric acid solution. Using the simple bonding model described in the review by Ibach, a reduction in the tensile stress of the surface (i.e. an increase of compressive surface stress) would be expected to lead to an increased outward relaxation [24]. By contrast, we observed the opposite trend, namely Au(1 1 1), in electrolyte solution, exhibits compressive stress changes (reduced tensile stress) and related inward relaxation of the top layer if it is positively charged. The simple bonding fails to explain this behaviour, since it does not take account of important energy contributions to the electronic structure of the surface. In this re-
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spect, it is noted that there is an intricate balance between cohesive energy and band energy contributions of single Au atoms. It is shown in this paper, that this balance in turn shifts the energetic groundstate (energy minimum) of the uncharged surface to the configuration with an extended interlayer distance between the first and second atomic layer. This trade-off between band energy and layer relaxation is also found in other transition metals, e.g. within the 4d series [18]. In this communication we consider how positive charging effects this trade-off of energetic contributions to electronic structure.
2. Experimental The experimental arrangement for the surface stress measurements was similar to that used in previous studies of surface stress at the electrochemical interface [4,14,25]. For these quantitative studies a cantilever sample is used, the deflection of which is tracked by the z-piezo of an STM [14,24]. The cantilever glass substrates, with dimensions of 24 2:5 0:55 mm3 (AF45, E ¼ 66 kN/mm2 , V ¼ 0:235, Berliner Glass K.G.), were coated on one side by evaporation of 2 nm of chromium followed by 200 nm of gold. The stress was evaluated from the measured deflection of the cantilever in the standard procedure according to Stoney’s equation [14,24]. Stress changes have been recorded against applied potential or charge. Compressive stress has been plotted as a negative stress change while tensile stress has been plotted with positive sign. A decrease in the natural tensile stress of the surface is referred to as a ‘‘stress change in the compressive direction’’. Prior to measurement the gold samples were flame annealed to produce (1 1 1) terraces [4]. The electrolyte solution used throughout the study was 1 M H2 SO4 . All electrode potentials are measured with reference to an oxidized gold wire and have been converted to the standard calomel reference electrode (SCE). The surface X-ray diffraction experiments were performed with a Au(1 1 1) single crystal on the XMaS CRG beamline (BM28) at the ESRF, Grenoble, and beamline 16.3 at the Daresbury
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Synchrotron Radiation Source. The crystal was aligned to <1° of the (1 1 1) surface, mechanically polished, and then electrochemically polished in a solution of 95% ethanol/5% HCl at 20 V for 15 s. Approximately 20 electropolishing cycles were conducted, each one followed by a careful annealing in a butane flame, to produce only a slight orange hue. The crystal was also flame annealed directly prior to an experiment. The crystal was then allowed to cool in air and transferred to the X-ray cell with a drop of ultra pure water protecting its surface. The electrochemical X-ray cell [26] was mounted on the X-ray diffractometer and measurements of the cyclic voltammetry confirmed that the cell was free of contamination. For the (1 1 1) surface an hexagonal unit cell is defined as used in LEED experiments, such that the surface normal is along the (0, 0, l)hex direction and the (h, 0, 0)hex and (0, k, 0)hex vectors lie in the plane of the surface and subtend 60°. Surface relaxation of Au(1 1 1) was computed using first principle density functional theory (DFT), the Vienna ab initio simulation program [27,28]. The program uses ultrasoft Vanderbilt type pseudopotentials [29] for the ionic cores and a repeated slab geometry (supercell). The twodimensional Brillouin zone was sampled with (8 8 1) k-points of a Monkhorst–Pack grid [30], the exchange correlation was parameterized following Perdew et al. (PW91) [31]. It should be noted that the relaxations depend critically on the crystal lattice constant [18]. For this reason we first computed the lattice constant within the PW91 by minimizing the bulk energy of fcc Au. This lattice (2.96 A for the reduced cell) constant of 4.19 A was used in our calculation. The set-up of the 13layer film for the simulation is shown in Fig. 1. The vacuum gap between successive films was chosen
Fig. 1. The set-up for the DFT calculations. The unit cell for vacuum gap. the simulation consists of 13 layers and a 5 A
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, which in practice is sufficient to deto be 5 A couple the two surfaces.
3. Results Fig. 2 shows a cyclic voltammogram for Au(1 1 1) in 0.1 M sulfuric acid, recorded in a hanging meniscus arrangement in a three-electrode electrochemical cell. The broad peak centered at about 0.45 V is due to the adsorption of sulfate. The peak at about p 0.3 V marks the potential at which the (23 3) reconstruction is lifted. The small current peaks close to 0.85 V have been shown to be associated with the formation of an ordered sulfate overlayer, with a coverage of 0.2 ML [32]. Between about 0.3 and 0.85 V the coverage of the adsorbed anion varies with electrode potential on the unreconstructed (1 1) gold surface. The voltammetric features shown in Fig. 2 could also be reproduced in both the X-ray diffraction cell and the surface stress electrochemical cell. The compromised electrode geometries of both cells meant that the peaks were not as sharply defined as in the hanging meniscus arrangement. The surface relaxation at the Au(1 1 1) surface was probed by X-ray diffraction using crystal truncation rod (CTR) measurements. CTRs are rods of scattering oriented along the h0; 0; li re-
Fig. 2. Cyclic voltammogram for Au(1 1 1) in 0.1 M sulfuric acid solution, sweep rate 5 mV/s.
ciprocal lattice direction passing through the bulk Au Bragg reflections. As has been demonstrated in numerous publications, the CTRs are extremely sensitive to surface atomic structure and, in the case of an unreconstructed metal surface, can be used to accurately probe surface relaxation effects [33]. In particular, expansion of the surface atomic layer causes an asymmetry around the Bragg reflections, for example, expansion of the surface will cause an increase in the scattered X-ray intensity at (1, 0, 3.5) and a decrease at (1, 0, 4.5) as these two positions are either side of the (1, 0, 4) Bragg reflection. Monitoring the X-ray intensity at these positions as the electrode potential is scanned gives a potentiodynamic measurement of the surface expansion and/or structural changes, a technique termed ‘X-ray voltammetry’ (XRV) [34,35]. In the experiments described here the potential dependence of the Au(1 1 1)-(1 1) surface expansion was determined by XRV measurements, as shown in Fig. 3. The sweep rate for the mea-
Fig. 3. The top panel shows the measured X-ray intensity at the reciprocal lattice positions (1, 0, 3.5) and (1, 0, 4.5) as a function of the electrode potential during a cathodic sweep, sweep rate ¼ 5 mV/s. The lower panel shows the data at the (1, 0, 3.5) position converted to surface expansion of the topmost Au atomic layer (as a percentage of the bulk Au(1 1 1) lattice spacing). This curve was calibrated by fits to CTR data at 0.4, 0.6 and 1.0 V (see text for details).
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surements shown corresponds to 5 mV/s. The data are consistent with expansion of the surface as the potential is stepped cathodically until the surface p reconstructs into the (23 3) phase (at 0.35 V) and the simple interpretation of the CTR data breaks down. In order to calibrate the XRV curves, the potential was held at 0.4, 0.6 and 1.0 V, and CTR data were measured, i.e., the (0, 0, l), (1, 0, l) and (0, 1, l) CTR’s from l ¼ 0:5–5:7 were measured by performing rocking scans and fixed l values, which were then numerically integrated to give CTR data that can be modeled (after the appropriate instrumental corrections) using a kinematical scattering theory [33–35]. Fits to the data were made using a structural model of the bulk-terminated Au(1 1 1)-(1 1) surface in which the only parameter that was allowed to vary in fitting the three data sets (0.4, 0.6 and 1.0 V) was the relaxation of the topmost Au atomic layer (a scale factor and the roughness factor for the topmost atomic layer were kept constant for the fits to all of the data). The results allow the intensity variation at the (1, 0, 3.5) reciprocal lattice position (top panel of Fig. 3) to be reinterpreted in terms of the potential dependence of the surface expansion, as shown in the lower part of Fig. 3. The surface expansion is plotted as a percentage of . the bulk Au(1 1 1) interplanar spacing, 2.354 A Fig. 3 shows that the outward lattice expansion of the Au(1 1 1) surface is a sensitive function of electrode potential. The potential of zero charge (PZC) of Au(1 1 1) is estimated as about þ0.35 V (vs. SCE). At 0.35 V the surface is expanded outward by 1.5% with respect to the bulk equilibrium lattice spacing of Au(1 1 1). As the potential is swept to positive potentials the lattice expansion decreases to 0.15% outward expansion at 1.0 V. At potentials negative of p the PZC the Au(1 1 1) surface forms the (23 3) reconstruction [5,32] and the scattered intensity along the CTRs depends on the restructuring of the surface; analysis of this region is not included in this paper. In order to evaluate the changes in outward surface relaxation the surface expansion data has been replotted in Fig. 4 against surface charge. Integration of the electrochemical current was made from the PZC to a potential of 1.0 V. This potential range spans the region of positive surface charge, where
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Fig. 4. The top-layer surface expansion as a percentage of the bulk Au(1 1 1) lattice spacing plotted against the surface charge.
the sulfate anions adsorb onto the electrode surface. A monotonous decrease in the outward surface relaxation occurs over this region. This decrease in surface expansion arises from the positive charging of the metal surface. The effect of positive surface charging on the surface stress has also been measured [25]. As for the X-ray data the data is plotted against surface charge. Fig. 5 shows the dependence of stress Dg on charge for Au(1 1 1) cantilever samples in sulfuric
Fig. 5. The dependence of the stress Dg on charge for a Au(1 1 1) cantilever sample in 1 M sulfuric acid solution.
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acid electrolyte. As for the in situ X-ray diffraction experiments the PZC had been chosen as 0.35 V. As before the sulfate anions are adsorbed towards positive potentials and there is a concomitant decrease in surface stress. The value of the slope og=or is 0.85 V [25]. In order to understand the outward expansion of the uncharged Au(1 1 1) surface we performed first principle simulations of a 13-layer Au(1 1 1) slab. In the crystal groundstate the outermost surface layer is relaxed outwards by 1.3% compared to the ideal bulk interlayer spacing. The charging of the gold surface could not be directly simulated, however, an indirect method to assess the effect of surface charging on interlayer spacing proved to be as efficient. When an adsorbate removes negative charge from the gold surface atom the effect must be similar to the existence of adjacent negative ions, i.e. to a positively charged surface. As the chemical element suitable to produce such an effect we chose Cl, which is an electronegative element with a Pauling electronegativity of 3.0 (c.f. 2.4 for Au). The Cl atom removes electron charge from the vicinity of the Au atom and, since the charge at the Fermi level of a metal possesses the highest mobility, the removed charge is preferably near the Fermi level. In the presence of Cl we find that the relaxation of the gold surface is reversed; the simulation then yields an inward relaxation of 1.05%. The calculated relaxations of the first six layers of the slab, with and without Cl adsorbate, are shown in Fig. 6.
Fig. 6. Summary of the relaxation of the six topmost layers of a 13 layer slab. DFT calculations for the clean and Cl-covered Au(1 1 1) surface.
4. Discussion The results show that charging of the Au(1 1 1) electrode surface can have a significant effect on both the surface stress and the outward surface relaxation. Taking a value of 2.77 N m1 for the tensile stress of the clean Au(1 1 1) surface from reference [15], positive charging of the surface by 60 lC cm2 (or a charge of about a quarter of the charge of an electron per surface atom) results in a decrease in the natural tensile stress of the Au(1 1 1) surface from about 2.77 to 2.27 N m1 . This is a change of 0.5 N m1 , with the negative sign indicating a compressive stress change (or rather a decrease in the tensile stress). On the other hand, the diffraction data shows that the uncharged Au(1 1 1)-(1 1) surface is relaxed outwards by 1.5%, which is then reduced to 0.2% on positively charging the surface by 80 lC cm2 . As pointed out in Section 1, the compressive stress changes would be expected, on the basis of a simple bonding model, to be accompanied by outward relaxation. Such a simple model would consider the surface bonds to be effectively weakened by positive charge, with the complementary effects of causing compressive stress changes within the surface plane and an accompanying outward surface relaxation. However, the results show that the opposite trend is observed with positive surface charging leading to stress changes in the compressive direction and concomitant inward surface relaxation. To provide a quantitative estimate of the influence of surface charge changes on surface stress, a model has been used which has been described in earlier publications [25]. This model involves the application of a fundamental thermodynamic equation, which states that the change of surface stress (og) with surface charge (or) at constant total area (A) is equal to the change in electrode potential with strain (e) at constant total charge. This is mathematically expressed as og oE ¼ or A oe Q (For the thermodynamic derivation, see Ref. [25]). The term ðog=orÞA is the experimentally measured
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parameter from the slope of the surface stress versus charge relationship (Fig. 5). On the other hand it is the term ðoE=oeÞQ that can be interpreted within a jellium model, since it represents the variation of work function / (/ ¼ eE þ constant, where e is the elementary charge and E the electrode potential) upon deformation of a sample (e) at constant total charge. The work function and its dependence on electron density can be calculated from a simple jellium model [36]. This can then be used to calculate ðoE=oeÞQ by making use of the inverse relation between density (of the jellium) and strain. As detailed in Ref. [25] a value of 0.45 V has then been obtained for ðoE=oeÞQ . This is the correct sign and magnitude when compared with the experimentally observed value of 0.85 V for Au(1 1 1) in sulfuric acid solution. However, the model, which has been described in the text above, although explaining the surface stress changes, cannot be used to rationalize the observed outward surface relaxation and it seems appropriate to apply DFT. The calculated surface relaxation of þ1.3% is in excellent agreement with the measured value of þ1.5%. A similar problem has been analyzed by Methfessel, Hennig and Scheffler, who found that Nb relaxes outward [18]. Relaxation is a trade off between two different effects: (i) cohesion between adjacent atoms, and (ii) the band energy due to the band structure of the crystal. In order to investigate this trade-off between atomic cohesion and band energy effects we have calculated the density of states (DOS) of the Au surface atom for the relaxed and unrelaxed surfaces (Fig. 7). In this way the energy gain for the relaxed surface can be assessed. The density of states calculated for the Au ) has its major contrisurface atom (radius 1.5 A bution from the d-states, but there is also a small contribution from s-states. The third graph in Fig. 7 shows the integrated difference ðDOS ðrelaxedÞ DOS ðunrelaxedÞÞ. It is positive for low energies and negative only close to the Fermi edge. This means that the relaxed surface is depleted of DOS near the Fermi edge and enriched in the energy interval from 4 to 1 eV. The net effect is a gain in energy, with the crystal gaining this energy by moving the atoms outwards from their unrelaxed positions. The crystal bands then are shifted to
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) for the Fig. 7. The DOS of the Au surface atom (radius 1.5 A relaxed and unrelaxed surfaces. Both the contributions from sand d-states are included. The third graph shows the integrated difference ðDOS ðrelaxedÞ DOS ðunrelaxedÞÞ, demonstrating the net gain in energy in the 4 to 1 eV region.
lower energies. This shift of energy is the driving force for the outward relaxation. This accounts for the outward relaxation of the clean surface.
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ities at the HiPerSPACE center were funded by the Higher Education Funding Council for England.
References
Fig. 8. The DOS of the Au surface atom for the clean surface and a Cl-covered surface. The lower line shows the difference, clearly indicating that Cl removes DOS around the Fermi level.
In order to see whether the model can also explain the inward relaxation of the surface upon positive charging we simulate the removal of states (reduction of the DOS) at the Fermi level with the aid of an adsorbate. Unlike oxygen, Cl, our element of choice, causes no restructuring of the surface. Fig. 8 shows the DOS for the clean surface and a Cl covered surface. The lower line shows the difference, clearly indicating that, as desired, the Cl removes DOS around the Fermi level. The relaxation of the surface with Cl is inward by 1.05%. By removing DOS the Cl adsorbate has blocked the outward relaxation and reversed the actual trend. In much the same way, positive surface charging reduces the outward relaxation of the surface Au atomic layer.
Acknowledgements This work was supported under EPSRC grant #GR/M23762. CAL acknowledges the support of an EPSRC Advanced Research Fellowship and TN the award of an EPSRC studentship. We are also grateful to the support of beamline 16-3 at Daresbury Laboratory (Steve Collins, Bridget Murphy) and the EPSRC-funded XMaS beamline at the ESRF (Simon Brown, Paul Thompson). WAH acknowledges support from the British Council and the Canadian Research Council. Computing facil-
[1] G. Somorjai, New York, Chichester, Wiley, 1994. [2] W. Savich, S. Sun, J. Lipkowski, A. Wieckowski, J. Electroanal. Chem. 388 (1995) 233. [3] C. Bach, M. Giesen, H. Ibach, T. Einstein, Phys. Rev. Lett. 78 (1997) 4225. [4] W. Haiss, J. Sass, Langmuir 12 (1996) 4311. [5] J. Wang, A. Davenport, H. Isaacs, B. Ocko, Science 255 (1992) 1416. [6] H. Ibach, C. Bach, M. Giesen, A. Grossmann, Surf. Sci. 375 (1997) 107. [7] M. Seo, T. Makino, N. Sato, Denki Kagaku 53 (1985) 266. [8] T. Miyatani, M. Fujihira, J. Appl. Phys. 81 (1997) 7099. [9] T. Brunt, T. Rayment, S. Oshea, M. Welland, Langmuir 12 (1996) 5942. [10] A. Gokhshtein, Elektrokhimya 2 (1966) 1204. [11] R. Fredlein, A. Damjanovic, J. Bockris, Surf. Sci. 25 (1971) 261. [12] H. Butt, J. Colloid Interf. Sci. 180 (1996) 251. [13] S.D. Cattarin, F. Dini, D. Margesin, J. Electroanal. Chem. 474 (1999) 182. [14] W. Haiss, Reports Progr. Phys. 64 (2001) 591. [15] H. Ibach, Surf. Sci. Reports 29 (1997) 195. [16] Y. Li, F. Jona, P. Marcus, Phys. Rev. B 43 (1991) 6337. [17] A. Begley, S. Kim, F. Jona, P. Marcus, Phys. Rev. B 48 (1993) 12326. [18] M. Methfessel, D. Hennig, M. Scheffler, Phys. Rev. B 46 (1992) 4816. [19] J.L. Quinn, Ys. Tian, D. Li, H. Jona, F. Marcus, Phys. Rev. B 42 (1990) 11348. [20] W. Oed, B. Dotsch, L. Hammer, K. Heinz, K. Muller, Surf. Sci. 207 (1988) 55. [21] see, for example P.J. Feibelman, Surf. Sci. 360 (1996) 297. [22] O.M. Magnussen, J. Hagebock, J. Hotlos, R.J. Behm, Faraday Discuss. (1992) 329. [23] G.J. Edens, X.P. Gao, M.J. Weaver, J. Electroanal. Chem. 375 (1994) 357. [24] H. Ibach, Surf. Sci. Rep. 29 (1997) 195. [25] W. Haiss, R. Nichols, J. Sass, K. Charle, J. Electroanal. Chem. 452 (1998) 199. [26] Based on the design described in I.M. Tidswell, N.M. Markovic, C.A. Lucas, P.N. Ross, Phys. Rev. B 47 (1993) 16542. [27] G. Kresse, J. Furthmuller, Phys. Rev. B 54 (1996) 11169. [28] G. Kresse, J. Hafner, Phys. Rev. B 47 (1993) 558. [29] D. Vanderbilt, Phys. Rev. B 41 (1990) 7892. [30] H. Monkhurst, Phys. Rev. B 13 (1976) 5188. [31] J.P. Perdew, J.A. Chevary, S.H. Vosko, K.A. Jackson, M.R. Pederson, D.J. Singh, C. Fiolhais, Phys. Rev. B 46 (1992) 6671.
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Surface relaxation and surface stress of Au(1 1 1) R.J. Nichols
a,*
, T. Nouar b, C.A. Lucas b, W. Haiss a, W.A. Hofer
c
a
Department of Chemistry, University of Liverpool, Liverpool L69 7ZE, UK Oliver Lodge Laboratory, Department of Physics, University of Liverpool, Liverpool L69 7ZE, UK Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT, UK b
c
Received 1 November 2001; accepted for publication 27 February 2002
Abstract Changes in surface stress and in the top-layer expansion of Au(1 1 1) electrodes in sulfuric acid have been measured as a function of electrode potential by combining surface stress and X-ray diffraction measurements. Both are linear functions of interfacial charge in the electrode potential range of changing anion coverage. Over this range the surface stress changes by 0.5 N m1 (compressive direction), while the outward top-layer relaxation decreases from þ1.5% to þ0.2%. The surface stress changes can be rationalized in terms of a jellium model, while ab initio simulations are needed to explain the top-layer expansion. These simulations yield þ1.3% relaxation for the uncharged gold surface, in good agreement with the X-ray diffraction measurements. They also demonstrate that the outward relaxation of the surface is curbed in the presence of an electron withdrawing adsorbate (Cl), which mimics the effects of positive surface charging. Ó 2002 Elsevier Science B.V. All rights reserved. Keywords: Surface stress; Surface relaxation and reconstruction; X-ray scattering, diffraction, and reflection; Density functional calculations; Gold
1. Introduction The bonding and electronic structure of substrate surfaces can be affected by molecular chemisorption. The bonding in the outmost substrate layers can have significant effects on surface structure and dynamics, leading to phenomena such as surface reconstruction or enhanced substrate mobility [1]. Electrochemists have the unique ability to affect the bond strengths of the substrate surface, by tuning the electrode potential and consequently altering the surface electronic
*
Corresponding author.
structure. These changes in surface bond strengths are not at present directly measurable, but they result in changes in the surface energy, surface stress, top-layer surface relaxation and in extreme cases surface reconstruction; all of which can now be monitored in situ [2–5]. In this paper in situ measurements of surface stress and outward surface relaxation are presented and compared. Surface stress has been measured previously at the metal–electrolyte interface using a number of mechanical methods to monitor strain changes in the electrode [4,6–13]. Although some of the results on polycrystalline samples were ambiguous, the more recent experiments for single crystals show that the tensile surface stress decreases linearly with increasing
0039-6028/02/$ - see front matter Ó 2002 Elsevier Science B.V. All rights reserved. PII: S 0 0 3 9 - 6 0 2 8 ( 0 2 ) 0 1 5 1 0 - 8
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electrode potential [14]. Both the natural tensile stress of metals and the increase in surface stress upon positively charging the surface can be explained by a simple qualitative model of the surface bonds, which is described in a review by Ibach [15]. This ‘‘simple bonding model’’ considers that upon cleaving a surface, the bond charge in the missing bonds that are broken by the surface termination is relocated between the surface atoms and their backbonds. The resulting increase in charge density between the surface atoms can be used to explain the tensile stress of metal surfaces [15]. The adsorption of electronegative atoms or positive surface charging removes charge from the surface bonds, effectively weakening them and causing the tensile stress to decrease (compressive stress change). This qualitative bonding model, is described later in this paper in terms of a jellium model for the surface, which is used to quantify the stress changes with surface charging. It is described how this model predicts the correct sign and magnitude of the stress change. The qualitative bonding model described by Ibach also predicts a contraction of the distance between the first and second layers (top-layer relaxation), which should be lessened by positive surface charging [15]. Top layer relaxation is measured by an X-ray diffraction technique to monitor the interlayer spacing at the surface [16,17]. X-ray diffraction has been employed for some years to monitor surface and adsorbate structures in the electrochemical environment although it has not yet been widely used to monitor top-layer relaxation of singlecrystal surfaces. In ultra-high-vacuum (UHV) surface relaxation has been monitored by means of low energy electron diffraction (LEED) I–V analysis and a significant database now exists [16, 17]. Although the outermost atomic layer on most metal surfaces in UHV shows an inward relaxation, tantamount to a reduction of the interlayer spacing between the first two layers, a number of metals exhibit outward relaxation [18]. These include Pd(0 0 1) and Rh(0 0 1) surfaces, with an outward relaxation of (3:0 1:5)% and (0:5 2)%, respectively [19,20]. Attempts to establish trends in surface relaxation effects by state-of-the-art theoretical calculations have highlighted discrepancies
both in the theoretical results and the experimental studies [21]. The Au(1 1 1) surface in aqueous surface acid provides a good model system for studying the effects of electrode potential on the top-layer relaxation and surface stress of Au(1 1 1) electrodes. The surface electrochemistry of Au(1 1 1) in aqueous surface acid is relatively well understood. pffiffiffi Sulfate adsorption assists in lifting the 22 3 surface reconstruction and at very positive potentials, close to the onset of gold surface oxidation, the sulfate ions form an ordered pffiffiffi adsorbed pffiffiffi ð 3 7Þ structure [22,23]. In between the potential at which the surface reconstruction is lifted and that at which the ordered anion overlayer is formed, there exists a defined potential region in which the coverage of the adsorbed anion varies with electrode potential on the unreconstructed (1 1) gold surface. As the potential is increased in this region the coverage of the adsorbate anion increases creating a positive image charge in the Au surface that leads to changes in the band structure at the metal surface. These changes leads to the observed changes in surface stress and in the top-layer expansion of Au(1 1 1) electrodes. It is important to note that surface reconstruction can also lead to changes in surface stress and in the top-layer expansion, but the electrochemical environment allows measurements to be made for Au(1 1 1) in the absence of the reconstructed surface. Experimentally, we were at first puzzled by an unexpected trend in surface stress and layer relaxations, when we analyzed the changes in the atomic structure of a unreconstructed Au(1 1 1) surface in sulfuric acid solution. Using the simple bonding model described in the review by Ibach, a reduction in the tensile stress of the surface (i.e. an increase of compressive surface stress) would be expected to lead to an increased outward relaxation [24]. By contrast, we observed the opposite trend, namely Au(1 1 1), in electrolyte solution, exhibits compressive stress changes (reduced tensile stress) and related inward relaxation of the top layer if it is positively charged. The simple bonding fails to explain this behaviour, since it does not take account of important energy contributions to the electronic structure of the surface. In this re-
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spect, it is noted that there is an intricate balance between cohesive energy and band energy contributions of single Au atoms. It is shown in this paper, that this balance in turn shifts the energetic groundstate (energy minimum) of the uncharged surface to the configuration with an extended interlayer distance between the first and second atomic layer. This trade-off between band energy and layer relaxation is also found in other transition metals, e.g. within the 4d series [18]. In this communication we consider how positive charging effects this trade-off of energetic contributions to electronic structure.
2. Experimental The experimental arrangement for the surface stress measurements was similar to that used in previous studies of surface stress at the electrochemical interface [4,14,25]. For these quantitative studies a cantilever sample is used, the deflection of which is tracked by the z-piezo of an STM [14,24]. The cantilever glass substrates, with dimensions of 24 2:5 0:55 mm3 (AF45, E ¼ 66 kN/mm2 , V ¼ 0:235, Berliner Glass K.G.), were coated on one side by evaporation of 2 nm of chromium followed by 200 nm of gold. The stress was evaluated from the measured deflection of the cantilever in the standard procedure according to Stoney’s equation [14,24]. Stress changes have been recorded against applied potential or charge. Compressive stress has been plotted as a negative stress change while tensile stress has been plotted with positive sign. A decrease in the natural tensile stress of the surface is referred to as a ‘‘stress change in the compressive direction’’. Prior to measurement the gold samples were flame annealed to produce (1 1 1) terraces [4]. The electrolyte solution used throughout the study was 1 M H2 SO4 . All electrode potentials are measured with reference to an oxidized gold wire and have been converted to the standard calomel reference electrode (SCE). The surface X-ray diffraction experiments were performed with a Au(1 1 1) single crystal on the XMaS CRG beamline (BM28) at the ESRF, Grenoble, and beamline 16.3 at the Daresbury
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Synchrotron Radiation Source. The crystal was aligned to <1° of the (1 1 1) surface, mechanically polished, and then electrochemically polished in a solution of 95% ethanol/5% HCl at 20 V for 15 s. Approximately 20 electropolishing cycles were conducted, each one followed by a careful annealing in a butane flame, to produce only a slight orange hue. The crystal was also flame annealed directly prior to an experiment. The crystal was then allowed to cool in air and transferred to the X-ray cell with a drop of ultra pure water protecting its surface. The electrochemical X-ray cell [26] was mounted on the X-ray diffractometer and measurements of the cyclic voltammetry confirmed that the cell was free of contamination. For the (1 1 1) surface an hexagonal unit cell is defined as used in LEED experiments, such that the surface normal is along the (0, 0, l)hex direction and the (h, 0, 0)hex and (0, k, 0)hex vectors lie in the plane of the surface and subtend 60°. Surface relaxation of Au(1 1 1) was computed using first principle density functional theory (DFT), the Vienna ab initio simulation program [27,28]. The program uses ultrasoft Vanderbilt type pseudopotentials [29] for the ionic cores and a repeated slab geometry (supercell). The twodimensional Brillouin zone was sampled with (8 8 1) k-points of a Monkhorst–Pack grid [30], the exchange correlation was parameterized following Perdew et al. (PW91) [31]. It should be noted that the relaxations depend critically on the crystal lattice constant [18]. For this reason we first computed the lattice constant within the PW91 by minimizing the bulk energy of fcc Au. This lattice (2.96 A for the reduced cell) constant of 4.19 A was used in our calculation. The set-up of the 13layer film for the simulation is shown in Fig. 1. The vacuum gap between successive films was chosen
Fig. 1. The set-up for the DFT calculations. The unit cell for vacuum gap. the simulation consists of 13 layers and a 5 A
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, which in practice is sufficient to deto be 5 A couple the two surfaces.
3. Results Fig. 2 shows a cyclic voltammogram for Au(1 1 1) in 0.1 M sulfuric acid, recorded in a hanging meniscus arrangement in a three-electrode electrochemical cell. The broad peak centered at about 0.45 V is due to the adsorption of sulfate. The peak at about p 0.3 V marks the potential at which the (23 3) reconstruction is lifted. The small current peaks close to 0.85 V have been shown to be associated with the formation of an ordered sulfate overlayer, with a coverage of 0.2 ML [32]. Between about 0.3 and 0.85 V the coverage of the adsorbed anion varies with electrode potential on the unreconstructed (1 1) gold surface. The voltammetric features shown in Fig. 2 could also be reproduced in both the X-ray diffraction cell and the surface stress electrochemical cell. The compromised electrode geometries of both cells meant that the peaks were not as sharply defined as in the hanging meniscus arrangement. The surface relaxation at the Au(1 1 1) surface was probed by X-ray diffraction using crystal truncation rod (CTR) measurements. CTRs are rods of scattering oriented along the h0; 0; li re-
Fig. 2. Cyclic voltammogram for Au(1 1 1) in 0.1 M sulfuric acid solution, sweep rate 5 mV/s.
ciprocal lattice direction passing through the bulk Au Bragg reflections. As has been demonstrated in numerous publications, the CTRs are extremely sensitive to surface atomic structure and, in the case of an unreconstructed metal surface, can be used to accurately probe surface relaxation effects [33]. In particular, expansion of the surface atomic layer causes an asymmetry around the Bragg reflections, for example, expansion of the surface will cause an increase in the scattered X-ray intensity at (1, 0, 3.5) and a decrease at (1, 0, 4.5) as these two positions are either side of the (1, 0, 4) Bragg reflection. Monitoring the X-ray intensity at these positions as the electrode potential is scanned gives a potentiodynamic measurement of the surface expansion and/or structural changes, a technique termed ‘X-ray voltammetry’ (XRV) [34,35]. In the experiments described here the potential dependence of the Au(1 1 1)-(1 1) surface expansion was determined by XRV measurements, as shown in Fig. 3. The sweep rate for the mea-
Fig. 3. The top panel shows the measured X-ray intensity at the reciprocal lattice positions (1, 0, 3.5) and (1, 0, 4.5) as a function of the electrode potential during a cathodic sweep, sweep rate ¼ 5 mV/s. The lower panel shows the data at the (1, 0, 3.5) position converted to surface expansion of the topmost Au atomic layer (as a percentage of the bulk Au(1 1 1) lattice spacing). This curve was calibrated by fits to CTR data at 0.4, 0.6 and 1.0 V (see text for details).
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surements shown corresponds to 5 mV/s. The data are consistent with expansion of the surface as the potential is stepped cathodically until the surface p reconstructs into the (23 3) phase (at 0.35 V) and the simple interpretation of the CTR data breaks down. In order to calibrate the XRV curves, the potential was held at 0.4, 0.6 and 1.0 V, and CTR data were measured, i.e., the (0, 0, l), (1, 0, l) and (0, 1, l) CTR’s from l ¼ 0:5–5:7 were measured by performing rocking scans and fixed l values, which were then numerically integrated to give CTR data that can be modeled (after the appropriate instrumental corrections) using a kinematical scattering theory [33–35]. Fits to the data were made using a structural model of the bulk-terminated Au(1 1 1)-(1 1) surface in which the only parameter that was allowed to vary in fitting the three data sets (0.4, 0.6 and 1.0 V) was the relaxation of the topmost Au atomic layer (a scale factor and the roughness factor for the topmost atomic layer were kept constant for the fits to all of the data). The results allow the intensity variation at the (1, 0, 3.5) reciprocal lattice position (top panel of Fig. 3) to be reinterpreted in terms of the potential dependence of the surface expansion, as shown in the lower part of Fig. 3. The surface expansion is plotted as a percentage of . the bulk Au(1 1 1) interplanar spacing, 2.354 A Fig. 3 shows that the outward lattice expansion of the Au(1 1 1) surface is a sensitive function of electrode potential. The potential of zero charge (PZC) of Au(1 1 1) is estimated as about þ0.35 V (vs. SCE). At 0.35 V the surface is expanded outward by 1.5% with respect to the bulk equilibrium lattice spacing of Au(1 1 1). As the potential is swept to positive potentials the lattice expansion decreases to 0.15% outward expansion at 1.0 V. At potentials negative of p the PZC the Au(1 1 1) surface forms the (23 3) reconstruction [5,32] and the scattered intensity along the CTRs depends on the restructuring of the surface; analysis of this region is not included in this paper. In order to evaluate the changes in outward surface relaxation the surface expansion data has been replotted in Fig. 4 against surface charge. Integration of the electrochemical current was made from the PZC to a potential of 1.0 V. This potential range spans the region of positive surface charge, where
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Fig. 4. The top-layer surface expansion as a percentage of the bulk Au(1 1 1) lattice spacing plotted against the surface charge.
the sulfate anions adsorb onto the electrode surface. A monotonous decrease in the outward surface relaxation occurs over this region. This decrease in surface expansion arises from the positive charging of the metal surface. The effect of positive surface charging on the surface stress has also been measured [25]. As for the X-ray data the data is plotted against surface charge. Fig. 5 shows the dependence of stress Dg on charge for Au(1 1 1) cantilever samples in sulfuric
Fig. 5. The dependence of the stress Dg on charge for a Au(1 1 1) cantilever sample in 1 M sulfuric acid solution.
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acid electrolyte. As for the in situ X-ray diffraction experiments the PZC had been chosen as 0.35 V. As before the sulfate anions are adsorbed towards positive potentials and there is a concomitant decrease in surface stress. The value of the slope og=or is 0.85 V [25]. In order to understand the outward expansion of the uncharged Au(1 1 1) surface we performed first principle simulations of a 13-layer Au(1 1 1) slab. In the crystal groundstate the outermost surface layer is relaxed outwards by 1.3% compared to the ideal bulk interlayer spacing. The charging of the gold surface could not be directly simulated, however, an indirect method to assess the effect of surface charging on interlayer spacing proved to be as efficient. When an adsorbate removes negative charge from the gold surface atom the effect must be similar to the existence of adjacent negative ions, i.e. to a positively charged surface. As the chemical element suitable to produce such an effect we chose Cl, which is an electronegative element with a Pauling electronegativity of 3.0 (c.f. 2.4 for Au). The Cl atom removes electron charge from the vicinity of the Au atom and, since the charge at the Fermi level of a metal possesses the highest mobility, the removed charge is preferably near the Fermi level. In the presence of Cl we find that the relaxation of the gold surface is reversed; the simulation then yields an inward relaxation of 1.05%. The calculated relaxations of the first six layers of the slab, with and without Cl adsorbate, are shown in Fig. 6.
Fig. 6. Summary of the relaxation of the six topmost layers of a 13 layer slab. DFT calculations for the clean and Cl-covered Au(1 1 1) surface.
4. Discussion The results show that charging of the Au(1 1 1) electrode surface can have a significant effect on both the surface stress and the outward surface relaxation. Taking a value of 2.77 N m1 for the tensile stress of the clean Au(1 1 1) surface from reference [15], positive charging of the surface by 60 lC cm2 (or a charge of about a quarter of the charge of an electron per surface atom) results in a decrease in the natural tensile stress of the Au(1 1 1) surface from about 2.77 to 2.27 N m1 . This is a change of 0.5 N m1 , with the negative sign indicating a compressive stress change (or rather a decrease in the tensile stress). On the other hand, the diffraction data shows that the uncharged Au(1 1 1)-(1 1) surface is relaxed outwards by 1.5%, which is then reduced to 0.2% on positively charging the surface by 80 lC cm2 . As pointed out in Section 1, the compressive stress changes would be expected, on the basis of a simple bonding model, to be accompanied by outward relaxation. Such a simple model would consider the surface bonds to be effectively weakened by positive charge, with the complementary effects of causing compressive stress changes within the surface plane and an accompanying outward surface relaxation. However, the results show that the opposite trend is observed with positive surface charging leading to stress changes in the compressive direction and concomitant inward surface relaxation. To provide a quantitative estimate of the influence of surface charge changes on surface stress, a model has been used which has been described in earlier publications [25]. This model involves the application of a fundamental thermodynamic equation, which states that the change of surface stress (og) with surface charge (or) at constant total area (A) is equal to the change in electrode potential with strain (e) at constant total charge. This is mathematically expressed as og oE ¼ or A oe Q (For the thermodynamic derivation, see Ref. [25]). The term ðog=orÞA is the experimentally measured
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parameter from the slope of the surface stress versus charge relationship (Fig. 5). On the other hand it is the term ðoE=oeÞQ that can be interpreted within a jellium model, since it represents the variation of work function / (/ ¼ eE þ constant, where e is the elementary charge and E the electrode potential) upon deformation of a sample (e) at constant total charge. The work function and its dependence on electron density can be calculated from a simple jellium model [36]. This can then be used to calculate ðoE=oeÞQ by making use of the inverse relation between density (of the jellium) and strain. As detailed in Ref. [25] a value of 0.45 V has then been obtained for ðoE=oeÞQ . This is the correct sign and magnitude when compared with the experimentally observed value of 0.85 V for Au(1 1 1) in sulfuric acid solution. However, the model, which has been described in the text above, although explaining the surface stress changes, cannot be used to rationalize the observed outward surface relaxation and it seems appropriate to apply DFT. The calculated surface relaxation of þ1.3% is in excellent agreement with the measured value of þ1.5%. A similar problem has been analyzed by Methfessel, Hennig and Scheffler, who found that Nb relaxes outward [18]. Relaxation is a trade off between two different effects: (i) cohesion between adjacent atoms, and (ii) the band energy due to the band structure of the crystal. In order to investigate this trade-off between atomic cohesion and band energy effects we have calculated the density of states (DOS) of the Au surface atom for the relaxed and unrelaxed surfaces (Fig. 7). In this way the energy gain for the relaxed surface can be assessed. The density of states calculated for the Au ) has its major contrisurface atom (radius 1.5 A bution from the d-states, but there is also a small contribution from s-states. The third graph in Fig. 7 shows the integrated difference ðDOS ðrelaxedÞ DOS ðunrelaxedÞÞ. It is positive for low energies and negative only close to the Fermi edge. This means that the relaxed surface is depleted of DOS near the Fermi edge and enriched in the energy interval from 4 to 1 eV. The net effect is a gain in energy, with the crystal gaining this energy by moving the atoms outwards from their unrelaxed positions. The crystal bands then are shifted to
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) for the Fig. 7. The DOS of the Au surface atom (radius 1.5 A relaxed and unrelaxed surfaces. Both the contributions from sand d-states are included. The third graph shows the integrated difference ðDOS ðrelaxedÞ DOS ðunrelaxedÞÞ, demonstrating the net gain in energy in the 4 to 1 eV region.
lower energies. This shift of energy is the driving force for the outward relaxation. This accounts for the outward relaxation of the clean surface.
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ities at the HiPerSPACE center were funded by the Higher Education Funding Council for England.
References
Fig. 8. The DOS of the Au surface atom for the clean surface and a Cl-covered surface. The lower line shows the difference, clearly indicating that Cl removes DOS around the Fermi level.
In order to see whether the model can also explain the inward relaxation of the surface upon positive charging we simulate the removal of states (reduction of the DOS) at the Fermi level with the aid of an adsorbate. Unlike oxygen, Cl, our element of choice, causes no restructuring of the surface. Fig. 8 shows the DOS for the clean surface and a Cl covered surface. The lower line shows the difference, clearly indicating that, as desired, the Cl removes DOS around the Fermi level. The relaxation of the surface with Cl is inward by 1.05%. By removing DOS the Cl adsorbate has blocked the outward relaxation and reversed the actual trend. In much the same way, positive surface charging reduces the outward relaxation of the surface Au atomic layer.
Acknowledgements This work was supported under EPSRC grant #GR/M23762. CAL acknowledges the support of an EPSRC Advanced Research Fellowship and TN the award of an EPSRC studentship. We are also grateful to the support of beamline 16-3 at Daresbury Laboratory (Steve Collins, Bridget Murphy) and the EPSRC-funded XMaS beamline at the ESRF (Simon Brown, Paul Thompson). WAH acknowledges support from the British Council and the Canadian Research Council. Computing facil-
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