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Chemical Physics Letters 400 (2004) 26–29

Changes in the surface energy during the reconstructionof Au(100) and Au(111) electrodes

Elizabeth Santos a, W. Schmickler b,*

a Facultad de Matematica, Astronomia y Fisica Universidad Nacional de Cordoba, 5000 Cordoba, Argentinab Abteilung Elektrochemie, University of Ulm, D-89069 Ulm, Germany

Received 18 October 2004; in final form 19 October 2004

Available online 6 November 2004

Abstract

The reconstruction of Au(100) and Au(111) electrodes is lifted at sufficiently positive potentials. From capacity data the differ-

ence in surface energy for the reconstructed and the bulk-terminated surface can be obtained; this energy difference is much larger

for Au(100) than for Au(111). For non- or weakly adsorbing electrolytes the interaction between the surface dipole and the double

layer field or, equivalently, the surface charge, determines the lifting of the reconstruction.

� 2004 Elsevier B.V. All rights reserved.

1. Introduction

In the vacuum, a fair number of single crystal metal

surfaces exhibit reconstruction: They do not terminate

with the bulk structure, but the surface atoms rearrange

to form a more compact, energetically more favorable,

structure. In some cases the reconstruction is lifted by

suitable adsorbates, and there has been some discussion

if this lifting is caused by the adsorption bond or by theredistribution of charges accompanying the adsorption.

Obviously, experiments in ultra-high vacuum cannot

distinguish between these two mechanism, since it is

not possible to vary the surface charge to an appreciable

extent.

In contrast, electrochemistry offers the unique advan-

tage that the surface charge can be controlled through

the electrode potential. By performing experiments innon- or weakly adsorbing electrolytes the effects of

adsorption and charge can be separated. Much atten-

0009-2614/$ - see front matter � 2004 Elsevier B.V. All rights reserved.

doi:10.1016/j.cplett.2004.10.072

* Corresponding author. Fax: +731 502 5409.

E-mail address: Wolfgang.Schmickler@Chemie.Uni-Ulm.de (W.

Schmickler).

tion has been given to the reconstruction of the princi-ple surfaces of single-crystal gold electrodes, which can

be lifted by applying a suitable potential [1,2]. However,

the understanding of these electrochemical phenomena

has been impeded by two facts: (1) The analysis was

often based on faulty thermodynamics; in particular

there has been some confusion about the proper ther-

modynamic potential, a point to which we will return

below. (2) Ab initio calculations have been restrictedto reconstruction of the Au(110) surface, because this

requires only a small unit cell in the directions parallel

to the surface. However, for Au(110) the reconstruction

entails only a small change in the work function; there-

fore, as we shall argue below, the effect of the charge is

small.

In the following, we shall briefly outline the correct

thermodynamics to describe the reconstruction of elec-trodes, and show how standard electrochemical meas-

urements can be used to obtain the difference in the

surface energy between the reconstructed and the bulk-

terminated surface. Explicit evaluations will be per-

formed for Au(100) and Au(111); in particular we will

show that the reconstruction of the former surface

entails a much larger change in energy.

E. Santos, W. Schmickler / Chemical Physics Letters 400 (2004) 26–29 27

2. The thermodynamics of surface reconstruction in

electrochemistry

In the literature, there has been some confusion about

the correct thermodynamic potential for the surface en-

ergy of electrodes. In particular, the most recent reviewarticle on surface reconstruction [2] does not distinguish

between the surface free energy and the surface tension

and thus obfuscates the issue. Therefore, we briefly sum-

marize the correct thermodynamic relations.

Electrode surfaces are regions of constant electro-

static potential, therefore the reconstruction occurs at

constant electrode potential, which is the electrostatic

potential measured with respect to a reference electrode.At the transition point the reconstructed and the non-

reconstructed surfaces are in equilibrium; then they have

the same potential, but different surface charge densities.

As is well known, under these condition the correct ther-

modynamic potential describing equilibrium conditions

is the surface tension c [3], which has the electrode

potential / as its natural variable. However, electronic

structure calculations do not give c but the free energyf per surface area as a function of the surface-charge

density r. As was recently emphasized by Lozovoi and

Alavi [4], such calculations must be performed for a sys-

tem which carries zero total charge – the same paper

also gives a good summary of the thermodynamics from

a quantum-chemical point of view. The surface tension

is obtained from the free energy through a Legendre

transformation [5]:

c ¼ f � r~l=e0; with � ~l=e0 ¼ofor

; ð1Þ

where ~l is the electrochemical potential of the electrons

in the metal; ~l=e0 is also the electrode potential on the

absolute (or vacuum) scale [3].At constant chemical composition of the electrolyte,

the differential of the surface tension is simply:

dc ¼ �r d/: ð2ÞStrictly, this equation should contain an additional term

accounting for the variation of the surface stress with

potential; however, this term is smaller by several ordersof magnitude and can be safely neglected [6,7]. Eq. (2)

can be integrated:

cð/Þ ¼ c0 �Z /

/0

rð/0Þ d/0; ð3Þ

where c0 is the surface tension at the potential /0 of zero

charge (pzc), which is equal to the free energy of the un-

charged surface per unit area. Eq. (3) holds both for the

reconstructed and for the non-reconstructed surfaces,

but they have a different potential of zero charge and,

possibly, a different relation between charge and poten-

tial. Since o2c/o/2 = �C, where C is the interfacialcapacity, the c vs. / curves are convex and roughly

parabolic. This makes it possible to obtain the differ-

ence Dc0 ¼ cunrecon0 � crecon0 in surface tension between

the uncharged unreconstructed and reconstructed

surfaces: By twice integrating the interfacial capacity

data the surface tension curves for both surfaces are

obtained up to the unknown values at the pzc. Thetwo curves must cross at the potential where the sur-

face reconstruction is lifted. This condition uniquely

determines Dc0.This procedure is valid no matter if there is specific

adsorption or not; in the former case one simply obtains

Dc0 in the presence of the adsorbate. The value in the ab-

sence of specific adsorption is of particular interest. For

this purpose it is sufficient to choose an electrolyte whichdoes not adsorb at the pzc. It is not relevant if there is

specific adsorption at other potentials.

Of course, the difference in surface tension, or surface

free energy, obtained in this way refers to surfaces cov-

ered with water. For metals such as gold, which interact

but weakly with water, we may expect this electrochem-

ical value to be close to the vacuum value.

3. Application to Au(100) and Au(111)

Throughout this section, we focus on the case where

the electrolyte is not or only weakly adsorbed. We will

consider the Au(100) and Au(111) surfaces in turn,

and make a few comments about Au(110).

The surface of Au(100) is reconstructed into a hexag-onal structure, which is also denoted as (5 · 20). In

weakly adsorbing electrolytes it is lifted at potentials

positive of the pzc, which is evidenced by a peak in a

slow cyclic voltammogram. When the potential is

scanned back towards negative potentials, the recon-

struction is slow, so that the capacities for both surfaces

can be measured. In order to determine the energy

change Dc0 associated with the reconstruction ofAu(100) we have used data for aqueous solutions of

perchloric acid. The corresponding capacity curves are

well documented in the literature [1,8] so we do not

show them here. We have used data from our own group

[9], which agree well with the published data where they

overlap. Using the procedure outlined above, we have

determined Dc0 from four data sets with concentrations

in the range 10–100 mM. The reconstruction potentialswere identified with the foot of the peak in the cyclic vol-

tammograms (sweep rate 50 mV/s), since the position of

the peak itself is governed by kinetics. Fig. 1 shows two

examples of calculated surface tension curves for

the lowest and the highest concentrations investigated.

The surface tensions c0 of the reconstructed surfaces

at the pzc were set to zero. The difference in c0 for the

two unreconstructed surfaces reflects the experimentaluncertainty. From our four data sets we obtain a value

of Dc0 = (4.1 ± 0.3) · 10�2 J/m2.

8.0.604.02.00.02.0-.40-8-

6-

4-

2-

0

2

4

6

6.05.04.0

2-

0

γ x1

02 / J

m-2

φECS

V/

Fig. 1. Surface tensions for reconstructed and bulk terminated

Au(100) electrodes in perchloric acid solutions. Boxes: 10 mM;

triangles: 100 mM; open symbols refer to bulk terminated surfaces,

filled symbols to reconstructed surfaces.

28 E. Santos, W. Schmickler / Chemical Physics Letters 400 (2004) 26–29

Since the unit cell of the reconstructed Au(100) sur-

face is large, ab initio calculations for Dc0 are not avail-able. Estimates based on various approximate methods

span the range of (1–10) · 10�2 J/m2 [10,11] and are thusconsistent with our experimental value. Bohnen and

Kolb [12] identify the reconstructed Au(100) surface

with the unreconstructed Au(111) surface and obtain

Dc0 = 0.2 J/m2, but this is certainly too high since the

reconstructed Au(100) surface should have a higher sur-

face energy than Au(111).

Though the Au(111) surface is already densely

packed, it exhibits a hexagonal reconstruction in thevacuum. Similarly to Au(100), this reconstruction is

lifted at sufficiently positive potentials. Fig. 2 shows

capacity curves for the reconstructed and for the bulk-

6.04.02.00.02.0-4.0-01

02

03

04

05

06

07

C /

µF c

m.2

φ V /

Fig. 2. Interfacial capacities for reconstructed and bulk terminated

Au(111) electrodes in 10 mM perchloric acid (triangles) and 5 mM

KPF6 (circles) solutions; open symbols refer to bulk terminated

surfaces, filled symbols to reconstructed surfaces.

terminated electrodes for 10 mM HClO4 and 5 mM

KPF6 solutions. The adsorption of KPF6 is still weaker

than that of perchloric acid; the positions of the pzc are

the same for both types of solutions. The capacity at the

minimum is lower for KPF6 because the concentration is

smaller.The corresponding surface tensions are shown in

Fig. 3; again, c0 was set to zero for the reconstructed sur-

face. From these plots we obtain Dc = (3–5) · 10�3 J/m2;

thus, the change in surface energy accompanying the

reconstruction of Au(111) is about one order of magni-

tude smaller than for Au(100). In view of the fact, that

the perfect Au(111) surface is already densely packed,

this result is quite plausible. We have not found any the-oretical estimates, probably because of the large unit cell

and the smallness of the effect. Our value is in line with the

estimate ofWu et al. [13], who obtained�2 · 10�3 J/m2 <

Dc < 4 · 10�3 J/m2 using a procedure equivalent to ours.

As mentioned in the introduction, there has been

some discussion whether the lifting of the reconstruction

can be induced by charging the surface. For the two gold

surfaces considered here the answer is affirmative: Inboth cases the reconstructed surfaces have the higher

work function and, hence, higher values of the pzc. Since

the average interfacial capacity, which according to Eq.

(2) determines the second derivative of the surface ten-

sion, is about the same for the reconstructed and the

bulk-terminated surfaces the two surface tensions curves

must cross at sufficiently positive potentials. Physically,

the lifting of the reconstruction can be explained by theinteraction of the surface dipole with the electric field in

the double layer. In general, metal surfaces have an

intrinsic electronic dipole moment, which has its nega-

tive end pointing out of the surface. The concomitant

potential drop makes a sizable contribution to the work

6.04.02.00.02.0-4.0-01-

5-

0

6.04.02.01-

0

1

γ 10

2 /J m

-2

φECS

V/

Fig. 3. Surface tensions for reconstructed and bulk terminated

Au(111) electrodes in 10 mM perchloric acid (triangles) and 5 mM

KPF6 (circles) solutions; open symbols refer to bulk terminated

surfaces, filled symbols to reconstructed surfaces.

E. Santos, W. Schmickler / Chemical Physics Letters 400 (2004) 26–29 29

function. Since the workfunction of the reconstructed

surface is higher, it carries a larger surface dipole mo-

ment, and hence its interaction energy with the electric

field increases faster as the electrode potential is raised,

making it eventually energetically less stable than the

unreconstructed surface. The gist of this argument canbe seen by assuming, to a good first approximation, that

the interfacial capacities C of the two surfaces are equal

and constant. A simple calculations shows that the two

surfaces are in equilibrium if:

Dc ¼ C /recon0 � /unrecon

0

� �/� ð/unrecon

0 þ /recon0 Þ=2

� �¼ DlEave; ð4Þ

where Dl is the difference in the surface dipole moment

between the two surfaces, and Eave is the average electric

field in the double layer. Thus, at equilibrium the differ-

ence Dc0 is balanced by the difference in the dipole-field

interactions.

Of course, the above argument does not hold in the

presence of strong specific adsorption, which has a large

effect on the the interfacial capacity. Otherwise the samemechanism should operate whenever the work functions

of the reconstructed and the bulk-terminated surfaces

differ substantially. However, the crossing of the two

surface tension curves need not necessarily lie within

the experimentally accessible region.

Our results are at variance with the findings of

Bohnen and Kolb [12], who concluded that the recon-

struction of Au(100) is not lifted by charging. However,these authors based there arguments on the behaviour of

the surface free energy f; as pointed out above, this is not

the correct thermodynamic potential for a system at

constant electrostatic potential.

On Au(110) electrodes, bulk termination, 1 · 2 and

1 · 3 reconstruction have all been observed; however,

the reconstruction and its lifting are fast [14]. Therefore

it is not possible to measure the capacities for the varioussurface structures, and the differences in the surface ten-

sions cannot be obtained from experimental data. Lozo-

voi and Alavi [4] have calculated the surface energies for

these surfaces, and review the values obtained by other

groups. They obtain only small differences in the work

functions between the three surfaces; according to our

argument above this entails a small influence of the sur-

face-charge density. So in this respect Au(110) seems tobehave differently from the other principal surfaces.

4. Conclusions

Based on a correct thermodynamic analysis, we have

obtained the differences in the surface energies between

the bulk-terminated and the reconstructed surfaces of

Au(100) and Au(111) from experimental data. As ex-pected, the reconstruction of Au(100) entails a much

larger change in energy than that of Au(111). The

same procedure can be used to obtain such energy

changes whenever the capacities of both the recon-

structed and the unreconstructed surfaces are available.

For the two cases considered we can ascertain that the

lifting of the reconstruction at positive potentials can

be induced by charging the surface. Of course, thisdoes not exclude that it can also be effected by specific

adsorption.

Acknowledgements

Financial support by the Deutsche Forschungsgeme-

inschaft, the DAAD and CONICET is gratefullyacknowledged. We thank Prof. J. Lipkowski, Guelph,

for an enlightening scientific exchange.

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