Surface Science 602 (2008) 2840–2844
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Surface Science
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Reversed surface segregation in palladium-silver alloys due to hydrogen adsorption
O.M. Løvvik a,b,*, Susanne M. Opalka c
a
b
c
Department of Physics, University of Oslo, P.O. Box 1048 Blindern, N-0316 Oslo, Norway
Institute for Energy Technology, P.O. Box 40, N-2027 Kjeller, Norway
United Technologies Research Center, 411 Silver Lane, East Hartford, CT 06108, USA
a r t i c l e
i n f o
Article history:
Received 14 May 2008
Accepted for publication 1 July 2008
Available online 26 July 2008
Keywords:
Density-functional calculations
Surface segregation
Palladium
Silver
Hydrogen
a b s t r a c t
It is well known that silver segregates to the surface of pure and ideal Pd–Ag alloy surfaces. By first-principles band-structure calculations it is shown in this paper how this may be changed when hydrogen is
adsorbed on a Pd–Ag(1 1 1) surface. Due to hydrogen binding more strongly to palladium than to silver,
there is a clear energy gain from a reversal of the surface segregation. Hydrogen-induced segregation may
provide a fundamental explanation for the hydrogen or reducing treatments that are required to activate
hydrogen-selective membrane or catalyst performance.
Ó 2008 Elsevier B.V. All rights reserved.
1. Introduction
Palladium-silver alloy surfaces are important for a number of
applications including heterogeneous catalysis and hydrogen separation membranes [1,2]. Dense metal membranes for hydrogen
separation may be used to purify hydrogen or to enhance the outcome of e.g. a water gas shift reactor [3,4].
An understanding of the impact of segregation tendencies on local surface alloy composition is crucial to designing alloys for various applications. For instance, one of the alloying elements may be
more catalytically active than the other(s), making the presence of
that element in the surface layer important. For Pd–Ag alloys, the
pure low-index surfaces are dominated by silver under vacuum;
the (1 1 1) surface of Pd67Ag33 contains only between 5% and 11%
palladium between 720 and 920 K, while the (1 0 0) surface has a
very low equilibrium surface concentration of Pd at similar temperatures [5]. The same tendency has been described in a number
of previous modeling papers [6–10]. The Ag segregation tendency
may be rationalized as a combination of geometric and electronic
effects; the slightly larger Ag atoms induce less strain at the surface
than in the subsurface and the surface energy of Ag is significantly
lower than that of Pd [7].
The situation may change when various adsorbates are present:
adsorbate-induced segregation or desegregation of binary metal
alloys are well known for a number of metallurgical and catalytic
applications (e.g. Refs. [11–15] for recent examples). This is obvi* Corresponding author. Address: Department of Physics, University of Oslo, P.O.
Box 1048 Blindern, N-0316 Oslo, Norway. Tel.: +47 22840689.
E-mail address: o.m.lovvik@fys.uio.no (O.M. Løvvik).
0039-6028/$ - see front matter Ó 2008 Elsevier B.V. All rights reserved.
doi:10.1016/j.susc.2008.07.016
ously of high relevance to the Pd–Ag alloy applications; for example, Pd–Ag alloy surfaces are routinely exposed to hydrogen-rich
atmospheres when used as hydrogen separation membranes or
heterogeneous hydrogenation catalysts. Recent modeling and
experimental papers studies have primarily focused on the effect
of oxygen adsorption on metal alloy segregation (see, e.g. Refs.
[16–18,12,19,13]), and not so many papers have investigated the
effect of hydrogen adsorption on segregation. One early experimental paper reported no change in surface segregation after
exposing a Mo/Re surface to hydrogen; this was attributed to the
hydrogen desorption temperature (around room temperature)
being lower than that required to achieve significant metallic diffusion (around 600 °C) [20].
Hydrogen-induced segregation is significant on Pd–Ag alloys,
however, due to the stronger adsorption of hydrogen on Pd. Hydrogen adsorbing on Pd–Ag alloy surfaces is for this reason closely
related to Pd atoms in the surface, and hydrogen may be ‘‘trapped”
around single Pd atoms [21]. The difference in adsorption energy
between Ag and Pd is approximately 0.25 eV per metal neighbor
when hydrogen is adsorbed on a (1 1 1) surface fcc site with three
nearest neighbors. This difference is apparently large enough to
facilitate reversal of surface segregation, which has been demonstrated experimentally [22] and theoretically [23]. Also, a recent
experimental study indicated that hydrogen adsorption on top of
a multi-crystalline Pd–Ag film led to surface segregation of Pd
[24]. The formation of a Pd-rich surface layer in Pd–Ag alloys can
be used to support other explanations on why these alloys exhibit
superior hydrogen flux over pure Pd membranes [1,2,25], even
when the membranes are thin enough to make surface adsorption
the rate-limiting step. Also, it can lead to enhanced catalytic
O.M. Løvvik, S.M. Opalka / Surface Science 602 (2008) 2840–2844
2841
activity of Pd–Ag alloys, since Pd is more active than Ag for most
reactions.
This paper presents density-functional band-structure investigations of the influence of hydrogen adsorption on the uppermost
layers of a (1 1 1) surface slab with an overall Pd3Ag stoichiometry.
Several different models representing possible arrangements of the
atoms in the slab are evaluated by relaxation of the internal forces
and accurate calculation of the total energy of the final configurations. The present study is complementary to the recent modeling
study on the same subject, which focused on varying hydrogen
coverage and exchange of Ag positions between the subsurface
and surface layers [23]. Here, rather, the focus is on the detailed
overall distribution of Pd and Ag atoms with the adsorbed hydrogen concentration fixed at 0.25 monolayers (ML). Together with
the previous study, this will give a comprehensive picture of the
hydrogen-induced segregation of Pd–Ag alloys.
2. Computational method
Density-functional calculations at the generalized gradient
approximation level [26] were employed as implemented in the
Vienna ab initio simulation package (VASP) [27,28]. The energy cutoff of the plane-wave expansion was 500 eV, and the nearest
neighbour k-point distances within the slab were always less than
0.17 Å1. Only the C point was used perpendicular to the slab. The
criterion for self-consistency was that the total energy difference
between two consecutive cycles converged to less than 0.01 meV.
A five-layer 20 atom 2 2 (1 1 1) surface unit cell was formed from
the relaxed Pd3Ag Pm3m bulk phase. Varying Ag distributions were
simulated by breaking the overall Pm3m symmetry with the exchange of Pd and Ag positions. The slabs were separated by a
1 nm vacuum layer; this was found sufficient to achieve converged
adsorption energies. The unit cell was kept fixed at the bulk relaxed size during all relaxations, with the bottom layer frozen to
mimick bulk continuation. Relaxation of the atomic positions was
performed using the residual minimization method with direct
inversion in iterative subspace; an implementation of the quasinewton method. The force convergence criterion was less than
0.03 eV/Å. Relaxation of the 0.25 ML hydrogen adsorption models
were performed in two steps. First the height of the hydrogen
atoms above the surface z was optimized by a harmonic fit of the
calculated total energy of a number of z values. The optimized value of z was then used as input to a complete automatic relaxation
including the metal atoms of the slab. This two-step procedure ensured that the relaxed position was not a local minimum with
incorrect z. After relaxation of the atomic coordinates (except the
frozen bottom layer), the total energy was calculated in a separate
self-consistent calculation using high accuracy. The ground state
energies in eV per unit cell were uncorrected for the zero-point
energy.
To keep track of the 15 different Pd–Ag alloy configuration
models investigated in this paper, they are indexed by the number
of Ag atoms within the 4 atomic positions of each unit cell layer. As
an example, the Pd3Ag{2 0 1 1 1} model had two silver atoms in the
first (top) layer, while the second layer contained four Pd atoms.
One out of the four atoms in the remaining layers were Ag. Fig. 1
shows the unit cell of this model from the side. The periodic distribution of silver atoms was in all the models chosen to maximize
the Pd–Ag mixing and the Ag–Ag distances, especially when expanded to a supercell respresentation. This is supported by experiments which have shown repulsive interactions between surface
Pd atoms in Pd-doped Ag surfaces [5], and by recent modeling
studies predicting ordered bulk phases maximizing the Ag–Ag distance [29,30]. Hydrogen adsorption was performed at a coverage of
0.25 ML, always selecting the fcc site with the largest number of Pd
Fig. 1. The model Pd3Ag{2 0 1 1 1} with 0.25 ML adsorbed H, seen from the side.
Each number in the index {2 0 1 1 1} denotes the number of Ag atoms out of four
total atoms in each layer of the unit cell, starting from the first layer (top). Silver
atoms are shown as dark grey balls, Pd atoms are shown as light yellow balls, while
the H atom is shown as a small, red ball. The unit cell is outlined, as are the unit cell
directions x, y, and z, which are in the h1 1 2i, h1 1 2i, and h1 1 1i directions,
respectively. (For interpretation of the references to colour in this figure legend, the
reader is referred to the web version of this article.)
neighbors – this was shown to be the most stable configuration in a
previous study [7].
3. Results and discussion
3.1. Pure slabs
Previous modeling results on pure Pd–Ag alloy (1 1 1) surfaces
[21,7,8] are reproduced and complemented here as shown in the
ground state energy changes in Table 1 and in Fig. 2: the total energy is significantly lower when silver is located in the first (surface) or second (subsurface) layers, than in the middle layer
(bulk). As an example, the Pd3Ag{2 1 0 1 1} and {1 2 0 1 1} models
are more stable than the isotropic Pd3Ag{1 1 1 1 1} model by
0.15 eV, and 0.03 eV, respectively. The energy gained from moving
a silver atom from the middle to the top layer ranges between
0.09 eV (from {3 0 1 0 1} to {4 0 0 0 1}) and 0.33 eV (from {0 1 2 1 1}
to {1 1 1 1 1}). Likewise, the energy gained when moving a silver
atom from the middle layer to the second layer varies from around
0.03 (energy lost when moving from {2 0 1 1 1} to {2 1 0 1 1}) to
0.17 eV (from {2 0 2 0 1} to {2 0 1 1 1}).
To see the influence of the number of silver atoms in the first
and second layer more clearly, we have created a simple linear
model in which the difference in energy is calculated as
DEslab-model ¼ 1 ðn1 1Þ þ 2 ðn2 1Þ:
ð1Þ
Here n1 and n2 are the number of silver atoms in the first (surface) and second (subsurface) layers, and 1 and 2 are fitted parameters. They correspond to the typical energy of bringing a silver
atom from the bulk (mid-layer) to the first and second layers, when
repulsive interactions between neighbor silver atoms are not taken
into account. The fitted values are 1 = 0.25 eV and 2 = 0.10 eV.
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O.M. Løvvik, S.M. Opalka / Surface Science 602 (2008) 2840–2844
Table 1
The difference in total energy between the various models and the isotropic {1 1 1 1 1}
model (DEslab) is listed, together with the difference in total energy between models
with adsorbed hydrogen and the isotropic {1 1 1 1 1} model with adsorbed hydrogen
(DEads)
DEslab (eV)
DEads (eV)
{0 0 4 0 1}
{0 1 2 1 1}
{0 2 1 1 1}
{0 3 0 1 1}
{0 4 0 0 1}
{1 1 1 1 1}
{1 2 0 1 1}
{2 0 1 1 1}
{2 0 2 0 1}
{2 1 0 1 1}
{2 2 0 0 1}
{3 0 0 1 1}
{3 0 1 0 1}
{3 1 0 0 1}
{4 0 0 0 1}
0.48
0.33
0.22
0.12
0.16
0.00
0.03
0.17
0.02
0.15
0.15
0.23
0.24
0.28
0.32
0.50
0.32
0.24
0.16
0.17
0.00
0.01
0.06
0.10
0.00
0.06
0.06
0.17
0.13
0.49
A negative DEslab means that the model is more stable than the {1 1 1 1 1} model. The
index numbers refer to the distribution of silver atoms in each layer of the slab, as
explained in Fig. 1 and in the text. The energies are calculated from total electronic
energies without zero-point energy corrections, and are measured in eV per unit
cell (20 metal atoms). The hydrogen coverage was 0.25 ML.
Slab with adsorbed H
0.3
0.1
0.0
-0.1
31001
40001
30101
21011
30011
22001
20111
12011
20201
11111
03011
02111
04001
-0.5
Surface unit cells
01211
-0.3
Pure slab
00401
Energy difference (eV)
0.5
Fig. 2. The difference in total energy between the various models and the isotropic
{1 1 1 1 1} model (DEslab) is plotted, together with the difference in total energy
between models with adsorbed hydrogen and the isotropic {1 1 1 1 1} model with
adsorbed hydrogen (DEads). A negative DEslab means that the model is more stable
than the {1 1 1 1 1} model. The index numbers refer to the distribution of silver
atoms in each layer of the slab, as explained in Fig. 1 and in the text. The energies
are calculated from total electronic energies without zero-point energy corrections), and are measured in eV per unit cell (20 metal atoms). The hydrogen
coverage was 0.25 ML.
The simple model is compared to the calculated data in Fig. 3.
The fit is relatively good, taken into account the simplicity of the
model. The most important failure of the model is the underestimation of the energy differences (and thus the total energy of
the slab) when going to large (positive or negative) energy differences. This is probably due to repulsive interactions between silver
atoms, which gives higher DFT calculated energies than expected
from the simple model. This is consistent with the fact that the discrepancy increases as the number of silver atoms per layer increases. As an example, the {0 3 0 1 1} and {0 4 0 0 1} models both
have a total of four silver atoms in the second and fourth subsurface layers, but the latter model is less stable than the former by
0.05 eV. Thus, there is an effective repulsive interaction between
silver atoms in the same layer. There may be an additional asymmetry effect from freezing the bottom layer, but we do not expect
this to be notable in the subsurface layer.
0.4
Linear model
Model
0.6
0.2
0.0
-0.2
-0.4
-0.6
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
DFT calculated
Fig. 3. The simple linear model in Eq. (1) of the energy difference is plotted as a
function of the DFT calculated values. The dotted line is where the model would
correspond perfectly to the DFT calculated data.
The fitted single atom segregation energies from the wide range
of configurations, 1 = 0.25 eV and 2 = 0.10 eV, compare reasonably well to the equivalent energy differences arising from moving
a single impurity Ag atom in a 20 atom Pd slab from the middle to
the top (0.29 eV) or from the middle to the second layer (0.06 eV)
in our previous study [7]. Similarly, Gonzalez et al. report a segregation energy for Ag from the second to the first layer as 0.16 eV
[23]. The difference between this study and our former one [7] is
most probably due to repulsive Ag–Ag interactions in the present
slabs with 25% silver. This is supported by another modeling study
by Ropo et al. using the concentration of silver in each layer as free
variables [8]. Here it was found that the segregation energy of Ag
from the bulk to the surface changed from 0.08 to 0.20 eV when
the surface concentration of silver varied from 1.0 to 0.7 [8]. Similarly, the segregation energy from the bulk to the subsurface changed from 0.03 to 0.04 eV when the second layer concentration of
Ag varied from 0.0 to 0.30 [8]. The latter study had a rather high
concentration of Ag (50% in the bulk), which is the most likely
explanation of their lower segregation energies compared to what
we have found.
The silver concentration is also important for the local relaxation of the slabs. Silver in this work was found to be between 12
and 24 pm higher than palladium after relaxation, while our previous modeling study with 5% silver concluded that Ag was 28 pm
higher than Pd in the surface [7]. The same trend is found by Gonzalez et al., who found the Ag atoms to be located around 10 pm
above the surface Pd atoms on average. The differences between
the modeling studies are probably due to different unit cell sizes
and different concentration of Ag in the upper layers. Apart from
this, the modeling results are consistent. Experiments, however,
have shown the opposite effect, with Pd being 25 pm higher than
Ag in the Pd67Ag33 (1 1 1) surface [5]. To check if our results were
artifacts due to local minima, we tried to restart the relaxation
from a configuration with Pd placed higher than Ag in the surface
layer. This model relaxed directly back to the same situation as before, with Pd being lower than Ag. The most probable explanation
to this discrepancy is the difference in Pd concentration in the surface layer between the experiments (5–11%) and our modeling
studies (25–75%). Another possible explanation is temperature;
our calculations are performed at 0 K, while the experiments were
done at 720–920 K.
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O.M. Løvvik, S.M. Opalka / Surface Science 602 (2008) 2840–2844
We have previously investigated the various high-symmetry
adsorption sites of hydrogen on a Pd3Ag(1 1 1) surface [21]. It
was there found that hydrogen binding was always stronger at
fcc surface sites, and that the adsorption was stabilized with
increasing number of (up to three) nearest neighbour (NN) Pd
atoms. We have therefore in this study only investigated adsorption on the fcc sites with the highest number of NN Pd on each
surface.
The relaxed H position depended on the NN surface atoms. The
optimized Pd–H distance was 180–181 pm when H had three NN
Pd atoms; this decreased to 174–175 pm and 167–169 pm when
the number of NN Pd atoms decreased to two and one, respectively. The decreasing Pd–H distance can be understood from the
higher affinity between Pd and H relative to that between Ag and
H; when the number of NN Pd atoms decreases, the bonding between the remaining NN Pd atom(s) and the adsorbed hydrogen
gets stronger, and the Pd–H distance is reduced. Consistent with
this picture is the variation in Ag–H distance as the number of
NN Ag atoms changes: it exhibits the opposite behaviour. The
Ag–H distance is thus largest for the models where H had only
one NN Ag atom, 210–223 pm. When H had two NN Ag atoms,
the Ag–H distance was 203–204 pm, and in the model where H
had three NN Ag atoms {4 0 0 0 1}, the Ag–H distance was 192
pm. The relatively large variation in Ag–H distance for the one
NN Ag models is because of different numbers of Ag atoms in the
subsurface layer; the Ag atoms in the subsurface layer act as a
repulsive force in the {2 2 0 0 1} model. The present results compare
very well with previously published values for hydrogen adsorption on pure (1 1 1) metal surfaces, where the Pd–H distance is
181 pm [31] and the Ag–H distance is 189 pm [32].
In order to compare the segregation tendency of the different
surfaces directly, we have found it most instructive to study the total energy of the slab with 0.25 ML H at the equilibrium position
relative to the same energy of the isotropic {1 1 1 1 1} model. This
may be viewed as a ‘‘hydrogen corrected” segregation energy, that
is: how much energy is gained (or lost) from moving silver atoms
between the bulk, surface, and subsurface layers? The resulting
energies have been shown in Table 1 and Fig. 2. It is seen that,
while the energy of the pure slabs decreases monotonically when
going from Pd-rich to Ag-rich surfaces (when only regarding the
most stable model for each surface concentration), there is a minimum in the energy of the slabs with 0.25 ML adsorbed H at 50%
silver, that is two out of the four atoms in the surface unit cell. This
is a strong indication that the presence of hydrogen can indeed reverse the surface segregation in this alloy. Our results are consistent with those of Gonzalez et al. [23]. They compared three
different slab models with four different hydrogen coverages, and
found that a hydrogen coverage of approximately 0.25 ML was sufficient to obtain a segregation reversal. Since our slab models are
quite different from theirs, and the hydrogen coverage is not the
same, the numbers are not directly comparable.
We have in this study only investigated 0.25 ML hydrogen, but
an increased coverage would of course mean an even stronger promotion of the reversal effect. This would have to compete with the
repulsive interaction between the hydrogen atoms at higher coverage, which is in the order of 0.1 eV up to a coverage of 1.0 on a pure
Pd (1 1 1) surface [31]. On the other hand, since the interaction between Pd and H is so much stronger than that between Ag and H,
we can expect clustering of Pd in the surface at low H coverage.
We have created a linear model of the hydrogen adsorption,
using the number of palladium atoms among the adsorbed hydrogen nearest neighbours(nPd) as the variable:
DEads-model ¼ DEslab nPd Pd :
ð2Þ
The parameter Pd is the effective energy difference between
having a silver atom and a palladium atom as a nearest neighbour
for a hydrogen atom. The best fit is shown in Fig. 4, with Pd =
0.20 eV. It includes the cost of moving the Pd out to the surface,
and is thus a direct measure of the strength of the effect.
The previously cited experimental study of hydrogen on Mo/Re
bimetallic surfaces showed no change in surface segregation after
hydrogen exposure, rationalized by hydrogen desorption taking
place at temperatures lower than that required for metallic diffusion [20]. Will this be the case for the surfaces in study here as
well, reducing the relevance for real systems? We believe that this
is not the case, due to the very strong affinity of hydrogen to palladium. The energy gained by moving from the most stable pure
slab model {4 0 0 0 1} to the most stable adsorption model with
25% Pd in the surface layer {3 0 0 1 1} is more than 0.43 eV, which
is significant. Kinetic barriers would certainly hinder diffusion
needed to achieve the reversed segregation at perfect (1 1 1) surfaces. In real systems, however, there is an abundance of different
surface terminations, faults, impurities, etc. We expect that there
will be many stable adsorption sites for hydrogen in the vicinity
of Pd atoms in the ‘‘bulk” (subsurface and beyond) that can reach
the surface through relatively low barriers. Also, even though H
can be desorbed, there can be a relatively high turnover of H, so
that the surface may be continually covered with H. Thus, our results are in good correspondence with the reported experimental
reversal of segregation in this system [22].
We lend further support to the supposed segregation reversal in
real systems from the fact that Pd–Ag membranes improve their
performance significantly by activation [2]. This is a procedure in
which the membrane is exposed to hydrogen gas or air at elevated
temperature for several hours or even days. The mechanism behind this effect is not fully understood. We believe that our results
indicate that one likely explanation of this effect is hydrogen-induced reversed surface segregation of Pd to the surface layer.
Our results may also have relevance for catalysis. Bimetallic surfaces may have very high theoretical catalytic activity, but surface
segregation can be detrimental on their performance [33]. Hydrogen activation may be a new way to reverse such segregation to
significantly improve catalysts that otherwise would be of no
interest.
0.6
0.4
Linear model
3.2. Hydrogen covered slabs
0.2
0.0
-0.2
-0.2
0.0
0.2
0.4
0.6
DFT calculated
Fig. 4. A simple linear model of the difference energy of the slabs with adsorbed
hydrogen compare to the bare slab surfaces. The dotted line is a linear fit to the DFT
calculated data, according to Eq. (2). This relationship takes into account the
influence of the number of Pd nearest neighbors bonded to H on slab energy.
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O.M. Løvvik, S.M. Opalka / Surface Science 602 (2008) 2840–2844
4. Conclusions
In conclusion, we have studied the effect of hydrogen adsorption on the surface segregation of Pd–Ag bimetallic (1 1 1) surfaces,
using density-functional calculations. This showed that there is a
significant energy gain from moving a palladium atom from the
bulk to the surface when hydrogen adsorbs on the surface. This
may explain the mechanism behind hydrogen activation of Pd–
Ag membranes. Also, such an activation may have relevance for
heterogeneous catalysis.
Acknowledgements
Economic support from the Norwegian Research Council
through the NANOMAT program and a grant of computational resources via the NOTUR project are acknowledged by OML. SMO
acknowledges financial support through US Department of Energy,
Contract No: DE-FG26-05NT42453.
References
[1]
[2]
[3]
[4]
[5]
[6]
[7]
[8]
S. Uemiya, Sep. Purif. Meth. 28 (1999) 51.
S.N. Paglieri, J.D. Way, Sep. Purif. Meth. 31 (2002) 1.
R. Bredesen, K. Jordal, O. Bolland, Chem. Eng. Proc. 43 (2004) 1129.
P.A. Sheth, M. Neurock, C.M. Smith, J. Phys. Chem. B 109 (2005) 12449.
P.T. Wouda, M. Schmid, B.E. Nieuwenhuys, P. Varga, Surf. Sci. 417 (1998) 292.
B.C. Khanra, M. Menon, Physica B 291 (2000) 368.
O.M. Løvvik, Surf. Sci. 583 (2005) 100.
M. Ropo, K. Kokko, L. Vitos, J. Kollar, Phys. Rev. B 71 (2005) 045411.
[9] H.Y. Kim, H.G. Kim, J.H. Ryu, H.M. Lee, Phys. Rev. B 75 (2007) 212105.
[10] T. Marten, O. Hellman, A.V. Ruban, W. Olovsson, C. Kramer, J.P. Godowski, L.
Bech, Z.S. Li, J. Onsgaard, I.A. Abrikosov, Phys. Rev. B 77 (2008) 125406.
[11] R.D. Adams, J. Organomet. Chem. 600 (2000) 1.
[12] J.K. Edwards, B.E. Solsona, P. Landon, A.F. Carley, A. Herzing, C.J. Kiely, G.J.
Hutchings, J. Catalysis 236 (2005) 69.
[13] M. Hirsimaki, M. Lampimaki, K. Lahtonen, I. Chorkendoff, M. Valden, Surf. Sci.
583 (2005) 157.
[14] P.A.J. Bagot, A. Cerezo, G.D.W. Smith, T.V. de Bocarme, T.J. Godfrey, Surf. Interf.
Analysis 39 (2007) 172.
[15] T. Kravchuk, A. Hoffman, Surf. Sci. 601 (2007) 87.
[16] T. Kangas, N. Nivalainen, H. Pitkänen, A. Puisto, M. Alatalo, K. Laasonen, Surf.
Sci. 600 (2006) 4103.
[17] B.C. Han, A.V. der Ven, G. Ceder, B.J. Hwang, Phys. Rev. B 72 (2005) 205409.
[18] E. Christoffersen, P. Stoltze, J.K. Nørskov, Surf. Sci. 505 (2002) 200.
[19] M. Okada, M. Hashinokuchi, M. Fukuoka, T. Kasai, K. Moritani, Y. Teraoka, Appl.
Phys. Lett. 89 (2006) 201912.
[20] L. Hammer, M. Kottcke, K. Heinz, K. Muller, D.M. Zehner, Surf. Rev. Lett. 3
(1996) 1701.
[21] O.M. Løvvik, R.A. Olsen, J. Chem. Phys. 118 (2003) 3268.
[22] J. Shu, B.E.W. Bongondo, B.P.A. Grandjean, A. Adnot, S. Kaliaguine, Surf. Sci. 291
(1993) 129.
[23] S. Gonzalez, K.M. Neyman, S. Shaikhutdinov, H.J. Freund, F. Illas, J. Phys. Chem.
C 111 (2007) 6852.
[24] Borgschulte, et al., unpublished.
[25] C.G. Sonwane, J. Wilcox, Y.H. Ma, J. Chem. Phys. 125 (2006) 184714.
[26] J.P. Perdew, K. Burke, M. Ernzerhof, Phys. Rev. Lett. 77 (1996) 3865.
[27] G. Kresse, J. Hafner, Phys. Rev. B 47 (1993) 558.
[28] G. Kresse, J. Furthmuller, Phys. Rev. B 54 (1996) 11169.
[29] S. Müller, A. Zunger, Phys. Rev. Lett. 8716 (2001) 165502.
[30] A.V. Ruban, S.I. Simak, P.A. Korzhavyi, B. Johansson, Phys. Rev. B 75 (2007)
054113.
[31] O.M. Løvvik, R.A. Olsen, Phys. Rev. B 58 (1998) 10890.
[32] O.M. Løvvik, unpublished.
[33] J. Greeley, J.K. Nørskov, Surf. Sci. 601 (2007) 1590.