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Effect of Strain on the Reactivity of Metal Surfaces
Mavrikakis, Manos; Hammer, Bjørk; Nørskov, Jens Kehlet
Published in:
Physical Review Letters
Link to article, DOI:
10.1103/PhysRevLett.81.2819
Publication date:
1998
Document Version
Publisher's PDF, also known as Version of record
Link back to DTU Orbit
Citation (APA):
Mavrikakis, M., Hammer, B., & Nørskov, J. K. (1998). Effect of Strain on the Reactivity of Metal Surfaces.
Physical Review Letters, 81(13), 2819-2822. https://doi.org/10.1103/PhysRevLett.81.2819
VOLUME
81, NUMBER 13 PHYSICAL REVIEW LETTERS 28S
EPTEMBER
1998
Effect of Strain on the Reactivity of Metal Surfaces
M. Mavrikakis,
1
B. Hammer,
2
and J.K. Nørskov
1
1
Center for Atomic-scale Materials Physics, Department of Physics, Technical University of Denmark, DK-2800 Lyngby, Denmark
2
Institute of Physics, Aalborg University, DK-9220 Aalborg, Denmark
(Received 15 May 1998)
Self-consistent density functional calculations for the adsorption of O and CO, and the dissociation
of CO on strained and unstrained Ru(0001) surfaces are used to show how strained metal surfaces have
chemical properties that are significantly different from those of unstrained surfaces. Surface reactivity
increases with lattice expansion, following a concurrent up-shift of the metal d states. Consequences
for the catalytic activity of thin metal overlayers are discussed. [S0031-9007(98)07198–1]
PACS numbers: 82.65.My, 82.20.Pm, 82.30.Lp, 82.65.Jv
The ability to grow and characterize one metal on top
of another has developed rapidly over the last few years.
In a number of cases it has become possible to epitaxially
grow several layers of one metal on top of another. If
the lattice constants of the two metals differ, strained
overlayers are formed. It has been shown experimentally
that such strained overlayers can have chemical properties
that are significantly different from those of the pure
overlayer metal [1–3]. Most recently strain in the surface
region has been introduced not just by growing one metal
epitaxially on another, but by local deformation of a single
metal phase [4]. Such strain has been shown to modify
the chemisorption properties of the metal considerably.
If strain generally induces changes in the ability of a
surface to form bonds to adsorbed atoms or molecules,
the possibility arises of using strain to manipulate the
reactivity of a metal.
In the present Letter we investigate the generality of
the effect of strain on surface reactivity and its origin by
performing a set of density functional (DFT) calculations.
We study a metal [Ru(0001)] slab under compressive or
tensile stress and show that both molecular (CO) and
atomic (O) chemisorption energies as well as barriers for
surface reactions (CO dissociation) vary substantially on
strained lattices. We further proceed to show that this
effect can be explained on the basis of shifts in the metal
d bands induced by the stress. This allows us to develop
a model for the effect which can be readily extended to
several catalytically important systems.
We used a three layer slab of Ru periodically repeated
in a super cell geometry with five equivalent layers of
vacuum between any two successive metal slabs. O
adsorption and CO dissociation were treated within a
s2 3 2d unit cell, whereas CO chemisorption was studied
on a
p
3 3
p
3 unit cell. These specific choices represent
the most stable overlayer structures for the corresponding
systems, as determined by experiments [5,6]. Adsorption
is allowed on only one of the two surfaces exposed and
the electrostatic potential is adjusted accordingly [7]. The
top surface layer was relaxed for the atomic and molecular
chemisorption problems, but kept fixed at its initial
position for the calculation of the CO dissociation barrier.
Ionic cores are described by ultrasoft pseudopotentials
[8] and the Kohn-Sham one-electron valence states are
expanded in a basis of plane waves with kinetic energies
below 25 Ry. The surface Brillouin zone is sampled at
18 special k points. The exchange-correlation energy
and potential are described by the generalized gradient
approximation (PW91) [9,10]. The self-consistent PW91
density is determined by iterative diagonalization of the
Kohn-Sham Hamiltonian, Fermi population of the Kohn-
Sham states (k
B
T 0.1 eV), and Pulay mixing of the
resulting electronic density [11]. All total energies have
been extrapolated to k
B
T 0 eV.
We first examine the effect of changing the lattice
constant parallel to the surface of the Ru(0001) slab on
the chemisorption properties of the surface. In this way
we focus directly on the strain effects. For thin layers of
one metal on top of another it can be difficult to isolate the
strain effects because they are folded with the effects due
to the interaction of the overlayer with the substrate. We
will later return to the overlayer structures. The calculated
equilibrium lattice constant (d
eq
) for bulk Ru(0001) was
found to be 2.74 Å, in reasonable agreement with the
experimental value of 2.70 Å [12]. The equilibrium cya
value used for Ru is 1.582 [12]. For the purposes of the
present study, we vary the lattice constant (d) parallel to
the surface between 2.70 and 2.80 Å corresponding to
a maximum absolute value of relative strain (Ddyd
eq
)
of ca. 2%. All the results shown here were obtained
from calculations on a three-metal-layer slab, where the
distance between the middle and bottom metal layers
was kept fixed at the value of the interlayer distance
corresponding to the equilibrium structure (d
eq
). We have
also tested an alternative model, where the interlayer
distance between these two layers is changed with in
plane strain according to Ru’s Poisson ratio [13] of 0.29.
We found no significant difference between the results
of these two approaches. Furthermore, additional test
calculations performed with up to six metal layers show
that the results presented here remain practically invariant
with the number of metal layers used.
0031-9007y98y81(13)y2819(4)$15.00 © 1998 The American Physical Society 2819
VOLUME
81, NUMBER 13 PHYSICAL REVIEW LETTERS 28S
EPTEMBER
1998
First, consider the adsorption of CO and O. Figure 1
shows the calculated adsorption energy
DE
ads
Esadsymetald 2 Esadsd 2 Esmetald (1)
as a function of the surface strain Ddyd
eq
. The geometry
of adsorption is illustrated in Fig. 2. O is chemisorbed
on its preferred hcp site in a 2 3 2 overlayer structure
as suggested by several experiments, including LEED
studies [5]. CO on the other hand, preferentially adsorbs
on an atop site in a
p
3 3
p
3 overlayer structure, in
accord with experimental evidence [6]. The results for O
and CO adsorption on the unstrained surface are in good
agreement with previous DFT calculations [14,15].
The results illustrated in Fig. 1 suggest that there
is a considerable variation in adsorption energy with
strain, and in both cases the chemisorption bond gets
stronger as the lattice constant increases. However, the
effect on O chemisorption strength is about 5 times
more pronounced than the corresponding effect for CO.
The trend calculated for O adsorption is in accord with
scanning tunneling microscopy (STM) observations on a
strained Ru(0001) surface [4], where oxygen atoms were
found to preferentially adsorb on sites at the expanded
regions of the surface. The same experiments suggest two
possibilities for CO: (i) either the opposite chemisorption
trend with lattice strain holds (i.e., CO prefers sites at the
compressed regions of the surface), or (ii) a dense CO
overlayer is formed at the expanded regions, rendering
-2.5 -1.5 -0.5 0.5 1.5 2.5
∆d/d
eq
%
0.60
0.80
1.00
-2.03
-2.01
-1.99
-5.45
-5.35
-5.25
E
CO
diss
(eV) E
CO
ads
(eV) E
O
ads
(eV)
(a)
(b)
(c)
FIG. 1. Effect of relative change in surface lattice constant
sd 2 d
eq
dyd
eq
of a Ru(0001) surface on the (a) binding energy
of atomic oxygen (E
ads
O
) (top panel), (b) binding energy of
molecular CO (E
ads
CO
) (middle panel), and (c) CO dissociation
barrier (E
diss
CO
), referenced to a zero of the clean surface plus
a gas phase CO molecule (bottom panel). Dashed lines are
drawn as a guide to the eye.
molecules invisible to the STM in these regions. Gsell
et al. [4] suggest that further experiments are needed to
clarify the situation with CO. We believe that the second
of the proposed possibilities is most likely describing the
actual events. The high mobility of CO molecules on
this surface (calculated diffusion barrier of ca. 0.15 eV)
adds to the degree of difficulty for the CO experiment.
Therefore, the above mentioned room temperature STM
experiments had to trace very mobile CO molecules and
differentiate between adsorption sites with only slightly
different binding energies between each other. Results
pertaining to O adsorption are much easier to interpret,
since the binding energy difference between competing
sites is considerably larger, and the diffusion barrier for O
atoms is much higher (calculated ca. 0.40 eV) compared
to CO. In support of these arguments, several studies
of CO adsorption on strained overlayers show that an
expansion of the lattice constant increases the CO binding
energy (see, for example, [1]).
We next consider the dissociation of CO on Ru(0001).
The barrier for CO dissociation over several metal sur-
faces has been determined in the past [16]. Extending this
work to CO dissociation on Ru(0001), we determined the
transition state (TS) for the unstrained surface as shown
in Fig. 2. The TS is very stretched compared to the bond
length of the gas phase molecule (calculated at 1.15 Å,
versus an experimental value [17] of 1.12 Å), and the
reaction proceeds almost entirely as a stretch of the CO
bond with the C end of the molecule already in its final,
hcp site on the surface. When the surface lattice con-
stant is varied, we search for the new transition state by
making variations in this reaction coordinate. This is il-
lustrated in Fig. 3, where, as the lattice constant increases,
the TS moves slightly towards smaller C-O distances, but
the overall trend is not affected significantly. In the bot-
tom panel of Fig. 1 the variation in the energy of the TS,
defined similarly to Eq. (1), is also shown as a function
of strain. Again the interaction strength increases with in-
creasing tensile strain (ca. 0.15 eV for each 1% of strain,
on the average), making the stretched slab considerably
more reactive towards CO dissociation.
It seems that molecular and atomic adsorption energies
as well as activation energies for dissociation show similar
FIG. 2. A top view of the preferred geometry for chemisorbed
O and CO, and the TS for CO dissociation on a Ru(0001) sur-
face for the equilibrium (unstrained) lattice constant (2.74 Å).
The TS is very close to a center (C)-bridge (O) configuration.
Shaded metal atoms illustrate the unit cell used. Smaller cir-
cles, above the surface plane, represent the respective adsorbed
species.
2820
VOLUME
81, NUMBER 13 PHYSICAL REVIEW LETTERS 28S
EPTEMBER
1998
FIG. 3. Calculated energy along the reaction coordinate of
C-O distance during CO dissociation over three different
Ru(0001) surfaces. The corresponding surface lattice constants
are shown as labels to the curves. Continuous lines represent
the best fits through the calculated data points shown with
circles, squares, or diamonds. Calculated forces along the
reaction coordinate have been used for the slopes of these
lines. The highest point on each curve is taken as the respective
activation energy barrier shown in the bottom panel of Fig. 1.
The energy scale is referenced to a zero of the clean surface
plus a gas phase CO molecule.
trends. We will now discuss possible explanations for
this, trying to elucidate the underlying mechanism leading
to the observed behavior. In particular, we will examine
if the effect of strain on surface chemisorption and
reactivity can be reduced to the strain-induced change in a
more fundamental parameter determining these variations.
Finally, the generality of the strain effect for different
surfaces and adsorbates within the framework of both
uniformly strained slabs and thin overlayers is argued.
We will start by postulating that the underlying parame-
ter determining the strain-induced variations shown in
Fig. 1 is the position of the center of the metal d bands.
There are good reasons for this [18]. The interaction be-
tween the adsorbate states and the metal d states is an
important part of the interaction energy, and while the
sp bands of the metal are broad and structureless, the
d bands are narrow, and small changes in the environment
can change the d states and their interaction with adsor-
bate states significantly. The d-band center (e
d
) is the
simplest possible measure for the position of the d states.
In Fig. 4 we show the data of Fig. 1 as a function of the
center of mass of the density of states projected onto the
atomic d states of the clean surface. For convenience, we
use all the d states here, instead of the ones with the cor-
rect symmetry for bonding with the various adsorbates.
This makes no major difference, when the adsorption ge-
ometry remains similar. When the lattice is expanded par-
allel to the surface, the overlap between the d electrons on
neighboring metal atoms becomes smaller, the bandwidth
decreases and to keep the d occupancy fixed, the d states
FIG. 4(color). Molecular (E
CO
chem
) and atomic (E
atomic
chem
) binding
energy as a function of the d-band center (e
d
) of the metal
surface (top and middle panel, respectively). The barrier
for dissociation of small molecules, referenced to gas phase
zero, as a function of e
d
is shown in the bottom panel.
Common colors are used for data corresponding to the same
metal throughout the three panels. Lines drawn represent best
linear fits. X:XY reflects chemisorption on or dissociation
over atom X in an XY -alloy surface. X@Y means an X
atom impurity in a Y surface. Specific data points are taken
from: [20] for N, O, and NO on Pd; [23,24] for CO on
Pt, Ni, Cu, and Pd; [22,25] for CH
4
on Ni; [21] for H
2
on Cu. Data for O and CO on Ru are those shown in
Fig. 1.
2821
VOLUME
81, NUMBER 13 PHYSICAL REVIEW LETTERS 28S
EPTEMBER
1998
have to move up in energy [19]. According to Fig. 4 this
gives a stronger interaction in all cases.
In order to show that the d-band center is the under-
lying parameter we have included in Fig. 4 a large num-
ber of data from the literature [20–25], all extracted from
similar DFT calculations. These data represent calculated
adsorption energies of atomic and molecular adsorbates as
well as activation energies for surface reactions. They all
describe a situation, where the adsorbate interacts with the
same kind of metal atom(s) in the same local geometry,
but the environment varies. In particular, the environment
has been changed in several cases by considering different
facets and stepped surfaces. Here the local d-projected
density of states has not been changed due to strain, but
due to a change in the number of metal neighbors, the
general rule being that the lower the coordination num-
ber, the smaller the local bandwidth and the higher the e
d
(for metals with more than half-filled d bands). The fact
that these data follow the same trend when plotted as a
function of e
d
strongly suggests that e
d
is the underlying
parameter determining reactivity to a first approximation.
This data set also includes alloys and overlayers, where
a large portion of the change in e
d
can be attributed to
changes in the metal-metal distances in the surface [26],
as is the case for the strained slab.
Data in Fig. 4 also show that the correlation between
interaction strength (adsorption energy or activation en-
ergy barrier) and e
d
holds for many different adsorbates
and metals. Similar calculations for H
2
dissociation on
transition and noble metals have shown such a relation-
ship to hold also when different metals are compared
[18,27]. The generality of this correlation is a simple
manifestation of the fact that the coupling to the d states
depends on the position of the d states relative to the
Fermi level. This tendency is also elucidated by simple
models describing interactions between atomic or molec-
ular adsorbates and transition states with metal surfaces
[18]. In addition, the correlation between the interaction
strength and the d-band center found in the framework
of these simple models appears to be independent of the
adsorbate and the metal, in agreement with the trends re-
vealed with our large-scale total energy calculations, as il-
lustrated with the data in Fig. 4. The identity of the metal
involved shows up only in the strength of the effect, that
is, the slope of Ese
d
d through the size of the coupling
matrix element. The relative ordering in the coupling
strength is 5d . 4d . 3d following the relative sizes of
the d wave functions [18].
In conclusion, we have shown that there is a general
correlation between surface strain and adsorption energies
and activation energy barriers. We have also shown that
this effect can be attributed to a shift in the center of
the metal d bands (e
d
) with strain. The parameter e
d
,
which is a property of the local adsorption site of the
unperturbed metal surface, also describes variations in
reactivity for metal overlayers and for different surface
structures. Our results suggest that surface strain can
in general be used to tailor the catalytic activity of
metals.
The present work was in part financed by The Danish
Research Councils through The Center for Surface Reac-
tivity and Grant No. 9501775. The Center for Atomic-
scale Materials Physics is sponsored by the Danish
National Research Foundation. M.M. gratefully acknowl-
edges financial support from EU through a Marie-Curie
grant (Contract ERBFMBICT No. 961691).
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