Multi-Lattice Kinetic Monte Carlo Simulations from First-Principles: Reduction of the Pd(100) Surface Oxide by CO

8.2 MB·English

by  Max J. Hoffmann

Multi-Lattice Kinetic Monte Carlo Simulations from
First-Principles:
Reduction of the Pd(100) Surface Oxide by CO
5
1 Max J. Hoffmann,∗,† Matthias Scheffler,‡ and Karsten Reuter∗,†
0
2
ChairforTheoretical Chemistryand CatalysisResearchCenter, TechnischeUniversität

n
München,Lichtenbergstr. 4,85747Garching(Germany), andFritz-Haber-Institutder
a
J Max-Planck-Gesellschaft,Faradayweg4-6, 14195Berlin(Germany)

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E-mail: [email protected];[email protected]
]
l
l
a
h
- Abstract ysis.1–6 On the one hand, this approach employs
s
e material-specific rate constants for the elemen-
m
We present a multi-lattice kinetic Monte Carlo tary processes, presently typically computed by
.
t (kMC) approach that efficiently describes the density-functional theory (DFT) and transition-
a
m atomistic dynamics of morphological transitions state theory (TST). On the other hand, and in
- between commensurate structures at crystal sur- contrast to still prevalent mean-field rate equation
d
n faces. As an example we study the reduction of based microkineticmodels, the 1p-kMC approach
o a(√5 √5)R27 PdO(101)overlayeronPd(100) explicitlyaccountsforspatialheterogeneities,cor-
c × ◦
[ in a CO atmosphere. Extensivedensity-functional relations, and fluctuations of the atomic structure.

theory calculations are used to establish an atom- Thedownsideoftheapproachisthecomputational
1
v istic pathway for the oxide reduction process. cost of the underlying DFT-TST calculations. In
0
First-principles multi-lattice kMC simulations on practice, 1p-kMC simulations are therefore hith-
1
7 the basis of this pathway fully reproduce the ex- ertoperformedonlatticemodels. Thisexploitsthe
1 perimental temperature dependence of the reduc- translational symmetry of the crystalline lattice to
0
. tion rate [Fernandes et al., Surf. Sci. 2014, 621, dramaticallyreducetherequirednumberofdiffer-
1
0 31-39]andhighlightthecrucialroleofelementary ent 1p rate constants.7,8 For simple reaction net-
5 processes special to the boundary between oxide works liketheCO oxidationreaction at low-index
1
and metaldomains. single-crystal model catalyst surfaces, this num-
:
v
ber of 1p rate constants can be as low as 10-20,
i
X comprising adsorption, desorption, diffusion and
r 1 Introduction reaction steps at and between the different lattice
a
sites.5,9,10
In recent years first-principles (1p) kinetic Monte By construction, the conventional lattice 1p-
Carlo (kMC) simulations have established a new kMC approach cannot directly be applied to (sur-
standard for the microkinetic modeling of sur- face) morphological rearrangements, i.e. any type
face chemical processes and heterogeneous catal- of phase transition that includes changes in the
consideredlatticesitearrangement. Notwithstand-
Towhomcorrespondenceshouldbeaddressed
∗
†ChairforTheoreticalChemistryandCatalysisResearch ing, for the (late) transition-metal catalysts typi-
Center,TechnischeUniversitätMünchen,Lichtenbergstr. 4, cally employed in oxidation catalysis, a possible
85747Garching(Germany) formation of (surface) oxides has been discussed.
‡Fritz-Haber-InstitutderMax-Planck-Gesellschaft,Fara-
Possibly, especially the continuous formation and
dayweg4-6,14195Berlin(Germany)
1
reductionofsuchoxidicfilmscouldbeamajorac- to which they are bound. Only rarely, i.e. after
tuator for the observed catalytic activity.11–19 As very many such vibrations, an elementary process
a first step to make such systems and phenomena changes this population at the lattice sites, where
accessible to 1p-kMC we here describe a multi- the duration of this process itself is very short.
lattice 1p-kMC approach, which is applicable to A diffusion process brings a reaction intermediate
morphological transitions between commensurate to another site, adsorption and desorption fill and
crystalline lattices. The simple concept is that we empty sites at the surface, surface reactions con-
work on a super-lattice that contains both lattices vert reaction intermediates into another etc. Dur-
simultaneously. In a spatial region describing one ing the long time intervals between such individ-
stable phase, only the sites of the corresponding ual elementary processes the reaction intermedi-
lattice are "enabled". The actual morphological ates equilibrate fully and thereby are assumed to
transitionisthendescribedthroughtheelementary forget through which elementary process they ac-
processes of its atomistic pathway, which "dis- tuallyreached theircurrent siteorstate.
able" sites of one lattice and "enable" sites of the Viewing the entire population at all sites as one
otherlattice. possible configuration, individual events in form
We illustrate this multi-lattice 1p-kMC idea by ofelementaryprocessesthusadvancethesystem’s
modeling the surface oxide reduction at Pd(100). state from one configuration to another. In each
Recent experimental work20 observed significant configuration reaction intermediates are assumed
changes in the rate of oxide reduction in the tem- to have forgotten their past. In this Markov ap-
peraturerangefrom300-400K,whenexposingan proximation events will occur uncorrelated from
initially prepared (√5 √5)R27 PdO(101) sur- previousonesandthetimeevolutionofthesystem
◦
×
face oxide film (henceforth coined √5-oxide for isdescribed byaMarkovianmasterequation
brevity)21,22 to a 5 10 11bar CO atmosphere.
Analysisofthedatau×sing−fittedmean-fieldkinetic r˙u(t)=(cid:229) wuvr v(t) wvur u(t) , (1)
−
v
models suggested that the reduction is controlled
by boundary processes between surface oxideand where r (t)is the probability for the system to be
u
metal domains.20 In the present paper, we use ex-
in configuration u at time t, and w is the transi-
vu
tensive DFT calculations to establish an atomistic tion rate (in units of time 1) at which configura-
−
pathway for the oxide reduction process. Based
tion u changes to configuration v. For heteroge-
on this pathway, our multi-lattice 1p-kMC simu-
neous catalysis, solving this equation is in prac-
lations perfectly reproduce the observed trends in tice not feasible by any direct approach.7,8 The
thereductionrates,andshowthatthecriticalsteps
kMC approach addresses this problem by gener-
inthereductionofthesurfaceoxidecorrespondin-
atingconfiguration-to-configurationtrajectoriesin
deedtocross-reactionsbetweenthemetaldomains
such a way that an average over an ensemble of
and thesurface oxide.
suchtrajectoriesyieldsthecorrectprobabilityden-
sity r (t) of eq. 1.7,8 Instead of evaluating and
u
storingtheentiretransitionmatrixw, a kMCcode
2 Theory
thus only focuses on-the-fly on those transition
matrix elements w that are actually required to
vu
2.1 Kinetic Monte Carlo simulations
propagatethetrajectory.
for heterogeneous catalysis
2.2 Efficient 1p-kMC on one or more
Wefocusonthermallydrivensurfacechemicalre-
actions that involve a site-specific (covalent-type) lattices
binding of the reaction intermediates. Such reac-
Even with this focus on the required w , a kMC
tions generally follow a so-called rare-event time vu
simulation can still be an extremely demanding
evolution. Thatis,ontimescalesthatcanbesimu-
task, if the rate constants determining the w are
lated by ab initio molecular dynamics all reaction vu
to be provided through 1p-calculations. Emerg-
intermediates only vibrate around the lattice sites
2
ing so-called adaptive or self-learning kMC ap- elementary processes that require an empty site
proaches23–26 address this problem by generat- explicitly look for the sites to be empty and not
ing look-up tables of already computed w in "occupied" by null. In a corresponding region
vu
the course of the simulation. However, an orders where all sites belonging to the other lattices are
of magnitude higher efficiency is needed to make disabled through null species, multi-lattice 1p-
comprehensive 1p-kMC simulations tractable for kMCthusreducestoaregularlattice1p-kMCsim-
systems as complex as the present one. This effi- ulation and only the elementary processes corre-
ciency is achieved when the sites involved in the sponding to the 1p-kMC model of this lattice can
surface catalysis can be mapped onto a static lat- possiblyoccur.
tice. Due to the translational symmetry of the lat- Inthissetup,localtransitionsbetweenthediffer-
tice, each equivalent site type then features the ent lattices are finally enabled by introducing new
same group of in principle possible elementary elementary processes which involve the removal
processes, and these elementary processes typi- or placement of the null species at sites belong-
cally depend only on the occupation of nearby ing to the lattices involved. Trivially, for the ox-
sites. While this does not reduce the number of ide reduction example this could be as simple as
w required during a 1p-kMC trajectory, it dra- an elementary process placing the null species
vu
maticallyreducesthetotalnumberofinequivalent on one or more sites of the oxide lattice and re-
w and therewith 1p rate constants that need to movingthenull speciesfrom nearby sitesofthe
vu
be computed with DFT-TST. In lattice 1p-kMC metallattice. AsshownbelowforthePdoxidere-
these1prateconstantsaretheninpracticeprecom- duction, local lattice transitions are unlikely that
putedandstored,tobelookedupondemandinthe simple, but follow complex, multi-stepped reac-
evolvingkMCsimulation. tion paths. The additional challenge of setting up
Assuming a static arrangement of sites, lattice andperformingamulti-lattice1p-kMCsimulation
1p-kMCcannotdirectlybeappliedtosystemsun- ascomparedtotraditionallattice1p-kMCisthere-
dergoingamorphologicaltransition. Inthepresent fore to establish such atomistic pathways for the
context,thiswouldbethereductionoftheinitially lattice transitions and implement them in form of
oxidized surface to a metallic state, where the ox- correspondingelementaryprocesses.
ide overlayer and metal substrate exhibit different From a purely algorithmic point of view as
crystal lattices. With our suggested generaliza- implemented in the kMC modeling framework
tion to multi-lattice 1p-kMC transitions between kmos multi-lattice kMC is identical to single-
commensurable lattices become accessible. The lattice kMC which underlines that multi-lattice
essenceoftheapproach ishereby tochooseas ba- kMCishighlyefficient. Theonlydifferenceisthat
sic unit cell of the lattice employed in the kMC thoseelementary stepsaccountingformorpholog-
simulations a suitable, large enough commensu- ical changes typically involve significantly more
ratecellthatembracesallprimitiveunitcellsofthe sites(10-20sites)thantypicalordinarysurfacere-
differentlatticestobetreated. Thiscommensurate actionsteps (1-8 sites). Thescaling withthenum-
cell (and the lattice built up from it) then contains ber of conditions (i.e. here sites) has been studied
as sitessimultaneouslyall sitesofalllattices. inapreviouspaper.8 Thisshowsthatthecomputa-
In order to efficiently distinguish (during a sim- tionalscalingwiththenumberofconditionsissig-
ulation) in which lattice state a given local region nificant, (O(nlog(n) to O(n2)). Howeverin terms
is currently in, we introduce an additional artifi- ofoverheadthereisnofundamentaldifferencebe-
cial species (canonically named null) to repre- tweensingle-latticekMCand multi-latticekMC.
sent "disabled" sites. If say, a certain region is
currently in one lattice structure, then the null
species are placed on all sites corresponding to
the other lattices in this region. A site "occupied"
with a null species is hereby to be distinguished
from an empty site. No elementary processes are
available at sites occupied by a null species, i.e.
3
2.3 Literature 1p-kMC models of CO cesses are time-reversals of these non-activated
oxidation at the √5-surface oxide adsorption processes, with rate constants ful-
filling detailed balance. Oxygen diffusion oc-
and at Pd(100)
curs between nearest-neighbor hollow sites, CO
Our multi-lattice 1p-kMC simulations describing diffusion between nearest-neighbor bridge sites.
the reduction of the Pd(100) surface initially cov- Strong short-range repulsive interactions between
eredwitha√5-surfaceoxidefilmbuildonexisting adsorbed reaction intermediates as calculated by
1p-kMCmodelsforCOoxidationatthe√5-oxide DFT33,34 are accounted for through site-blocking
and for CO oxidation at Pd(100). These single- rules that prevent processes leading to O-O pairs
lattice models and the elementary processes con- at nearest-neighbor hollow-hollow distances, to
sideredinthemhavebeenestablishedbyextensive CO-CO pairs closer or at next-nearest-neighbor
DFT calculations and have been described in de- bridge-bridgedistance,andO-COpairsatnearest-
tail before.27,28 Here, we only briefly recapitulate neighbor hollow-bridge distance.28 CO oxidation
theiressentialsforcompletenessandasameansto proceeds via a Langmuir-Hinshelwood mecha-
introducethetwolatticetypes. nismandatthetemperaturesofinterestleadstoan
instantaneouslydesorbingCO molecule. Therate
2
constants for all these elementary processes have
been computed with DFT-TST, specifically em-
ploying the PBE exchange-correlation (xc) func-
tional.35 Typical for CO oxidation at transition
metal surfaces, O and CO diffusion barriers are
significantlylowerthanthebarriersofallotherel-
ementary processes involved. In the1p-kMCsim-
ulations this leads to frequent executions of diffu-
sioneventsatminutetimeincrements. Toincrease
the numerical efficiency and be able to simulate
theextendedtimescalesnecessarytofollowoxide
Figure 1: Illustration of the lattice employed in reduction we artificially increased diffusion barri-
the 1p-kMC model of CO oxidation at Pd(100). ers for CO of 0.14eV and for O of 0.28eV28 by
Shown is a top view of the Pd(100) surface with 0.5eV.Thisispermissible,ifdiffusionisthenstill
a primitive unit cell and its hollow (yellow circle) fast enough to achieve an equilibration of the ad-
and bridge (green rectangle) sites. CO molecules layer ordering in between the other (rare) elemen-
adsorb at bridge sites and oxygen molecules ad- tary processes.7 We validated that this is indeed
sorb (dissociatively) at hollow sites. Here and the case, by performing the 1p-kMC simulations
henceforth Pd atoms in fcc(100) positions are de- with diffusion barriers increased by 0.6eV and
picted as large blue spheres, O atoms as small red 0.7eV without obtaining any significant changes
spheres,and C as smallgrey spheres. intheoxidereductionrates reported below.
As established by detailed first-principles statis-
Systematic DFT calculations identified the hol- tical mechanics simulations by Rogal et al.9 only
low and bridge sites offered by the Pd(100) sur- two ofthe high-symmetryadsorptionsites offered
face, cf. Fig. 1, as stable high-symmetry adsorp- by the intact √5-oxide are relevant for the re-
tion sites for O and CO, respectively.28 The 1p- ducing environments considered here: a bridge
kMCCOoxidationmodelonPd(100)correspond- and a hollow site as illustrated in Fig. 2. Equiv-
ingly considers all non-concerted adsorption, des- alent to the Pd(100) case, the 1p-kMC CO ox-
orption,diffusion,andLangmuir-Hinshelwoodre- idation model at the √5-oxide correspondingly
action processes involving these sites.28 Oxygen considers all non-concerted adsorption, desorp-
molecules adsorb dissociatively on two empty tion, diffusion, and Langmuir-Hinshelwood re-
next-nearest neighbor hollow sites,29–32 CO ad- action processes involving these sites.27,28 Eley-
sorbs on an empty bridge site. Desorption pro- Ridealreactionprocessesasrecentlysuggestedby
4
the same PBE xc functional35 as used in the
Pd(100) and √5-oxide 1p-kMC models. Employ-
ing the same computational setup as detailed in
ref. 28,theDFTcalculationshavebeenperformed
with the CASTEP package38 via the Atom-
ic Simulation Environment.39 Previous
work28 established that the employed standard li-
brary ultrasoft pseudopotentials accurately repro-
duce the full-potential √5-oxide adsorption ener-
getics of Rogal et al.27 Geometry optimizations
andtransition-statesearchesweredonewithsuper-
cell geometries containing asymmetric slabs with
Figure 2: Illustration of the lattice employed one (frozen) layer of Pd(100) and one layer of
in the 1p-kMC model of CO oxidation at the PdO(101),separatedbyatleast10Åvacuum. Ge-
√5-oxide. Shown is a top view of the (√5 ometry optimizations were performed using the
×
√5)R27 PdO(101) surface oxide reconstruction BFGSmethodwithaforcethresholdof0.05eV/Å.
◦
with a primitive unit cell of the oxide layer and The energetics of the thus obtained intermediate
its hollow (yellow circle) and bridge (green rect- geometries were refined in single-point calcula-
angle) sites. O and CO adsorb at both site types. tions with further Pd(100) layers added to the
In the stoichiometric termination shown, O atoms slab. Transition state searches have been per-
occupy all hollow sites. Here and henceforth Pd formed with the climbing-image nudged elastic
atoms in surface oxide positions are depicted as bandmethod40 orsimpledragprocedureswiththe
largegreen spheres. nature of the transition state confirmed through
frequency calculations. From test calculations
with additional Pd(100) layers added we estimate
Hirvi et al.36 are in principle also considered, but
the uncertainty in the thus determined barrier val-
do not play a role at the low CO pressures ad-
ues as 0.1 eV. The gas-phase calculations for O
2
dressed here. Adsorption is non-activated, apart
and CO were performed in a cubic supercell of
from dissociative adsorption of O into neighbor-
2 15ÅboxlengthandG -pointsampling. Ataplane-
ingbridgesites,whichishinderedbyasizablead-
wave cutoff of 400eV and a [4 4 1] k-point
sorption barrier of 1.9eV. As for the Pd(100) 1p- × ×
grid for the commensurate surface oxide unit cell
kMCmodel,all1prateconstantsofthis√5-oxide
and a [2 2 1] k-point grid for the (2 2) sur-
model have been computed with DFT-TST, em- × × ×
faceoxideunitcellintheslabcalculationsconver-
ploying the PBE xc functional.35 DFT-computed
gence tests demonstrate a numerical convergence
nearest-neighborlateral interactionsare takeninto
ofthe obtained DFT barriers and bindingenergies
account in these rate constants as detailed by Ro-
towithin0.1eV.
galet al.27
All 1p-kMC simulations have been performed
usingthekmosframework.8 Theperiodicbound-
2.4 Computational DFT and kMC ary simulation cell contains (40 20) √5-unit
×
settings cells and thus 1600 sites in case of the single-
lattice 1p-kMC simulations on the surface oxide.
The multi-lattice 1p-kMC simulations of the ox-
Systematictestswithvaryingsimulationcellsizes
ide reduction process consider additional ele-
showed the obtained oxide reduction rates to be
mentary processes to model the atomistic path-
fully converged at this setting. In the multi-lattice
way from oxide to metal lattice. This pathway
case one commensurate unit-cell contains already
and the involved elementary processes are de-
a total of 19 sites from both the metal and the
scribed in Sections 3.2-3.4 below. Their 1p rate
oxide lattice. We employed periodic boundary
constants have been calculated with DFT em-
simulation cells comprising (10 20), (20 20)
ploying the same TST-based expressions37 and × ×
and (40 20) such commensurate unit-cells to
×
5
specificallyassesstheroleofelementaryprocesses
acrossoxideandmetaldomains(seebelow). Inall
cases, averages over 10 kMC trajectories starting
withdifferentrandomnumberseedsweretakento
obtainthecorrect transientquantities.
100
3 Results
80
3.1 Single-lattice 1p-kMCsimulations %] 60 303 K
[ 343 K
of oxide reduction θOh 40 393 K
As mentioned initially the central objective of 20
our simulations is to analyze the oxide reduction
0
ratesobtainedinrecenthigh-resolutionX-raypho- 0 20 40 60 80 100 120
toelectron spectroscopy experiments by Fernan- t [min]
(a)
deset al.20 Within a small range of temperatures,
100
they reported large variations for thetotal timere-
quired to fully reduce an initially prepared √5-
80
oxide layer by exposure to a pure CO atmosphere
of 5 10 11bar. Specifically, at 303K the ox- %] 60 303 K
−
× [ 343 K
ide was reduced after approximately 90minutes, h
θO 40 393 K
while the same process took only approximately
12min at 343K and less than 4minat 393K. Pre- 20
vious theoretical work addressing the surface ox-
0
ide stability employed the 1p-kMC approach with 0 20 40 60 80 100 120
a single lattice, namely the √5-oxide 1p-kMC (b) t [min]
model. They monitored the coverage of O in the
Figure 3: Single-lattice kMC simulations for
hollow sites as an indicator for the oxide stabil-
ity.27 Usingthiscriterion1p-kMCsimulationsfail √5-oxide reduction at the three temperatures em-
ployed in the experiments and using the O cov-
qualitatively to reproduce the experimental find-
erage at the hollow sites (q ) as indicator for
ings of Fernandeset al.. Even at the highest tem- O
h
theprogressingreductionofthesurfaceoxide(see
perature of 393K no reduction of the oxide is ob-
text). The1prateconstantsaremodifiedtoachieve
served at all after 120mins, i.e. the oxygen cover-
at least some agreement with the experimental
age remainsessentially intactovertheentiretime.
findings: (a) CO adsorption energy lowered by
This can be explained by the lack of CO on the
0.2eV. The reduction times for all three tempera-
surface, which impliesthat an efficient removalof
turesareintherightorderofmagnitude,buttheor-
oxygenviaCO oxidationis notpossible.
dering with temperature is wrong. (b) CO adsorp-
Since an error in the reported experimental con-
tion energy lowered by 0.5eV; CO oxidation bar-
ditions large enough to explain this discrepancy
rierincreasedby0.15eV.Theoxidereductiontime
seems unlikely we focus on the uncertainty in the
correctly decreases with temperature, but the re-
DFT parameters deployed in the model. A pos-
duction time at 303K disagrees qualitatively with
sible reason for this discrepancy could be that
experiment.
the relevant CO adsorption energy of 0.92eV
−
as calculated by DFT-PBE is too small, and/or
the CO reaction barrier towards CO formation of
2
0.9eV27istoohigh. Weexplorethesepossibilities
by running the 1p-kMC simulations using modi-
fied rate constants. Specifically, we vary the CO
6
oxidationbarrierandtheCOadsorptionenergyon
the bridge and hollow sites within 1eV. How-
±
ever, no such kMC simulation reproduces the ex-
perimentally observed behavior: Either the time
scale for reduction is too long or too short for all
three temperatures, or if the simulations exhibit a
correct time scale for at least one of the temper-
atures, then the trend with temperature is wrong,
i.e. the reduction time does not decrease for each
higher temperature as found in the measurements.
We illustrate this in Fig. 3 for two cases where
at least partial agreement with experiment is ob-
I II
tained: When the CO adsorption energy is low-
ered by 0.2eV and the CO reaction barrier is left
unchanged, reasonable reduction time scales are
obtained for all three temperatures, but the order-
ing is wrong: At the intermediate temperature of C D
343Kreductionisslowerthanatthelowertemper-
III
ature of 303K. When instead the CO adsorption
A B
energy is lowered by 0.5eV and the CO oxidation
barrierissimultaneouslyincreasedby0.15eV,this
orderingiscorrect, butthetimescaleforoxidere-
ductionat 303Kis muchtoolong.
It is difficult to generally rule out that also vary-
ing the rate constants of all other elementary pro-
cesses would not coincidentally yield a parame-
Figure 4: Top view of the supercell model em-
ter set that reproduces the experimental reduction
ployed in the oxide reduction DFT calculations,
times. Nevertheless, the failure to obtain such a
spanning four √5-oxide unit cells in a (2 2) ar-
parameter set when modifying the two processes ×
rangement. Each intact √5-oxide unit cell con-
thatmostobviouslyrelatetothereductiontime,let
tains four O atoms, labeled from A to D, and four
us believe that a shortcoming of the employed 1p
Pd atoms, two of which (marked through hatch-
rate constants is unlikely the reason for the quali-
ing) are located in hollow sites of the underlying
tativediscrepancytothemeasurements. Wethere-
Pd(100) substrate. The arrows in the upper right
foretendtoconcludethatthereductionofthe√5-
threeunit-cellsindicatethedirectionsinwhichthe
oxidelayerdoesnothappenatintactoxidepatches
twoPdatomscanbeshiftedtogenerateaminimal
(for which the O coverage at the hollow sites is a
Pd(100) patch: This defines the three cases I (up-
usefulstabilityindicator).
per left unit-cell), II (upper right unit-cell) and III
(lowerrightunit-cell)referred to inthetext.
3.2 Atomistic pathway for the √5-
oxide reduction
In the context of oxide formation and reduction
efficient cross-reactions at the boundary between
oxide and metal domains have long been dis-
cussed.41 Fernandesetal. reportedlonginduction
times of theorder of minutes at all measured tem-
peratures.20 This renders a crucial role of cross-
reactions at extended surface imperfections like
steps or dislocations rather unlikely. Instead we
7
suspect that a slow initial reduction of ideal ox- does not constitute a pathway with at least a very
ide terraces locally generates minimal Pd(100) low activation barrier. This pathway centers on
patches that then enable an efficient continued re- the above mentioned realization that two of the
duction through cross-reactions. Admittedly, also four Pd atoms in the √5-oxide unit cell are al-
for this suggestion the observed induction time is ready located infourfold hollowsiteswithrespect
somewhat long. In order to scrutinize this picture to the underlying Pd(100) substrate. A direct way
with multi-lattice 1p-kMC simulations we there- to convert one entire √5 cell into a Pd(100)-type
fore establish an atomistic pathway from the in- patch would therefore be to simply shift the other
tact √5-oxide to reduced Pd(100) and focus on two Pd atoms from their close to bridge positions
the structural evolution of the surface oxide film to adjacent hollow sites. As illustrated in Fig. 4
when progressively removing O atoms. These there are three ways to realize this: Either both
studies are consistently performed with large su- Pd atoms move to hollow sites in the same direc-
percell models spanning four √5-oxide surface tion (cases I and II), or the two Pd atoms move
unit cells in a (2 2) arrangement as shown in to hollow sites in opposite directions (case III). If
×
Fig. 4. This model is large enough to study the we enforce such lateral shifts on the Pd atoms of
effects of O removal on one √5 cell that is still one unit cell for the intact surface oxide, they re-
surrounded by intact √5-oxide units in every di- lax back to theiroriginal positionsupon geometry
rection. For these studies, an important structural optimization. The same holds, if this is done with
aspectofthecommensurate√5-oxide/Pd(100)in- one O vacancy in the √5-oxide unit cell, or when
terface is that in every √5-oxide unit cell two of movingonlyoneofthetwoPd atoms.
the four Pd atoms in the oxide layer are located Incontrast,metastablestructuresresultwhenthe
in fourfold hollow sites of the underlying Pd(100) samemovementsare appliedinthepresenceofan
substrate, with the other two being rather close to Odivacancy. UnderreactionconditionssuchanO
bridge sites, cf. Fig. 4. After complete reduction, divacancy could arise from the random reduction
the Pd atoms of the surface oxide will form do- of neighboring O atoms in the oxide but possibly
mains of a new Pd(100) layer,21,42 in which they also due to a consequential reaction step next to
are also located in the fourfold hollow sites. This a metal to surface oxide boundary. Following a
means that during the local oxide decomposition systematic development from the fully intact sur-
two out of four Pd atoms in theoxide layer do not face oxide similar to a cluster expansion divacan-
necessarily have to significantly change their lat- cies are an obviousnext candidate motifafter sin-
eral position. gle vacancies. Specifically this is when removing
Inthestoichiometric√5-oxideterminationthere thetwo upper O atoms, labeled A and B in Fig. 4,
arefourOatomsper√5unitcell. Twoarelocated that are directly coordinated to one of the moving
above the Pd atoms of the oxide layer (occupying Pd atoms. For the three cases defined in Fig. 4
the hollow sites described above) and two below, we calculate the relative energies of the resulting
as shown in Fig. 4. In agreement to previous DFT metastable structures compared to the original di-
studies performed in smaller supercells,9 we find vacancy structure with the Pd atoms in their regu-
no significant structural changes upon removal of larpositions. Theyare 0.40eV(I), 0.25eV(II)
− −
any single of these four O atoms in one √5 unit and+0.17eV(III).CasesIandIIleadthereforeto
cell of our model. In particular, none of the oxide more stable intermediate structures. In particular
Pdatomschangetheirlateralregistry. Thesameis forthemoststablecaseIwefurthermorefindonly
observed, when removing pairs of O atoms in all anegligiblysmallactivationbarrierbelow0.1eV.
possible combinations. Apparently neither single This suggests the following initial steps in the
O vacancies, nor O divacancies lead to an unacti- oxide reduction pathway: Upon local formation
vateddestabilizationofthe√5-oxidestructure. of an O divacancy as shown in Fig. 5a, the two
In this situation, we focus on a straightforward bridge-site Pd atoms of the corresponding √5-
way to generate a minimal Pd(100) patch within oxide cell shift laterally and essentially unacti-
the surface oxide layer. We explore if this (to- vated to yield the intermediate structure shown in
gether with an increasing number of O vacancies) Fig. 5b. This metastable structure is more stable
8
(a) (b) (c)
Figure5: Topviewofintermediatestructuresalongthesuggestedoxidereductionpathway. (a)Divacancy
created by removaloftwoneighboringupperO atomsin one√5-oxideunit-cell(labeled A andB inFig.
4). (b) Intermediate structure formed from (a) through an essentially unactivated shift of the two bridge-
sitePd atomsas in case I ofFig. 4. Thisstructure is by 0.4eV morestablethan structure(a). (c) Pd(100)
patchformedfrom(b)aftertheactivateddiffusionofthesub-surfaceOlabeledDinFig. 4tothefourfold
on-surfacesiteinthecenterofthethusformed Pd(100)patch (seetext).
than the divacancy by 0.4eV. It already features a that to the formation of extended Pd(100) islands
minimalPd(100)patch with fourPd atoms in hol- as seen inexperiment.15–17,44
low sites, but stillcontains thetwo O atoms of the
√5-oxide cell that were originally below the Pd
3.3 Elementary processes at the
layer. One of these two, labeled C in Fig. 4, auto-
Pd(100) patch under reduction
matically moves to a position above the Pd atoms
conditions
of the Pd(100) patch along with the lateral shift
of the bridge-site Pd atoms. The other O atom
D remains in a sub-surface positionas depicted in
Fig. 5b.
We calculate a barrier of 0.66eV for the diffu-
sionprocessthatletsthisOatompopuptotheon-
surface site E in the center of the Pd(100) patch,
cf. Fig. 5c. There the O atom is by 0.11eV more
stable than in its original sub-surface site. From
there and as further detailed below, the on-surface
O atom can be reacted off through Langmuir-
Hinshelwood-type CO oxidation. Alternatively, it
can diffuse away. Both cases leave a bare mini-
mal Pd(100) patch as the end product of the here
suggestedoxidereductionpathway. Continuedre-
duction of the oxide layer will then lead to an in-
creasing number of such Pd(100) patches. As the
Pddensityintheintactsurfaceoxideis20%lower
Figure6: TopviewofthePd(100)patchasformed
than in a Pd(100) layer, Pd vacancies will emerge
during the oxide reduction process. Shown are all
along with the formation of these patches. The
high-symmetrybindingsitesexploredtoassessthe
diffusion of such Pd vacancies will be very fast.
binding properties of the patch itself (sites A-E)
The calculated activation barrier of only 0.2eV
∼ and at its boundary (sites F-K). Pd atoms of the
is similar to the diffusion of Pd on Pd(100).43–47
formedpatch are darkened.
Quickly, this fast diffusion will lead to the coales-
cence of the individual Pd(100) patches and with
The Pd(100) patch is the central new feature
9
withintheobtainedoxidereductionpathway. Dur-
inginitialoxidereductionitmayemergeuponsuf-
ficientlocaloxygendepletionofthe√5-oxide. Its
existence may then enable new elementary pro-
cesses specific to either the patch itself or the
boundary between patch and surrounding oxide.
As the next step we therefore proceed to a sys-
tematic identification and description of corre-
sponding processes. As starting point for this we
first consider the binding at the different high-
symmetry sites illustrated in Fig. 6. This com-
Table 1: Calculated DFT binding energies for
prises sites on top of the patch and at its bound-
CO and O at high-symmetry sites on top of the
ary. Specifically, sites labeled A-D and site E cor-
Pd(100) patch and at its boundary. Shown are re-
respond to Pd(100)-type bridge and hollow sites
sultsfor the situationwith thesub-surface O atom
on the patch, respectively. Sites F-J are sites di-
still beneath the patch (labeled "w/ sub-surf O")
rectly at thepatch/oxideboundary, whereas siteK
and without the sub-surface O atom (labeled "w/o
corresponds to a √5-oxide bridge site in the im-
sub-surf O"). Sites A-K are defined in Fig. 6.
mediatevicinityof the patch. Table 1 summarizes
Fieldsmarkedwithaletterindicatethattheadsor-
thecomputedbindingenergiesatthesesitesforthe
bate moved to the respective site during geometry
two"oxidation"stagesofthepatchalongtheoxide
optimization. Fields marked " " indicatesites for
reduction pathway: With the sub-surface oxygen −
which no binding was obtained. Binding in sites
atom still beneath it, cf. Fig. 5b, and without it.
marked with an asterisk ended up in a threefold
Thelattersituationresultsasaconsequenceofthe
coordination after geometry optimization. All en-
activateddiffusionoftheOatomtotheon-surface
ergies arein eV.
hollowsiteofthepatchandsubsequentreactionor
diffusion, vide infra, and is the situation depicted w/sub-surfO w/o sub-surfO
inFig. 6. CO O CO O
With the exception of site B directly adjacent
A -1.72 E -1.85 E
to the sub-surface O atom, the effect of the latter
B -1.73 I
atom on the binding properties of the sites on top − −
C -1.40 D -1.62 -0.98
∗
of the patch is rather small. Quite similar bind-
D -2.06 -0.96 -2.06 -1.00
ing energies are obtained for these sites for the
E D -1.22 -1.90 -1.25
∗
two cases. Cum grano salis these binding ener-
F -1.49 -0.96 -1.72 -1.25
gies on the patch sites are also quite similar to
G -1.27 -0.40 -1.31 -0.47
those computed for the extended Pd(100) surface.
H -0.83 J -1.56 J
Roughly we obtain a preferred O binding at the
I B -0.96
hollow site E of about 1.25eV. This should be − −
J H -0.39 H -0.75
−
comparedto 1.25eVatthecorrespondingsiteon
K -1.03 -0.30 -1.10 -0.37
−
Pd(100). Inturn,thecalculatedpreferredCObind-
ingatthebridgesitesA-Dofabout 1.4-2.1eV
∼−
shouldbecomparedto 1.93eV atbridgesitesof
−
Pd(100). Without the presence of the sub-surface
O atom this also extends to the bridge sites F and
H at the interface between the patch and the √5-
oxide. Again the CO binding properties are very
similartoregularbridgesitesatextendedPd(100).
Furthermore considering the close geometric and
energeticvicinityofthesedifferent sites wethere-
forealsoexpect similarlylowdiffusionbarriers as
10