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Multi-Lattice Kinetic Monte Carlo Simulations fromFirst-Principles:

Reduction of the Pd(100) Surface Oxide by CO

Max J. Hoffmann,∗,† Matthias Scheffler,‡ and Karsten Reuter∗,†

Chair for Theoretical Chemistry and Catalysis Research Center, Technische UniversitätMünchen, Lichtenbergstr. 4, 85747 Garching (Germany), andFritz-Haber-Institut der

Max-Planck-Gesellschaft, Faradayweg 4-6, 14195 Berlin (Germany)

E-mail: max.hoffmann@ch.tum.de; karsten.reuter@ch.tum.de

Abstract

We present a multi-lattice kinetic Monte Carlo(kMC) approach that efficiently describes theatomistic dynamics of morphological transitionsbetween commensurate structures at crystal sur-faces. As an example we study the reduction ofa (

√5×

√5)R27◦ PdO(101) overlayer on Pd(100)

in a CO atmosphere. Extensive density-functionaltheory calculations are used to establish an atom-istic pathway for the oxide reduction process.First-principles multi-lattice kMC simulations onthe basis of this pathway fully reproduce the ex-perimental temperature dependence of the reduc-tion rate [Fernandeset al., Surf. Sci. 2014, 621,31-39] and highlight the crucial role of elementaryprocesses special to the boundary between oxideand metal domains.

1 Introduction

In recent years first-principles (1p) kinetic MonteCarlo (kMC) simulations have established a newstandard for the microkinetic modeling of sur-face chemical processes and heterogeneous catal-

∗To whom correspondence should be addressed†Chair for Theoretical Chemistry and Catalysis Research

Center, Technische Universität München, Lichtenbergstr.4,85747 Garching (Germany)

‡Fritz-Haber-Institut der Max-Planck-Gesellschaft, Fara-dayweg 4-6, 14195 Berlin (Germany)

ysis.1–6 On the one hand, this approach employsmaterial-specific rate constants for the elemen-tary processes, presently typically computed bydensity-functional theory (DFT) and transition-state theory (TST). On the other hand, and incontrast to still prevalent mean-field rate equationbased microkinetic models, the 1p-kMC approachexplicitly accounts for spatial heterogeneities, cor-relations, and fluctuations of the atomic structure.The downside of the approach is the computationalcost of the underlying DFT-TST calculations. Inpractice, 1p-kMC simulations are therefore hith-erto performed on lattice models. This exploits thetranslational symmetry of the crystalline lattice todramatically reduce the required number of differ-ent 1p rate constants.7,8 For simple reaction net-works like the CO oxidation reaction at low-indexsingle-crystal model catalyst surfaces, this num-ber of 1p rate constants can be as low as 10-20,comprising adsorption, desorption, diffusion andreaction steps at and between the different latticesites.5,9,10

By construction, the conventional lattice 1p-kMC approach cannot directly be applied to (sur-face) morphological rearrangements,i.e. any typeof phase transition that includes changes in theconsidered lattice site arrangement. Notwithstand-ing, for the (late) transition-metal catalysts typi-cally employed in oxidation catalysis, a possibleformation of (surface) oxides has been discussed.Possibly, especially the continuous formation and

1

reduction of such oxidic films could be a major ac-tuator for the observed catalytic activity.11–19 Asa first step to make such systems and phenomenaaccessible to 1p-kMC we here describe a multi-lattice 1p-kMC approach, which is applicable tomorphological transitions between commensuratecrystalline lattices. The simple concept is that wework on a super-lattice that contains both latticessimultaneously. In a spatial region describing onestable phase, only the sites of the correspondinglattice are "enabled". The actual morphologicaltransition is then described through the elementaryprocesses of its atomistic pathway, which "dis-able" sites of one lattice and "enable" sites of theother lattice.

We illustrate this multi-lattice 1p-kMC idea bymodeling the surface oxide reduction at Pd(100).Recent experimental work20 observed significantchanges in the rate of oxide reduction in the tem-perature range from 300-400 K, when exposing aninitially prepared(

√5×

√5)R27◦ PdO(101) sur-

face oxide film (henceforth coined√

5-oxide forbrevity)21,22 to a 5× 10−11bar CO atmosphere.Analysis of the data using fitted mean-field kineticmodels suggested that the reduction is controlledby boundary processes between surface oxide andmetal domains.20 In the present paper, we use ex-tensive DFT calculations to establish an atomisticpathway for the oxide reduction process. Basedon this pathway, our multi-lattice 1p-kMC simu-lations perfectly reproduce the observed trends inthe reduction rates, and show that the critical stepsin the reduction of the surface oxide correspond in-deed to cross-reactions between the metal domainsand the surface oxide.

2 Theory

2.1 Kinetic Monte Carlo simulationsfor heterogeneous catalysis

We focus on thermally driven surface chemical re-actions that involve a site-specific (covalent-type)binding of the reaction intermediates. Such reac-tions generally follow a so-calledrare-eventtimeevolution. That is, on time scales that can be simu-lated byab initio molecular dynamics all reactionintermediates only vibrate around the lattice sites

to which they are bound. Only rarely, i.e. aftervery many such vibrations, an elementary processchanges this population at the lattice sites, wherethe duration of this process itself is very short.A diffusion process brings a reaction intermediateto another site, adsorption and desorption fill andempty sites at the surface, surface reactions con-vert reaction intermediates into another etc. Dur-ing the long time intervals between such individ-ual elementary processes the reaction intermedi-ates equilibrate fully and thereby are assumed toforget through which elementary process they ac-tually reached their current site or state.

Viewing the entire population at all sites as onepossible configuration, individual events in formof elementary processes thus advance the system’sstate from one configuration to another. In eachconfiguration reaction intermediates are assumedto have forgotten their past. In this Markov ap-proximation events will occur uncorrelated fromprevious ones and the time evolution of the systemis described by a Markovian master equation

ρ̇u(t) = ∑v

wuvρv(t)−wvuρu(t) , (1)

whereρu(t) is the probability for the system to bein configurationu at timet, andwvu is the transi-tion rate (in units of time−1) at which configura-tion u changes to configurationv. For heteroge-neous catalysis, solving this equation is in prac-tice not feasible by any direct approach.7,8 ThekMC approach addresses this problem by gener-ating configuration-to-configuration trajectories insuch a way that an average over an ensemble ofsuch trajectories yields the correct probability den-sity ρu(t) of eq. 1.7,8 Instead of evaluating andstoring the entire transition matrixw, a kMC codethus only focuses on-the-fly on those transitionmatrix elementswvu that are actually required topropagate the trajectory.

2.2 Efficient 1p-kMC on one or morelattices

Even with this focus on the requiredwvu, a kMCsimulation can still be an extremely demandingtask, if the rate constants determining thewvu areto be provided through 1p-calculations. Emerg-

2

ing so-called adaptive or self-learning kMC ap-proaches23–26 address this problem by generat-ing look-up tables of already computedwvu inthe course of the simulation. However, an ordersof magnitude higher efficiency is needed to makecomprehensive 1p-kMC simulations tractable forsystems as complex as the present one. This effi-ciency is achieved when the sites involved in thesurface catalysis can be mapped onto a static lat-tice. Due to the translational symmetry of the lat-tice, each equivalent site type then features thesame group of in principle possible elementaryprocesses, and these elementary processes typi-cally depend only on the occupation of nearbysites. While this does not reduce the number ofwvu required during a 1p-kMC trajectory, it dra-matically reduces the total number ofinequivalentwvu and therewith 1p rate constants that need tobe computed with DFT-TST. In lattice 1p-kMCthese 1p rate constants are then in practice precom-puted and stored, to be looked up on demand in theevolving kMC simulation.

Assuming a static arrangement of sites, lattice1p-kMC can not directly be applied to systems un-dergoing a morphological transition. In the presentcontext, this would be the reduction of the initiallyoxidized surface to a metallic state, where the ox-ide overlayer and metal substrate exhibit differentcrystal lattices. With our suggested generaliza-tion to multi-lattice 1p-kMC transitions betweencommensurable lattices become accessible. Theessence of the approach is hereby to choose as ba-sic unit cell of the lattice employed in the kMCsimulations a suitable, large enough commensu-rate cell that embraces all primitive unit cells of thedifferent lattices to be treated. This commensuratecell (and the lattice built up from it) then containsas sites simultaneously all sites of all lattices.

In order to efficiently distinguish (during a sim-ulation) in which lattice state a given local regionis currently in, we introduce an additional artifi-cial species (canonically namednull) to repre-sent "disabled" sites. If say, a certain region iscurrently in one lattice structure, then thenullspecies are placed on all sites corresponding tothe other lattices in this region. A site "occupied"with anull species is hereby to be distinguishedfrom an empty site. No elementary processes areavailable at sites occupied by anull species, i.e.

elementary processes that require an empty siteexplicitly look for the sites to be empty and not"occupied" bynull. In a corresponding regionwhere all sites belonging to the other lattices aredisabled throughnull species, multi-lattice 1p-kMC thus reduces to a regular lattice 1p-kMC sim-ulation and only the elementary processes corre-sponding to the 1p-kMC model of this lattice canpossibly occur.

In this setup, local transitions between the differ-ent lattices are finally enabled by introducing newelementary processes which involve the removalor placement of thenull species at sites belong-ing to the lattices involved. Trivially, for the ox-ide reduction example this could be as simple asan elementary process placing thenull specieson one or more sites of the oxide lattice and re-moving thenull species from nearby sites of themetal lattice. As shown below for the Pd oxide re-duction, local lattice transitions are unlikely thatsimple, but follow complex, multi-stepped reac-tion paths. The additional challenge of setting upand performing a multi-lattice 1p-kMC simulationas compared to traditional lattice 1p-kMC is there-fore to establish such atomistic pathways for thelattice transitions and implement them in form ofcorresponding elementary processes.

From a purely algorithmic point of view asimplemented in the kMC modeling frameworkkmos multi-lattice kMC is identical to single-lattice kMC which underlines that multi-latticekMC is highly efficient. The only difference is thatthose elementary steps accounting for morpholog-ical changes typically involve significantly moresites (10-20 sites) than typical ordinary surface re-action steps (1-8 sites). The scaling with the num-ber of conditions (i.e. here sites) has been studiedin a previous paper.8 This shows that the computa-tional scaling with the number of conditions is sig-nificant, (O(nlog(n) to O(n2)). However in termsof overhead there is no fundamental difference be-tween single-lattice kMC and multi-lattice kMC.

3

2.3 Literature 1p-kMC models of COoxidation at the

√5-surface oxide

and at Pd(100)

Our multi-lattice 1p-kMC simulations describingthe reduction of the Pd(100) surface initially cov-ered with a

√5-surface oxide film build on existing

1p-kMC models for CO oxidation at the√

5-oxideand for CO oxidation at Pd(100). These single-lattice models and the elementary processes con-sidered in them have been established by extensiveDFT calculations and have been described in de-tail before.27,28 Here, we only briefly recapitulatetheir essentials for completeness and as a means tointroduce the two lattice types.

Figure 1: Illustration of the lattice employed inthe 1p-kMC model of CO oxidation at Pd(100).Shown is a top view of the Pd(100) surface witha primitive unit cell and its hollow (yellow circle)and bridge (green rectangle) sites. CO moleculesadsorb at bridge sites and oxygen molecules ad-sorb (dissociatively) at hollow sites. Here andhenceforth Pd atoms in fcc(100) positions are de-picted as large blue spheres, O atoms as small redspheres, and C as small grey spheres.

Systematic DFT calculations identified the hol-low and bridge sites offered by the Pd(100) sur-face, cf. Fig. 1, as stable high-symmetry adsorp-tion sites for O and CO, respectively.28 The 1p-kMC CO oxidation model on Pd(100) correspond-ingly considers all non-concerted adsorption, des-orption, diffusion, and Langmuir-Hinshelwood re-action processes involving these sites.28 Oxygenmolecules adsorb dissociatively on two emptynext-nearest neighbor hollow sites,29–32 CO ad-sorbs on an empty bridge site. Desorption pro-

cesses are time-reversals of these non-activatedadsorption processes, with rate constants ful-filling detailed balance. Oxygen diffusion oc-curs between nearest-neighbor hollow sites, COdiffusion between nearest-neighbor bridge sites.Strong short-range repulsive interactions betweenadsorbed reaction intermediates as calculated byDFT33,34 are accounted for through site-blockingrules that prevent processes leading to O-O pairsat nearest-neighbor hollow-hollow distances, toCO-CO pairs closer or at next-nearest-neighborbridge-bridge distance, and O-CO pairs at nearest-neighbor hollow-bridge distance.28 CO oxidationproceeds via a Langmuir-Hinshelwood mecha-nism and at the temperatures of interest leads to aninstantaneously desorbing CO2 molecule. The rateconstants for all these elementary processes havebeen computed with DFT-TST, specifically em-ploying the PBE exchange-correlation (xc) func-tional.35 Typical for CO oxidation at transitionmetal surfaces, O and CO diffusion barriers aresignificantly lower than the barriers of all other el-ementary processes involved. In the 1p-kMC sim-ulations this leads to frequent executions of diffu-sion events at minute time increments. To increasethe numerical efficiency and be able to simulatethe extended time scales necessary to follow oxidereduction we artificially increased diffusion barri-ers for CO of 0.14 eV and for O of 0.28 eV28 by0.5 eV. This is permissible, if diffusion is then stillfast enough to achieve an equilibration of the ad-layer ordering in between the other (rare) elemen-tary processes.7 We validated that this is indeedthe case, by performing the 1p-kMC simulationswith diffusion barriers increased by 0.6 eV and0.7 eV without obtaining any significant changesin the oxide reduction rates reported below.

As established by detailed first-principles statis-tical mechanics simulations by Rogalet al.9 onlytwo of the high-symmetry adsorption sites offeredby the intact

√5-oxide are relevant for the re-

ducing environments considered here: a bridgeand a hollow site as illustrated in Fig. 2. Equiv-alent to the Pd(100) case, the 1p-kMC CO ox-idation model at the

√5-oxide correspondingly

considers all non-concerted adsorption, desorp-tion, diffusion, and Langmuir-Hinshelwood re-action processes involving these sites.27,28 Eley-Rideal reaction processes as recently suggested by

4

Figure 2: Illustration of the lattice employedin the 1p-kMC model of CO oxidation at the√

5-oxide. Shown is a top view of the(√

5×√5)R27◦ PdO(101) surface oxide reconstruction

with a primitive unit cell of the oxide layer andits hollow (yellow circle) and bridge (green rect-angle) sites. O and CO adsorb at both site types.In the stoichiometric termination shown, O atomsoccupy all hollow sites. Here and henceforth Pdatoms in surface oxide positions are depicted aslarge green spheres.

Hirvi et al.36 are in principle also considered, butdo not play a role at the low CO pressures ad-dressed here. Adsorption is non-activated, apartfrom dissociative adsorption of O2 into neighbor-ing bridge sites, which is hindered by a sizable ad-sorption barrier of 1.9 eV. As for the Pd(100) 1p-kMC model, all 1p rate constants of this

√5-oxide

model have been computed with DFT-TST, em-ploying the PBE xc functional.35 DFT-computednearest-neighbor lateral interactions are taken intoaccount in these rate constants as detailed by Ro-galet al.27

2.4 Computational DFT and kMCsettings

The multi-lattice 1p-kMC simulations of the ox-ide reduction process consider additional ele-mentary processes to model the atomistic path-way from oxide to metal lattice. This pathwayand the involved elementary processes are de-scribed in Sections 3.2-3.4 below. Their 1p rateconstants have been calculated with DFT em-ploying the same TST-based expressions37 and

the same PBE xc functional35 as used in thePd(100) and

√5-oxide 1p-kMC models. Employ-

ing the same computational setup as detailed inref. 28, the DFT calculations have been performedwith the CASTEP package38 via the Atom-

ic Simulation Environment.39 Previouswork28 established that the employed standard li-brary ultrasoft pseudopotentials accurately repro-duce the full-potential

√5-oxide adsorption ener-

getics of Rogalet al.27 Geometry optimizationsand transition-state searches were done with super-cell geometries containing asymmetric slabs withone (frozen) layer of Pd(100) and one layer ofPdO(101), separated by at least 10 Å vacuum. Ge-ometry optimizations were performed using theBFGS method with a force threshold of 0.05 eV/Å.The energetics of the thus obtained intermediategeometries were refined in single-point calcula-tions with further Pd(100) layers added to theslab. Transition state searches have been per-formed with the climbing-image nudged elasticband method40 or simple drag procedures with thenature of the transition state confirmed throughfrequency calculations. From test calculationswith additional Pd(100) layers added we estimatethe uncertainty in the thus determined barrier val-ues as 0.1 eV. The gas-phase calculations for O2

and CO were performed in a cubic supercell of15 Å box length andΓ-point sampling. At a plane-wave cutoff of 400 eV and a [4× 4× 1] k-pointgrid for the commensurate surface oxide unit celland a [2×2×1] k-point grid for the (2× 2) sur-face oxide unit cell in the slab calculations conver-gence tests demonstrate a numerical convergenceof the obtained DFT barriers and binding energiesto within 0.1 eV.

All 1p-kMC simulations have been performedusing thekmos framework.8 The periodic bound-ary simulation cell contains(40× 20)

√5-unit

cells and thus 1600 sites in case of the single-lattice 1p-kMC simulations on the surface oxide.Systematic tests with varying simulation cell sizesshowed the obtained oxide reduction rates to befully converged at this setting. In the multi-latticecase one commensurate unit-cell contains alreadya total of 19 sites from both the metal and theoxide lattice. We employed periodic boundarysimulation cells comprising(10× 20), (20× 20)and (40× 20) such commensurate unit-cells to

5

specifically assess the role of elementary processesacross oxide and metal domains (see below). In allcases, averages over 10 kMC trajectories startingwith different random number seeds were taken toobtain the correct transient quantities.

3 Results

3.1 Single-lattice 1p-kMC simulationsof oxide reduction

As mentioned initially the central objective ofour simulations is to analyze the oxide reductionrates obtained in recent high-resolution X-ray pho-toelectron spectroscopy experiments by Fernan-deset al.20 Within a small range of temperatures,they reported large variations for the total time re-quired to fully reduce an initially prepared

√5-

oxide layer by exposure to a pure CO atmosphereof 5× 10−11bar. Specifically, at 303 K the ox-ide was reduced after approximately 90 minutes,while the same process took only approximately12 min at 343 K and less than 4 min at 393 K. Pre-vious theoretical work addressing the surface ox-ide stability employed the 1p-kMC approach witha single lattice, namely the

√5-oxide 1p-kMC

model. They monitored the coverage of O in thehollow sites as an indicator for the oxide stabil-ity.27 Using this criterion 1p-kMC simulations failqualitatively to reproduce the experimental find-ings of Fernandeset al.. Even at the highest tem-perature of 393 K no reduction of the oxide is ob-served at all after 120 mins, i.e. the oxygen cover-age remains essentially intact over the entire time.This can be explained by the lack of CO on thesurface, which implies that an efficient removal ofoxygen via CO oxidation is not possible.

Since an error in the reported experimental con-ditions large enough to explain this discrepancyseems unlikely we focus on the uncertainty in theDFT parameters deployed in the model. A pos-sible reason for this discrepancy could be thatthe relevant CO adsorption energy of−0.92 eVas calculated by DFT-PBE is too small, and/orthe CO reaction barrier towards CO2 formation of0.9 eV27 is too high. We explore these possibilitiesby running the 1p-kMC simulations using modi-fied rate constants. Specifically, we vary the CO

(a)

0 20 40 60 80 100 120

t [min]

0

20

40

60

80

100

θO

h[%

] 303 K

343 K

393 K

(b)

0 20 40 60 80 100 120

t [min]

0

20

40

60

80

100

θO

h[%

] 303 K

343 K

393 K

Figure 3: Single-lattice kMC simulations for√5-oxide reduction at the three temperatures em-

ployed in the experiments and using the O cov-erage at the hollow sites (θOh) as indicator forthe progressing reduction of the surface oxide (seetext). The 1p rate constants are modified to achieveat least some agreement with the experimentalfindings: (a) CO adsorption energy lowered by0.2 eV. The reduction times for all three tempera-tures are in the right order of magnitude, but the or-dering with temperature is wrong. (b) CO adsorp-tion energy lowered by 0.5 eV; CO oxidation bar-rier increased by 0.15 eV. The oxide reduction timecorrectly decreases with temperature, but the re-duction time at 303 K disagrees qualitatively withexperiment.

6

oxidation barrier and the CO adsorption energy onthe bridge and hollow sites within±1 eV. How-ever, no such kMC simulation reproduces the ex-perimentally observed behavior: Either the timescale for reduction is too long or too short for allthree temperatures, or if the simulations exhibit acorrect 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 eachhigher temperature as found in the measurements.We illustrate this in Fig. 3 for two cases whereat least partial agreement with experiment is ob-tained: When the CO adsorption energy is low-ered by 0.2 eV and the CO reaction barrier is leftunchanged, reasonable reduction time scales areobtained for all three temperatures, but the order-ing is wrong: At the intermediate temperature of343 K reduction is slower than at the lower temper-ature of 303 K. When instead the CO adsorptionenergy is lowered by 0.5 eV and the CO oxidationbarrier is simultaneously increased by 0.15 eV, thisordering is correct, but the time scale for oxide re-duction at 303 K is much too long.

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-ter set that reproduces the experimental reductiontimes. Nevertheless, the failure to obtain such aparameter set when modifying the two processesthat most obviously relate to the reduction time, letus believe that a shortcoming of the employed 1prate constants is unlikely the reason for the quali-tative discrepancy to the measurements. We there-fore tend to conclude that the reduction of the

√5-

oxide layer does not happen at intact oxide patches(for which the O coverage at the hollow sites is auseful stability indicator).

3.2 Atomistic pathway for the√

5-oxide reduction

In the context of oxide formation and reductionefficient cross-reactions at the boundary betweenoxide and metal domains have long been dis-cussed.41 Fernandeset al. reported long inductiontimes of the order of minutes at all measured tem-peratures.20 This renders a crucial role of cross-reactions at extended surface imperfections likesteps or dislocations rather unlikely. Instead we

A B

C D

I II

III

Figure 4: Top view of the supercell model em-ployed in the oxide reduction DFT calculations,spanning four

√5-oxide unit cells in a(2×2) ar-

rangement. Each intact√

5-oxide unit cell con-tains four O atoms, labeled from A to D, and fourPd atoms, two of which (marked through hatch-ing) are located in hollow sites of the underlyingPd(100) substrate. The arrows in the upper rightthree unit-cells indicate the directions in which thetwo Pd atoms can be shifted to generate a minimalPd(100) patch: This defines the three cases I (up-per left unit-cell), II (upper right unit-cell) and III(lower right unit-cell) referred to in the text.

7

suspect that a slow initial reduction of ideal ox-ide terraces locally generates minimal Pd(100)patches that then enable an efficient continued re-duction through cross-reactions. Admittedly, alsofor this suggestion the observed induction time issomewhat long. In order to scrutinize this picturewith multi-lattice 1p-kMC simulations we there-fore establish an atomistic pathway from the in-tact

√5-oxide to reduced Pd(100) and focus on

the structural evolution of the surface oxide filmwhen progressively removing O atoms. Thesestudies are consistently performed with large su-percell models spanning four

√5-oxide surface

unit cells in a(2× 2) arrangement as shown inFig. 4. This model is large enough to study theeffects of O removal on one

√5 cell that is still

surrounded by intact√

5-oxide units in every di-rection. For these studies, an important structuralaspect of the commensurate

√5-oxide/Pd(100) in-

terface is that in every√

5-oxide unit cell two ofthe four Pd atoms in the oxide layer are locatedin fourfold hollow sites of the underlying Pd(100)substrate, with the other two being rather close tobridge sites, cf. Fig. 4. After complete reduction,the Pd atoms of the surface oxide will form do-mains of a new Pd(100) layer,21,42 in which theyare also located in the fourfold hollow sites. Thismeans that during the local oxide decompositiontwo out of four Pd atoms in the oxide layer do notnecessarily have to significantly change their lat-eral position.

In the stoichiometric√

5-oxide termination thereare four O atoms per

√5 unit cell. Two are located

above the Pd atoms of the oxide layer (occupyingthe hollow sites described above) and two below,as shown in Fig. 4. In agreement to previous DFTstudies performed in smaller supercells,9 we findno significant structural changes upon removal ofany single of these four O atoms in one

√5 unit

cell of our model. In particular, none of the oxidePd atoms change their lateral registry. The same isobserved, when removing pairs of O atoms in allpossible combinations. Apparently neither singleO vacancies, nor O divacancies lead to an unacti-vated destabilization of the

√5-oxide structure.

In this situation, we focus on a straightforwardway to generate a minimal Pd(100) patch withinthe surface oxide layer. We explore if this (to-gether with an increasing number of O vacancies)

does not constitute a pathway with at least a verylow activation barrier. This pathway centers onthe above mentioned realization that two of thefour Pd atoms in the

√5-oxide unit cell are al-

ready located in fourfold hollow sites with respectto the underlying Pd(100) substrate. A direct wayto convert one entire

√5 cell into a Pd(100)-type

patch would therefore be to simply shift the othertwo Pd atoms from their close to bridge positionsto adjacent hollow sites. As illustrated in Fig. 4there are three ways to realize this: Either bothPd atoms move to hollow sites in the same direc-tion (cases I and II), or the two Pd atoms moveto hollow sites in opposite directions (case III). Ifwe enforce such lateral shifts on the Pd atoms ofone unit cell for the intact surface oxide, they re-lax back to their original positions upon geometryoptimization. The same holds, if this is done withone O vacancy in the

√5-oxide unit cell, or when

moving only one of the two Pd atoms.In contrast, metastable structures result when the

same movements are applied in the presence of anO divacancy. Under reaction conditions such an Odivacancy could arise from the random reductionof neighboring O atoms in the oxide but possiblyalso due to a consequential reaction step next toa metal to surface oxide boundary. Following asystematic development from the fully intact sur-face oxide similar to a cluster expansion divacan-cies are an obvious next candidate motif after sin-gle vacancies. Specifically this is when removingthe two upper O atoms, labeled A and B in Fig. 4,that are directly coordinated to one of the movingPd atoms. For the three cases defined in Fig. 4we calculate the relative energies of the resultingmetastable structures compared to the original di-vacancy structure with the Pd atoms in their regu-lar positions. They are−0.40 eV (I),−0.25 eV (II)and+0.17 eV (III). Cases I and II lead therefore tomore stable intermediate structures. In particularfor the most stable case I we furthermore find onlya negligibly small activation barrier below 0.1 eV.

This suggests the following initial steps in theoxide reduction pathway: Upon local formationof an O divacancy as shown in Fig. 5a, the twobridge-site Pd atoms of the corresponding

√5-

oxide cell shift laterally and essentially unacti-vated to yield the intermediate structure shown inFig. 5b. This metastable structure is more stable

8

(a) (b) (c)

Figure 5: Top view of intermediate structures along the suggested oxide reduction pathway. (a) Divacancycreated by removal of two neighboring upper O atoms in one

√5-oxide unit-cell (labeled A and B in Fig.

4). (b) Intermediate structure formed from (a) through an essentially unactivated shift of the two bridge-site Pd atoms as in case I of Fig. 4. This structure is by 0.4 eV more stable than structure (a). (c) Pd(100)patch formed from (b) after the activated diffusion of the sub-surface O labeled D in Fig. 4 to the fourfoldon-surface site in the center of the thus formed Pd(100) patch (see text).

than the divacancy by 0.4 eV. It already features aminimal Pd(100) patch with four Pd atoms in hol-low sites, but still contains the two O atoms of the√

5-oxide cell that were originally below the Pdlayer. One of these two, labeled C in Fig. 4, auto-matically moves to a position above the Pd atomsof the Pd(100) patch along with the lateral shiftof the bridge-site Pd atoms. The other O atomD remains in a sub-surface position as depicted inFig. 5b.

We calculate a barrier of 0.66 eV for the diffu-sion process that lets this O atom pop up to the on-surface site E in the center of the Pd(100) patch,cf. Fig. 5c. There the O atom is by 0.11 eV morestable than in its original sub-surface site. Fromthere and as further detailed below, the on-surfaceO atom can be reacted off through Langmuir-Hinshelwood-type CO oxidation. Alternatively, itcan diffuse away. Both cases leave a bare mini-mal Pd(100) patch as the end product of the heresuggested oxide reduction pathway. Continued re-duction of the oxide layer will then lead to an in-creasing number of such Pd(100) patches. As thePd density in the intact surface oxide is 20 % lowerthan in a Pd(100) layer, Pd vacancies will emergealong with the formation of these patches. Thediffusion of such Pd vacancies will be very fast.The calculated activation barrier of only∼ 0.2 eVis similar to the diffusion of Pd on Pd(100).43–47

Quickly, this fast diffusion will lead to the coales-cence of the individual Pd(100) patches and with

that to the formation of extended Pd(100) islandsas seen in experiment.15–17,44

3.3 Elementary processes at thePd(100) patch under reductionconditions

Figure 6: Top view of the Pd(100) patch as formedduring the oxide reduction process. Shown are allhigh-symmetry binding sites explored to assess thebinding properties of the patch itself (sites A-E)and at its boundary (sites F-K). Pd atoms of theformed patch are darkened.

The Pd(100) patch is the central new feature

9

within the obtained oxide reduction pathway. Dur-ing initial oxide reduction it may emerge upon suf-ficient local oxygen depletion of the

√5-oxide. Its

existence may then enable new elementary pro-cesses specific to either the patch itself or theboundary 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 wefirst consider the binding at the different high-symmetry sites illustrated in Fig. 6. This com-prises sites on top of the patch and at its bound-ary. Specifically, sites labeled A-D and site E cor-respond to Pd(100)-type bridge and hollow siteson the patch, respectively. Sites F-J are sites di-rectly at the patch/oxide boundary, whereas site Kcorresponds to a

√5-oxide bridge site in the im-

mediate vicinity of the patch. Table 1 summarizesthe computed binding energies at these sites for thetwo "oxidation" stages of the patch along the oxidereduction pathway: With the sub-surface oxygenatom still beneath it, cf. Fig. 5b, and without it.The latter situation results as a consequence of theactivated diffusion of the O atom to the on-surfacehollow site of the patch and subsequent reaction ordiffusion, vide infra, and is the situation depictedin Fig. 6.

With the exception of site B directly adjacentto the sub-surface O atom, the effect of the latteratom on the binding properties of the sites on topof the patch is rather small. Quite similar bind-ing energies are obtained for these sites for thetwo cases.Cum grano salisthese binding ener-gies on the patch sites are also quite similar tothose computed for the extended Pd(100) surface.Roughly we obtain a preferred O binding at thehollow site E of about−1.25 eV. This should becompared to−1.25 eV at the corresponding site onPd(100). In turn, the calculated preferred CO bind-ing at the bridge sites A-D of about∼−1.4-2.1 eVshould be compared to−1.93 eV at bridge sites ofPd(100). Without the presence of the sub-surfaceO atom this also extends to the bridge sites F andH at the interface between the patch and the

√5-

oxide. Again the CO binding properties are verysimilar to regular bridge sites at extended Pd(100).Furthermore considering the close geometric andenergetic vicinity of these different sites we there-fore also expect similarly low diffusion barriers as

Table 1: Calculated DFT binding energies forCO and O at high-symmetry sites on top of thePd(100) patch and at its boundary. Shown are re-sults for the situation with the sub-surface O atomstill beneath the patch (labeled "w/ sub-surf O")and without the sub-surface O atom (labeled "w/osub-surf O"). Sites A-K are defined in Fig. 6.Fields marked with a letter indicate that the adsor-bate moved to the respective site during geometryoptimization. Fields marked "−" indicate sites forwhich no binding was obtained. Binding in sitesmarked with an asterisk ended up in a threefoldcoordination after geometry optimization. All en-ergies are in eV.

w/ sub-surf O w/o sub-surf OCO O CO O

A -1.72 E -1.85 EB − − -1.73 IC -1.40 D -1.62 -0.98∗

D -2.06 -0.96 -2.06 -1.00E D -1.22 -1.90∗ -1.25F -1.49 -0.96 -1.72 -1.25G -1.27 -0.40 -1.31 -0.47H -0.83 J -1.56 JI − − B -0.96J H -0.39 H -0.75K -1.03 -0.30 -1.10 -0.37

10

on Pd(100). Correspondingly, there will be a pre-dominant presence of the adsorbates in the mostfavorable sites, i.e. CO in the bridge site D and Oin the hollow site E at the temperatures employedin the oxide reduction experiments.

Multiple adsorption on one patch in form of COadsorption at several bridge sites, or O and COcoadsorption on hollow and bridge site, respec-tively, is not possible according to our DFT cal-culations. Also in this respect, adsorption at thePd(100) patch seems very similar to adsorptionat extended Pd(100). Likewise the disturbance ofthe

√5-oxide created by the Pd(100) patch seems

quite short-ranged. Already at the oxide bridgesite K directly adjacent to the patch, O and CObinding is essentially identical to the binding at thebridge site on the stoichiometric

√5 termination.

The CO binding is calculated as−1.03 eV and−1.10 eV at site K (with and without sub-surfaceO underneath the adjacent Pd(100) patch) and as−1.08 eV on the intact

√5-oxide. The O binding

energy is 0.30 eV,−0.37 eV and−0.19 eV for thethree cases, respectively. Finally, the binding at theinterfacial sites F, G, H and I in the presence of thesub-surface oxygen atom and at the interfacial siteH without the sub-surface O atom is intermediateto the one obtained on the patch and on the intact√

5-oxide.In light of these results, we can now systemat-

ically analyze the new elementary processes thatmay arise due to the patch under the reducing con-ditions of the experiment and assess their qualita-tive relevance for the oxide reduction process. COadsorption and desorption processes can take placeat the patch bridge sites, with a maximum cover-age of one CO molecule on a patch. This is re-gardless of whether the sub-surface O atom is stillpresent underneath the patch or not. CO diffusionon the patch itself will be fast, and will lead to apreferential population of bridge site D at the tem-peratures employed in the reduction experiments.After coalescence of nuclei to larger Pd(100) do-mains, equivalent processes (CO adsorption, des-orption, diffusion) will occur, with properties ason extended Pd(100). In principle, CO diffusioncould also occur from patch (or Pd(100) domain)to oxide or vice versa. An important point to real-ize here, however, is that CO binding at the patch(and at Pd(100)) is about 1 eV more stable than at

the hollow or bridge sites of the√

5-oxide. This al-ready imposes a quite large mere thermodynamicbarrier for CO diffusion onto the oxide. Simulta-neously CO diffusion processes from the oxide tothe patch will be rare, owing to the near zero COcoverage on the surface oxide under the conditionsof the reduction experiments, cf. Section 3.1.

If all sites A-E of the patch are unoccupied, thesub-surface O atom can pop up into the on-surfacefourfold hollow site E of the patch, with a cal-culated barrier of 0.66 eV. The reverse process ispossible with a corresponding barrier of 0.77 eV.From the patch site E the oxygen atom can dif-fuse to an adjacent vacant hollow site of the sur-rounding oxide, or vice versa. Since O binding isabout 0.4 eV more stable at the oxide hollow sites,this diffusion will preferentially take oxygen awayfrom the patch (or coalesced larger Pd(100) do-mains). For O diffusion between the oxide hollowsites directly adjacent to the patch (those above siteK in Fig. 6) we find a slightly lowered diffusionbarrier of 1.1 eV as compared to the 1.4 eV for thediffusion over the intact surface oxide. This lower-ing can be rationalized with the higher geometricflexibility of the underlying Pd atoms in the par-tially reduced surface oxide environment. Oxy-gen diffusion from site E to adjacent bridge sitesof the

√5-oxide face a similarly large thermody-

namic barrier as the CO diffusion processes due tothe much weaker O binding at these oxide sites.As these bridge sites are furthermore essentiallyall unoccupied under the conditions of the reduc-tion experiments, the reverse diffusion processesbringing O atoms from adjacent oxide bridge sitesto the patch will also occur at a negligibly lowrate. Associative oxygen desorption requires twonearby O atoms. It can thus only take place eitherafter coalescence of nuclei (which creates next-nerest neighbor Pd(100)-type hollow sites) or incase of an individual patch by involving one Oatom from the patch site E and one O atom fromnearest neighbor O hollow sites of the oxide. Dueto the similar binding energies of O on both metaland oxide, such processes are as rare as they werein the single-lattice 1p-kMC simulations focusingonly on the surface oxide. Correspondingly, suchprocesses are unlikely to have a relevant effect onthe reduction kinetics.

Finally, new CO oxidation reactions can be en-

11

Figure 7: Top view of the Pd(100) patch illus-trating possible CO oxidation reactions across thepatch/oxide boundary. The CO molecule is ad-sorbed at the most stable bridge site D of thePd(100)-patch. The calculated barriers for the fourreaction processes are: NW 1.63 eV, SW 1.46 eV,SE 1.54 eV, and E 0.95 eV.

abled at the patch or its boundary. One possibil-ity is a reaction of a CO molecule adsorbed onthe patch with the sub-surface O atom. For a COmolecule occupying the preferred bridge site D wecalculate a barrier of 1.27 eV for this process. Thisis rather high for this process to play a significantrole at the temperatures employed in the experi-ments. Alternatively, the CO molecule could reactwith O atoms of the surrounding

√5-oxide. Fo-

cusing on the preferred binding site D Fig. 7 illus-trates the four corresponding reactions to the clos-est such O atoms and compiles the calculated bar-riers for these processes. Only one of these pro-cesses exhibits a barrier below 1 eV and shouldtherewith exhibit a similar reactivity as the reac-tion processes occurring on either Pd(100) or onthe

√5-oxide. As last possibility, an O atom oc-

cupying the on-surface site E of the patch couldreact with a nearby adsorbed CO molecule. Dueto the near zero CO coverage on the oxide duringthe reduction experiments, such a process is un-likely to occur with a CO molecule adsorbed onthe

√5 though. At the same time, the strong re-

pulsive interactions prevent CO adsorption at thebridge sites A-D of the patch, if an O atom occu-

pies the hollow site E. This leaves as only possi-bility for such a cross-reaction, the reaction with aCO molecule adsorbed at the bridge site F, cf. Fig.6. In general, such a reaction process can not havea strong influence on the oxide reduction processthough. As O diffusion from the

√5-oxide onto

the patch is rare, this process will predominantlyoccur after the sub-surface O atom has popped upto the surface. The process then takes place onceper formed patch and is thereafter unlikely to re-occur.

Summarizing these insights, the qualitativelynew feature emerging from the presence of aformed Pd(100) patch during the oxide reductionprocess is the significantly enhanced stabilizationof CO at the patch as compared to the

√5-oxide.

Whereas the CO coverage on the latter is close tozero under the reducing conditions of the experi-ment, a much higher CO coverage can thus be ex-pected at formed patches. An oxidation reactionof such CO molecules across the patch/oxide in-terface with O atoms of the surface oxide then pro-vides a much more efficient means to deplete thesurface oxygen compared to the two mechanismspossible at the

√5-oxide alone. There the asso-

ciative O desorption is a rare process due to thestrong O binding energy on the oxide. Similarlythe CO oxidation is a rare process due to the lowCO coverage at the surface. In contrast, the newreduction process enabled at the oxide/patch inter-face only depends on the CO adsorption, whichis comparatively frequent in the reducing environ-ment of the experiment, and on the replenishmentof the created O vacancies at the oxide sites at theinterface. The latter occurs via O diffusion on thesurface oxide, which is not a very fast process. Yet,it is still faster than the oxide-only reaction mech-anism, considering in particular that the numberof formed Pd(100) patches will scale with the in-creasing number of concomitantly created O va-cancies in the oxide layer.

3.4 Multi-lattice 1p-kMC model

We now proceed by casting the established pic-ture of the reduction process via the formation ofPd(100) patches into an explicit multi-lattice 1p-kMC model. For regions of Pd(100) and intact√

5-oxide this multi-lattice 1p-kMC model will

12

employ the literature single-lattice 1p-kMC mod-els as before. The new elementary processes aris-ing in the context of the Pd(100) patches and theirDFT calculated barriers are listed as follows:

A local reduction begins whenever an oxygen di-vacancy involving two neighboring hollow sites onthe

√5-oxide, cf. Fig. 5, is formed during the

1p-kMC simulation. The patch formation is thenmodeled as a non-activated process, i.e. it auto-matically follows the formation of the divacancy.In terms of the multi-lattice representation thepatch formation corresponds to deactivating thetwo bridge and two hollow sites associated withthe corresponding

√5-oxide unit cell by changing

their occupation status tonull. In their place,Pd(100) lattice sites are activated. Specifically,this concerns Pd(100) bridge sites at sites labeledA, B, C, D, F, H in Fig. 6, the occupation of whichis changed fromnull to empty. Furthermore,a Pd(100) hollow site is createdempty at thesite labeled E in Fig. 6. The quenched-in oxygenatom is modeled to remain at its sub-surface

√5-

oxide site. However, now that the Pd(100) hollowsite labeled E in Fig. 6 is created, this sub-surfaceO atom can hop there with a barrier of 0.66 eV.However, this only, if the Pd(100) hollow siteand its four nearest-neighbor Pd(100) bridge sitesare empty in accordance with the site-blockingrules used in the Pd(100) single-lattice 1p-kMCmodel.28 From there, the oxygen atom can reversethe diffusion with a barrier of 0.77 eV. Alterna-tively, if there are already other immediately adja-cent Pd(100) patches, it can also regularly diffuseto corresponding nearest-neighbor Pd(100) hollowsites. O diffusion from the patch to surrounding√

5-oxide (and the reverse back-diffusion process)exhibits a barrier of 0.5 eV (0.9 eV). The hollow-hollow diffusion of oxygen on the

√5-oxide im-

mediately adjacent to a Pd(100)-patch has a bar-rier of 1.1 eV, and is therewith accelerated as com-pared to diffusion on the intact

√5 with its barrier

of 1.4 eV.The second oxygen atom that is originally in the

sub-surface√

5-oxide site and pops up to the sur-face during the formation of the Pd(100) patch, cf.Fig. 5b, has a binding energy of−1.42 eV, irre-spective of whether the other adjacent quenched-in sub-surface O atom is still present or not. Eventhough thus exhibiting a somewhat stronger bind-

ing by 0.17 eV, we still approximate this as a reg-ular O atom in a Pd(100) hollow site. In themulti-lattice scheme we correspondingly activateanother Pd(100) hollow lattice site at the locationthat is obtained by going from site E one latticeconstant to the left in Fig. 6 and directly occupyit with the popped-up O atom. Simultaneously,the sub-surface

√5-oxide site in which the oxygen

atom resided before the patch formation is deacti-vated by setting its occupation tonull.

If the new patch lies next to already existingpatches, CO diffusion from neighboring Pd(100)sites onto bridge sites of the new Pd(100) patchis possible, if the nearest-neighbor hollow as wellas all up to next-nearest-neighbor bridge sites areempty – again in accordance with the site-blockingrules for CO diffusion in the Pd(100) single-lattice1p-kMC model.28 If all Pd(100) patch bridge andhollow sites are empty, non-activated CO adsorp-tion is possible onto a bridge site. CO desorptionhas a desorption barrier of 1.93 eV and obeys de-tailed balance with the adsorption process as inthe Pd(100) single-lattice 1p-kMC model. As ad-ditional reaction processes we only consider themost likely process labeled E in Fig. 7 with a bar-rier of 0.95 eV, involving a CO molecule adsorbedat site D of the patch and an O atom adsorbed at adirectly adjacent upper hollow

√5-oxide site.

With these prescriptions and new processes themulti-lattice 1p-kMC simulation will allow for thegeneration of Pd(100) patches, which if generatednext to each other will increasingly lead to largerPd(100)-type domains in the course of a reduc-tion condition simulation. As a Pd(100) unit-cellof the commensurate

√5-oxide/Pd(100) interface

exhibits only 4/5 of the Pd atom density, thesepatches will not correspond to dense Pd(100) ter-races though. Instead, they will contain a regu-lar array of Pd vacancies. In reality, fast Pd self-diffusion will lead to the coalescence into closelypacked Pd(100) islands, and connected with it toan entire class of additional elementary processes.However, in the here proposed atomistic pathway,cf. Fig. 5, the Pd(100)-patch formation step shiftsthe two mobile Pd atoms in such a way that theemerging Pd(100) vacancy is located furthest fromthe relevant

√5-oxide/Pd(100) domain boundary,

where the cross-reaction E of Fig. 7 can take place.As such we anticipate that the coalescence of Pd

13

vacancies through Pd self-diffusion occurs pre-dominantly displaced from the reduction front andthen has no effect on the actual reduction kinetics.Within this view, we neglect Pd self-diffusion inthe multi-lattice 1p-kMC model, such that the endproduct of a complete reduction of the

√5-oxide

film corresponds to a Pd(100) surface with a regu-lar array of Pd vacancies.

Table 2: DFT parameters entering rate constantsof elementary processes near Pd(100)/PdO(

√5×√

5)R27◦ domain boundary. All energies are in eV.

process barrieroxide reconstruction 0.0O spillover 0.66O reverse spillover 0.77O hollow diffusion near nucleus 1.1cross-reaction (E) 0.95

3.5 Multi-lattice 1p-kMC simulationsof oxide reduction

Within the multi-lattice 1p-kMC model we nowaddress the oxide reduction experiments of Fer-nandeset al.. The qualitatively new feature in-troduced by the explicit account of reduced ox-ide patches in the multi-lattice simulations is thepossibility of reduction through cross-reactions at√

5-oxide/Pd(100) domain boundaries. Within thepicture of some initial slow reduction during thelong induction time seen in the experiments, weemploy kMC simulation cells, in which initiallyone row of

√5-oxide along the[010]-direction is

already removed, cf. Fig. 8. To assess the sensitiv-ity on this point, we conduct the multi-lattice 1p-kMC simulations using(10×20), (20× 20) and(40×20) cells, thereby systematically varying thewidth of the initially intact

√5-oxide domain. As

demonstrated in Fig. 9 we obtain only small vari-ations in the oxide reduction times. These do notaffect at all the conclusions put forward below andconfirm the understanding that the oxide reductionrates seen in experiment are governed by a fast re-duction following some slow activation during theinduction period.

Figure 9 shows the surface oxide coverage asa function of time using the experimental con-

Figure 8: Illustration of the initial configurationused in the multi-lattice 1p-kMC simulations. Forclarity, only a small(4× 8) commensurate

√5-

oxide cell area of the larger simulation cell isshown. One row of

√5-oxide cells has been re-

duced to Pd(100) nuclei along the (100) directionof the multi-lattice kMC model. Shown in paren-thesis are the corresponding crystallographic axesof the PdO crystal.

14

Figure 9: Multi-lattice 1p-kMC simulations of the√5-oxide reduction at the three experimentally

employed temperatures. Shown is the fraction ofthe surface covered by the surface oxide as a func-tion of time using a(20×20) (solid, bold lines),a (10× 20) (dashed, thin lines), and a(40× 20)(dotted, thin lines) simulation cell. The slight dif-ference in the initial

√5-oxide fraction for the dif-

ferent cell sizes results from the fact that in everycell initially one row of oxide is removed.

ditions of 5× 10−11 bar CO pressure, and tem-peratures of 303 K, 343 K, and 393 K. In con-trast to the single-lattice 1p-kMC simulations dis-cussed in Section 3.1, very good agreement withthe experimentally observed times and trends isobtained – without the need to modify any of the1p rate constants. In order to better understandhow the new cross-reaction feature leads to thisdramatic improvement, we analyze which elemen-tary process immediately precedes the formationof an appropriate divacancy and therewith trig-gers the creation of a Pd(100) patch in the sim-ulations. Figure 10 shows these relative contri-butions and reveals that at lower temperatures re-duction is predominately caused by CO oxidationprocesses within the surface oxide domain, whileat the higher temperatures the ongoing reductionis primarily driven by cross-reactions over

√5-

oxide/Pd(100) domain boundaries. The latter is anatural consequence of the enhanced CO bindingat the Pd(100) nuclei as compared to the

√5-oxide.

At the higher temperatures CO is then predomi-nantly stabilized on the Pd(100) patches at the sur-face, concomitantly enhancing the cross-reactioncompared to the regular CO oxidation within thesurface oxide domain. This change in the mech-

anism behind the oxide reduction leads to a tem-perature dependence of the reduction time that isimpossible to grasp within a single-lattice model,regardless of how one tries to tweak the underlyingrate constants.

300 320 340 360 380 400

T [K]

0

20

40

60

80

100

%of

divacan

cycreation

O diffusioncr

oss-reaction

oxidereaction

Figure 10: Relative contribution of elemen-tary processes leading to the creation of divacan-cies and therewith to the ongoing oxide reductionthrough the formation of Pd(100) patches at thesurface. "Oxide reaction" denotes divacancy cre-ation through a CO oxidation reaction within the√

5-oxide domain, "cross-reaction" denotes diva-cancy creation through a cross-reaction over the√

5-oxide/Pd(100) domain boundary, and "O dif-fusion" denotes divacancy creation through diffu-sion of O atoms on the

√5-oxide. The data is ob-

tained using a(20×20) simulation cell.

4 Summary and Conclusions

We presented a general multi-lattice 1p-kMC ap-proach that allows to describe surface morpho-logical transitions within lattice kMC, as long asthese transitions occur between structures exhibit-ing commensurate lattices. This approach allowsto evaluate long-time kinetic behavior subject tocorresponding transitions and is efficient enoughto be based on 1p rate constants. Additionallyrequired compared to traditional single-lattice 1p-kMC is a detailed atomistic pathway for the tran-sition, which then needs to be mapped into the 1p-kMC model in form of new elementary processes.

We illustrated the approach by addressing recentoxide reduction experiments at a Pd(100) modelcatalyst by Fernandeset al.20 Single-lattice 1p-kMC simulations monitoring the O coverage as

15

an oxide stability indicator can not account forthe temperature dependence of the reduction timeobserved in the experiments. This holds, evenwhen abandoning the first-principles character ofthe simulations and optimizing the rate constantsof relevant elementary processes to fit the experi-mental data. In particular at more elevated temper-atures, the limitations in stabilizing CO at the sur-face oxide lead to reduction times that are muchtoo long. This leads us to conclude that the contin-ued oxide reduction subsequent to a long inductionperiod seen in the measurements is not governedby processes at intact oxide patches.

Extensive DFT calculations were correspond-ingly used to establish an atomistic reduction path-way that generates local Pd(100) patches. An im-portant rational in this development was the real-ization that several oxide metal atoms do not nec-essarily have to change their geometric positionduring the transition from oxide to pristine metal.The choice to only consider pathways where cor-responding position changes are not taking placethen leads to a drastic reduction in the space ofpossibly stable intermediates and could also be auseful strategy to conceive complex reconstructionmechanisms in other systems.

Very good agreement with the measurementsis obtained with the multi-lattice 1p-kMC sim-ulations on the basis of the proposed oxide re-duction pathway. The crucial new feature lead-ing to this improvement is the possibility for COoxidation reactions across

√5-oxide/Pd(100) do-

main boundaries. These cross-reactions constitutea largely varying contribution to the overall ox-ide reduction within the temperature range cov-ered by the experiments, and therewith generate atemperature-dependence of the reduction rate thatcannot be effectively described by a single-latticemodel.

In the catalysis context an interface controlledreactivity is often emphasized. As long as phaseswith commensurate lattices are involved, multi-lattice 1p-kMC offers the exciting perspective toscrutinize this perception within comprehensivemicrokinetic modeling. The present work alreadycontributes to this by highlighting that even thoughreaction barriers may be quite similar on the metal,the surface oxide and across the metal/oxide do-main boundary, the latter could still be the dom-

inant reaction mechanism due to the steady-statecoverages around the metal/oxide interface. Forthe present model to directly address steady-stateCO oxidation activity primarily additional elemen-tary processes are required that describe surfaceoxidation, in particular dissociative oxygen ad-sorption at highly O-precovered surfaces e.g. fea-turing Pd(100) patches surrounded by

√5-oxide.

Acknowledgements

We gratefully acknowledge support from the Ger-man Research Council (DFG) and the TUM Fac-ulty Graduate Center Chemistry, as well as gener-ous computing time at the Supercomputing Centerof the Max-Planck-Society, Garching.

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