Nanometric chemical clocksJean-Sabin McEwena,1, Pierre Gasparda, Thierry Visart de Bocarmeb, and Norbert Kruseb

aCentre for Nonlinear Phenomena and Complex Systems, CP 231, Universite Libre de Bruxelles, B-1050 Brussels, Belgium; and bChemical Physics of Materials,CP 243, Universite Libre de Bruxelles, B-1050 Brussels, Belgium

Edited by Stuart A. Rice, University of Chicago, Chicago, IL, and approved December 30, 2008 (received for review November 24, 2008)

Field ion microscopy combined with video techniques and chemicalprobing reveals the existence of catalytic oscillatory patterns at thenanoscale. This is the case when a rhodium nanosized crystal—conditioned as a field emitter tip—is exposed to hydrogen andoxygen. Here, we show that these nonequilibrium oscillatorypatterns find their origin in the different catalytic properties of allof the nanofacets that are simultaneously exposed at the tip’ssurface. These results suggest that the underlying surface anisot-ropy, rather than a standard reaction–diffusion mechanism, playsa major role in determining the self-organizational behavior ofmultifaceted nanostructured surfaces. Surprisingly, this nanoreac-tor, composed of the tip crystal and a constant molecular flow ofreactants, is large enough for the emergence of regular oscillationsfrom the molecular fluctuations.

field ion microscopy � heterogeneous catalysis � nanopatterns �nonequilibrium oscillations

The Belousov–Zhabotinskii reaction is probably the mostfamous example of an oscillating chemical reaction in the

liquid phase (1, 2). However, studies of oscillations in hetero-geneous catalysis begun in the 1970s (3, 4). One decade later,Ertl et al. demonstrated for the first time (5, 6) that oscillatorysurface reactions are associated with the occurrence of specificpattern formations ranging from tens to hundreds of microme-ters. More recently, oscillations have been discovered on thenanoscale in field electron and field ion microscopes by usingvideo techniques (FEM and FIM, respectively) (7–10). At thislength scale of tens of nanometers, self-sustained oscillatorypatterns are observed about which little is known. This iscertainly the case for the catalytic water production whenexposing oxygen and hydrogen to a rhodium field emitter tip (11,12). Our purpose in the present article is to show that thisnonequilibrium self-organizational behavior can be understoodby taking into account the structural anisotropy of the crystallinetip that results in different catalytic properties on the variousnanofacets. Moreover, we demonstrate that the external electricfield, as applied in a FIM (of the order of 10 V/nm), promotessurface oxidation thus giving way to a feedback mechanism toexplain self-sustained rate oscillations in the H2/O2/Rh system.

The understanding of self-sustained oscillations at the mac-roscale was pioneered by Prigogine who showed that suchphenomena are consistent with thermodynamics as long as thesystem is open and far from equilibrium (13). Such self-organization phenomena are understood in terms of reaction–diffusion processes, which also explains the mesoscopic patternsobserved on oriented metal single-crystal surfaces (14, 15).However, the nanopatterns observed during a catalytic reactionin a FIM have a spatial scale smaller than typical diffusionlengths. Moreover, one may wonder how the molecular fluctu-ations that manifest themselves in such small systems (16, 17)affect the oscillations. Indeed, their regularity disappears if thenumber of molecules involved in the reaction is too small,suggesting the existence of a minimum number of moleculesrequired for a nanometric system to act as a chemical clock (18,19). Field emission techniques (20) stunningly meet such arequirement because they demonstrate the appearance of chem-ical clocks down to the nanoscale, as first observed in FEM (7,8) and later in FIM with a higher (close to atomic) resolution (9,

10). Despite these intriguing results, only little information iscurrently available on how the different crystal planes of a fieldemitter tip interact during a nonlinear chemical reaction (21, 22).This need is addressed in the present work.

Experimental ObservationsThe video-FIM is operated as a flow reactor while imaging thedynamic reaction behavior with nanoscale lateral resolution onthe surface of a nano-sized rhodium tip. A large variety ofnanofacets are simultaneously exposed at the surface of this tip.In the absence of reactive gases, atomic resolution is obtained sothat a clear structural correlation with dynamic reaction patternscan be established. As illustrated in Fig. 1 A and B, the fieldemitter tip approximates the 3D morphology of a single nanometer-sized metal catalyst particle in the absence of an oxide support (23).

Our system was examined through a series of micrographsbetween 400 and 550 K at a fixed oxygen pressure PO2

and avarying hydrogen pressure PH2

, which allows the catalytic for-mation of water to occur (11, 12). In our experiments, it wasconcluded that for small PH2

/PO2ratios the surface is predomi-

nantly covered by oxygen, whereas for large PH2/PO2

ratios it ismainly covered by hydrogen (11). In an intermediate region thesystem becomes bistable, with hysteresis extending over a certainrange of PH2

/PO2, which narrows considerably toward higher

temperatures, as it did in the catalytic formation of water onplatinum (22) (see Fig. 2). Depending on temperature (400 K �T � 500 K), local and erratic f luctuations of the surfacecomposition between a hydrogen-covered and an oxygen-covered rhodium tip are observed within a specific range ofPH2

/PO2ratios. This defines the bistability region. Under well

reproducible PH2/PO2

ratios, the micrographs clearly demonstratestructural transformations. In a hydrogen-rich H2/O2 mixture,the main features of Fig. 1 A are still visible, i.e., the (001) and{111} planes are discernible along with their respective symme-tries. With a decreasing H2 partial pressure while keeping the O2

pressure constant, a ‘‘granular’’ structure emerges at theapex of the tip, as illustrated in Fig. 1C. Previous atom-probestudies during the ongoing reaction have shown that this is dueto the presence of RhxOy indicating the formation of a surfaceoxide (12).

Reaction SchemeThe above observations can be rationalized in terms of thepartial coverages of the various adsorbed species and the kineticequations governing these coverages. The kinetic parametersused in this mean-field approach are fixed so as to be in line withab initio calculations and experimental data. This allows us to

Author contributions: J.-S.M., P.G., T.V.d.B., and N.K. designed research, performed re-search, contributed new reagents/analytic tools, analyzed data, and wrote the paper.

The authors declare no conflict of interest.

This article is a PNAS Direct Submission.

1To whom correspondence should be addressed. E-mail: jmcewen@ulb.ac.be.

This article contains supporting information online at www.pnas.org/cgi/content/full/0811941106/DCSupplemental.

© 2009 by The National Academy of Sciences of the USA

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determine the rate coefficients and their activation energies onseveral of the main crystalline planes, which show importantdependences on the Miller indices characterizing the planarorientation.

We have taken this essential feature into account by deter-mining for each reaction how the activation energy E and theprefactor k0 of each rate coefficient depend on the unit vectorn perpendicular to the crystalline plane

k � k0 �n; F� exp � �E�n; F�

kBT � [1]

where F is the electric field at the surface, T is the temperature,and kB is the Boltzmann constant. The normal unit vector n itselfdepends on the Miller indices (hkl) of the nanofacet where thereaction takes place (see Fig. 3). Because the Miller indices varyfor the different nanofacets composing the field emitter’s tip, therate coefficients have a spatial dependence describing the an-isotropy of the crystalline tip as given in Eq. 1, which is centralto explaining the nanopatterns observed in the experiment.

Moreover, the electric-field component F perpendicular to thefield emitter surface also depends on its location at the tip’ssurface. The spatial dependence of the electric field F is deter-mined by the geometry of the tip according to electrostatics,which results in a higher field value at the tip’s apex than at itsf lanks.

In Eq. 1, the normal unit vector n and the electric field F aredefined with respect to the mean shape of the tip (here taken asa paraboloid). Such an approach is justified because the atomicscale (Rh lattice constant of 0.38 nm) is significantly smaller thanthe scale of the nanopatterns and the tip’s radius of curvature

(�10 nm). Remarkably, the corresponding spatial dependenceof the rate coefficients allows us to understand the observednanopatterns.

The reaction network leading to water formation starts withthe dissociative adsorption of hydrogen and oxygen, as illustratedin Fig. 4. Note that oxygen is molecularly adsorbed in a precursorstate before dissociating (24, 25). Although the adsorption of

B12.3 V/nm

400 450 5000.00

0.01

0.02H2 P

ress

ure

(Pa)

Temperature (K)

0.00

0.01

0.02

A11.0 V/nm

Fig. 2. The bistability diagram showing hysteresis for PO2 � 5 � 10�4 Paduring catalytic water formation on rhodium at 11.0 V/nm (A) and 12.3 V/nm(B). The circles and stars indicate the experimental pressures (with correspond-ing error bars) for which the structural transformation occurred when de-creasing and increasing the hydrogen pressure, respectively. The area inbetween marks the coexistence region of bistability. The full lines mark thetheoretical delimitation of the bistability region with a kinetic model of thefield emitter tip.

(001)

(101) (011)

(111)

θ

φ

n = (h,k,l)

h2+k2+l2

nanofacet (hkl)

•

Fig. 3. Ball model of the field emitter tip with the unit vector n � (sin � cos�, sin � sin �, cos �) perpendicular to the nanofacet of Miller indices (hkl) of anunderlying fcc crystal. All of the balls inside a paraboloid are retained in thismodel of the field emitter. We notice that the mean electric field points in thesame direction F � Fn because the electric field is always perpendicular to thesurface of a conductor such as the field emitter tip. The (001) nanofacet is atthe tip’s apex (green balls). The nanofacets {011} (resp. {111}) are in red (resp.in blue).

A B

C D

Fig. 1. The field ion microscope, unlike the scanning tunneling microscope,allows us to study the cooperative effects and concerted behavior in a non-linear chemical reaction because a large number of nanosized facets aresimultaneously exposed at the surface of a 3D tip. (A) Field ion micrographs ofa clean (001)-oriented Rh tip imaged by neon at PNe � 10�3 Pa, T � 55 K, F �35V nm�1. The radius of curvature is �10 nm. (B) Ball model of the surfacestructure encountered in A. (C) Micrograph showing the structural transfor-mation of the surface at 450 K, 12.3 V/nm, and PO2 � 5.0 � 10�4 Pa in thebistability regime (PH2/PO2 � 10.0). Areas of the tip that are covered by oxygenand by hydrogen are indicated by arrows. (D) The subsurface oxygen distri-bution on a logarithmic scale in the bistability regime (PH2/PO2 � 2.0) asobtained within a kinetic model of the reaction on the tip. The bright areas inthe theoretical model correspond to a high site occupation value and the darkareas have a vanishing site occupation.

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oxygen is essentially irreversible in the temperature range of theexperiment, the hydrogen adsorption is reversible because of itslow desorption energy on rhodium. As for the diffusion of theadsorbed species, oxygen is strongly bound such that its diffusioncan be neglected. However, hydrogen is known to be highlymobile on rhodium (26). Indeed, its diffusion time over adistance of �10 nm is of the order of 10�8 to 10�9 s at 500 K,which is much smaller than the timescales of the other kineticprocesses. Accordingly, hydrogen adatoms quickly achieve aquasi-equilibrium spatial distribution in the effective energypotential determined by the local hydrogen desorption energy oneach nanofacet and the local electric field. This spatial distribu-tion varies slowly, on the timescales of the longer differentreactions [see details in supporting information (SI)].

Afterward, the interactions between the adsorbed speciesgovern how the system evolves. In particular, the repulsionbetween the oxygen adatoms drives them subsurface when theirdensity at the surface is high enough. Alternatively, oxygen canalso react with hydrogen to form water. These considerationsallow us to correlate the presence of subsurface oxygen with theexistence of the ‘‘granular’’ structure as observed with our FIM(compare Fig. 1D with Fig. 1C). Recently, the penetration ofsurface oxygen has been shown to be facilitated by the presenceof a positive external electric field (27, 28). Indeed, such asubsurface site occupation reduces the field force acting on theelectronegative oxygen atoms. Overall, the formation of water issustained by using 2 reservoirs of oxygen, namely, surfaceadsorbed and subsurface atoms.

BistabilityAs for the bistability, the role of the external electric field has,however, remained obscure (22). Here, we show in Fig. 2 A andB that the corresponding bistability region depends in a funda-mental way on the applied external electric field and that anincrease in its value results in a larger bistability regime. Weinterpret this increase of the bistability region as being due to thefield’s dependence of the rate coefficients in Eq. 1 for theassociative desorption of hydrogen, the passage of oxygen be-tween the adsorption and subsurface sites, and the reaction ofwater formation. The values of the activation energies and theother kinetic parameters are given in Tables S1 and S2.

The influence of the anisotropy of the tip on the bistabilityregion can also be clearly seen experimentally in Fig. 1C andtheoretically with the oxygen subsurface distribution depicted inFig. 1D. The tip in both cases is divided into 4 quadrants, wherethe oxygen-covered region correlates well with the subsurfaceoxygen distribution. This anisotropy finds its origin in thedependence of the rate coefficients on the crystalline plane

orientation, as expressed in Eq. 1. This is the case, in particular,for the rates of hydrogen desorption and oxygen adsorption, aswell as for the oxidation rates of the metal or the correspondingreduction rates of the oxide. In this regard, we find that the widthof the bistability region sensitively depends on the energeticdifference between the latter 2 barriers. A smaller difference inthe energy barriers results in a larger bistability region at a fixedexternal electric field value.

Oscillatory NanopatternsPrevious atom-probe studies with short field pulses have pro-vided local information on the chemical surface compositionduring the oscillations (12). A direct correlation of the tipcatalytic activity with the brightness of field ion micrographs hasbecome possible since it was found that the water signal (con-sisting of single charged H2O� and H3O� ions) dominates themass spectra for most of the time during one oscillating reactioncycle (12, 29). More recent additional experiments have shownthat oxygen ionization may contribute significantly to the imagebrightness once the surface runs into a catalytically less activestate that is associated with the formation of a surface oxide. Fig.5 displays the evolution of the calculated surface oxygen/hydrogen coverages and the oxygen subsurface occupation alongwith the brightness of the field ion micrographs. A fast clean-offreaction is seen to start the oscillating cycle corresponding to thepeak in the brightness. Afterward, the system goes into thecatalytically less active state, with a corresponding decrease ofthe image brightness. However, we find that the water coverageand thus the number of ionized species on the tip will be smallat our experimental conditions compared with the number ofoxygen, subsurface oxygen, and hydrogen atoms adsorbed on thetip. This can be understood because the tip temperature (550 K)is well above the desorption temperature of water on rhodium[�300 K for water on Rh (001) (30)] so that the formed watermolecules will desorb rapidly. Thus, the ionization should only

gas phase

precursor state

adsorbates

subsurface oxygen

Fig. 4. Two-dimensional schematic illustration of the different processesthat we consider in the reaction scheme: (i) the dissociative adsorption ofoxygen via a precursor state; (ii) the formation of a surface oxide trilayer whenoxygen atoms migrate below the surface; (iii) the dissociative adsorption ofhydrogen; and (iv) the formation of water. The double-arrowed lines indicatethat these processes are reversible in the model (see SI, Theoretical Methods,for more details). The red disks represent oxygen atoms and the gray disksrhodium atoms, whereas the blue ones are hydrogen atoms.

↓ ↓

0 500

20

40

Brig

htne

ss (a

.u.)

Time (s)

0 50

0.00.20.40.60.81.0

A

θ O,θ

S

10-510-410-310-2

θ H

B

C

Fig. 5. Time dependence of the oxygen and hydrogen site occupations aswell as the experimental total brightness during the rate oscillations. (A) Thetime evolution of the oxygen coverage (solid line) and the oxygen subsurfaceoccupation (dashed line) at the (001) plane in the kinetic model. (B) Corre-sponding oscillations of the hydrogen coverage at the (001) plane. (C) Exper-imental total brightness in the oscillatory regime. The temperature, electricfield and partial pressures of oxygen in A, B, and C are T � 550 K, F0 � 12 V/nm,PO2 � 2 � 10�3 Pa, respectively. However, the hydrogen pressure is PH2 � 2 �10�3 Pa in the FIM experiments and 4 � 10�3 Pa in our kinetic model. Thearrows indicate the transition from a metallic rhodium field emitter tip to onethat is invaded by subsurface oxygen.

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perturb weakly the population of the neutral species. We willtherefore assume that the ionization is driven by the dynamics ofthe neutral species. This conclusion is supported when compar-ing Fig. 5 A and B with Fig. 5C. Indeed, in Fig. 5C, the subsequenttrend of decreasing intensities, which are reflecting the increas-ing contribution of oxygen ionization, correlates well with theevolution of the oxygen subsurface occupation as given in Fig.5A. However, the peak in the experimental brightness is re-f lected with an increase of the hydrogen coverage on the surfaceas depicted in Fig. 5B.

Our nanometric chemical clock begins to work at tempera-tures near 500 K and continues up to 550 K. Starting from ametallic surface, a Rh oxide is first formed at the topmost (001)layer of the tip that is marked by a bright area extending nofurther than the {012} planes (Fig. 6A). We correlate this brightarea with the subsurface oxygen distribution that extends slightlybeyond the {012} facets (Fig. 6D). The oxide layer then expandsanisotropically toward the peripheral regions with a preferencefor kink-site nanofacets in zone lines between the (001) and the{011} orientations. At 13 s, a nanometric cross-like structure isclearly formed (Fig. 6B). We rationalize the formation of thisnanometric structure with the one obtained for the oxygensubsurface occupation that extends out to the shank of the tip(Fig. 6E). Surface oxidation proceeds with an associated de-crease of the overall brightness as shown at t � 36 s in Fig. 6C.The oxide now invades nearly all of the visible area of the tip,except in areas near the {111} facets. Remarkably, this is exactlywhat we obtain for the subsurface oxygen distribution (Fig. 6F).The presence of subsurface oxygen is central in our explanationof the self-sustained oscillations, because a key feature of ourinterpretation is that an increasing subsurface site occupationmust hinder the adsorption of oxygen onto the surface (see theSI for details). At �36 s, this results in an oxygen subsurfaceoccupation that is larger than the oxygen coverage that isthermodynamically unstable (28, 31) and induces a suddenreduction of the surface oxide from the outskirts toward the apexof the tip, with a considerable increase of the brightness (seeMovie S1 and Movie S2). Structural features of the metallic

surface are recovered at this stage of the cycle. The essential roleof the external electric field for our chemical clock’s behavioralso emerges once again, because in its absence there is nosubsurface oxygen and thus no oscillations are present. Theimportant effect of the electric field is to facilitate the formationof a surface oxide at low oxygen pressures, which is otherwiseonly possible at high pressures in the absence of a field. Thus, theelectric field, in the present study, turns out to bridge the gapbetween low-pressure single-crystal surface studies and high-pressure heterogeneous catalysis.

ConclusionsThe present findings provide a comprehensive understanding ofthe emergence of oscillatory patterns in the H2/O2/Rh systemunder FIM conditions. They show how this chemical clock canfunction with only a few thousand atoms despite the presence ofmolecular fluctuations. We demonstrated that the tip’s anisot-ropy and the external electric field play a major role in deter-mining the nanopatterns and the time evolution of this chemicalclock. Such results suggest how the observed self-sustainedoscillations can be controlled. They also indicate how one canmanipulate the reaction rates and selectivities for nanotechnol-ogy applications (32, 33).

Materials and MethodsThe field ion microscope used for these studies has been described in detailelsewhere (34) and provides micrographs of the extremity of a sharp tip, withatomic lateral resolution under best imaging conditions (traditional mode ofimaging, see Fig. 1A). To obtain a clean rhodium field emitter tip, severalcycles of field evaporation, noble gas sputtering, and heat treatment werenecessary. The clean rhodium specimen served as a reference to calculate thevalues of the field strength. Its radius of curvature was calculated by countingthe number of atomic layers between 2 facets of known orientation. StandardFIM images were taken with a high dynamic range Roper Scientific CCDcamera (512 � 512 pixels, 16 bits per pixel). The same field ion microscope wasused for dynamic reaction imaging. A high-sensitivity video camera with atime resolution of 20 ms was used for this purpose. Local brightness was thenevaluated by pixel analysis of the digitized data.

A B C

D E F

Fig. 6. Series of FIM micrographs covering the complete oscillatory cycle and the corresponding time evolution of the subsurface oxygen distribution on alogarithmic scale as obtained within a kinetic model of the field emitter tip. Starting from a surface in the quasi-metallic state (A and D), an oxide layer invadesthe topmost plane and grows along the {011} facets forming a nanometric cross-like structure (B and E). The oxide front spreads to finally the whole visible surfacearea (C and F). The temperature, electric field, and partial pressures of oxygen are as those in Fig. 5. For the subsurface site occupation, the white areas indicatea high site occupation value whereas the dark areas indicate a low site occupation value.

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Rhodium tips were prepared by electrochemically etching a thin wire (Rh,0.127 mm diameter, 99.8% purity) in a molten mixture of NaCl and NaNO3 saltsat 520 °C (20).

In a second setup, the field ion microscope is part of a 1-dimensional atomprobe allowing a chemical identification of adsorbed layers during the ongo-ing catalytic reaction. To do so, field pulses (�100 ns width) are applied to acounter electrode (with a hole) in front of the rhodium tip. Pulses rupture

species as ions that pass the probe hole of the microscope screen and enter atime-of-flight mass spectrometer for chemical identification.

Theoretical methods are presented as SI.

ACKNOWLEDGMENTS. This work was supported by Communaute francaisede Belgique Contract ‘‘Actions de Recherche Concertees’’ 04/09-312. T.V.d.B.and J.-S.M. were supported by Fonds National de la Recherche Scientifique.

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