Density fluctuations as door-opener for diffusion on crowded surfaces

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Science  15 Feb 2019:
Vol. 363, Issue 6428, pp. 715-718
DOI: 10.1126/science.aav4143

A path through a crowd

Catalytic reactions on surfaces occur at pressures at which the surfaces are completely covered with adsorbed molecules. It would seem that this arrangement would interfere with reactants encountering one another through diffusion processes. Henß et al. used high-speed scanning tunneling microscopy to follow the diffusion of oxygen atoms on a ruthenium surface that was fully covered with carbon monoxide (CO) molecules (see the Perspective by Magnussen). Oxygen-atom diffusion was unexpectedly fast. A theoretical model revealed that CO diffusion appears to open pathways for oxygen-atom movement.

Science, this issue p. 715; see also p. 695


How particles can move on a catalyst surface that, under the conditions of an industrial process, is highly covered by adsorbates and where most adsorption sites are occupied has remained an open question. We have studied the diffusion of O atoms on a fully CO-covered Ru(0001) surface by means of high-speed/variable-temperature scanning tunneling microscopy combined with density functional theory calculations. Atomically resolved trajectories show a surprisingly fast diffusion of the O atoms, almost as fast as on the clean surface. This finding can be explained by a “door-opening” mechanism in which local density fluctuations in the CO layer intermittently create diffusion pathways on which the O atoms can move with low activation energy.

We investigated the question of how atoms can move on a “crowded surface,” the situation on solid catalysts under operation conditions. Surface diffusion, which determines the mixing of the reactant particles on the catalyst surface and their lateral transport—for example, to defects acting as “active sites”—is generally regarded as extremely fast. This assumption is based on the low hopping barriers that the adsorbed particles can easily overcome at the applied elevated temperatures (1). Surface diffusion is thus usually not even included in the kinetics of catalytic reactions.

On the other hand, at the high pressures of industrial processes, catalyst surfaces can be highly covered by molecules adsorbing from the gas phase, reaction intermediates, and by-products. Whether the picture of an extremely mobile layer still holds for such crowded surfaces on which most adsorption sites are occupied is an open question. Measurements of macroscopic surface diffusion coefficients usually show a decrease with increasing coverages of the adsorbates (26) so that one may expect just the opposite: complete immobility at saturation. However, such macroscopic data are difficult to interpret with respect to atomic processes; simple site-blocking usually seems insufficient, and more complex effects—such as repulsive or attractive interactions between the particles, phase formation, and trapping at defects—play a role. For atomic diffusion mechanisms on crowded catalyst surfaces, one thus usually relies on kinetic Monte Carlo simulations (7, 8).

Some experimental, atomic-scale information of how particles may move when embedded in a close-packed two-dimensional (2D) layer has been obtained with scanning tunneling microscopy (STM). For In and Pd atoms embedded in the first layer of a Cu(100) surface, these “tracer atoms” moved by means of a vacancy mechanism (911), which is also the most prominent diffusion mechanism in 3D solids (12). The tracer atom can only jump to a neighboring lattice site when one of the mobile vacancies, which exist in a solid at a finite temperature, comes near the tracer atom, so that it can exchange sites with the vacancy. For Cl atoms on an H-covered Si(100) surface, a direct exchange of the tracer atom with neighboring H atoms was suggested (13). Such a direct exchange mechanism has also been postulated for 3D solids but is usually not observed because of the high activation energies involved. On Cl- and Br-covered Cu(100) electrodes in an electrolyte solution, S tracer atoms were proposed to move by means of two other mechanisms known from 3D solids: a ring-exchange mechanism or a mechanism resembling the so-called interstitialcy mechanism (14). In both cases, the dynamics were strongly affected by the electrical potential and thus specific to the electrochemical environment.

Here, we show that in an adsorbate layer on a catalyst, which is chemically and structurally quite different from these systems, diffusion may follow a different mechanism. Using a combined high-speed/variable-temperature STM that achieves imaging rates of up to 50 frames s−1, we investigated the dynamics of individual O atoms on a fully CO-covered Ru(0001) surface. This system was chosen because the CO oxidation on Pt group metals is a well-studied model for catalysis (15). Because (metallic) Ru is the least active of these metals (16), diffusion could be studied without competing CO2 formation. By means of statistical analysis of movies that consist of a large number of STM images over an extended range of temperatures and complementary density functional theory (DFT) calculations, we obtained a complete description of the atomic mechanism. In a “door-opening” mechanism, local density fluctuations of the CO layer open paths on which the O atom can move with surprisingly low activation energy.

Three consecutive images from an STM movie taken at 300 K (movie S1) show a single O atom surrounded by CO molecules (Fig. 1, A to C). Close inspection revealed that the position of the O atom was not exactly on a lattice site of the CO structure but displaced somewhat to the left in Fig. 1A, up in Fig. 1B, and to the right in Fig. 1C. This asymmetry resulted from the different adsorption sites of O atoms and CO molecules (Fig. 1, D to F). The O atom occupied a hexagonal close-packed (hcp) site (a threefold hollow site with a Ru atom of the second layer underneath) (17, 18), whereas CO occupied a top site (19), so that the O atom is necessarily displaced with respect to the CO lattice site. Occupation of the face-centered cubic (fcc) site, the threefold site without a Ru atom underneath, was not observed for the O atoms, which is consistent with the calculated lower binding energy of O on this site (18). We ruled out that the lattice site marked by the “x” in Fig. 1 was occupied by a CO molecule because in such a configuration, CO and O would bind to the same Ru atom, which would result in a strongly repulsive interaction (20). The short time interval of 0.1 s between the movie frames already indicates that at 300 K, the O atom readily hopped between the three hcp positions in a “cage” defined by the neighboring CO molecules.

Fig. 1 Hopping of O in a CO cage.

(A to C) Three consecutive STM images of the position of a single O atom embedded in the layer of CO molecules on Ru(0001). The bright dot is the O atom, and the hexagonal pattern is the (3×3)R30° structure of CO molecules (dark dots); the “x” marks a (3×3)R30° lattice point (300 K, 10 frames s−1, tunneling voltage Vt = –0.22 V, tunneling current It = 10 nA). (D to F) Corresponding structure models. The O atom is indicated in red, the CO molecules in blue, and the Ru atoms in gray.

To record O atom trajectories over longer time periods, an automatic particle-tracking algorithm was developed that could identify the positions of the O atoms in the STM images and record position changes over several thousand images (supplementary materials, materials and methods, and movie S2). An example obtained from an experiment at 273 K is shown in Fig. 2. The trajectory displayed a striking sequence of equilateral triangles, with side lengths of ~2.5 Å, each triangle consisting of several lines and connected to a neighboring triangle by (mostly) a single line of the same length. An obvious explanation is that each triangle represents the three hcp positions, separated by the Ru lattice constant of 2.7 Å, which the O atom can occupy in a CO cage (Fig. 1). The trajectory can then be understood as a path where the O atom spends a large fraction of time hopping between the three positions within a cage but occasionally leaves it, after which it becomes trapped in a neighboring cage.

Fig. 2 Trajectory of an O atom through the CO layer on Ru(0001).

The series was constructed from 1512 consecutive frames of an STM movie (273 K, 12 frames s−1, Vt = –0.7 V, It = 3 nA). The positions of the O atom in the individual frames are connected by lines, and frame numbers are color-coded.

An example for such a cage-leaving event is shown in Fig. 3. The O atom, first located at the upper tip of the original triangular cage (Fig. 3A), appeared in the following image at the base of a neighboring triangular cage (Fig. 3B). Because the O atom, after this event, was again coordinated by six CO molecules (Fig. 3B), this process represents a site exchange between the O atom and a CO molecule (Fig. 3, C and D). The arrows shown in Fig. 3C are not meant to suggest that this process must be a direct exchange of the O atom with the marked CO molecule. The connected triangles in the O trajectories (Fig. 2) that represent the diffusion of the O atom on the CO-covered surface are thus explained by two processes, local hopping within the CO cages and exchanges with neighboring CO molecules.

Fig. 3 Studies of O/CO exchange.

(A and B) STM images of an exchange event between an O atom and a CO molecule (300 K, 10 frames s−1, Vt = –0.22 V, It = 10 nA). (C and D) Corresponding structure models. The site marked by the “x” is the same in both frames. (E) Oxygen displacement distribution and hopping model. The magenta bars are the experimental displacement distribution Pt0(x,y), determined from 10,889 frames (291 K, 10 frames s−1); the blue bars are the corresponding fit, and (0,0) is the starting position of the O atom. Green arrows in the model indicate jumps within the CO cage, and black arrows indicate exchange jumps with CO molecules. (F) Arrhenius plot of the two hopping frequencies. Green dots indicate jump rates Γ1 within the triangles, and black dots indicate exchange rates Γ2 with CO.

To test the validity of this diffusion model and to extract hopping frequencies, we developed a statistical analysis method. The model assumes that the individual hopping events of the O atom are statistically independent of each other—a most certainly fulfilled assumption because the time between the hopping events is much longer than the 10−12 to 10−13 s time scale of the hopping events themselves. The hopping should then follow a Poisson distributionP˜t0(n)=(Γt0)nn!eΓt0(1)where P˜t0(n) is the probability that an O atom jumps n times during the time period t0. t0 is the time for an STM image, and Γ is the hopping frequency, defined as Γ=1/τ, where τ is the mean time the particle spends on an adsorption site.

In the present case, the O atom can either hop with or without a site exchange with CO. For example, when the O atom is localized on the upper of the three hcp sites in the cage (Fig. 3E, inset), it can jump to one of the two lower hcp sites without exchanging sites with CO (“triangle jumps”) (Fig. 3E, green arrows). Alternatively, it can exchange sites with one of the three surrounding CO molecules from above (“exchange jumps”), along one of the four black arrows. Exchange jumps to the left and right are pairwise equivalent because of symmetry. Exchange jumps with the top CO and with one of the two lateral COs, although appearing different, are also equivalent: When the O atom has exchanged sites with the top CO (Fig. 3, C and D), the reverse of this process (Fig. 3, D to C) would involve a lateral CO. Because of microscopic reversibility, the back-and-forth processes must have the same rates, so that the exchange rates with the top and lateral COs must have the same rates. Therefore, there are only two different types of processes that have to be considered, triangle and exchange jumps. P˜t0(n1,n2) is then the probability that within the time period t0, the O atom jumps n1 times within the cage and n2 times through an exchange with CO. For the same reason as above, the two processes can be assumed to be statistically independent of each other, so that P˜t0(n1,n2) is given by the product of two Poisson distributionsP˜t0(n1,n2)=(Γ1t0)n1n1!eΓ1t0(Γ2t0)n2n2!eΓ2t0(2)Γ1 and Γ2 are the frequencies of the triangle and the exchange jumps, respectively. Because the STM does not see the individual jumps but only records the particle position in a frame with respect to the preceding frame, P˜t0(n1,n2) is not a directly measurable quantity. What is measurable is the displacement distribution Pt0(x,y), the probability that a particle located at x = 0 and y = 0 in one frame is found on a site with displacement coordinates x and y in the following frame. Pt0(x,y) is related to P˜t0(n1,n2) byPt0(x,y)=n1=0n2=0P˜t0(n1,n2)wn1,n2(x,y)(3)wn1,n2(x,y) is the probability that the O atom can travel from x = 0, y = 0 to the coordinates x and y by a given combination of n1 triangle jumps and n2 exchange jumps. For example, for the starting configuration of Fig. 3E, inset, wn1,n2(x,y) to land on one of the two other triangle positions by the combination n1 = 1, n2 = 0 is 1/2 each. For general n1 and n2 combinations, the wn1,n2 values are obtained with recursion by using the geometry of the O/CO configuration, assuming that only jumps to neighboring hcp sites occur, for both processes (supplementary materials, materials and methods). Multiplication by P˜t0(n1,n2) and adding overall n1 and n2 gives the theoretical displacement distribution Pt0(x,y). For the temperature range investigated, the infinite sums could be terminated at n1 = 100 and n2 = 10. An analog equation has previously been derived for the analysis of field ion microscopy data, for the simpler case of one jump type in one dimension (21).

The experimental displacement distributions were determined, for each temperature, from several thousand to several tens of thousands successive frames by using trajectories such as that shown in Fig. 2. An example of the displacement distribution from measurements at 291 K is shown in Fig. 3E as the magenta bars. The high three central bars reflect the relatively long time the O atom spends within its cage, whereas the lower bars at larger distances are the result of the rarer exchanges with neighboring CO molecules. This distribution was least-square fitted with Eq. 3 (Fig. 3E, blue bars), where the only fitting parameters were the two hopping frequencies, Γ1 and Γ2. The agreement of the fit with the experimental data is excellent (coefficient of determination R2 = 0.99994). The frequencies obtained were Γ1 = 28.5 s–1 and Γ2 = 0.997 s–1. Similarly good agreement was obtained for the other temperatures.

The experimental distribution was well reproduced by Eq. 3, meaning that the two-process model provides a good description of O atom diffusion on the CO-crowded surface. A vacancy mechanism—the main mechanism in 3D solids, and also observed for atoms embedded in metal surfaces—can be ruled out. Vacancy diffusion displays characteristic spatial correlations of successive jumps resulting from the high probability after exchange with a vacancy that the tracer atom jumps back to the vacancy that is now located on the opposite side (911). Such correlations are absent here. However, the mechanism obtained here is also not a simple random walk. For example, for the O atom on the upper hcp site (Fig. 3E, inset) to exchange sites with one of the CO molecules in the lower half, it first must jump to one of the two lower hcp positions. The resulting displacement is not independent of the order of the two jump types. This effect is fully implemented in the statistical model.

Displacement distributions were analyzed for several temperatures between 234 and 303 K. At temperatures <234 K, the O atom jumped too rarely—a few times on the time scale of 1 hour—to give statistically relevant data. At higher temperatures, the rapid oscillations of the O atom in the CO cage prevented accurate determination of its position. Nevertheless, the frequencies measured in the accessible temperature range (table S1) span five orders of magnitude (very high for dynamic STM experiments), a result of the combined high imaging rate and low thermal drift enabling long observation times. The results for Γ1 and Γ2 plotted in Fig. 3F as functions of temperature gave straight lines on the Arrhenius plot for both processes over the entire temperature range. The activation energies obtained were E1*=0.57±0.02 eV for the jumps in the triangles and E2*=0.63±0.03 eV for the exchanges with CO. The preexponential factors, Γ10=1011.4±0.4 s−1 and Γ20=1011.1±0.7 s−1, were only marginally lower than the expected 1012 to 1013 s−1 range.

The two jump processes identified may consist of several elementary steps. The STM images show the particles in their stable positions, and metastable intermediate positions occupied by the O atom or the CO molecules may be too short-lived to be observable. Thus, in order to obtain further insights, we used DFT to calculate the energy landscape in which the jump processes take place using a technical setup (supplementary materials, materials and methods) that has been shown to be well suited for the CO/Ru(0001) system (22, 23).

For the triangle jumps, the hcp position of the O atom is most stable, and the fcc position is a 0.30 eV higher local minimum. The barrier for the jumps from the hcp to the fcc position is 0.56 eV, which is in very good agreement with the experimental value for E1* of 0.57 eV. Thus, the most likely path that the O atom takes within a cage is from the hcp site via the fcc site to the neighboring hcp site.

For the exchange jumps, three scenarios were investigated: A direct exchange in which the O atom and the CO molecule moved concertedly (Fig. 3C), a sequential mechanism in which the O atom moved first, and a sequential mechanism in which a CO molecule moved first. Concerted mechanisms did not give low-energy paths along which a CO molecule actually exchanged sites with the O atom. A direct concerted exchange intermediately forced O and CO into a strongly repulsive conformation that resembled a deformed CO2 molecule (fig. S2). The activation energy was very high, close to 1.5 eV, a value also found for the CO oxidation on Ru(0001) (20). Thus, a concerted, direct exchange mechanism could be ruled out.

A sequential mechanism in which the O atom moved first is indicated in Fig. 4A as the black arrows. In the initial step, the O atom moved from its original position (hcp 1) to an fcc site near the rim of the CO cage and then to an hcp site on the rim between two CO molecules (hcp 2). The energy profile of this path (Fig. 4B, dotted black line) showed a high barrier for the first step, 0.98 eV, resulting from O and CO sharing one Ru atom and strongly repelling each other in the intermediate Ofcc/CO configuration. The second step, the transfer of the O atom to the hcp 2 site, had a lower barrier of 0.35 eV. Also, the subsequent rearrangements of several CO molecules, such as along the indicated orange and cyan arrows, had low barriers of ~0.30 eV and were fast. In the final configuration, a CO molecule occupied the central top site in the cage originally occupied by the O atom. The net effect is a complete O/CO site exchange. However, the barrier of the first step is >50% higher than the experimental E2* value, which, given the high quality of the Arrhenius plot, we consider a substantial difference. Thus, we also rule out this mechanism.

Fig. 4 Paths and energy diagram of the exchange jump of an O atom with CO.

(A) Unit cell used for the DFT calculations. The black arrows indicate the path along which the O atom moves; the orange and blue arrows are paths taken by two CO molecules with possible intermediate positions 1 and 2. (B) Energy profile when the O atom moves first (dotted black line), and when a CO molecule moves first and then the O atom (solid black line).

In the sequential mechanism in which a CO molecule moved first, the initializing step could, for example, be a move of a CO to the top position 1 (Fig. 4A, orange arrow). The related barrier is 0.30 eV (Fig. 4B, orange line), and the energy of the O/CO configuration increased by 0.16 eV (Fig. 4B, solid black line). The same barriers and energy shifts were found when the CO initially moved to one of the other neighboring top sites. The increase in energy was caused by the mutual repulsions of the CO molecules on adjacent top sites, but this effect was relatively small. This repulsion also led to an outward tilt of the CO axes in the range of 5° to 9°, depending on the particular configuration. When, in the following step, the O atom moved to the indicated fcc site (Fig. 4A, black arrow), the barrier was considerably reduced to 0.62 eV (Fig. 4B, solid black line). The subsequent transfer of the O atom to hcp site 2 only had a barrier of 0.29 eV, and the consecutive rearrangements of the CO molecules, such as along the blue arrows in Fig. 4A, were again fast. Once the O atom moved to the hcp 2 site, it was much more likely for the CO molecules to rearrange than for the O atom to jump back. If we assume that the initial CO shift to a neighboring top site is a fast preequilibrium, the activation energy for the full process is the sum of the initial energy shift of 0.16 eV and the barrier for the O atom to jump to the fcc site of 0.62 eV, giving 0.78 eV. This value is the lowest from all mechanisms tested, and it was in reasonable agreement with the experimental E2* value of 0.63 eV.

The sequential mechanism in which a CO molecule moved first followed by the movement of the O atom described the STM data best. It resembles the ring-exchange mechanism in 3D solids, in which the tracer atom and several matrix atoms move in a ringlike fashion (12), but the classical ring exchange is a concerted mechanism. We ruled out a concerted movement here because, in this case, the barriers of all elementary steps would add, giving unreasonably high activation energies. The mechanism is sequential, and it is better described as a local density fluctuation of the CO layer that occasionally opens a door, allowing the O atom to escape from its cage. Once the O atom has escaped, the locally disordered CO molecules quickly reorder, closing the door and preventing the O atom from immediately jumping back, which completes the exchange.

Such a diffusion mechanism is not known in 3D solids and has also not been reported for the diffusion of particles in close-packed surfaces. That such a mechanism occurred here can be understood by the CO molecules—despite forming an ordered overlayer—not being very densely packed, so that density fluctuations could occur with low activation energy. The mechanism is efficient, allowing the O atom to move at a surprising speed. For example, the frequency of the exchange jumps at 300 K of 4.7 s−1 [normalized by 6/4 to account for the reduced number of four directions in which the O atom can exchange with CO (Fig. 3E, inset)] is only by a factor of 3.5 lower than the hopping frequency of 16.6 s−1 of an O atom on the empty Ru surface (only measured at room temperature, so that no barrier is available) (24). The O atom could thus travel on the crowded surface almost as fast as on the empty one. Additional effects of a weakened O–Ru bond by the coadsorbed CO have been investigated but played a minor role (supplementary materials).

We propose that the door-opening mechanism may play a general role for diffusion on catalyst surfaces. Strongly bound particles such as O, N, or C atoms are intermediates in many catalytic reactions, and the door-opening mechanism would allow them to diffuse rapidly even in a crowded layer of weakly bound coadsorbates. High surface mobility in catalytic reactions is relevant for a correct formulation of the kinetics. Kinetic equations are usually formulated with coverages as variables. Coverages represent mean-field averages, which is reasonable as long as the distribution of the particles on the adsorption sites is random. Because in a catalytic process the random distribution is permanently disturbed by the reaction, this condition is only fulfilled if the surface mobility is high enough to randomize the particles on a time scale fast with respect to the reaction.

Supplementary Materials

Materials and Methods

Supplementary Text

Figs. S1 to S3

Table S1

References (2534)

Movies S1 and S2

References and Notes

Acknowledgments: A.-K.H. and J.Win. thank F. Kreuzer, T. Gisicius, and R. Hiermaier, LMU Munich, for expert precision mechanics support. Funding: S.S. and A.G. acknowledge support by the Baden-Württemberg Foundation through the project MSMEE within the High-Performance Computing II program and computer time through bwHPC and the German Research Foundation (DFG) through grant INST 40/467-1 FUGG. Author contributions: A.-K.H. performed the STM measurements, developed the data recording and analysis software, and evaluated the data. A.-K.H. and J.Win. wrote the manuscript and designed Figs. 1 to 3. J.Win. supervised the project and developed the mathematical diffusion model. S.S. and A.G. performed the DFT calculations and designed Fig. 4. P.K.M. and D.C.L. provided the atom-tracking algorithm. R.S. wrote a first version of the data recording software. J.Wie. built the I/V converter for the high-speed STM. All authors reviewed and commented on the manuscript. Competing interests: The authors declare no competing interests. Data and materials availability: The particle tracking algorithm is available under All data are available in the main text or the supplementary materials.

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