range investigated, theinfinite sums could be
terminated atn 1 =100andn 2 = 10. An analog
equation has previously been derived for the
analysis of field ion microscopy data, for the sim-
pler 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 dis-
placement distribution from measurements at
291KisshowninFig.3Easthemagentabars.
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 neighbor-
ing 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,G 1 andG 2. The agreement
of the fit with the experimental data is excellent
(coefficient of determinationR^2 = 0.99994). The
frequencies obtained wereG 1 =28.5s–^1 andG 2 =
0.997 s–^1. Similarly good agreement was obtained
for the other temperatures.
The experimental distribution was well re-
produced 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 suc-
cessive 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 ( 9 – 11 ). Such correla-
tionsareabsenthere.However,themechanism
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 tem-
peratures, the rapid oscillations of the O atom in
the CO cage prevented accurate determination of
its position. Nevertheless, the frequencies mea-
sured in the accessible temperature range (table
S1) span five orders of magnitude (very high for
dynamic STM experiments), a result of the com-
bined high imaging rate and low thermal drift
enabling long observation times. The results for
G 1 andG 2 plottedinFig.3Fasfunctionsoftem-
perature gave straight lines on the Arrhenius plot
for both processes over the entire temperature
range. The activation energies obtained wereE 1 ¼
0 : 57 T 0 :02 eV for the jumps in the triangles and
E 2 ¼ 0 : 63 T 0 :03 eV for the exchanges with CO.
The preexponential factors,G^01 ¼ 1011 :^4 T^0 :^4 s−^1
andG^02 ¼ 1011 :^1 T^0 :^7 s−^1 ,wereonlymarginallylower
than the expected 10^12 to 10^13 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 positionis 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 forE 1 of 0.57 eV. Thus,
the most likely path that the O atom takes within
acageisfromthehcpsiteviathefccsitetothe
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 de-
formed CO 2 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 theHenßet al.,Science 363 , 715–718 (2019) 15 February 2019 3of4
Fig. 3. Studies of O/CO exchange.(AandB) 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). (CandD) 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 distributionPt 0 ðx;yÞ, 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 ratesG 1 within the triangles, and
black dots indicate exchange ratesG 2 with CO.RESEARCH | REPORT
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