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
takenat300K(movieS1)showasingleOatom
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 ad-
sorption 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 be-
cause 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.
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 con-
nected to a neighboring triangle by (mostly) a
single line of the same length. An obvious ex-
planation 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.
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 ex-
change of the O atom with the marked CO mol-
ecule. 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.
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 hoppingevents 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~t 0 ðnÞ¼ðGt^0 Þn
n!
eGt^0 ð 1 Þwhere~Pt 0 ðnÞis the probability that an O atom
jumpsntimes during the time periodt 0 .t 0 is
thetimeforanSTMimage,andGis the hop-
ping frequency, defined asG¼ 1 =hti,where
htiis 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 sur-
rounding CO molecules from above (“exchange
jumps”), along one of the four black arrows. Ex-
change 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.~Pt 0 ðn 1 ;n 2 Þis then the probability that
within the time periodt 0 ,theOatomjumps
n 1 times within the cage andn 2 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
~Pt 0 ðn 1 ;n 2 Þis given by the product of two Poisson
distributionsP~t 0 ðn 1 ;n 2 Þ¼ðG^1 t^0 Þn 1
n 1!eG^1 t^0
ðG 2 t 0 Þn^2
n 2!eG^2 t^0 ð 2 ÞG 1 andG 2 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~t 0 ðn 1 ;n 2 Þis
not a directly measurable quantity. What is
measurable is the displacement distribution
Pt 0 ðx;yÞ, the probability that a particle located at
x=0andy=0inoneframeisfoundonasite
with displacement coordinatesxandyin the fol-
lowing frame.Pt 0 ðx;yÞis related to~Pt 0 ðn 1 ;n 2 ÞbyPt 0 ðx;yÞ¼X∞n 1 ¼ 0Xn 2 ¼ 0∞
~Pt 0 ðn 1 ;n 2 Þwn 1 ;n 2 ðx;yÞð 3 Þwn 1 ;n 2 ðx;yÞis the probability that the O atom can
travel fromx=0,y= 0 to the coordinatesxandy
by a given combination ofn 1 triangle jumps and
n 2 exchange jumps. For example, for the starting
configuration of Fig. 3E, inset,wn 1 ;n 2 ðx;yÞto land
on one of the two other triangle positions by the
combinationn 1 =1,n 2 = 0 is 1/2 each. For general
n 1 andn 2 combinations, thewn 1 ;n 2 values are ob-
tained 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 meth-
ods). Multiplication byP~t 0 ðn 1 ;n 2 Þand adding
overalln 1 andn 2 gives the theoretical displace-
ment distributionPt 0 ðx;yÞ.ForthetemperatureHenßet al.,Science 363 , 715–718 (2019) 15 February 2019 2of4
Fig. 2. Trajectory of
an O atom through
the CO layer on
Ru(0001).The
series was con-
structed from 1512
consecutive frames
of an STM movie
(273 K, 12 frames s−^1 ,
Vt=–0.7 V,It=3nA).
The positions of the
Oatomintheindi-
vidual frames are
connected by lines,
and frame numbers
are color-coded.RESEARCH | REPORT
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