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Yu. Suchorski et al. / Surface Science 454–456 (2000) 331–336
employed by Graham et al. to analyze spatiotem-
poral temperature patterns [10].
vacuum (UHV) system, is described elsewhere
[3,5,11].
In this paper we show that POD is also a very
useful tool for the analysis of FEM images. We
demonstrate this by applying POD to the fluctua-
tion-induced transitions that occur during catalytic
CO oxidation on a platinum field-emitter tip in
the vicinity of the (110) plane, as reported in an
earlier paper using ‘conventional’ analysis of FEM
images [6].
An atomically clean platinum surface as shown
by the inset in Fig. 1 was prepared by field evapora-
tion under visual control [12]. FEM images during
the reaction were recorded with a CCD video
camera and the recorded images were digitized
with 8 bit resolution. For POD typically about
1000 frames were taken, with a rectangular probing
window (7.5 nm×7.5 nm surface area correspond-
ing to a 15 pixel×15 pixel matrix) positioned in
the vicinity of the (110) plane. The resolution of
FIM (#0.2–0.3 nm) allowed a precise crystallo-
graphic identification of the probed area.
For a spatiotemporal signal, w(x, t), POD yields
an ‘optimal’ basis of orthogonal functions Y (x)
n
modes which represent the signal as
2
w(x, t)= ∑ A (t) · Y (x),
(1)
n
n
n=1
where A (t) are the time-dependent amplitudes of
n
3. Results and discussion
the corresponding basis functions. The basis func-
tions Y (x) are the eigenvectors of the equation
n
Catalytic CO oxidation exhibits two branches
which coexist in the bistable range: an inactive
ˆ
SY (x)=l Y (x),
(2)
n
n n
branch where a high CO coverage inhibits O
adsorption, poisoning the reaction, and a reactive
ˆ
with eigenvalues l and correlation matrix S, with
2
n
S =ꢀw(x , t)w(x , t)ꢁ representing the two-points
correlation functions, where x , x are the image
pixels and ꢀꢁ means time average. In our case,
w(x, t) represents the fluctuations of the FEM
ij
i
j
t
branch where a predominantly oxygen-covered
surface still allows CO to adsorb and react [14].
The difference in the local work function (WF)
between the oxygen-covered surface (high WF,
low emission) and the CO-covered and bare surface
(low WF, high emission) is reflected in the varia-
tions of the local FEM intensity; i.e., the oxygen-
covered surface appears dark and the
CO-covered/bare surface appears bright. In the
bistable regime one observes, upon variation of
the temperature, a hysteresis in the local FEM
intensity measured here in the vicinity of the (110)
plane (Fig. 1).
In a recent FEM study, fluctuation-driven trans-
itions between the two stable branches of catalytic
CO oxidation were observed in the vicinity of the
Pt(110) facet [6]. As experimental evidence for
such transitions, a bimodal (non-Gaussian) ampli-
tude distribution of the local fluctuations was
taken. Such a bimodal distribution was also repro-
duced in a Monte Carlo simulation with a system
size comparable to the area probed in the FEM
experiments [6]. In the following we study the
fluctuations with the same experimental parame-
ters and in the same crystallographic region as in
i
j
t
image intensity.
The amplitudes A (t) are obtained by projecting
n
the space–time evolution on the basis Y (x).
n
Effectively, POD is a method of data reduction
but, applied to complex spatiotemporal dynamics,
the resulting modes can be viewed as degrees of
freedom of the system. Each spatial mode together
with its corresponding amplitude capture a certain
percentage of the overall dynamics called its weight
or energy. Thus, when the spatiotemporal
dynamics are governed by only a few degrees of
freedom, only the first few modes are associated
with a high weight.
2. Experimental
The fluctuations were investigated on the apex
of a [100]-oriented platinum tip. The apparatus,
constructed on the basis of a standard field ion
microscope (FIM) in a bakeable, metal, ultrahigh
Suchorski
