Oscillations in the N2O-H2 reaction over Ir(1 1 0). Route to chaos

Article abstract of DOI:10.1016/S0039-6028(03)00086-4

The study described in the present paper is focused on the N₂O-H₂ reaction on the Ir(1 1 0) surface and, in particular, on different kinds of oscillatory behaviour, including the route to chaos. Oscillations in rate were observed in the temperature range between 460 and 464 K, at a N₂O pressure of 1 × 10^-6 mbar with H₂/N₂O ratios close to 1. Upon minor changes in the H₂/N₂O ratio, a series of period doublings is observed, resulting finally in aperiodic behaviour.

Full text of DOI:10.1016/S0039-6028(03)00086-4

Surface Science 532–535 (2003) 96–102
www.elsevier.com/locate/susc
Oscillations in the N2O–H2 reaction over Ir(1 1 0). Route
to chaos
a
Sonia A.C. Carabineiro , Wibo D. van Noort , Bernard E. Nieuwenhuys
b
a,
*
ꢀ
a
Surface Science and Heterogeneous Catalysis Group, Leiden Institute of Chemistry, Leiden University,
Einsteinweg 55, 2333 CC Leiden, The Netherlands
Philips Research Leuven, Kapeldreef 75, B-3001 Leuven, Belgium
b
Abstract
The study described in the present paper is focused on the N2O–H2 reaction on the Ir(1 1 0) surface and, in par-
ticular, on different kinds of oscillatory behaviour, including the route to chaos. Oscillations in rate were observed in the
temperature range between 460 and 464 K, at a N2O pressure of 1 ꢀ 10ꢁ6 mbar with H2/N2O ratios close to 1. Upon
minor changes in the H2/N2O ratio, a series of period doublings is observed, resulting finally in aperiodic behaviour.
Ó 2003 Elsevier Science B.V. All rights reserved.
Keywords: Nitrogen oxides; Nitrogen molecule; Catalysis; Surface chemical reaction; Iridium; Models of surface chemical reactions
1. Introduction
scribed [19]. The present work deals with more
recent results obtained with this surface that indi-
cate different kinds of oscillatory behaviour, in-
cluding the route to chaos.
NO reduction reactions and its oscillatory be-
haviour have been studied in detail on several
metal surfaces because of its importance in auto-
motive catalysis [1–13]. However less attention has
been given to N2O, which is an important green-
house gas and it participates in cyclic reactions
that lead to ozone destruction [14–18]. In a pre-
vious paper the oscillatory behaviour of the N2O
reaction with H2 on the Ir(1 1 0) surface was de-
However, proving that a given time series re-
sults from chaotic, rather than noisy, irregular or
multi-periodic behaviour is far from trivial [4,20].
Chaotic behaviour is not just any kind of disorder;
it appears to be completely unpredictable (equiv-
alent to aperiodicity), but nevertheless obeys de-
terministic laws [4,20,21]. The experimental history
of the system is essential to distinguish between
chaotic and a noisy behaviour. The observation of
period doublings in the oscillatory signals (where a
single period is replaced by two, four, or eight
periods and more) is a strong indication that a
system is moving towards chaotic behaviour where
periodicity is no longer present. That is to say that
the system first starts to exhibit a one period one
amplitude/shape oscillation and will start to exhibit
* Corresponding author. Address: Faculty of Mathematics
and Sciences, Gorlaeus Laboratories, Leiden University, Ein-
steinweg 55, P.O. Box 9502, 2300 RA Leiden, The Netherlands.
Tel.: +31-71-527-4545; fax: +31-71-527-4451.
E-mail addresses: s.carabineiro@chem.leidenuniv.nl (S.A.C.
Carabineiro), b.nieuwe@chem.leidenuniv.nl (B.E. Nieuwen-
huys).
0039-6028/03/$ - see front matter Ó 2003 Elsevier Science B.V. All rights reserved.
doi:10.1016/S0039-6028(03)00086-4

S.A.C. Carabineiro et al. / Surface Science 532–535 (2003) 96–102
97
3. Results and discussion
one large and one small amplitude/shape oscilla-
tion, which will repeat every cycle. The same will
be true for the second period doubling, except that
then the system will have four different amplitudes/
shapes. Period doublings can continue until finally
a transition occurs to non-systematic variations in
amplitude/shape, a state of so called ‘‘deterministic
chaos’’. Moreover, very small perturbations are
sufficient to induce these doublings, and the in-
tensity of the chaotic signal is comparable to the
ones of previous period doublings, which excludes
the possibility that the system simply goes (gradu-
ally) into an extremely noisy regime.
In a previous paper, it was shown that in the
temperature range between 460 and 464 K, rate
oscillations were observed at a N2O pressure of
1 ꢀ 10ꢁ6 mbar, with H2/N2O ratios close to 1 [19].
The procedure to obtain those oscillations is de-
scribed in the same paper, and consists of heating
the crystal in N2O with a very low amount of H2,
from room temperature to 800 K and cool it down
to the temperature expected for oscillations and
then increase stepwise the pressure of H2 until
sustained oscillations start [19].
In the present work, oscillatory behaviour was
established at a constant temperature (461 K),
through the procedure described above. Once os-
cillations started, it was shown that a tentative
change in the H2 pressure resulted in loss of the
oscillations. In contrast, small changes in the
pressure of N2O (originally 1 ꢀ 10ꢁ6 mbar) re-
sulted in changes in the oscillatory behaviour.
These changes were very small (around 1%),
sometimes hardly noticeable by the ion gauge.
With an initial H2/N2O ratio of 1.4, upon those
slight changes in the N2O pressure, a series of
period doublings was observed, finally resulting in
aperiodic behaviour (Fig. 1). Fig. 1a shows a se-
quence of all kinds of behaviour observed: It
started with period-1 oscillations (I). Then upon
minor changes in the H2/N2O ratio, a series of
period doublings was obtained: period-2 (II), pe-
riod-4 (III) and period-8 (IV). Finally, another
minor change in the N2O pressure resulted in
aperiodic behaviour (V). During all those changes
the system took only a few periods to reach a new
‘‘steady-state’’ oscillatory behaviour (this inter-
mediate periods are not shown in Fig. 1a. Instead,
to make it simpler, gaps in pressure and the time
scale are shown). Those five types of oscillatory
behaviour (single period, period-2, period-4, peri-
od-8, aperiodic) are shown in detail in Fig. 1b–f,
respectively. The transition between oscillatory
states were shown to be completely reversible (by a
‘‘reverse’’ change in the N2O pressure), but only
between the periods 1, 2, 4 and 8. Once in the
aperiodic ‘‘zone’’, reversion was not possible any-
more. Moreover, these oscillations are very sensi-
tive to experimental factors and fade away easily,
Grassberger and Procaccia used correlation in-
tegrals that facilitate determination of the mini-
mum number of variables that are required to
describe the system mathematically, which can
give valuable information for determining a reac-
tion scheme [22–24]. Periodic and aperiodic oscil-
lations can be distinguished by examination of the
Fourier transformation of a measured time series
(i.e., the power spectrum) [1,2,4,21,25].
In high pressure studies, the chaotic behaviour
has been identified for massive metallic [26] and
supported catalysts [27,28]. In low pressure single
crystal surface studies, chaos has been demon-
strated only for a few systems: Pt(1 1 0)/CO þ O2
reaction [25,29], Pt(1 0 0)/NO þ H2 [1,2], Pt(1 0 0)/
NO þ NH3 [2–4], Pt(1 0 0)/NO þ CO [30–33]. In all
those systems, a transition from regular oscilla-
tions to chaos took place via the sequence of period
doublings described above, i.e., the Feigenbaum
scenario. By stepwise changing the pressure of one
of the reactants in these systems, the oscillations
undergo transitions from periodic to aperiodic (or
chaotic) behaviour through a sequence of period
doublings.
2. Experimental
Measurements were carried out in a UHV sys-
tem with facilities for LEED, AES and quadrupole
mass spectrometry. Further details of the experi-
mental set-up, preparation of the Ir(1 1 0) surface,
and the procedure used for the mass spectrometric
analysis of reactant and reactions are described
elsewhere [19].

98
S.A.C. Carabineiro et al. / Surface Science 532–535 (2003) 96–102
(I)
(II)
(III)
(IV)
(V)
1x10-6 N2O 9.9x10-7 N2O
9.8x10-7 N2O
9.7x10-7 N2O
9.6x10-7 N2O
N2
H2O
P=2.7 0.2min
P=1.2 0.2 min
10 20
P=5.0 0.2 min
P=9.7 0.2 min
aperiodic
0
0
10
0
10 20 30 0
10 20
30
40 50
0
10
20
30
40 50
60 70
Time (min)
(a)
7.1x10-8
6.9x10-8
6.7x10-8
6.5x10-8
7.0x10-8
6.8x10-8
6.6x10-8
6.4x10-8
(I)
P=1.2 0.2 min
(II)
P=2.7 0.2 min
0
0
0
2
4
6
8
10
0
2
4
6
8
10
(b)
Time (min)
Time (min)
(c)
7.0x10-8
6.8x10-8
6.6x10-8
6.4x10-8
6.2x10-8
7.0x10-8
6.8x10-8
6.6x10-8
6.4x10-8
(IV)
P=9.7 0.2 min
(III)
P=5.0 0.2 min
3
6
9
12
15
18
21
24
0
3
6
9
12
15
8
21
24
27
(d)
Time (min)
Time (min)
(e)
7.0x10-8
6.8x10-8
6.6x10-8
6.4x10-8
(V)
aperiodic
5
10
15
20
25
30
35
40
45
50
Time (min)
(f)
Fig. 1. Oscillations in the partial pressures of H2O and N2, at a starting N2O pressure of 1 ꢀ 10ꢁ6 mbar, at 461 K and a H2/N2O ratio
of 1.4. A sequence of all kinds of oscillatory behaviour found is shown (a). The oscillations show first: (I) single period behaviour (b),
followed by a series of period doublings: (II) period-2 (c), (III) period-4 (d), and (IV) period-8 (e), resulting finally in: (V) aperiodic
behaviour (f).
which is shown in the last part of Fig. 1a. Oscil-
latory behaviour thus ended spontaneously, start-
ing by a decrease in the amplitude of oscillations
and finally total loss of oscillations (a completely

S.A.C. Carabineiro et al. / Surface Science 532–535 (2003) 96–102
99
straight line). This made it impossible to obtain
more points for the aperiodic ‘‘zone’’. The oscil-
lations could only be triggered again by heating
the crystal up to 800 K and cooling down to the
desired temperature (around 460 K), as described
to obtain them [19]. This procedure could always
be used to recover oscillatory behaviour, if oscil-
lations faded away.
The correlation integrals were calculated ac-
cording to the method described by Grassberger
and Procaccia [22–24]. The results obtained by this
method were inconclusive, due to the limited
number of points that were available. Obtaining
more points is hampered by the difficulty to sustain
these oscillations for an extended period of time.
The Fourier-transform power spectra of the
time series were also obtained (Fig. 2). The power
spectrum of a period-1 oscillation revealed the
main frequency (Fig. 2a). In the power spectra of
the period-2 (Fig. 1b), period-4 (Fig. 1c) and pe-
riod-8 (not shown) oscillations, higher order fre-
quencies appeared. Finally, for the aperiodic
oscillations (Fig. 1d), several frequencies appeared
in the Fourier-transform power spectrum, giving it
a ‘‘noisy’’ appearance. Similar results were ob-
tained by other authors [1,2,4].
Period-3 and period-5 oscillations were ob-
tained by the same authors while searching for the
chaos in other reactions [1,2,4]. Here, this type of
oscillations was also observed, as is shown in Figs.
1.0
(a)
ω
1.0
(b)
ω
0.8
0.6
0.4
0.8
0.6
1/2 ω
0.4
0.2
0.2
0.0
0.0
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3
Frequency (Hz)
Frequency (Hz)
1.0
1.0
(c)
(d)
ω
1
2
/ ω
3
0.8
0.6
0.4
0.8
0.6
0.4
/ ω
5
3
/ ω
3
0.2
0.0
0.2
0.0
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5
2.0
1.5
0.0
0.5
1.0
2.5
3.0
Frequency (Hz)
Frequency (Hz)
Fig. 2. Power spectra of single period oscillations (a), period-2 (b), period-4 (c) and aperiodic oscillations (d) in the N2 partial pressure.

100
S.A.C. Carabineiro et al. / Surface Science 532–535 (2003) 96–102
9.45x10-7
9.35x10-7
9.25x10-7
9.15x10-7
9.05x10-7
8.95x10-7
-8
(a)
7.0x10
(a)
-8
6.9x10
-8
6.8x10
-8
6.7x10
-8
6.6x10
-8
P=5.0 0.2 min
6.5x10
P=2.7 0.2 min
0
2
4
6
8
10
12
14
0
2
4
6
8
Time (min)
Time (min)
1.0
0.8
0.6
0.4
1.0
(b)
ω
(b)
ω
1/3 ω
0.8
0.6
0.4
4/3 ω
2ω
2/3 ω
4ω
0.2
0.0
2ω
0.2
0.0
1.5 1.6 1.7
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4
Frequency (Hz)
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3
Frequency (Hz)
Fig. 4. Five period oscillations in the N2 partial pressure, at a
pressure of 9.75 ꢀ 10ꢁ7 mbar N2O, at 460 K, and a H2/N2O
ratio of 1.44 (a). The corresponding power spectrum is shown
(b).
Fig. 3. Three period oscillations in the N2O partial pressure, at
a pressure of 9.85 ꢀ 10ꢁ7 mbar N2O, at 460 K, and a H2/N2O
ratio of 1.42 (a). The corresponding power spectrum is shown
(b).
each period doubling increases, resulting in longer
cycles. For the aperiodic regime, no repeating cycle
was found, at least within the limits of the exper-
imental data. The observed period doublings, and
the extremely small pressure differences associated
with them, strongly indicate that a route to chaos
was observed, which is further emphasized by the
‘‘zone’’ where no periodicity was found.
Fig. 5 shows the first 8 min of oscillations at 463
K. It can be seen that N2O oscillates in counter-
phase with N2 and the maxima in H2O formation
are ‘‘delayed’’ compared to the maxima of N2 for-
mation. That relationship had already been pointed
out in the previous paper [19]. The following steps
were proposed as part of the mechanism:
3 and 4, for N2O and N2 pressures, respectively. It
can be observed that the total period of this kind
of oscillations (Figs. 3a and 4a) was not much
different from the period-2 and period-4 oscilla-
tions (Fig. 1c and d), that is 2.7 Æ 0.2 min and
5 Æ 0.2 min, respectively. However, by observation
of the power spectrum of period-2 (Fig. 2b) and
period-3 oscillations (Fig. 3b), it can be seen that
the main frequency changed from 0.55 to 0.25 Hz
and that other overtones appeared (2x and 4x).
As for the differences between the power spectra of
period-4 (Fig. 2c) and period-5 (Fig. 4b) oscilla-
tions, it can be seen that the main frequency is
maintained, however the frequency at 5=3x, dis-
appears and is replaced by another one at 4=3x.
The frequency at 2=3x becomes smaller and also
an additional overtone appears at 2x.
N2O ! N2ðgÞ þ Oads
ð1Þ
ð2Þ
ð3Þ
ðgÞ
H2ðgÞ ! 2Hads
The number of points needed to describe a
single period oscillation is 12. For the first period
doubling, the number of points needed to describe
a double period oscillatory cycle is 25. Moving
further, the amount of points needed to describe
Oads þ 2Hads ! H2O
ðgÞ
The model is based on different rates of Oads re-
moval by (3), formation of Oads by (1) and a large

S.A.C. Carabineiro et al. / Surface Science 532–535 (2003) 96–102
101
Research (lab. report no. UL 01-2-03) and of
NRSC-Catalysis. The project was supported by
the NRSC-Catalysis and partly by INTAS (99-
01882).
N2O
N2
H2O
References
[1] P.D. Cobden, J. Siera, B.E. Nieuwenhuys, J. Vac. Sci.
Technol. A. 10 (1992) 2487.
0
1
2
3
4
5
6
7
8
Time (min)
[2] J. Siera, Ph.D. Thesis, Leiden University, 1992.
[3] M.F.H. van Tol, J. Siera, P.D. Cobden, B.E. Nieuwenhuys,
Surf. Sci. 274 (1992) 63.
Fig. 5. Detail of oscillations in the partial pressures of N2O,
H2O and N2, at 463 K. N2O pressure of 1 ꢀ 10ꢁ6 mbar and H2/
N2O ratio of 0.9. The N2O conversion was 7%.
[4] M.F.H. van Tol, Ph.D. Thesis, Leiden University, 1993.
[5] D.Y. Zemlyanov, M.Yu. Smirnov, V.V. Gorodetskii, J.H.
Block, Surf. Sci. 329 (1995) 61.
[6] P.D. Cobden, N.M.H. Janssen, Y. van Breugel, B.E.
Nieuwenhuys, Faraday Discuss. 105 (1996) 57.
[7] N.M.H. Janssen, P.D. Cobden, B.E. Nieuwenhuys, J.
Phys.: Condens. Matter. 9 (1997) 1889.
effect of Oads on the N2O dissociation (1). A build-
up of atomic oxygen on the surface (observed by
AES), has a large effect on the rate of N2O dis-
sociation, until oxygen is released in the form of
water. Rate oscillations for the N2O–H2 reaction
are related to periodic transitions between O-rich
and O–poor surfaces [19]. Work is being carried
out in order to model these reactions [34]. It has
been shown that the unusual phase shift between
production rates of N2 and H2O (Fig. 5) is closely
connected with the character of lateral interactions
in the adlayer [34]. At a certain stage, hydrogen
removes the oxygen from the surface, resulting in
H2O production and affecting the dissociation of
N2O [19,34].
[8] C.A. de Wolf, B.E. Nieuwenhuys, A. Sasahara, K. Tanaka,
M.M. Slinko, M.Yu. Smirnov, Surf. Sci. 411 (1998) L904.
[9] C.A. de Wolf, B.E. Nieuwenhuys, M.M. Slinko, M.Yu.
Smirnov, Surf. Sci. 433–435 (1999) 63.
[10] B.E. Nieuwenhuys, Adv. Catal. 44 (1999) 259.
[11] P.D. Cobden, C.A. de Wolf, M.Yu. Smirnov, A. Makeev,
B.E. Nieuwenhuys, J. Molec. Catal. A: Chem. 158 (2000)
115.
[12] C.A. de Wolf, M.O. Hattink, B.E. Nieuwenhuys, Surf. Sci.
471 (2001) 114.
ꢀ
[13] T.V. de Bocarme, N. Kruse, Chaos 12 (2002) 118.
[14] J.N. Armor, Appl. Catal. B: Environ. 1 (1992) 221.
[15] F. Kapteijn, J. Rodriguez-Mirasol, J.A. Moulijn, Appl.
Catal. B: Environ. 9 (1996) 25.
[16] G. Centi, L. DallÕOlio, S. Perathoner, J. Catal. 192 (2000)
224.
4. Conclusions
[17] H. Horino, S. Liu, A. Hiratsuka, Y. Ohno, T. Matsushima,
Chem Phys. Lett. 341 (2001) 419.
Oscillations in rate were observed for the N2O–
H2 reaction over Ir(1 1 0), at a N2O pressure of
1 ꢀ 10ꢁ6 mbar, with H2/N2O ratios close to 1, from
460 to 464 K. Upon a little change in the H2/N2O
ratio, a series of period doublings is observed,
which result finally in aperiodic behaviour. These
observed period doublings and the extremely small
pressure differences associated with them are a
strong indication that a route to chaos for this
reaction was observed.
[18] H. Horino, S. Liu, M. Sano, S. Wako, A. Hiratsuka, Y.
Ohno, I. Kobal, T. Matsushima, Topics Catal. 18 (2002) 21.
[19] S.A. Carabineiro, B.E. Nieuwenhuys, Surf. Sci. 495 (2001) 1.
[20] R. Imbihl, G. Ertl, Chem. Rev. 95 (1995) 697.
[21] M.M. Slinko, N.I. Jaeger, Oscillating heterogeneous cata-
lytic systems, in: Studies in Surface Science and Catalysis,
Vol. 86, Elsevier Science BV, Amsterdam, The Nether-
lands, 1994, p. 249.
[22] P. Grassberger, I. Procaccia, Phys. Rev. Lett. 50 (1983)
364.
[23] P. Grassberger, I. Procaccia, Phys. Rev. A 28 (1983)
2591.
[24] P. Grassberger, I. Procaccia, Physica D9 (1983) 189.
[25] M. Eiswirth, K. Krischer, G. Ertl, Surf. Sci. 202 (1988)565.
[26] L.F. Razon, S.-M. Chang, R.A. Schmitz, Chem. Eng. Sci.
41 (1986) 1561.
Acknowledgements
This work has been done under the auspices of
NIOK, The Netherlands Institute for Catalysis
[27] H.U. Onken, E. Wocke, Ber. Bunsen-Ges. Phys. Chem. 90
(1986) 976.

102
S.A.C. Carabineiro et al. / Surface Science 532–535 (2003) 96–102
[28] M.M. Slinko, A.A. Ukharskii, N.V. Peskov, N.I. Jaeger,
Catal. Today 70 (2001) 341.
[31] G. Veser, R. Imbihl, J. Chem. Phys. 100 (1994) 8492.
[32] N. Khrustova, A.S. Mikhailov, R. Imbihl, J. Chem. Phys.
107 (1997) 2096.
[29] M. Eiswirth, T.-M. Kruel, G. Ertl, F.W. Schneider, Chem.
Phys. Lett. 193 (1992) 305.
[33] R. Imbihl, G. Veser, J. Vac. Sci. Technol. A. 12 (1994) 2170.
[34] N.V. Peskov, M.M. Slinko, S.A.C. Carabineiro, B.E.
Nieuwenhuys, Chem. Sustain. Develop., in press.
[30] G. Veser, F. Mertens, A.S. Mikhailov, R. Imbihl, Phys.
Rev. Lett. 71 (1993) 935.