We analyze a model for CO oxidation on surfaces which incorporates both rapid diffusion of adsorbed CO, and superlattice ordering of adsorbed immobile oxygen on a square lattice of adsorption sites. The superlattice ordering derives from an “eight-site adsorption rule,” wherein diatomic oxygen adsorbs dissociatively on diagonally adjacent empty sites, provided that none of the six additional neighboring sites are occupied by oxygen. A “hybrid” formalism is applied to implement the model. Highly mobile adsorbed CO is assumed randomly distributed on sites not occupied by oxygen (which is justified if one neglects CO–CO and CO–O adspecies interactions), and is thus treated within a mean-field framework. In contrast, the distribution of immobile adsorbed oxygen is treated within a lattice–gas framework. Exact master equations are presented for the model, together with some exact relationships for the coverages and reaction rate. A precise description of steady-state bifurcation behavior is provided utilizing both conventional and “constant-coverage ensemble” Monte Carlo simulations. This behavior is compared with predictions of a suitable analytic pair approximation derived from the master equations. The model exhibits the expected bistability, i.e., coexistence of highly reactive and relatively inactive states, which disappears at a cusp bifurcation. In addition, we show that the oxygen superlattice ordering produces a symmetry-breaking transition, and associated coarsening phenomena, not present in conventional Ziff–Gulari–Barshad-type reaction models.

1.
R.
Imbihl
and
G.
Ertl
,
Chem. Rev.
95
,
697
(
1995
).
2.
J.
Wintterlin
,
S.
Volkening
,
T. V. W.
Janssens
,
T.
Zambelli
, and
G.
Ertl
,
Science
278
,
1931
(
1997
).
3.
M.
Tammaro
and
J. W.
Evans
,
Surf. Sci. Lett.
395
,
L207
(
1998
).
4.
E. V.
Albano
,
Heterog. Chem. Rev.
3
,
389
(
1996
);
J. W.
Evans
and
M.
Sabella
,
Trends Stat. Phys.
1
,
107
(
1994
);
V. P.
Zhdanov
and
B.
Kasemo
,
Surf. Sci. Rep.
20
,
111
(
1994
);
J. W.
Evans
,
Langmuir
7
,
2514
(
1991
).
5.
W. H.
Weinberg
,
Annu. Rev. Phys. Chem.
34
,
217
(
1983
);
K.
Binder
and
D. P.
Landau
,
Adv. Chem. Phys.
26
,
91
(
1989
).
6.
J. W.
Evans
and
T. R.
Ray
,
Phys. Rev. E
50
,
4302
(
1994
).
7.
M.
Tammaro
,
M.
Sabella
, and
J. W.
Evans
,
J. Chem. Phys.
103
,
10277
(
1995
).
8.
M.
Tammaro
and
J. W.
Evans
,
J. Chem. Phys.
108
,
762
(
1998
).
9.
J. W. Evans and M. Tammaro, in Computer Simulation Studies in Condensed Matter Physics XI, edited by D. P. Landau and H. B. Schuettler (Springer, Berlin, 1998), pp. 103–117;
M.
Tammaro
and
J. W.
Evans
,
Phys. Rev. E
57
,
5087
(
1998
).
10.
M.
Silverberg
and
A.
Ben-Shaul
,
J. Chem. Phys.
87
,
3178
(
1989
);
H. C.
Kang
,
T. A.
Jachimowiski
, and
W. H.
Weinberg
,
J. Chem. Phys.
93
,
1418
(
1990
).
11.
G. A. Somorjai, Introduction to Surface Chemistry and Catalysis (Wiley, New York, 1994).
12.
Y.
Suchorski
,
J.
Beben
,
E. W.
James
,
J. W.
Evans
, and
R.
Imbihl
,
Phys. Rev. Lett.
82
,
1907
(
1999
).
13.
C. R.
Brundle
,
R. J.
Behm
, and
J. A.
Barker
,
J. Vac. Sci. Technol. A
2
,
1038
(
1984
).
14.
S.-L.
Chang
and
P. A.
Thiel
,
Phys. Rev. Lett.
59
,
296
(
1987
);
S.-L. Chang, D. E. Sanders, J. W. Evans, and P. A. Thiel, in The Structure of Surfaces II, Proceedings of ICSOS II, edited by J. F. van der Veen and M. A. Van Hove (Springer, Berlin, 1988), pp. 231–237.
15.
J. W.
Evans
,
J. Chem. Phys.
87
,
3038
(
1987
);
J. W.
Evans
and
D. E.
Sanders
,
Phys. Rev. B
39
,
1587
(
1989
).
16.
R. M.
Ziff
,
E.
Gulari
, and
Y.
Barshad
,
Phys. Rev. Lett.
56
,
2553
(
1986
).
17.
V. P.
Zhdanov
and
B.
Kasemo
,
Surf. Sci.
412/413
,
527
(
1998
).
18.
F. H.
Ree
and
D. A.
Chesnut
,
J. Chem. Phys.
45
,
3983
(
1966
).
19.
J. W.
Evans
,
Rev. Mod. Phys.
65
,
1281
(
1993
).
20.
The density of “internal defects” or “holes,” H, in c(2×2) domains is given by
21.
Lattice–gas reaction models with finite adspecies hop rates can have only one true stable steady state, perhaps coexisting with a metastable steady state with a finite lifetime.
22.
R. M.
Ziff
and
B. J.
Brosilow
,
Phys. Rev. A
46
,
4630
(
1992
).
23.
E. W. James, D.-J. Liu, and J. W. Evans (unpublished).
24.
If only one sublattice is populated, except for randomly distributed “defects,” then the probability on the LHS of Eq. (6) equals the average of (1−[A]−2[B])2 and (1−[A])2(1−2[B])6. These terms correspond to choosing the central empty sites on the B-populated and B-unpopulated sublattices, respectively. The result differs from that obtained via Eq. (9), but is still inaccurate.
25.
J. W.
Evans
,
J. Chem. Phys.
98
,
2463
(
1993
).
26.
S. M.
Allen
and
J. W.
Cahn
,
Acta Metall.
27
,
1085
(
1979
);
I. M.
Lifshitz
,
Sov. Phys. JETP
15
,
939
(
1962
).
27.
M. A. Van Hove, W. H. Weinberg, and C.-M. Chan, Low-Energy Electron Diffraction (Springer, Berlin, 1986).
28.
A.-L. Barabasi and H. E. Stanley, Fractal Concepts in Surface Growth (Cambridge University Press, Cambridge, 1995).
29.
R. H.
Goodman
,
D. S.
Graff
,
L. M.
Sander
,
P.
Lerox-Hugon
, and
E.
Clement
,
Phys. Rev. E
52
,
5904
(
1995
);
H. C.
Kang
and
W. H.
Weinberg
,
Phys. Rev. E
47
,
1604
(
1993
);
H. C.
Kang
and
W. H.
Weinberg
,
Phys. Rev. E
48
,
3464
(
1994
).
30.
Let Q+ denote the probability that a dimer does not adsorb when a B+ is removed from the + sublattice (cf. Sec. V C). Then, the rate of loss of B+ due to monomer desorption equals Q+[B+], and the rate of gain due to dimer adsorption equals (1−Q+)[B+]. Thus, one has d/dt [B+]=(1−Q+)[B+]−Q+[B+]=(1−2Q+)[B+]. This is the lowest order equation in an exact hierarchy.
31.
V. Privman, in Annual Reviews of Computational Physics III, edited by D. Stauffer (World Scientific, Singapore, 1995).
32.
E. W. James, D.-J. Liu, and J. W. Evans, Colloids Surf. A (to be published).
33.
D.-J.
Liu
and
J. W.
Evans
,
Bull. Am. Phys. Soc.
44
,
1387
(
1999
).
This content is only available via PDF.
You do not currently have access to this content.