Table Of ContentTHE CHEMICAL PHYSICS OF SOLID SURFACES
Volume 1
CLEAN SOLID SURFACES
Volume 2
ADSORPTION AT SOLID SURFACES
Volume 3
CHEMISORPTION SYSTEMS
Volume 4
FUNDAMENTAL STUDIES OF HETEROGENEOUS CATALYSIS
Volume 5
SURFACE PROPERTIES OF ELECTRONIC MATERIALS
Volume 6
COADSORPTION, PROMOTERS AND POISONS
Volume 7
PHASE TRANSITIONS AND ADSORBATE
RESTRUCTURING AT METAL SURFACES
THE CHEMICAL PHYSICS
OF SOLID SURFACES
EDITED BY
D.A. KING
B.Sc, Ph.D. (Rand), Sc.D. (East Anglia), F.R.S.
1920 Professor of Physical Chemistry,
University of Cambridge
AND
D.P.WOODRUFF
B.Sc. (Bristol), Ph.D., D.Sc (Warwick)
Professor of Physics,
University of Warwick
VOLUME 7
P H A SE T R A N S I T I O NS A ND
A D S O R B A TE R E S T R U C T U R I NG
AT M E T AL S U R F A C ES
ELSEVIER
AMSTERDAM - LONDON - NEW YORK - TOKYO
1994
ELSEVIER SCIENCE B.V.
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ISBN 0-444-81924-X (Vol. 7)
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ν
Contributors to Volume 7
P. BAK Department of Physics,
Brookhaven National Laboratory,
Upton, NY 11973, U.S.A.
C.J. BARNES School of Chemical Sciences,
Dublin City University,
Glasnevin, Dublin 9, Ireland
F. BESENBACHER Institute of Physics and Astronomy,
Aarhus University,
DK-8000 Aarhus C, Denmark
J.C. CAMPUZANO Department of Physics,
University of Illinois at Chicago,
P.O. Box 4348,
Chicago, IL 60680, U.S.A.
and
Materials Science Division,
Argonne National Laboratory,
9700 S. Cass Ave.,
Argonne, IL 60439, U.S.A.
N. DORAISWAMY Department of Materials Science and Engineering,
Northwestern University,
Evanston, IL 60208, U.S.A.
J.W.M. FRENKEN FOM-Institute for Atomic and Molecular Physics,
Kruislaan 407,
1098 SJ Amsterdam, The Netherlands
J. JUPILLE Laboratoire CNRS-Saint-Gobain 'Surface du
Verre et Interfaces',
B.P. 135,
93303 Aubervilliers Cedex, France
K. KERN Institut de Physique Experimental,
EPF-Lausanne,
CH-1015 Lausanne, Switzerland
D.A. KING Department of Chemistry,
University of Cambridge,
Lensfield Road,
Cambridge, CB2 1EW, U.K.
vi
A.C. LEVI Dipartimento di Fisica,
Universita di Genova,
16146 Genova, Italy
R.M. LYNDEN-BELL Department of Chemistry,
University of Cambridge,
Lensfield Road,
Cambridge, CB2 1EW, U.K.
L.D. MARKS Department of Materials Science and Engineering,
Northwestern University,
Evanston, IL 60208, U.S.A.
A.G. NAUMOVETS Institute of Physics,
Academy of Sciences of the Ukraine,
Prospect Nauki 46, UA-252650 Kiev 28, Ukraine
M. DEN NIJS Department of Physics,
FM-15, University of Washington,
Seattle, WA 98195, U.S.A.
M. PACZUSKI Department of Physics,
Brookhaven National Laboratory,
Upton, NY 11973, U.S.A.
H.M. VAN PINXSTEREN FOM-Institute for Atomic and Molecular Physics,
Kruislaan 407,
1098 SJ Amsterdam, The Netherlands
I. STENSGAARD Institute of Physics and Astronomy,
Aarhus University,
DK-8000 Aarhus C, Denmark
M.C. TRINGIDES Department of Physics and Astronomy,
Ames Laboratory, Iowa State University,
Ames, IA 50011, U.S.A.
D.P. WOODRUFF Department of Physics,
University of Warwick,
Coventry, CV4 7AL, U.K.
vii
Preface
Our objective in initiating this series of volumes, which began appearing in
1980, was to provide an in-depth review of advances made in understanding
key aspects of surface chemistry and physics through the application of new
techniques to the study of well-defined surfaces. Since that time the field of
surface science has greatly matured, and further important techniques,
particularly scanning probe microscopies, have been successfully assimilated
into the applications armoury of the surface scientist.
The present volume is a series of timely reviews by many of the current
experts in the field of phase transitions and adsorbate-induced surface
restructuring. No aspect of the science of solid surfaces can be fully
understood without accounting for the structural diversity of surfaces, now
revealed in atomic detail by techniques based on diffraction and scanning
probe microscopies. For example, it is now clear to those working in
heterogeneous catalysis that adsorbate-induced restructuring of surfaces can
play a crititcal role in phenomena such as bistability, kinetic oscillations, and
promotion and poisoning. Structural transitions at surfaces can also play a key
role in determining the electronic properties of surfaces, reviewed in volume
5.
The first chapter in this volume, by Bak and Paczuski, provides an
overview of the principles involved in phase transitions in two dimensions.
In subsequent chapters the most thoroughly characterised clean surface phase
transitions are reviewed in detail: on W{100}, by Jupille and King; and on
Au{110}, by Campuzano. Transitions at clean surfaces associated with
roughening and wetting phenomena have been widely studied in recent years
and are covered in chapters by den Nijs, Frenken and Pinxteren, Kern, and
Levi, covering both experimental and theoretical work in some detail.
Growth kinetics and surface self diffusion are given an experimental appraisal
by Tringides and a theoretical analysis by Lynden-Bell. Two dimensional
phase transitions in alkali metal adlayers have been well characterized, and are
reviewed by Naumovets; while adsorbate-induced restructuring of f.c.c. metal
{100} and {110} surfaces are reviewed, respectively, by Woodruff and by
Barnes. The detailed information available on adsorbate-induced
restructuring of metal surfaces by scanning probe microscopy is reviewed by
Besenbacher and Stensgaard. Finally, Marks and Doraiswamy provide a
timely review of structural transitions in small metal particles. The length of
this volume is a reflection of the tremendous advances made in this field over
the past decade.
D.A. King
April 1994 D.P. Woodruff
1
Chapter 1
Principles of Phase Transitions
in Two-dimensional Systems
Per Bak and Maya Paczuski
Department of Physics, Brookhaven National Laboratory, Upton, NY
1 INTRODUCTION
Experiments probing phase transitions on surfaces can provide
'ideal' examples for testing fundamental theories of two dimensional (2D)
physics. Based on symmetry principles, these theories make strong pre
dictions for 2D critical phenomena. In recent years, investigations of the
structure and phase behavior of clean metal surfaces and adsorbates on
metal surfaces at elevated temperatures have provided model systems
for comparison with theory. This chapter focuses on critical phenom
ena which may be observed on high symmetry metal surfaces including
order-disorder and commensurate-incommensurate (CT) transitions, as
well as more general surface reconstruction. These pnase transitions are
driven by fluctuations of in-plane positional order in the top surface layer.
Thus, a metal surface can be treated as a strictly 2D layer independent
of the 3D bulk properties.
However, the thermodynamic behavior of clean metal surfaces differs
from that of conventional epitaxial layer systems, e.g. adsorbed mono
layers of noble gases on graphite, via the presence of height fluctuations
(steps) and the possibility of thermal roughening. In this case, the im
portant excitations are out of plane undulations, involving multiple crys
talline layers under a metal facet. Above the roughening transition, the
width of the interface region over which the height of different parts of
the facet varies, diverges. Since the dominant fluctuations near a rough
ening transition point are mediated by surface tension; the physics is
again two dimensional. Depending on the symmetries of the excitations,
in plane fluctuations may be independent or coupled to out of plane un
dulations. In the former case, the order parameters for roughening and
e.g. an order-disorder transition are decoupled, so that the two tran
sition, if they occur, do so independently. In the latter case, however,
the order parameters are coupled and new types of roughening transi
tions may occur. Clean metal surfaces differ also from epitaxial layers
2
by the possibility of different symmetries present and stronger couplings
between surface fluctuations and the substrate, giving rise to long range
interactions in the surface or multiple layer melting. These differences
may also affect the critical behavior.
The two dimensional Ising and XY magnetic phase transitions are
prototypes capturing the essential symmetries of many surface phase
transitions. The up-down symmetry of the Ising model reflects the dom
inant order associated with lattice gas melting of a surface. A striking
example of 2D Ising behavior is the 2x1 'missing row 5 reconstruction of
metal surfaces, including Au(llO) and Pt(llO). In the second section, we
describe the mapping of the 'missing row' surface to the Ising model and
the critical behavior. This discussion is illustrative, introducing funda
mental concepts. In section three, we consider CI transitions generally:
in the uniaxial case as variants of the 2D XY model, and in the isotropic
case as a 2D elastic network. In both cases, the phase transitions are me
diated by topological defects, or solitons, which cause divergences in the
elastic constants. A brief discussion of the elastic theory for solitons and
the singularities associated with their fluctuations is given. Roughening
of crystalline facets is described by solid-on-solid (SOS) models, and the
roughening transition is simply an inverted XY transition, as shown in
section 4. Finally, novel roughening transitions coupling both the Ising
and XY order parameter fluctuations are discussed.
2 SURFACE RECONSTRUCTIONS
2.1 Au and Pt 2x1 reconstruction: the mystery of the missing row.
When clean (110) surfaces of Pt and Au are cooled from high tem
peratures, X-ray and LEED measurements show the emergence of ex
tra diffraction peaks at half-integer positions [l],[2],[3],[4l. Although at
low temperatures the diffraction pattern is consistent with a 2x1 surface
structure where every second row is missing (see Fig. lY the high tem
perature pattern indicates a complete surface layer. Tnus, where does
the 'missing row' go?
The apparent paradox originates from a misconception about the
nature of the phase transition. It is not a transition between two ordered
phases (one with a missing row, and the other with the missing row
restored) as it would be at zero temperature. It is an order-disorder
transition, driven by entropy and characterized by breaking an even-odd
symmetry [5]. In the low temperature structure, atoms in the top layer
preferentially occupy either the even or the odd rows. While above the
transition temperature, these surface atoms occupy both the even and
odd rows with equal probability. In fact, the answer to the paradox is:
there is no 'missing row'!
3
Figure 1. Missing row structure of the Au (110) surface.
A more detailed theory of the transition is given for the skeptical
reader. For clarity, we invoke a simple lattice gas model to describe the
behavior of the surface atoms near the phase transition. In this model,
it is assumed that atoms in the surface layer can occupy sites of a
regular (LxL) rectangular lattice (ideal (110) surfaces of Au and Pt have
rectangular symmetry). To each site, a variable nij is assigned; n;j = 1
if a site is occupied, and riij = 0 if it is empty. The energy, E, of a
configuration is given a simple form
Ε = - (Σ ii,jij+i + Knijn j + μη^) . (1.1)
Kn n 2 i+1
The constant K\ is positive, favoring occupied sites to have their nearest
neighbors within the same row also occupied. K is negative; so that
2
occupied sites prefer vacancies in neighboring rows. The surface chemical
potential, μ, can be positive or negative. It affects the density of occupied
sites on the surface, and is important in interpreting experiments.
This model is manifestly equivalent to an Ising model in a magnetic
field, with ferromagnetic interactions within a row, and antiferromag-
netic interactions between rows. A magnetic spin variable Sij — ±1 is
associated with each variable riij = (1 + Sij)/2. By direct substitution
4
into Eq. (1.1), the energy for a given configuration of spin variables
becomes
Ε = - I 2_\ + hSijSi+ij + HS{j I , (1.2)
where the exchange constants J\ = Ki/4 > 0, = Κ/4 < 0, and the
2
magnetic field Η = (Κχ + Κ2 + μ)/2. As long as \H\ is not too large , a
low temperature phase exists with even (odd) rows of mostly plus spins
alternating with odd (even) rows of mostly minus spins. It is useful to
define an order parameter, M, distinguishing between the ordered and
disordered phases;
(1.3)
The order parameter is positive if the even rows are preferentially oc
cupied, negative if the odd rows are preferentially occupied, and zero if
both types of rows are occupied with equal probability. Noting that the
energy in Eq.(1.2) is invariant under interchanging even and odd rows, at
the order-disorder phase transition an even-odd symmetry of the system
is spontaneously broken. The order parameter reflects this symmetry
breaking since Μ —> —Μ under interchange of even and odd rows. Thus
above the transition temperature, Μ = 0, and below M / 0.
At zero temperature, the phase behavior is determined by the
ground state energy, and for \H\ < —2J the ground state is antifer-
2
romagnetic, with every spin in an even row, 5i_ ven,j = 1 (say), and
e
every spin in an odd row 5i_ dd,j = — 1; so that Μ = 1. As the tem
0
perature is raised, small clusters, where the order parameter is negative,
emerge in the + region. Here, the rows are out of phase, as shown in
Fig. 2.
Clusters of spins in the wrong direction are the fundamental ex
citations out of the ground state. Although a positive surface energy,
coming from the unfavorable interactions at the boundary of a cluster,
inhibits these fluctuations, the clusters add entropy and become more
likely at higher temperature, reducing the size of the order parameter.
Eventually, as the temperature is raised to the critical temperature, T ,
c
cluster as large as the system size occur. In this case, there are as many
+ areas as - areas, and the system disorders. For a macroscopic system,
the length scale ξ characterizing the size of the clusters diverges at T .
c
Fig. 3 shows a configuration obtained by Monte Carlo simulation for the
Au (110) surface, slightly above T.
c
