Table Of ContentFilms on
Solid Surfaces
The Physics and Chemistry
of Physical Adsorption
J. G. DASH
Department of Physics
University of Washington
Seattle, Washington
ACADEMIC PRESS New York San Francisco London 1975
A Subsidiary of Harcourt Brace Jovanovich, Publishers
COPYRIGHT © 1975, BY ACADEMIC PRESS, INC.
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Library of Congress Cataloging in Publication Data
Dash, J G (date)
Films on solid surfaces.
Bibliography: p.
Includes index.
1. Adsorption. 2 Thin films. 3. Surface chem-
istry. I. Title.
QC182.D26 533'.1 74-30814
ISBN 0-12-203350-7
PRINTED IN THE UNITED STATES OF AMERICA
Preface
This book was written for the community of physical and biological
scientists now working in fields involving physical adsorption and sur-
face science. I have tried to cover most topics of contemporary interest,
some by detailed treatment and others less extensively, but I have at
least noted references to more complete accounts and guides to the
current literature. The chapters are ordered so that the book might be
used for graduate study following the plan of a course given at the
University of Washington in 1973.
The subject is introduced by chapters on the atomic nature of
physical adsorption and the states of single adsorbed atoms. There is a
review of experimental methods for studying solid surfaces and films,
and a discussion of substrate preparation. The equilibrium thermo-
dynamics of surface films is given an extensive treatment and is de-
veloped from general statistical principles. Four chapters are given
over to the various states of films and their phase transitions. The
complications caused by substrate heterogeneity are discussed as a
particularly challenging and important feature of all real films. Finally,
there is a review of thin film superfluidity, with its still largely un-
answered questions.
ix
Acknowledgments
Many people helped to write this book, and I wish to indicate here
my deep feelings of appreciation for all their contributions. The writ-
ing project was planned in collaboration with Frederick J. Milford.
Although not able to continue due to the pressure of other commit-
ments, he shares in the credit for its completion since I might never
have begun it alone, I feel a great debt to my former students David L.
Goodstein, G. Alec Stewart, Michael Bretz, and John A. Herb, who
taught me more than I taught them. I have been fortunate to have as
colleagues Michael Schick and Oscar E. Vilches, who with their in-
dependent talents in our common areas of interest have made our
group a more exciting and rewarding place in which to work. It is a
pleasure and an honor to thank Rudolf E. Peierls, who showed me how
to think about films, and who encouraged me to write this book.
Permission to reprint various figures and tables has been generously
granted by The American Chemical Society, The American Institute of
Physics, Marcel Dekker, Inc., North-Holland Publishing Co., Taylor
and Francis, Ltd., and John Wiley and Sons, Inc. I am grateful to
L. L. Ban, J. K. Kjems, A. J. Melmed, and J. M. Thomas for making
available photographic prints suitable for reproduction.
And finally, I thank my wife Joan, who has helped make my world
more than two-dimensional.
xi
1. Motivation
The study of thin surface films involves several fields of fundamental
and practical importance—surface science, statistical thermodynamics,
physics of condensed matter, and the experimental arts. Significant
developments in each of these separate disciplines are now bringing
about a revolution in film studies comparable to the advances in solid
state physics of the 1930s. It is now possible to make detailed macro-
scopic and microscopic measurements of films on well-characterized
solid surfaces, obtaining results that are highly reproducible from day
to day in the same apparatus, and more significantly, in several different
laboratories, and to correlate these results with the predictions of
sophisticated theoretical models. Initial successes have encouraged
more activity; fresh theoretical insights have stimulated new experi-
ments, and reliable precision measurements have led to more realistic
models. These advances have attracted new investigators into the
study of films, bringing novel approaches and techniques, both experi-
mental and theoretical, helping to generate an overall sense of en-
thusiasm and discovery.
What we find in the films is a rich succession of surface phases, some
of which resemble two-dimensional gases, liquids, and solids, together
with others that have no analogues in ordinary bulk matter. All are
important proving grounds for theory. They provide physical examples
of several theoretical models which were postulated many years ago
but which until recently could not be subjected to experimental tests.
1
2 1. MOTIVATION
Much of the current interest has to do with the influence of dimen-
sionality on long-range order. It has long been accepted that in 2D
matter there can be no perfectly ordered states or structures at any
finite temperature, which had been taken to imply that perfect 2D
crystals, magnets, superconductors, and superfluids cannot exist. These
sweeping implications have recently been called into question, and the
connections among various forms of long-range order and superfluidity,
magnetism, and crystallinity are now subjects for experimental and
theoretical investigation. Besides the question of long-range order, the
film phases can be used as novel systems to test ideas about conven-
tional matter. Theoretical techniques previously developed for bulk
matter have recently been modified to 2D systems, and applied to
several examples of monolayer gases, liquids, and solids. These tests
have been strikingly successful in some cases and in others have sug-
gested new paths toward the understanding of bulk matter. There also
are epitaxial phases in monolayers, in which the substrate structure
impresses some of its own regularity on the structure of the film. They
bear some resemblance to certain theoretical models which have been
studied intensively in connection with the phase transitions of bulk
matter. The Ising model of magnetism and the lattice gas model of
condensation occupy positions of great importance in the theory of
phase transitions in that exact solutions have been found for several
simple cases. Certain film phases show remarkable similarities to these
solutions in limited regimes but disagree in others, suggesting further
exploration of both theory and experiment.
The special regimes displayed by adsorbed films are not limited to
monolayer phases. Multilayers are in some ways more interesting and
complex than either the monolayer phases or bulk matter, for they
have the complications of both extremes. In multilayers there are the
interactions of bulk matter together with the strong gradients due to
substrate fields. In several systems there is evidence of distinctive
behavior of the individual layers of a two-layer and even three-layer
film. With greater substrate uniformity and lower temperatures it
should be possible to resolve the layers of even thicker films. These
results suggest some reformulation of the conventional thermodyna-
mics of films and interfaces reaching down to fundamentals, even to
the operative definitions of "phase."
1. MOTIVATION 3
The increased resolution of modern studies brings about a heightened
interest in substrate properties. Sophisticated theoretical models re-
quire increasingly detailed substrate characterization, and these theo-
ries are often subject to close comparison with experimental results.
This new discrimination not only requires a far higher degree of
substrate characterization than before, but permits physical adsorption
to be developed into a more sensitive and searching probe of surface
properties. Adsorption has been a most useful tool for studying sur-
faces, primarily used for gauging the effective areas and average attrac-
tive potentials of powders and porous bodies. But adsorption can yield
far more information in favorable instances. Current models involve
detailed knowledge of site symmetries and potentials, substrate phonon
spectra, surface electronic densities, and adsorption heterogeneity.
Heterogeneity can take many forms, involving variation in any of the
substrate properties that affect the films. The spatial distribution of
the heterogeneity can vary in magnitude, scale, and pattern. These
variations could be described by a kind of topographic map of the
surface, in which the altitude of the usual map is the substrate property
under question. The topographies that characterize different surfaces
reflect substrate treatment history and current condition, and the
possible patterns can rival ordinary topographical maps in their variety
of design and scale. Physical adsorption can in at least two thermo-
dynamic regimes give some measure of these variations, perhaps even-
tually leading to a complete tracing out of the surface property.
The preceding description of modern physisorption focuses on funda-
mental questions without regard to their practical implications. How-
ever, we recognize that a certain degree of stimulation comes from the
growing realization that surface science is extremely important to the
needs of society. One can recognize several areas of application: adhe-
sion, biological membranes, composite materials, heterogeneous cataly-
sis, corrosion, fracture, lubrication, and thin film electronics. Each of
these contains a strong element of surface science. They depend on the
results of fundamental studies for their continued progress, they supply
fresh problems and materials, and encourage the special efforts and
satisfaction that can come with social relevance.
2. The Atomic Basis
of Adsorption
2.1 THE ROLE OF THE SUBSTRATE IN
PHYSISORPTION
Physical adsorption deals with the behavior of atoms on weakly
attracting surfaces of bulk liquids and solids. The attraction is a general
phenomenon, which is due to the fluctuating electric dipole moments
mutually induced by all neutral materials. These interactions are in
contrast to the stronger and more specific bonding involved in chemical
adsorption. In physisorption the atoms and the surface are not strongly
perturbed from their isolated states; this fact and the lack of specificity
might suggest that the properties of physisorbed films can be under-
stood without any detailed knowledge of the nature of the adsorbing
surface. But this is not the case, for the interactions between the atoms
and the substrate have to be judged relative to the interactions between
the atoms in the film, and on this scale they are extremely important.
Therefore the study of adsorbed films rests upon the understanding of
the properties of the bare substrates and of their interactions with
individual atoms.
The characterization of surfaces has advanced greatly within the
past two or three decades, largely through the introduction and widen-
ing application of new experimental techniques, as indicated in Chap-
ter 3. With these probes it is possible to determine, in principle at
5
6 2. THE ATOMIC BASIS OF ADSORPTION
least, virtually all of the properties of an experimental solid surface:
the structure of the topmost layers, the amplitudes of the atomic
vibrations, its perfection with respect to chemical impurities and
crystalline order, and a good deal about the electronic structure.
Much of the new information comes as no surprise. The fact that
the surface atomic structure is related to that of the bulk, that conduc-
tion electron distributions extend beyond the ion cores, and that most
real surfaces are chemically and crystallographically imperfect are
easily accepted. The main impact is in the depth and details of under-
standing of specific surfaces and gas-surface combinations. In many
cases it is no longer necessary to invent a theoretical model for a
substrate-gas system, since it is now more likely that a similar system,
explored by means of one of the new microscopic techniques, is known
to have a definite set of physical parameters. Therefore, as more
microscopic results are obtained there will be greater interest in quanti-
tative models, where substrate parameters can be introduced at the
outset of the theoretical study of films. Nevertheless, current models of
surfaces, including the most elementary, will continue to be useful.
This is because there are certain domains of interest in which finer
details of the substrate are relatively unimportant. For example, where
the primary focus is on film properties that are largely determined by
the interactions of the atoms when they are in a restricted geometry, it
may be an unnecessary complication to include the periodic potential
of the adatom-surface interactions. But with a developing appreciation
for the properties of real surfaces, it will become increasingly important
to justify the application of any simplified model to an actual experi-
mental system.
The more general characteristics of substrates are contained within
the several idealizations listed below. These categories are given
roughly in order of increasing complexity; as mentioned earlier, each
is still useful in modern theory. Detailed considerations bearing on the
various models are taken up in subsequent sections of this chapter.
Models of solid surfaces
(i) Plane boundary A smooth, inert, mathematical surface; the
simplest model of a real substrate. Although this idealization is not
2.1 THE ROLE OF THE SUBSTRATE IN PHYSISORPTION 7
adequate in studies of very thin films, it can be a reasonable approxi-
mation in theories of surface effects on bulk phases, e.g., questions of
restricted geometry.
(ii) Attracting plane The sine qua non of physical adsorption is
a surface-normal attraction between substrate and adsorbate atoms.
This category contains two important subgroups.
(a) Adhesion The assumption of adhesion without explicit ac-
count of the magnitude and range of the attraction forms the basis for
the 2D abstraction of monolayer films. In this model one ignores
surface-normal excitation of the film and of the vapor phase. For
thicker films adhesion is assumed but gradients in the film are ne-
glected; in such "slab" models the surface acts only as a boundary
condition on the film.
(b) Explicit attractive forces More realistic models of surface-
normal forces are necessary when considering film-vapor equilibrium
and multilayer formation. Variations of film properties with distance
from the surface may become important in real systems, but are ne-
glected in the lowest order approximation. When the attractive inter-
action is relatively strong in comparison to thermal energies this model
approaches the 2D abstraction for monolayers.
(iii) Adsorption sites As a first approximation to a structured
surface, the substrate is treated as an array of potential wells or adsorp-
tion sites, each site capable of capturing a single atom. The internal
energy structure of the sites may be ignored and the potential energy
of the adatom taken to be a definite value with respect to the gas. This
category forms the basis for the Langmuir theory of adsorption and for
theories of 2D lattice gases and their ordering transitions.
(iv) Structured substrate The atomic texture of the surface is
treated more realistically than in (iii) by assuming a periodic variation
of attractive energy along the two directions parallel to the surface.
This model is the starting point for theories of localized-mobile transi-
tions in films and for translational surface band states of adatoms.
(v) Deformable substrate Models (i)-(iv) assume an inert and
rigid substrate. Each of those categories can be made more realistic by
the inclusion of excitations and deformations due to adsorption. Sub-
