Adsorption on Surfaces and Surface Diffusion of Adsorbates (Landolt-Börnstein: Numerical Data and Functional Relationships in Science and Technology - New Series Condensed Matter)

Landolt-Börnstein Numerical Data and Functional Relationships in Science and Technology New Series / Editor in Chief: W. Martienssen

Group III: Condensed Matter Volume 42

Physics of Covered Solid Surfaces Subvolume A Adsorbed Layers on Surfaces Part 1 Adsorption on Surfaces and Surface Diffusion of Adsorbates

Editor H.P. Bonzel Authors E.I. Altman, M. Bienfait, H.P. Bonzel, H. Brune, R. Diehl, M.Y.L. Jung, V.G. Lifshitz, M.E. Michel, R. Miranda, R. McGrath, K. Oura, A.A. Saranin, E.G. Seebauer, P. Zeppenfeld, A.V. Zotov

13

ISSN 1615-1925 (Condensed Matter) ISBN 3-540-41223-9 Springer-Verlag Berlin Heidelberg New York

Library of Congress Cataloging in Publication Data Zahlenwerte und Funktionen aus Naturwissenschaften und Technik, Neue Serie Editor in Chief: W. Martienssen Vol. III/42A1: Editor: H.P. Bonzel At head of title: Landolt-Börnstein. Added t.p.: Numerical data and functional relationships in science and technology. Tables chiefly in English. Intended to supersede the Physikalisch-chemische Tabellen by H. Landolt and R. Börnstein of which the 6th ed. began publication in 1950 under title: Zahlenwerte und Funktionen aus Physik, Chemie, Astronomie, Geophysik und Technik. Vols. published after v. 1 of group I have imprint: Berlin, New York, Springer-Verlag Includes bibliographies. 1. Physics--Tables. 2. Chemistry--Tables. 3. Engineering--Tables. I. Börnstein, R. (Richard), 1852-1913. II. Landolt, H. (Hans), 1831-1910. III. Physikalisch-chemische Tabellen. IV. Title: Numerical data and functional relationships in science and technology. QC61.23 502'.12 62-53136 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in other ways, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer-Verlag. Violations are liable for prosecution act under German Copyright Law. Springer-Verlag Berlin Heidelberg New York a member of BertelsmannSpringer Science+Business Media GmbH © Springer-Verlag Berlin Heidelberg 2001 Printed in Germany The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Product Liability: The data and other information in this handbook have been carefully extracted and evaluated by experts from the original literature. Furthermore, they have been checked for correctness by authors and the editorial staff before printing. Nevertheless, the publisher can give no guarantee for the correctness of the data and information provided. In any individual case of application, the respective user must check the correctness by consulting other relevant sources of information. Cover layout: Erich Kirchner, Heidelberg Typesetting: Authors and Redaktion Landolt-Börnstein, Darmstadt Printing: Computer to plate, Mercedes-Druck, Berlin Binding: Lüderitz & Bauer, Berlin SPIN: 10689660

63/3020 - 5 4 3 2 1 0 – Printed on acid-free paper

Editor H.P. Bonzel Forschungszentrum Jülich Institut für Grenzflächenforschung und Vakuumphysik (IGV) 52425 Jülich Germany

Authors E.I. Altman Department of Chemical Engineering Yale University New Haven, CT 06520 USA 3.4.3 Halogens on metals and semiconductors M. Bienfait CRMC2/CNRS Faculté de Luminy Physique - Case 910 F-13288 Marseille Cedex 9 FRANCE 3.1.2 Noble gases on graphite, lamellar halides, MgO, NaCl H.P. Bonzel Forschungszentrum Jülich Institut für Grenzflächenforschung und Vakuumphysik (IGV) 52425 Jülich Germany 1 Introduction to physical and chemical properties of adlayer/substrate systems 3.7.1 CO and N2 on metals W.A. Brown Department of Chemistry University College London London WC1H 0AJ U.K. 3.7.2 NO, CN, O2 on metals H. Brune Institut de Physique Expérimentale (IPE) École Polytechnique Fédérale de Lausanne (EPFL) PHB-Ecublens CH-1015 Lausanne 3.3.1 Metals on metals

K. Christmann Institut für Physikalische und Theoretische Chemie Freie Universität Berlin 14195 Berlin Germany 3.4.1 Chemisorbed hydrogen on metals and semiconductors R. Denecke Department of Physics Uppsala University S-751 21 Uppsala Sweden 4.3 Electron binding energy of metals and semiconductors R.D. Diehl Department of Physics Pennsylvania State University University Park, PA 16802 USA 3.2.1 Alkali metals on metals M. Enachescu Candescent Technologies 6320 San Ignacio Ave. San José, CA 95119 USA 3.4.4 P, S, As, Sb on metals and semiconductors N. Esser Institut für Festkörperphysik Technische Universität Berlin D-10623 Berlin Germany 4.6 Surface optical properties J.E. Fieberg Hillsdale College Hillsdale, MI 49242 USA 3.8.9 Halogen-substituted hydrocarbons on metals and semiconductors A. Föhlisch II. Institut für Experimentalphysik Universität Hamburg D-22761 Hamburg Germany 3.7.1 CO and N2 on metals H.-J. Freund Fritz-Haber-Institut der Max Planck Gesellschaft (MPG) D-14195 Berlin Germany 3.9 Adsorption on oxides

H.J. Grabke Max-Planck Institut (MPI) für Eisenforschung GmbH D-40074 Düsseldorf Germany 3.5 Surface segregation of atomic species (non-metal on metal) M. Grunze Institut für Angewandte Physikalische Chemie Universität Heidelberg D-69120 Heidelberg Germany 3.8.10 Polyatomic chain-like hydrocarbons on metals and semiconductors E. Hasselbrink Institut für Physikalische und Theoretische Chemie Universität Essen D-45117 Essen Germany 3.8.3 NH3 and PF3 on metals and semiconductors J. Heidberg Institut für Physikalische Chemie und Elektrochemie Universität Hannover D-30167 Hannover Germany 3.10 Adsorption on alkali halides G. Held Institut fuer Physikalische und Theoretische Chemie Universität Erlangen-Nürnberg D-91058 Erlangen Germany 3.8.7 Cyclic hydrocarbons on metals and semiconductors K. Hermann Fritz-Haber-Institut der Max-Planck Gesellschaft (MPG) Abteilung Theorie D-14195 Berlin Germany 4.1 Surface structure on metals and semiconductors K. Horn Fritz-Haber-Institut der Max-Planck Gesellschaft (MPG) Abteilung Theorie D-14195 Berlin Germany 3.7.4 Diatomic molecules on semiconductors

H. Ibach Institut für Grenzflächenforschung und Vakuumphysik (IGV) Forschungszentrum Jülich D-52425 Jülich Germany 4.4 Surface free energy and surface stress K. Jacobi Fritz-Haber-Institut der Max-Planck Gesellschaft (MPG) D-14195 Berlin Germany 4.2 Electron work function of metals and semiconductors W. Jaegermann Fachbereich Materialwissenschaft Fachgebiet Oberflächenforschung Technische Universität Darmstadt D-64287 Darmstadt Germany 3.8.2 H2O and OH on semiconductors M.Y.L. Jung Deppartment of Chemical Engineering University of Illinois Urbana, IL 61801 USA 3.11 Surface diffusion on metals, semiconductors and insulators B.E. Koel Department of Chemistry, SSC 606 University of Southern California Los Angeles, CA 90089-0482 USA 3.8.4 CO2, NO2, SO2, OCS, N2O, O3 on metals and semiconductors H. Kuhlenbeck Fritz-Haber-Institut der Max-Planck Gesellschaft (MPG) Abteilung Chemische Physik D-14195 Berlin Germany 3.9 Adsorption on oxides V.G. Lifshits Institute of Automation and Control Processes 690041 Vladivostok Russia 3.3.2 Metals on semiconductors

A.C. Luntz Fysik Institut Odense Universitet 5230 Odense M Denmark 3.12 Dynamics of activated adsorption N. Martensson Department of Physics Uppsala University S-751 21 Uppsala Sweden 4.3 Electron binding energy of metals and semiconductors T. Mayer Fachbereich Materialwissenschaft Fachgebiet Oberflächenforschung Technische Universität Darmstadt D-64287 Darmstadt Germany 3.8.2 H2O and OH on semiconductors R. McGrath Surface Science Research Centre and Department of Physics The University of Liverpool Liverpool L69 3BX U.K. 3.2.1 Alkali metals on metals E.G. Michel Departimento Fisica de la Materia Condensada C-III Instituto Universitario de Ciencia de Materiales "Nicolas Cabrera" Universidad Autonoma de Madrid 28049 Madrid Spain 3.2.2 Alkali metals on semiconductors R. Miranda Departimento Fisica de la Materia Condensada C-III Instituto Universitario de Ciencia de Materiales "Nicolas Cabrera" Universidad Autonoma de Madrid 28049 Madrid Spain 3.2.2 Alkali metals on semiconductors D.R. Mullins Oak Ridge National Laboratory Oak Ridge, TN 37831-6201 USA 3.8.5 Substituted hydrocarbons on metals

B.E. Nieuwenhuys Gorlaeus Laboratory Leiden University NL 2300 Ra Leiden The Netherlands 3.7.3 Diatomic molecules on alloys A. Nilsson Department of Physics Uppsala University S-751 21 Uppsala Sweden 3.7.1 CO and N2 on metals 4.3 Electron binding energy of metals and semiconductors K. Oura Department of Electronic Engineering Faculty of Engineering Osaka University Osaka 565-0871 Japan 3.3.2 Metals on semiconductors H. Over Fritz-Haber-Institut der Max-Planck Gesellschaft (MPG) D-14195 Berlin Germany 3.4.2 C, N, O on metals and semiconductors G. Pirug Institut für Grenzflächenforschung und Vakuumphysik (IGV) Forschungszentrum Jülich D-52425 Jülich Germany 3.8.1 H2O and OH on metals W. Richter Institut für Festkörperphysik Technische Universität Berlin D-10623 Berlin Germany 4.6 Surface optical properties M. Rocca Centro di Fisica delle Superfici e Basse Temperature del CNR Istituto Nazionale di Fisica della Materia I-16146 Genova Italy 4.5 Surface phonon dispersion

G. Rupprechter Fritz-Haber-Institut der Max-Planck Gesellschaft (MPG) Abteilung Chemische Physik D-14195 Berlin Germany 3.8.6 Linear hydrocarbons and CH4 on metals and semiconductors M. Salmeron Lawrence Berkeley Laboratory Materials Science Bldg. 66/208 Berkeley, CA 94720 USA 3.4.4 P, S, As, Sb on metals and semiconductors D. Sander Max-Planck Institut (MPI) für Strukturphysik D-06120 Halle Germany 4.4 Surface free energy and surface stress A.A. Saranin Institute of Automation and Control Processes 690041 Vladivostok Faculty of Physics and Engineering Far Eastern State University 690000 Vladivostok Russia 3.3.2 Metals on semiconductors E.G. Seebauer Deppartment of Chemical Engineering University of Illinois Urbana, IL 61801 USA 3.11 Surface diffusion on metals, semiconductors and insulators M. Sokolowski Institut für Physikalische und Theoretische Chemie Universität Bonn D-53115 Bonn Germany 3.8.11 Large aromatic adsorbates on metals and semiconductors G.A. Somorjai Department of Chemistry University of California Berkeley, CA 94720 USA 3.8.6 Linear hydrocarbons and CH4 on metals and semiconductors

H.-P. Steinrück Institut fuer Physikalische und Theoretische Chemie Universität Erlangen-Nürnberg D-91058 Erlangen Germany 3.8.7 Cyclic hydrocarbons on metals and semiconductors J. Suzanne Departement de Physique CRMC2 - Centre National de la Recherche Scientifique (CNRS) Faculte des Sciences de Luminy F-13288 Marseille, Cedex 9 France 3.6 Molecules on graphite, BN, MgO (except noble gases) W.T. Tysoe Department of Chemistry and Laboratory for Surface Studies University of Wisconsin - Milwaukee Milwaukee, WI 53211 USA 3.8.5 Substituted hydrocarbons on metals Ch. Uebing Department of Physics and Astronomy Rutgers, The State University of New Jersey Piscataway, NJ 08854-8019 USA 3.5 Surface segregation of atomic species (non-metal on metal) E. Umbach Lehrstuhl für Experimentelle Physik II Physikalisches Institut der Universität D-97074 Würzburg Germany 3.8.11 Large aromatic adsorbates on metals and semiconductors H. Viefhaus Max-Planck Institut (MPI) für Eisenforschung GmbH D-40074 Düsseldorf Germany 3.5 Surface segregation of atomic species (non-metal on metal) J.M. Vohs Department of Chemical Engineering University of Pennsylvania Philadelphia, PA 19104-6315 USA 3.8.8 Oxygenated hydrocarbons on metals and semiconductors

M.A. Van Hove Lawrence Berkeley National Laboratory Materials Science 66 Berkeley, CA 94720 and Department of Physics University of California-Davis Davis, CA 95616 USA 4.1 Surface structure on metals and semiconductors P.R. Watson Department of Chemistry Oregon State University Corvallis, OR 97331 USA 4.1 Surface structure on metals and semiconductors J.M. White Department of Chemistry and Biochemistry University of Texas at Austin Austin, TX 78712 USA 3.8.9 Halogen-substituted hydrocarbons on metals and semiconductors H. Wiechert Institut für Physik der Johann Gutenberg-Universität D-55099 Mainz Germany Molecules on graphite, BN, MgO (except noble gases) Ch. Wöll Lehrstuhl für Physikalische Chemie I Ruhr-Universität Bochum D-44801 Bochum Germany 2 Characterization of adsorbate overlayers: Measuring techniques P. Zeppenfeld Institut für Experimentalphysik Atom- und Oberflächenphysik Johannes-Kepler-Universität Linz A-4040 Linz, Austria 3.1.1 Noble gases on metals and semiconductors A.V. Zotov Faculty of Electronics Vladivostok State University of Economics and Service 690600 Vladivostok Institute of Automation and Control Processes 690041 Vladivostok Russia 3.3.2 Metals on semiconductors

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Preface Surface Science is understood as a relatively young scientific discipline, concerned with the physical and chemical properties of and phenomena on clean and covered solid surfaces, studied under a variety of conditions. The adsorption of atoms and molecules on solid surfaces is, for example, such a condition, connected with more or less drastic changes of all surface properties. An adsorption event is frequently observed in nature and found to be of technical importance in many industrial processes. For this reason, Surface Science is interdisciplinary by its very nature, and as such an important intermediary between fundamental and applied research. The beginning of Surface Science may be placed around the years 1900-1928, connected with seminal works by J.W. Gibbs, I. Langmuir, M. Knudsen, O. Stern, M. Volmer, C. Davisson and L. Germer, H.S. Taylor, J.E. Lennard-Jones, I.N. Stranski and others. In modern times, research activities in this field have literally exploded worldwide. Consequently, enormous progress can be recognized and it is no exaggeration, to note a high degree of maturity in this well-established scientific discipline. Tribute is being paid to this effect by the renowned Series of Landolt-Börnstein whose editor-in-chief Werner Martienssen, Frankfurt am Main, has initiated several volumes of collected scientific data in the field of Surface Science. Indeed, the point in time has arrived where all quantitative data, that have been generated over so many years, are worth being collected in tables and figures for critical review and reference purposes as well. The beginning has been made with Landolt-Börnstein volume 24, entitled Physics of Solid Surfaces. This volume, consisting of four subvolumes, appeared in 1993-96 and covers the properties of clean solid surfaces. The present volume 42 is devoted to Covered Solid Surfaces and, in particular, to Adsorbed Layers on Surfaces. It is as such a collection of data obtained for adsorbates on well-defined crystalline surfaces. "Well-defined" means surfaces of known crystallographic structure and chemical composition. These conditions can in most cases be realized by careful sample preparation in ultra-high vacuum. Work on the present volume started in late 1997 when I was first contacted by W. Martienssen. An initial outline of the volume was written in January of 1998. At this point I want to express my sincere gratitude to George Comsa, Bonn, and Gerhard Ertl, Berlin, for their support by making valuable suggestions, concerning both the outline and the choice of possible authors. In fact, the choices made at the time proved to be excellent ones, and the consulting of G. Comsa and G. Ertl turned out to be extremely helpful for the evolution of the present volume. It was almost clear at the beginning, that the amount of general information and quantitative data on Adsorbed Layers on Surfaces is enormous, too large to fit into a single volume. Hence, again several subvolumes had to be planned. Unfortunately, the chapters anticipated for each of the subvolumes did not arrive synchronously with the production schedule, such that the sequence of chapters actually printed in the subvolumes deviates from that in the general outline of the whole volume. We apologize for this inconvenience, but in the age of electronic information distribution this problem will be solved, once all volumes are available electronically. Search routines will guide the reader to the data of his desire. Until that time, the index of each subvolume will have to do. Finally and most importantly, I would like to extend my deep appreciation to all authors of this volume for their excellent contributions, and to the editing and production offices of Springer-Verlag for efficient cooperation and general support. Jülich, May 2001

The Editor

Survey of Volume III/42 Physics of Covered Solid Surfaces Subvolume A: Adsorbed Layers on Surfaces 1

2

Introduction to physical and chemical properties of adlayer/substrate systems

subvolume A1

Characterization of adsorbate overlayers: Measuring techniques

subvolume A2

3

DATA: Adsorbate properties of

3.1 3.1.1 3.1.2

Adsorption of noble gases Noble gases on metal substrates and semiconductors Noble gases on graphite, lamellar halides, MgO, and NaCl

subvolume A1 subvolume A1

3.2 3.2.1 3.2.2

Adsorption of alkali metals Alkali metals on metals Alkali metals on semiconductors

subvolume A1 subvolume A1

3.3 3.3.1 3.3.2

Adsorption of metals Metals on metals Metals on semiconductors

subvolume A1 subvolume A1

3.4 3.4.1 3.4.2 3.4.3 3.4.4

Non-metallic atomic adsorbates on metals and semiconductors Chemisorbed hydrogen on metals and semiconductors C, N, O on metals and semiconductors Halogens on metals and semiconductors subvolume A1 P, S, As, Sb on metals and semiconductors subvolume A3

3.5

Surface segregation of atomic species (non-metal on metal)

subvolume A3

3.6

Adsorption of molecules on graphite, BN, MgO (except noble gases)

subvolume A3

Molecular diatomic adsorbates CO and N2 on metals NO, CN, O2 on metals Diatomic molecules on alloys Diatomic molecules on semiconductors

subvolume A3 subvolume A3 subvolume A3 subvolume A3 subvolume A3

3.7 3.7.1 3.7.2 3.7.3 3.7.4

3.8 3.8.1 3.8.2 3.8.3 3.8.4 3.8.5 3.8.6 3.8.7 3.8.8 3.8.9

3.8.11

Molecular polyatomic adsorbates on metals and semiconductors H2O and OH on metals H2O and OH on semiconductors NH3 and PF3 on metals and semiconductors CO2, NO2, SO2, OCS, N2O, O3 on metals and semiconductors Substituted hydrocarbons on metals Linear hydrocarbons and CH4 on metals and semiconductors Cyclic hydrocarbons on metals and semiconductors Oxygenated hydrocarbons on metals and semiconductors Halogen-substituted hydrocarbons on metals and semiconductors Polyatomic chain-like hydrocarbons on metals and semiconductors Large aromatic adsorbates on metals and semiconductors

3.9

Adsorption on oxide surfaces

subvolume A3

3.10

Adsorption on alkali halide surfaces

subvolume A3

3.8.10

3.11

Surface diffusion of adsorbates on metals, semiconductors and insulators

subvolume A3 subvolume A3 subvolume A3 subvolume A3 subvolume A3 subvolume A3 subvolume A3 subvolume A3 subvolume A3 subvolume A3 subvolume A3

subvolume A1

3.12

Dynamics of activated adsorption

subvolume A3

4

Data: Adsorbate-induced changes of substrate properties

4.1

Surface structure on metals and semiconductors

subvolume A2

4.2

Electron work function of metals and semiconductors

subvolume A2

4.3

Electron binding energy of metals and semiconductors

subvolume A3

4.4

Surface free energy and surface stress

subvolume A2

4.5

Surface phonon dispersion

subvolume A2

4.6

Surface optical properties

subvolume A3

Ref. p. 59]

1 Introduction

1

1 Introduction to physical and chemical properties of adlayer/substrate systems H.P. BONZEL

1.1 General background The Physics and Chemistry of solid surfaces has been studied ever since the early work of Langmuir [13Lan, 18Lan], Lennard-Jones [28Len, 32Len, 36Len, 37Len], Davisson and Germer [27Dav], Stranski [28Str, 31Str], Stern [29Ste], Volmer [21Vol, 39Vol] and others. Prior to those, J.W. Gibbs defined important thermodynamic properties of solid surfaces for the first time with unprecedented rigor in the framework of thermodynamic theory [1876, 1878]. Further interest in surfaces, particularly in chemical reactions at surfaces, evolved from the discovery and technical implementation of heterogeneous catalytic reactions at the turn of the 18th century [39Mit, 72Sch]. Numerous studies of adsorption and surface reactions on metal surfaces, mostly on finely dispersed particles, appeared in the field of catalytic chemistry. In the late 1940s, intense work on semiconductor surfaces and interfaces provided a new powerful impetus for the growth of surface physics [47Bar, 94Gat]. In later years, the development of numerous quantitative surface analytical tools played a major role for a further rapid advancement of the new field of surface science. These new analytical techniques which often required good vacuum for their operation, enabled a widespread research of clean and covered surfaces of different materials, such as metals and alloys, semiconductors, alkali halides, oxides, etc. The additional basic desire to prepare a surface of a solid in a well-defined state and keep it in that state for a time long enough to carry out a microscopic or spectroscopic investigation, called for most experiments to be run under clean ultra-high vacuum (UHV) conditions (i.e. < 10–9 mbar). The latter was made possible by advances in vacuum technology, such as the development of new vacuum pumps and pressure measuring devices. Thus UHV of < 1x10–10 mbar became routine for many surface science experiments, increasing the lifetime of a "clean" surface and supporting electron, ion and atom beam scattering studies from surfaces. In general, the study of surfaces can be divided into those of clean surfaces where foreign atoms or molecules are totally undesirable, and into those of covered surfaces where atoms or molecules are intentionally added. The latter process is that of adsorption, and depending on the strength of interaction between the added species and the surface, we distinguish physisorption (weak) and chemisorption (strong) [60Ada, 64Hay, 70Cla, 72Som2]. The adsorbed species is called the adsorbate while the material with the exposed surface is called either substrate or adsorbent. The term adsorbent is verbally closely linked to adsorption and appears frequently in the older literature dealing strictly with the phenomenon of adsorption. Nowadays one prefers to use the term substrate because of the obvious link to vapor deposition of thin films on a substrate. Vapor deposition is also an adsorption process but there the object of interest is usually a structurally well defined multi-layer film. At this point it may be helpful to address briefly the distinction between adsorbed layers and thin films. First of all, there is no rigorous difference from a physics point-of-view but traditionally a distinction can be made on the grounds of energetics and coverage. Adsorbed layers, in the sense of this Landolt-Börnstein volume at least, are defined as ensembles of adsorbed atoms or molecules at effective coverages up to one monolayer, weakly or strongly bound to a substrate. Intra-layer interaction can be repulsive or attractive. All physical and chemical aspects of the adsorption process and of the adsorbate itself, often in relationship to the equivalent gas phase species, are of interest. The present volume will therefore cover the relevant research results obtained in this area of adsorption on structurally and chemically well-defined crystalline surfaces. Thin films, on the other hand, are mostly multi-layer configurations of several nanometer to micrometer thickness on a given substrate. Interfacial as well as intra-layer bonding is generally strong (always

Landolt-Börnstein New Series III/42A

2

1 Introduction

[Ref. p. 59

attractive interaction). Structural questions, such as the formation of thin films (including nucleation and growth), its crystallographic orientation with respect to the substrate (epitaxy) and its compactness, are of primary interest. Technical aspects, such as the crystallinity and possibly grain size, the mechanical and chemical resistance of thin films play an important role. The properties of thin films, in contrast to adsorbed layers as defined above, will not be considered in this volume. The distinction between physi- and chemisorption is historical and not rigid in a scientific sense. Once atoms or molecules are adsorbed, their properties are distinctly different from those of their gaseous counterpart. The stronger they are adsorbed, the more significant are these differences. For example, their intra-molecular bonds are weakened or strengthened, hence bondlengths are changed, the energies of molecular orbitals and molecular vibrational frequencies are changed, etc. If the interaction between adsorbate and substrate is very strong, certain intra-molecular bonds may weaken to the extent that they rupture resulting in the partial (or total) dissociation of the adsorbed species. Then we have a case of a heterogeneous surface reaction. It may happen that one part of the reaction products desorbs from the surface, leaving the other adsorbed as a fragment (radical). An adsorption process of this kind is more complex and may consist of several steps: (1) physisorption of the molecule; (2) surface diffusion and transition into a chemisorbed state; (3) breakup of the molecule into fragments; (4) chemisorption of tightly bound fragment(s); (5) diffusion, association and desorption of weakly bound fragments. The physisorbed molecule in this chain of surface events is called a precursor state to the chemisorbed state. The rate of surface diffusion in the weakly bound precursor state is generally high, enabling the molecule to find an empty site for chemisorption. This search is limited by the finite lifetime in the precursor state. As indicated by this brief description, the process of adsorption of atoms and molecules on solid surfaces involves kinetic as well as static aspects. Obviously, the sequence of steps (1)-(5) above is a complex kinetic phenomenon. On the other hand, measuring the physical properties of an adsorbed atom, molecule or fragment concerns the static nature of that species. In both cases the structure and chemical composition of the clean surface is of importance, because the properties of the adsorbed species depend sensitively on the local structure and chemistry of the adsorption site. Thus the description of adsorbed layers on surfaces is not thinkable without a detailed knowledge of clean surfaces. It is therefore no coincidence that the current volume of Adsorbed Layers follows the Landolt-Börnstein volume on Clean Surfaces. Important data characterizing clean surfaces of metals, semiconductors etc. are collected in the Landolt-Börnstein volumes III/24, subvolumes A-D. The current volume on Adsorbed Layers will introduce and summarize the knowledge obtained on all aspects of adsorption of atoms and molecules on solid surfaces of well-defined structure and chemical composition. A brief introduction to the surface thermodynamic concepts and equations in relationship to adsorption on solid surfaces will be given [66Def, 73Hir, 73Wag, 96Des]. The physical and chemical properties of the adsorbed species as well as the substrate related to thermodynamics will be introduced in this context. A more complete introduction, by means of examples, into the important physical and chemical properties of adsorbates, of both static and dynamic origin, follows. Adsorbate-induced changes of substrate properties will also be introduced. The following major chapter is devoted to a short description of surface analytical techniques for the investigation of adsorption. Modern experimental methods will be preferred over older less reliable ones which have been applied at high pressure or poor vacuum to samples with ill-defined structure and composition. This chapter will complement the description of techniques given in the Landolt-Börnstein volume III/24. The subsequent presentation of data will be grouped into two main parts: (1) properties of adsorbates, and (2) adsorbate-induced changes of substrate properties. In the first part, the presentation of properties is divided into groups of increasing molecular size, followed by more general chapters on material aspects, such as oxide, alkali halide, graphite and boron nitride surfaces, or certain property aspects, such as surface diffusion of adsorbed species, and the dynamics of activated adsorption. In the second part, various substrate properties, that are significantly changed by adsorbed species are described in six chapters. These changed substrate properties are: surface structure, electron work function, electron binding energies, surface free energy and surface stress, surface phonons, and optical properties.

Landolt-Börnstein New Series III/42A

Ref. p. 59]

1 Introduction

3

1.2 Surface thermodynamics From a historical and conceptual point of view it is useful, at the beginning of a survey of adsorption experiments and data, to introduce the concepts of surface thermodynamics and to define the fundamental quantities associated with adsorption. The origin of these concepts goes back to Gibbs [1876, 1878]. The following equations will be given for a two-phase system (solid/gas or solid/liquid or liquid/gas) of constant volume V, consisting of N chemical components with concentrations ci [in number of molecules/unit volume], immersed in a heat bath at temperature T, and connected with reservoirs of particles of each component. The interfacial area between both phases shall be A. The change in Helmholtz free energy of the total system for an infinitesimal deviation from equilibrium is dF = −SdT − PdV + γ dA + ∑ µ i dn i ,

(1)

i

where γ is the specific surface energy, equal to the work required to reversibly increase the surface area, µi the chemical potential of components i, and ni = ciVi the total number of species. The specific surface energy and chemical potentials of each component are thus defined as  ∂F  γ = and   ∂A  T,V , n i

 ∂F  . µi =    ∂n i  T,V,A ,n

(2)

j

The operational definition of γ via a small change in surface area may conceptually be connected with a concomitant change in the concentration of one or several of the chemical components, ∆ni, in the second phase. To keep all concentrations (intensive variables) constant, the amount of ∆ni has to be replenished in that phase by adding it to the system through a leak, keeping T and V constant. The only place where the small amount of component i can go is the incremental increase in interfacial area, ∆A. This operation therefore defines the adsorption of component i on the interface between the two phases 1 and 2. The adsorbed amount per unit area is called the surface excess, equal to  ∆n  . Γi =  i   ∆A  T,P ,V,n

(3)

j

Gibbs views the interface with the adsorbed material as a "third phase" but without treating this phase in the same thermodynamic rigor as the other two phases. Instead he proposes a mathematical "dividing surface" which is placed arbitrarily but parallel to and near the geometric interface. Formally, a free energy, entropy and particle concentrations, but no volume, are attributed to the surface phase, which is indicated by the superscript (S). Differences are defined as follows [73Hir] F(S ) = F − F(1) − F( 2 ) , S(S ) = S − S(1) − S( 2 ) , (2) n (i S ) = n i − n (1) . i − ni Due to the mathematical form of the dividing surface, the surface phase has no volume, i.e. V(S) = 0.

Landolt-Börnstein New Series III/42A

(4a) (4b) (4c)

1 Introduction

4

[Ref. p. 59

Fig. 1a, b. Plot of particle density c profiles vs. distance x vertical to an interface for a two component system A, B to illustrate a possible position of the dividing surface between solid phase and gas phase. (a) Component A in substrate solid phase; (b) component B: adsorbate. Note that densities are not drawn to scale [73Hir].

Figure 1 illustrates graphically the interfacial region of a two-phase system for two components A and B, with low concentrations of A,B in the gas phase (2) and also of B dissolved in the solid phase (1). The dividing surface is placed parallel to the interface, such that the excess concentration ΓA is zero. The extent of the adsorbed layer is just one monolayer of B in this simple picture, and its actual volume is practically insignificant compared to the volume of either phase (1) or (2). Even if the adsorbed layer would consist of two or three monolayers, this would still be true. The excess concentration ΓB is nonzero and equal to the coverage of B. Based on Eqs. (1)-(4), the free energy change for the surface phase is dF(S ) = −S(S )dT + γdA + ∑ µ i dn (i S ) .

(5)

i

The corresponding internal energy change is obtained by dE (S ) = dF(S ) − TdS(S ) − S(S ) dT . The expression for the differential internal energy can be integrated, yielding E(S ) = TS(S ) + γA + ∑ µ i n (i S ) .

(6)

i

Taking the total differential of this equation and subtracting it from the previous equation produces the following Gibbs-Duhem relationship [73Hir] S(S )dT + Adγ + ∑ n (i S )dµ i = 0 .

(7)

i

Subtracting Eq. (7) from Eq. (5), we obtain dF(S ) = d ( γA ) + d  ∑ n (i S )µ i  . Integrating this equation and i  dividing by the area A, an important definition of the system's specific surface free energy, f(S), results: f (S ) = γ + ∑ Γi µ i , with Γi = i

n (i S ) . A

(8)

Landolt-Börnstein New Series III/42A

Ref. p. 59]

1 Introduction

5

The excess concentration Γi of the adsorbed component i may also be called the surface coverage of i in units of molecules/cm2. Equation (8) shows that the specific surface free energy is only equal to the surface energy γ, if the sum over all chemical potentials on the r.h.s. of Eq. (8) is zero; for a onecomponent system this requires Γ1 = 0. In other words, for a clean surface, free of adsorbates, the first layer of the substrate has no surface excess, hence f (S ) = γ . Converting the extensive variables in Eq. (7) to quantities per unit surface area yields the Gibbs adsorption equation dγ = − s ( S ) dT − ∑ Γi dµ i ,

(9)

i

which governs the dependence of the surface energy on temperature and chemical potential. The following partial derivatives are equal to the specific surface entropy and the surface excess, −Γi, respectively:  ∂γ  (S )   = −s ,  ∂T  n

 ∂γ  = − Γi .    ∂µ i  T,µ

and

i

(10)

j

Note that the surface entropy is itself not a constant. For a two-component system, under isothermal conditions, we have dγ = − Γ1dµ1 − Γ2dµ 2 . Imagine a solid (1) in equilibrium with the gas phase (2), and a certain amount of gas adsorbed. The chemical potential of the adsorbing ideal gas at pressure p2 shall be µ 2 = µ 20 + kT ln p 2 ,

(11)

such that  ∂γ  ∂γ  ∂µ 2  = − Γ2 =     ∂p 2  ∂p 2   ∂µ 2  T,µ1

−1

=

1  ∂γ  .   kT  ∂ ln p 2  T,µ

(12)

1

If the dividing surface is placed at the geometric interface as shown schematically in Fig. 1, the excess concentration Γ1 is zero, and Γ2 is just the amount of adsorbed gas on the solid surface. A similar case would be the segregation of solute to the surface of a solid. This corresponds to a single phase system with two components. If the solute is component 2, the same equation (12) describes the variation of surface energy with surface concentration of solute. The negative sign of the surface excess indicates the lowering of γ with adsorption or segregation. Vice versa: only those particles will adsorb, either from the gas phase or the interior of the solid, that cause a lowering of the surface energy. It follows from Eqs. (10) and (12) that there is an intimate connection between the surface energy γ and the phenomenon of adsorption at the surface. This is the reason why thermodynamic relationships involving the surface energy term are important for the discussion of adsorption. Any type of adsorbed layer on a solid surface will change the surface energy, and when the latter is anisotropic, i.e. dependent on crystallography, this change will also imply morphological changes at the surface. This may be particularly significant for small particles, such as present on a finely dispersed catalyst used for heterogeneous catalysis. The interplay between adsorption, changing surface energy, morphology changes, and concomitant changes in surface reactivity is one of the most important ways to understand the complexity of heterogeneous catalytic reactions. Along the same lines of reasoning it is necessary to also consider the effect of curved surfaces which alter the surface energy as a function of curvature [52Her, 63Mul, 66Def]. Thus curvature at the surface introduces another dimension in the relationship between surface energy, adsorption and reactivity. Finally, we introduce the concept of intrinsic surface stress [52Her, 1876] which is equal to the work required to deform a surface. It is directly related to the surface energy and its derivative with respect to strain. For crystalline surfaces, strain is a tensor, and thus the surface stress, τij, is also a tensor of second Landolt-Börnstein New Series III/42A

1 Introduction

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[Ref. p. 59

rank. It may be defined by the derivative of the surface energy per atom, γA, with respect to the strain tensor, εij which leads to the Shuttleworth equation [50Shu] τ ij =

∂γ 1 d( γA ) = γ δ ij + . ∂ε ij A dε ij

(13)

On surfaces of two-fold symmetry the surface stress is expected to be anisotropic. This has been verified theoretically for Pd(110) and Pt(110) surfaces where the surface stress in the close-packed [1 1 0] direction is higher than in the [001] direction [95Fei]. Any change in γ will cause a change in surface stress, and vice versa. Thus adsorption will change both quantities [97Iba]. Curved surfaces The role of curved surfaces is very important in context with solid crystals and adsorption, regardless whether isotropic or anisotropic surface energy is considered [52Her, 63Mul]. Since the surface energy enters all expressions which govern the change of a physical quantity with the radius of curvature at the surface, these dependencies play also a role in context with adsorption because the latter influences the surface energy as well as its possible anisotropy. When the surface energy is isotropic, most relationships for liquid/liquid and liquid/gas two-phase systems can be transferred to the solid/liquid and solid/gas systems. The curved surface portion of a solid is characterized by an additional chemical potential relative to that of the flat surface, µ0. The result is the Gibbs-Thomson equation: 1 1 µ( M ) = µ 0 + Ω γ  +  ,  r1 r2 

(14)

where r1 and r2 are the principal radii of curvature at point M, and Ω is the atomic volume of the solid(liquid) phase. As a consequence of this dependence, several physical properties change with the radii of curvature, such as the vapor pressure of small spherical particles (droplets): ln

p( r ) Ω 2γ . =− p0 kT r

(15)

Secondly, the melting temperature of small crystals will be a function of their radii, i.e. they will melt at a lower temperature than the bulk material, Tm, according to: ln

T( r ) Ω 2γ sl , =− Tm ∆H f r

(16)

with ∆Hf = heat of fusion and γsl = interfacial energy at the liquid/solid interface. Also, small crystals have a heat of sublimation smaller than the value for the bulk solid [66Def]. The surface energy of solid crystals is generally anisotropic, i.e. it depends on the crystallographic orientation of the surface. In that case a generalisation of the Gibbs-Thomson equation (14) was given by Herring [52Her]:  ∂2 γ  1  ∂2 γ  1  µ( M ) = µ 0 + Ω   γ + 2  +  γ + 2   . ∂θ1  r1  ∂θ 2  r2   

(17)

Landolt-Börnstein New Series III/42A

Ref. p. 59]

1 Introduction

7

Here the sum of γ and its second derivative with respect to orientation is called the surface stiffness. For the special case of a 2-dimensional monatomic island on a single crystal surface, the surface energy is replaced by the step energy, and the equation for the chemical potential of the island edge, equivalent to Eq. (17), is d γ step  1  µ step ( M ' ) = µ '0 +  γ step +  . dθ 2  r 

(18)

Here the expression in parentheses is called the step stiffness. Both surface and step stiffnesses may be changed by adsorption. Adsorption heats and energies Different types of heats of adsorption have been defined in classical thermodynamics but they are numerically similar. Their relationship to experimental determinations is more or less straightforward [68Cer, 83Cer]. The molar differential heat of adsorption, Qdiff, of a component i from the gas phase (1) on a solid (2) is defined as the difference in enthalpy associated with the transfer of one mole of i to the surface of the substrate at constant T, P and other components nj. Assuming ideal gas behavior, the differential heat of adsorption is defined as [66Def]  ∂H   ∂ ln p i  = − kT2  Q diff =  (S )   .  ∂T  Γ  ∂n i  T,P ,n ,n i i

(19)

j

The value of Qdiff is thus defined for a particular coverage Γi. The r.h.s. of Eq. (19) is analogous to the Clausius-Clapeyron equation and contains a directive for the experimentalist to measure the differential heat of adsorption as a function of coverage [69Tra]. The isosteric heat of adsorption is defined very similarly and differs from the differential heat only by kT (about 50 meV at 600 K), Q iso = Q diff + kT . The name isosteric heat comes from the r.h.s. of Eq. (19) where the partial derivative of ln pi with respect to temperature is taken at constant coverage. The function pi(T) at constant Γi is called isoster and can be obtained experimentally, e.g. by measuring the coverage as a function of temperature, keeping the pressure constant (isobars), and subsequently cross-plotting the data as isosters [69Tra]. Both, differential and isosteric heats of adsorption, evaluated at several coverages of adsorbate, describe in principal the coverage dependence of the adsorption heat. This variation of Q with coverage can be very substantial, in particular for chemisorption systems, as many investigations have shown. There is usually a sharp drop in the heat of adsorption when the first chemisorbed layer is filled and a second layer begins to be populated. Finally, we mention the calorimetric heat of adsorption, Qcal, which is also frequently measured, recently even for single crystal samples [98Bro]. The calorimetric heat can be thought of as an integral heat of adsorption, because the measurement may extend over a larger range of increasing coverage of the adsorbate. Only if the calorimeter has sufficient resolution, in terms of temperature change versus time, can the coverage dependence also be determined. Then it is possible to measure differential calorimetric heats, as the coverage increases from zero to a monolayer, for example. The exact correlation of changes in temperature to coverage is then a necessary requirement. Generally, the calorimetric heat of adsorption can not be expected to be equal to the isosteric or differential heats of adsorption. Thermodynamically, an expression for Qcal has been derived which relates it to the differential heat of adsorption as follows [66Def, 70Cla]:  ∂p (1)   ∂p (1)  dT   . Q cal = Q diff + V (1)  (iS )  +  i   ∂n i  T  ∂ T  n( S ) dn (i S )  i  

Landolt-Börnstein New Series III/42A

(20)

1 Introduction

8

[Ref. p. 59

Here the coverage dependence is contained in the derivatives inside the parentheses. These are difficult to measure, such that Eq. (20) is not an easy directive to follow. Nevertheless, many different experimental approaches to measuring the calorimetric heat of adsorption have been proposed and tested. If the calorimeter can be operated differentially, e.g. by sending pulses of gas to the surface and by measuring the temperature rise due to adsorption simultaneously, the calorimetric heat can be determined for a certain coverage window. Under adiabatic conditions the calorimetric heat of adsorption is then equal to the isosteric heat at a given coverage [51Kin, 66Def, 70Cla]: Q cal ( n (i S ) ) = Q diff ( n (i S ) ) + kT = Q iso ( n (i S ) ) .

(21)

Experiments of this kind have recently been carried out with single crystal samples under vacuum conditions, using a molecular beam for gas dosing [91Bor, 98Bro]. An example for the differential heat of adsorption versus coverage measured calorimetrically is shown in Fig. 2 for CO on a Pd(100) surface [97Yeo]. The adsorption heat decreases with increasing coverage, indicative of repulsive interactions between adsorbed CO molecules. This result is in good agreement with a previous measurement of the isosteric heat of adsorption for the same system [69Tra]. Most older data in this field of adsorption calorimetry suffer from an insufficient characterization of the substrate surface structure and composition. 180

CO/Pd (100)

–1

Heat of adsorption Qdiff [kJ mol ]

160 140

0 ML C 0.05 ML C 0.07 ML C 0.20 ML C 0.45 ML C

120 100

Fig. 2. Calorimetric heat of adsorption Qdiff for CO, adsorbed at 300 K on clean Pd(100) (0 ML C) as well as Pd(100) precovered with various amounts of carbon (0.05-0.45 ML C), as a function of CO coverage θ [97Yeo].

80 60 0

0.2

0.4 0.6 CO coverage θ [ML]

0.8

1.0

Landolt-Börnstein New Series III/42A

Ref. p. 59]

1 Introduction

9

1.3 Kinetics of adsorption/desorption and adsorption isotherms 1.3.1 Thermal rates of adsorption / desorption Kinetic phenomena, such as rates of adsorption and desorption of atoms or molecules, measured as a function of pressure, temperature (substrate or gas), surface structure, etc., contain important information on the energetics of adsorption. Unambiguous relationships between kinetics and energetics are, however, at least in the field of adsorption, frequently not available. The simplest case is the rate of adsorption, rad, of atoms or simple molecules onto a uniform surface [64Hay]: rad (θ, T) =

p

(2πmkT)1 2

s (θ, T) ,

(22)

where p is the partial pressure of the adsorbing gas, m the atomic (molecular) weight, and s(θ,T) the sticking coefficient. The quantity θ is from now on the relative surface coverage, defined as θ = n ad N 0 , equal to the ratio of the number of adsorbed species, nad, over the number of surface atoms, N0. The surface coverage is thus equivalent to the formerly defined surface excess, Γ. The sticking coefficient, defined as the rate of adsorption divided by the rate of impinging molecules, may be written as a product of a coverage dependent function and a temperature dependent Boltzmann term, containing the activation energy of adsorption, Eac: E  s( θ, T) = c f (θ ) exp ac   kT 

(23)

The quantity c is the condensation coefficient (of the order of unity) which describes the energy accomodation of the adsorbing species. The activation energy of adsorption is illustrated by the onedimensional adsorption potential shown in Fig. 3.

Potential energy E

barrier Eac

precursor state

chemisorbed state

Fig. 3. Illustration of the activation energy E of adsorption between a physisorbed precursor and a chemisorbed state in a one-dimensional potential energy diagram.

Reaction coordinate z

This potential shows two minima, one characterizing a weakly adsorbed, physisorbed state, the other a more strongly adsorbed, chemisorbed state. The transition from one to the other shows a barrier, the activation energy of chemisorption, Eac. For many adsorbates, in particular atomic species, there is no Landolt-Börnstein New Series III/42A

1 Introduction

10

[Ref. p. 59

indication of an activation barrier. The rate of adsorption is then only weakly temperature dependent. For molecular species, that chemisorb intact, the activation barrier is generally very small. To note an effect of this barrier on the rate of adsorption, one has to perform the experiment at very low temperature [78Nor]. This was demonstrated for CO and O2 on Ni(111), for example, at 6 K [84Sha, 85Sha, 86Sha]. Electron spectroscopy and work funktion measurements show these species to populate exclusivly the physisorbed state. Only after raising the temperature to about 20 K, these molecules begin to transfer into the chemisorbed state, whereby O2 dissociates into atoms. A very low activation energy of 0.4 kJ/mol is estimated for CO chemisorption [85Sha]. For molecular species which adsorb dissociatively, the activation barrier can be substantial. A pronounced temperature dependence of the rate of adsorption is found in such cases [85Ste, 90Ber]. Furthermore, the angular dependence of the rate of adsorption (and desorption) responds sensitively to the presence of an activation energy of adsorption. This topic will receive more attention further below and in chapter 3.11 of this volume. The coverage dependent function, f(θ), includes details of the adsorption reaction (e.g. molecular or dissociative) and the statistics of site occupation on the surface, including possible surface diffusion prior to localized adsorption. The simplest case is f(θ) = 1 – θ, which means that empty sites can readily be occupied. For dissociative adsorption A2 → 2 A one has approximately a (1 – θ)2 dependence. More complicated cases have been proposed [55Ehr, 56Ehr, 57Kis, 58Kis]. It is frequently observed that the sticking coefficient does not follow a simple θ-dependence of the kind mentioned above. Figure 4 shows the measured sticking coefficient for CO on Pd(100) at 300 K [97Yeo]. Although CO adsorbs molecularly, the data do not support the simple site occupation formula. The explanation of this dependence rests on the existence of a precursor state to chemisorption, such as schematically shown in Fig. 3, which allows CO molecules bound in this state to migrate over a small portion of the surface looking for an empty chemisorption site. In addition, the transition from this precursor site to the chemisorption site is activated, causing the sticking coefficient to exhibit a complex temperature dependence. 0.90

CO/Pd (100)

0 ML C 0.05 ML C 0.07 ML C 0.20 ML C 0.45 ML C

Sticking probability

0.75

0.60

0.45

0.30

0.15 0

0.2

0.4 0.6 CO coverage θ [ML]

0.8

1.0

Fig. 4. Sticking probability of CO on clean Pd(100) (0 ML C) as well as Pd(100) precovered with various amounts of carbon (0.05-0.45 ML C), vs. CO coverage θ at 300 K [97Yeo].

The rate of desorption, rd, is always temperature dependent since atoms or molecules are transferred from a bound state to an unbound state in the gas phase. Nevertheless, this rate is coverage dependent and given by [75Kin, 75Men]  E  rd (θ, T) = θ n k d ( T) = θ n ν d ( T) N 0 exp − d  ,  kT 

(24)

Landolt-Börnstein New Series III/42A

Ref. p. 59]

1 Introduction

11

where kd(T) is the rate constant of desorption (in units of molecules/(cm2 s)), νd ( T) the pre-exponential frequency factor, N0 the density of surface sites, and Ed the activation energy of desorption. The activation energy of desorption is in general also coverage dependent, just as the heat of adsorption. At constant coverage, the activation energy of desorption is equal to the isosteric heat of adsorption plus the activation energy of adsorption. First order desorption implies that atoms or molecules desorb directly from their molecular physisorbed or chemisorbed state. Second order desorption occurs when a second order surface reaction, such as A + A → A2, preceeds the desorption. Complicated kinetics may be involved for combined surface reaction/desorption processes, resulting in other apparent order exponents of desorption [78Gor, 81Cas]. The experimentally determined order of desorption can not be straightforwardly interpreted in terms of a simple mechanism. A common technique for studying desorption kinetics is that of temperature programmed desorption (TPD) [53Bec, 56Ehr, 62Red]. A crystalline substrate containing a certain coverage of adsorbate is heated with a linear temperature ramp. Simultaneously the partial pressure of desorbing molecules is monitored by a mass spectrometer (or pressure gauge). For a sufficiently high pumping speed of the system one can show that the desorption rate is proportional to the partial pressure. A maximum in the rate of desorption is observed at a certain temperature T*, as illustrated in Fig. 5.

θ2

Pressure p

θ1

T* 250

300

350

400 450 500 Temperature T [K]

550

600

Fig. 5. Example of TDS traces of partial pressure p vs. substrate temperature T for two different initial coverages θ.

This temperature depends on the order of desorption, the activation energy of desorption, the initial coverage, etc. Under simple conditions, i.e. assuming Ed and νd to be constants, and for a first order desorption process, the peak temperature T* is related to the desorption energy: Ed ν T* = ln d − 3.64 . kT * dT dt

(25)

In general, however, the coverage dependence of Ed and νd has to be considered for almost any desorption process. One reason is adsorbate-adsorbate interactions which may not be negligible. In particular, the pre-exponential frequency factor may strongly depend on coverage and vary over many orders of magnitude [88See]. Advanced methods of experimentation, e.g. by relating the work function change of the substrate measured during desorption directly to the rate of desorption [83Pfn], and detailed data evaluation enable very accurate measurements of the coverage dependence of the isosteric heat of adsorption and the pre-exponential factor, respectively. A good example is CO on Ru(001) [82Men, 83Pfn] for which the results are shown in Fig. 6. The sudden decrease in the heat of adsorption and the

Landolt-Börnstein New Series III/42A

1 Introduction

12

[Ref. p. 59

frequency factor near the coverage of 0.3 is related to repulsive interactions within the adlayer causing a phase transition from an ordered 3 × 3 R 30° structure to a poorly ordered compressed CO layer.

Fig. 6a, b. Heat of adsorption Ead (a) and preexponential factor ν (b) vs. coverage θ for CO on Ru(001). Various quasi-equilibrium and kinetic measurements contributed to this data. The sudden decrease at 0.33 coverage is due to a structural change in the adsorbed layer [83Pfn].

Angular and kinetic energy dependence The principal questions concerning the angular and kinetic energy dependence of the rate of adsorption (or desorption) has been of great interest from early on [15Knu, 29Ste, 1879]. The starting point of this discussion is the velocity distribution of gas molecules under the condition of thermal equilibrium [85Com]. Here Maxwell's law is valid:  m  dn = 4πn    2πkT 

32

 mv 2  2 exp −  v dv ,  2kT 

(26)

where dn is the number density of molecules per unit volume, having a velocity between v and v+dv, and m the mass of the molecule. Introducing a solid surface into the gas phase creates a new situation in that directions of impinging and desorbing molecules relative to that surface can be defined. The differential flux of molecules impinging per unit time and unit solid angle in a given direction ( ϑ, ϕ ) , where ϑ is the polar angle relative to the surface normal and ϕ the azimuthal angle, and per unit time is then given by [85Com]:

Landolt-Börnstein New Series III/42A

Ref. p. 59]  m  df = n    2π kT 

1 Introduction 32

 mv 2  3 exp −  v cos ϑ dv .  2 kT 

13

(27)

Note the third power in velocity in Eq. (27) as compared to the square dependence in Eq. (26). This indicates that molecules in a flux directed onto a surface or leaving the surface will have an average kinetic energy different from that of molecules in the homogeneous gas phase. The average kinetic energy per molecule is (3/2)kT in the latter case, but 2kT for molecules directed towards or away from the surface if T is the gas temperature (here equal to the surface temperature). The angular distribution is cosine ("Knudsen distribution"). Based on the principle of microscopic reversibility ("detailed balance of fluxes"), the angular and kinetic energy distribution directed towards the surface, Eq. (27), and that of the molecules leaving the surface are the same in thermal equilibrium. The angular distribution of molecules leaving the surface are thus slightly peaked in the direction of the surface normal and the velocity distribution is Maxwellian. It was believed for a long time that Eq. (27) would be generally valid to describe the angle and velocity distribution of adsorbing and desorbing molecules. However, it was shown by Clausing [30Cla] and elaborated by Comsa [68Com] that this is not the case. The fundamental reason is simply that the sticking coefficient of adsorbing species is generally not unity, i.e. the probability of adsorption is not unity. This means that only a fraction of impinging molecules adsorb on the surface while others are scattered back. Vice versa, the probability of desorption must be also effected under equilibrium conditions, in that only some molecules desorb while others are scattered elastically or inelastically within the potential well without actually leaving the surface. Adsorption as well as desorption fluxes may therefore exhibit angle and energy dependencies which are markedly different from Eq. (27). Of course, the reason for sticking coefficients < 1 is the existence of an activation barrier of adsorption, Eq. (23). Molecules impinging in directions closer to normal incidence and/or with higher kinetic energy have a substantially higher probability of overcoming the barrier of adsorption, as their velocity component normal to the surface is larger. A similar argument holds for the desorption process. Thus the angular and velocity distributions of adsorbing and desorbing molecules are expected to deviate significantly from Eq. (27). In a qualitative sense, they will be more peaked in the normal direction than a cosine distribution and the mean kinetic energy of desorbing species will be higher than 2kT. There is then a two-fold task for the experimentalist. For adsorption systems with a unit sticking coefficient one may want to prove Eq. (27) and the principle of detailed balancing, i.e. the validity of Eq. (27) for adsorption and desorption. On the other hand, for systems with sticking coefficients < 1, one still expects to be able to prove equal adsorption and desorption rates as a function of polar angle, according to the principle of detailed balancing, but the actual measured dependencies should differ from that in Eq. (27). Strictly speaking, a rigorous proof of Maxwell and Knudsen distributions (or the deviations therefrom) is not possible under the conditions of thermal equilibrium because adsorbing and desorbing molecules can not be distinguished experimentally. Instead, separate experiments testing either fluxes have to be carried out utilizing the concept of molecular beams. Pressure or flux detectors selecting a small solid angle are used to probe the details of desorption [68Wil, 77Com, 79Com]. Molecular beams with a narrow angular cross section (and a narrow energy distribution) serve to probe the angular dependence of the sticking coefficient [85Ste]. Time-of-flight spectroscopy of desorbing molecules is used to measure the velocity dependence at a particular polar angle. The conditions are not those of a true equilibrium experiment, and it is therefore not a priori certain that the results will reflect the principle of detailed balancing [63Hir].

Landolt-Börnstein New Series III/42A

1 Introduction

14

Normalized integral flux

0.8

[011]

0.6

0.4

0 – 60°

Adsorption S0(ϑ) × cosϑ Desorption D(ϑ)

– 40°

– 20°

0° Angle ϑ

20°

40°

H2/Ni (111)

0.8

[011]

cosϑ

0.2

a

1.0

CO/Ni (111)

Normalized integral flux

1.0

[Ref. p. 59

[011]

0.6

0.4 Adsorption S0(ϑ) × cosϑ Desorption D(ϑ)

0.2

60°

Fig. 7a. Angular dependence of adsorption S and desorption D probability of CO from a Ni(111) surface. Equal probabilities are expected on the basis of detailed balancing. Gas and surface temperatures are 300 K [85Ste].

b

[011]

cos4.5ϑ

0 – 60°

– 40°

– 20°

0° Angle ϑ

20°

40°

60°

Fig. 7b. Angular dependence of adsorption S and desorption D probability of H2 from a Ni(111) surface. Equal probabilities are expected on the basis of detailed balancing. Non-cosine distributions for H2 indicate an activation barrier of adsorption. Gas temperature is 300 K, surface temperature 190 K [85Ste].

Examples of experimental angular distributions of adsorption and desorption are presented in Fig.7 for CO and H2 on a Ni(111) surface [84Ste, 85Rob, 85Ste]. In both cases the angular adsorption and desorption rates are clearly the same, confirming first of all the validity of detailed balancing and hence a quasi-equilibrium situation. Secondly, an excellent cosine distribution is found in the case of CO, in agreement with Eq. (27) and consistent with the sticking coefficient being close to unity for CO on Ni(111) [74Chr, 80Iba]. On the other hand, for H2 the distributions are non-cosine, i.e. in conflict with Eq. (27). They are more strongly peaked along the surface normal and can be described by cos4.5 ϑ . The sticking coefficient for H2 on Ni(111) was reported to be 0.025-0.07 [85Rob, 85Ste], and therefore the finding of non-cosine angular distributions is fully consistent with these low sticking coefficients. From measurements of the sticking coefficients of the two gases one knows that the adsorption of H2 is activated [85Rob] while that of CO on Ni(111) is probably not, or at least with a very small activation barrier [85Sha]. In the case of H2, measurements of the velocity distributions of desorbing D2 from Ni(111) at a surface temperature of 1134 K have shown that they are non-Maxwellian, with the gas temperature being substantially higher ("hot molecules") than the surface temperature, for polar angles of 0 - 55° [77Com, 79Com]. A particularly drastic example of this kind is shown in Fig. 8 by time-of-flight spectra of desorbing D2 from a Cu(100) surface at 1000 K and normal emission [82Com, 85Com]. The spectrum calculated for a Maxwell distribution at a gas temperature of 1000 K is shown for comparison. The measured distribution is very narrow and almost totally to the left of the Maxwell distribution, i.e. almost all desorbing molecules are much "hotter" than 1000 K. The mean kinetic energy of desorbing D2 is in this case about 4kT. Therefore the existence of an activation barrier of adsorption was also concluded from these results.

Landolt-Börnstein New Series III/42A

Ref. p. 59]

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15

Fig. 8. Time-of-flight spectra of D2 molecules desorbed from a clean (ο) and sulfur (x) (θS = 0.3) contaminated Cu(100) surface at 1000 K at normal emission. Short flight time corresponds to high kinetic energy. The dashed curve is a caculated spectrum based on a Maxwell distribution at a gas temperature of 1000 K [82Com]. The non-maxwellian experimental distribution for D2 indicates an activation barrier of adsorption.

Indeed, a number of experiments measuring the angular and velocity distributions have provided ample evidence for the correlation of non-cosine, non-Maxwellian distributions with activation barriers of adsorption and sticking coefficients less than unity [85Com]. Non-cosine distributions can be described phenomenologically by a coskϑ function, with values of k commonly between 10 and 1. Measured velocity distributions correspond to mean kinetic energies much higher than the surface temperature of the substrate, they are non-cosine and much narrower than the Maxwell distribution. All of these findings are relevant for chemisorption systems. By comparison, physisorption is not activated since there is no precursor state to physisorption. Further considerations in the context of activated adsorption can be made concerning the internal energy distributions of adsorbing and desorbing molecules. More detail about this and the effect of an activation barrier of adsorption on the characteristics of adsorption and desorption can be found in chapter 3.12.

1.3.2 Isotherms The relationship between the surface coverage and gas pressure p, at a constant temperature T, is called an isotherm, θ(p). The isotherm is a typical function characterizing the interaction between surface and gas molecules, under the conditions of thermodynamic equilibrium between solid and gaseous phases. A simple case is the Langmuir isotherm which is readily obtained from equating the rate of (non-activated) adsorption, assuming f(θ) = 1 – θ, and the rate of desorption, assuming first order. The result is θ( p ) =

p  E  12 , κ ( T) = ν d N 0 (2πmkT) exp − d  ,  kT  p + κ ( T)

(28)

where κ(T) (in units of pressure) depends exponentially on the activation energy of desorption, N0 the density of surface sites, and νd is the temperature dependent "frequency" of desorption, Eq. (24). A more detailed form of κ(T), which may be derived in the framework of statistical thermodynamics, depends on a number of assumptions concerning the degrees of freedom of the adsorbed species as well as their possible mutual interaction. No interactions are included in the derivation of Eq. (28). If nearest-neighbor interactions between the adsorbed species are taken into account, the same principal form of the isotherm, Eq. (28), is derived but κ(T) includes now a coverage dependent term containing the interaction energy, ε [39Fow, 96Des]. Therefore this isotherm is written as p(θ):

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θ (2πmkT) k F ( θ, T), k F (θ, T) = s 1− θ

12

p( θ ) =

 E + zθε νd exp − d  ,  kT 

[Ref. p. 59

(29)

where z is the average lateral coordination number between adspecies in the 2-dimensional lattice. If ε > 0, interactions are attractive, and below a critical temperature Tc < zε/2k, a two-phase adlayer can form for a certain range of coverage, consisting of a 2d ordered phase and a diluted disordered phase. For repulsive interactions, ε < 0, there is no critical temperature, i.e. a phase transition does not occur. For a case of non-activated adsorption, Ed + zθε = Qiso, we see that the isosteric heat of adsorption increases for attractive interaction between adspecies and decreases for repulsive interaction. The Langmuir isotherm shows that, at low pressure, the coverage is directly proportional to the pressure, while it approaches unity at high pressure. Single layer adsorption is frequently observed for chemisorbing molecules under vacuum conditions. However, this does not mean that isotherms are easily measured for single crystal samples of well-defined structure in vacuum. For example, if the heat of adsorption is > 20 kJ/mol, a measurement of an isotherm at low T would require low pressure and long equilibration times; on the other hand, at high T high pressures are needed which is not compatible with vacuum. Hence one prefers to measure a group of isobars θ(T)p which are replotted as isotherms. Multilayer adsorption can occur when the heat of adsorption of the second and higher layers are still appreciable compared to that of the first layer. This problem was considered by Brunauer, Emmet and Teller (BET) and led to the formula of the respective isotherm [38Bru]: θ( p ) =

k BET ( T) p p 0  Q − QL  , k BET ( T) = k 0 ( T) exp − iso  .  kT  (p 0 + k BET ( T)p − p)(p 0 − p)

(30)

The value p0 is the saturation pressure of the adsorbing gas at which an infinitely thick multilayer would form (condensation); QL is the heat of condensation. The model assumes a constant heat of adsorption for all layers beyond the first which is more strongly adsorbed. Interactions within each layer are not included. If the heat of adsorption varies from layer to layer, a more complex formula would result.

1.3.3 Non-thermal desorption In this introduction to adsorbate/substrate systems we have largely relied on the framework of thermodynamics for the phenomenological description of adsorption and desorption. Rates are governed by partial pressures in the gas phase and by gas and substrate temperatures, respectively. On the other hand, there is a group of adsorption/desorption phenomena where temperature is of secondary importance. Instead, rates are influenced decisively by non-thermal, non-equilibrium processes, induced by incident radiation with high energy photons, electrons or ions. Although both, the rate of adsorption as well as the rate of desorption, can be effected by energetic radiation, the process of desorption has received more attention in this context. Thus one speaks of ion-induced, electron-induced etc. desorption of atoms, molecules or fragments. The detailed mechanism of non-thermal desorption (and fragmentation) has been subject of intense investigation. In the case of infra-red radiation the distinction between thermal and non-thermal effects is particularly challenging, and the term laser-induced thermal desorption (LITD) should not be taken as an indication of a purely thermal mechanism. In many cases radiation induced electronic transitions to nonbonding states are the most important mechanistic step of this kind of desorption [64Men]. This gave rise to the term desorption induced by electronic transitions (DIET), a process that was subject of numerous conferences. DIET has become a sub-field of adsorption/desorption which will not be covered in this volume in any detail [83Tol, 85Bre, 88Stu, 90Bet, 93Bur].

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1.4 Physical and chemical properties of adsorbed species After the introduction to the general phenomenology of adsorption/desorption of gases on well-defined crystalline surfaces we will now give an overview of the main physical and chemical properties of adsorbed species. The adjective main relates to those properties which have been specifically analyzed in greater detail and with sufficient accuracy, for a large number of molecules, such that a listing and comparison in tables appears to be reasonable. Naturally, the number of investigations will vary widely from molecule to molecule, depending on several factors: ease of operation with gases in various environments; achieving stable adsorbate coverages under realizable conditions; applicability of several analytical techniques; relevance to technical processes, e.g. heterogeneous catalysis; corrosion, thin film formation, semiconductor device technology, etc. We will introduce and briefly discuss a few selected experimental results for each adsorbate property by referring to simple examples. One of the preferred systems to be used for the purpose of illustration is the reversible adsorption of CO on a Ni(110) surface. This is also one of the best studied systems in this field (compare section 3.7.1). For reference purposes we list here some general properties of gaseous CO. The electronic configuration is (1σ)2(2σ)2(3σ)2(4σ)2(1π)4(5σ)2, with the last three as valence molecular orbitals at 19.7, 16.8 and 14.0 eV binding energy, respectively [78Plu, 84Kra]. The bond length is 1.13 Å, the dissociation energy 11.2 eV, the static dipole moment 0.1 debye, and the C–O stretch vibration has a value of 2143 cm–1 [79Hub].

1.4.1 Sticking coefficient The sticking coefficient, defined as the rate of adsorption divided by the rate of impinging molecules, at a certain coverage and substrate temperature, is a quantity involving dynamic aspects as well as the energetics of adsorption. It is measured by following the coverage of the adsorbate as a function of gas exposure, either in the presence of a constant background pressure of this particular gas or in a molecular beam experiment where the flux of impinging molecules is known. The surface coverage is obtained by a surface sensitive chemical probe or a suitable physical indicator which has been calibrated, e.g. the change of work function versus coverage of adsorbate. A common way to determine coverage is also by stopping the exposure, desorbing all molecules by raising the temperature, recording and integrating the pressure pulse versus temperature. 0.8

1.0

CO/Ni

CO/Ni (110) 0.8

(110)

0.4 (100)

0.2

a

Rel.sticking coeff. s/s0

Sticking coeff. s

0.6

0

0.4 0.6 0.8 Apparent CO coverage θ [ML]

1.0

Fig. 9a. Sticking coefficient s of CO vs. apperent coverage θ on Ni(111) (- - -), Ni(100) ( ) and Ni(110) (....) surfaces at 300 K [93Stu]. Measured differences indicate surface structural sensitivity.

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0.4

0.2

(111)

0.2

0.6

b

0

0.2

0.4 0.6 CO coverage θ

0.8

1.0

Fig. 9b. Relative sticking coefficient s/s0 of CO vs. coverage θ on Ni(110) at 130 K [85Beh]. Comparison with Fig.9a illustrates the temperature dependence.

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[Ref. p. 59

Figure 9 compares the results of both approaches for CO on Ni(110) at two different temperatures, 130 K [85Beh] and 300 K [93Stu], respectively. In Fig. 9a the sticking coefficient is determined by the molecular beam technique for the low-index surfaces (111), (100) and (110). Its value at zero coverage is 0.75, independent of surface orientation, and decreases with increasing coverage until it reaches 0.3 at a monolayer of CO. Figure 9b shows the coverage variation of the relative sticking coefficient for the (110) surface (normalized to unity at zero coverage) determined continuously from the change in electron work function versus CO exposure. The behavior is qualitatively quite different than in Fig. 9a, partly due to the lower temperature of 130 K which may be responsible for an extended range of nearly constant sticking, compared to the faster decrease at 300 K. The observation of s0 < 1 and the rather pronounced temperature dependence of the sticking coefficient versus coverage point consistently towards the existence of a physisorbed CO precursor state and an activation barrier of adsorption.

1.4.2 Heat of adsorption The heat of adsorption is in general a function of the adsorbate coverage. Its value at a certain coverage is a direct measure of the strength of interaction between substrate and adsorbate and of the inter-molecular interaction. Therefore the heat of adsorption depends on the adsorption site and on the surface structure in general. If the adsorption of molecules is fully reversible, i.e. if no dissocation occurs, and if there is no significant activation barrier for adsorption, the heat of adsorption and the activation energy of desorption should be approximately the same. This comparison has been made for CO on Ni(110) for which calorimetric, isosteric and desorption measurements exist [73Mad, 90Fei, 92Dea, 93Stu]. 150

CO/Ni (110)

–1

Adsorption heat Q [kJ mol ]

140 130 120 110 100 90 0

0.2

0.4 0.6 0.8 Apparent CO coverage θ [ML]

1.0

Fig. 10. Heat of adsorption Q vs. apparent coverage θ for CO adsorbed on Ni(110) at 300 K. Comparison of data obtained by Stuckless et al. [93Stu] (full circle), Madden et al.[73Mad] (open circle), DeAngelis et al. [92Dea] (down triangle) and Feigerle et al. [90Fei] (up triangle).

Figure 10 shows a plot of these energies versus CO coverage between zero and one monolayer. The initial heat of adsorption is near 130 kJ/mol, decreasing towards higher coverages to about 100 kJ/mol. There are certain systematic differences in these results: The plateau of constant heat of adsorption extends up to a coverage of about 0.6 for the isosteric and desorption energies, respectively, while the calorimetric heat shows a decrease already at 0.3 coverage leveling off at 0.55. These differences may be due to rather different temperature ranges playing a role at these measurements. The calorimetric measurement is also an almost isothermal measurement while the measurements of the isosteric heat and the desorption energy involve a rather broad temperature menu. Measurements of isotherms as a source of the heat of adsorption are rare for single crystal substrates. Special techniques of experimentation are required to record isotherms under vacuum conditions. One such measurement is known for CO on Ni(110) [70Kli] which shall illustrate the case. The coverage of

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radioactively labelled 14CO is monitored [54Dil, 69Kli] at constant substrate temperature as a function of CO pressure. Pressure p [Torr] for T = 298 K –7 –5 10 10

–9

1.2

10

–3

10

CO/Ni (110)

–2

CO surface density [1015 cm ]

1.0

0.8

0.6 T = 298 K 182 K

0.4 0.2 16

19

22

25 ln (p/kT)

28

31

34

Fig. 11. Surface density N [1015cm−2] vs. pressure p (respectively ln(p/kT)) for CO adsorbed on Ni(110) measured at two temperatures of 182 and 298 K [70Kli].

The isotherms shown in Fig. 11 for T = 182 K and 298 K are then fitted to a theoretical isotherm based on the Devonshire cell model [37Dev]. Lateral interaction between adsorbed CO molecules as well as the substrate CO interaction are accounted for in this model. Under special assumptions, values of 106 kJ/mol and 15 kJ/mol are separately obtained for the heat of adsorption and the CO–CO interaction energy, respectively. These energies are not coverage-specific. Because of the separation of the heat of adsorption into an energy of adsorption of an isolated CO and the energy of lateral CO interaction, the value of 106 kJ/mol should be compared to the heat of adsorption at zero coverage in Fig. 10.

1.4.3 Orientation of adsorbed molecules With regard to the structure of an adsorbed molecule or radical on a crystalline metal or semiconductor surface, answers on different levels of complexity can be sought. One of the primary questions concerns the adsorption bond(s) itself, i.e. which molecular group(s) bonds to surface atoms of the substrate. Secondly, how is the molecule oriented relative to the surface normal? The first question can often be answered by referring to the cluster-surface analogy. There is a large group of molecular metal clusters which are ideal model systems of chemisorption [78Plu, 79Mue]. For example, the group of metal carbonyls consists of several metal atoms and CO molecules which are bonded through the carbon atom to the metal. In analogy, one expects CO to bond (involving the 5σ and 1π molecular orbitals of CO) via the carbon atom to a metal surface. Investigations of CO bonding to a large variety of metal surfaces have confirmed this cluster-surface analogy in many respects. From a techniques point of view three examples will be given here which demonstrate how adsorbed CO is oriented on a metal surface. The first technique rests on the phenomenon that linearly polarized light couples differently to molecular orbitals of π and σ symmetry [76Lie]. CO has three molecular orbitals of interest here: 4σ, 1π and 5σ (in order of decreasing binding energy). When a CO covered surface is irradiated with uv-photons, photoelectrons at characteristic kinetic energies are emitted. The emitted intensity is a measure of the interaction probability between photon and bound electron state (orbital). Figure 12 shows a series of spectra for p- and s-polarized light (28 eV) recorded for various polar angles of emission from a Ni(100) surface covered with adsorbed CO [76Smi]. Two peaks are observed at about 8 eV and 11 eV binding energy. The peak at 11 eV is only intense for p-polarized light at normal emission. Comparing the experimental results to theoretical calculations for oriented CO

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[Ref. p. 59

molecules [76Dav, 78Dav], agreement is found for perpendicularly adsorbed CO oriented and bound with the carbon atom towards the surface [76Smi, 77All]. The accuracy of determining the bond angle by this technique is not very high. ϑA = 47.7° A

hν ϑp

hν

ϑA = 90°

ϑp p

p ϕp A

ϕp

CO/Ni (100) clean ϑp = 0° N(E) [counts per incident photon]

N(E) [counts per incident photon]

clean ϑp = 0°

3L CO ϑp = 0°

3L CO ϑp = 0°

3L CO ϑp = 30°

a

– 14

– 12

– 10

–8 –6 –4 Initial energy Ei [eV]

3L CO ϑp = 23°

–2

0

b

– 14

– 12

– 10

–8 –6 –4 Initial energy Ei [eV]

–2

0

Fig. 12a, b. Angle resolved photoemission spectra of CO adsorbed on Ni(100) at a photon energy of 28 eV. (a) Nearly p-polarized light; (b) s-polarized light [76Smi].

The second technique utilizes the effect of stimulated ion desorption from adsorbates when the covered surface is irradiated with medium to high energy electrons. We consider the particular system CO adsorbed on Ni(110) at low and high CO coverage. The measurement of the angular distribution of desorbing ions (ESDIAD, electron stimulated desorption ion angular distribution) is then related to the orientation of the adsorbed species which supply the ions [79Mad1, 79Mad2, 85Rie, 86Alv]. ESDIAD distributions of mostly O+ ions, generated by 1000 eV incident electrons, from adsorbed CO at coverages of 0.5 and 1.0, respectively, are shown in Fig. 13 [86Alv]. A single emission peak perpendicular to the surface is observed at the lower coverage, attributed to perpendicularly adsorbed CO. A double peak, measured at polar angles of about 19° relative to normal, is clearly resolved at the saturation coverage of CO for which the well ordered (2×1)p2mg layer exists. This double peak is interpreted in terms of a tilted CO molecule whereby the projected tilt occurs along the [001] and [00 1 ] surface directions [85Rie, 86Alv]. The fact that these angular distributions are measured for O+ emission suggests that CO is Landolt-Börnstein New Series III/42A

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oriented with the carbon atom next to the surface (Ni–C bonding). The quantitative evaluation of the CO tilt is somewhat hampered by the attractive force between the emitted ion and its image charge, resulting in bent ion trajectories emitted at a polar angle larger than that of the tilted molecule.

Fig. 13. ESDIAD intensity distribution for CO adsorbed on Ni(110) showing perpendicularly adsorbed CO at low coverage and tilted CO at saturation coverage. The incident electron energy was 1000 eV [86Alv].

A third technique for locating the orientation of bond directions of adsorbed molecules is x-ray photoelectron diffraction (XPD) in the forward scattering mode [79Pet, 82Ord, 84Ege, 88Wes2, 89Wes]. Recording the angle-resolved intensities of core level photoelectrons, here either C1s or O1s from the carbon or oxygen atom of CO, respectively, allows the spatial localization of the CO bond axis and furthermore, an unambiguous distinction of the molecule's bonding through either the carbon or oxygen atom [79Pet]. Typical results for CO adsorbed on Ni(110) are presented in Fig. 14, for two different coverages [92Kna, 94Fri]. The angular distribution of C1s intensity versus polar angle at a CO coverage of about 0.6 shows a large narrow peak at normal emission and smaller maxima at 44° and 64° polar angles. The main peak at normal emission proves, firstly, that CO is bonded through the carbon atom to the Ni surface, since the corresponding O1s distribution is isotropic, and secondly, that CO is perpendicularly adsorbed. Checking the azimuthal variation of the C1s forward scattering peak width shows rather different values at half height, indicative of anisotropic amplitudes of "wagging" vibrations of CO [88Wes1, 94Fri]. The smaller peaks in Fig. 14 arise from inter-molecular scattering and are thus a sign of short range order within the CO layer. The second C1s intensity distribution shown in Fig. 14 was recorded along the [001] azimuth at 120 K, for the CO coverage of unity. This distribution shows a total of four peaks, located at polar angles of 20° and 67°, respectively. The peaks at 20° are due to intra-molecular scattering of C1s photoelectrons and indicate therefore the tilt angle of adsorbed CO molecules. The outer peaks at 67° are due to intermolecular scattering, i.e. scattering between neighboring CO molecules, and are consistent with a well ordered arrangement of CO on the Ni(110) surface (compare 1.4.5).

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CO/Ni (100) C1s in <110>

[Ref. p. 59

Intensity I

T = 300 K θCO = 0.55

a

90°

75°

60°

45°

30°

0° 15° 15° Polar angle ϑ

30°

CO(2×1) p2mg/Ni (110) C1s in <001>

45°

60°

75°

90°

T = 120 K θ=1 experiment theory

Intensity I

Fig. 14a, b. XPD C1s intensity distributions of CO adsorbed on Ni(110) at (a) 300 K and a coverage of 0.55, (b) 120 K at a coverage of unity. The dotted curve in (b) is the result of a multiple scattering calculation [92Kna, 94Fri].

b

90°

75°

60°

45°

30°

0° 15° 15° Polar angle ϑ

30°

45°

60°

75°

90°

1.4.4 Surface diffusion coefficients Adsorbed species, atoms and molecules, are mobile in their physisorbed precursor states and, depending on the surface temperature, also in their chemisorbed states. The mobility is generally higher, the lower the adsorption energy. Rates of surface diffusion have been measured for many chemisorbed species but only for a few physisorbed species [59Gom, 90Gom, 93Bon, 95See]. A number of different experimental techniques exist for the measurement of surface diffusion coefficients (compare section 3.11). Some techniques rely on rather macroscopic diffusion, i.e. over distances of the order of several µm or more. Others determine the local mobility, on the scale of nm. Hence the characteristic quantitative parameters describing the rate of surface diffusion can be different, depending on the technique. The main reason for observed differences in absolute values of measured surface diffusion coefficients and activation energies is the inhomogeneous potential that the adsorbed species encounters by diffusing across the surface [65Gjo, 66Gjo]. Even on a well oriented low-index single crystal surface there are defects sites, such as steps, kinks, small adatom or vacancy clusters, dislocation emerging points, which constitute in general higher binding energy sites than those on a flat terrace. Therefore, if a technique measures diffusion over a distance large compared to the averge separation between these defect sites, the activation energy of surface diffusion will include contributions due to transient binding to these sites. In this case one speaks Landolt-Börnstein New Series III/42A

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of mass transport surface diffusion. On the other hand, if a technique measures diffusion in an area small compared to the inter-defect separation, an activation barrier characteristic of terrace surface diffusion will be measured, provided the measured area is defect-free. In this case the diffusion coefficient is defined by statistical random walk and one speaks of tracer or intrinsic surface diffusion, if the coverage of the diffusing species is very low [83Gom]. For larger coverages, where interactions between diffusing species become important, a chemical surface diffusion coefficient has been defined that contains a thermodynamic derivative factor of the adlayer's chemical potential with respect to particle density [77Ehr]. In that case the surface diffusion coefficient may depend strongly on coverage, especially where ordered adsorbed layers exist. More about these distinctions can be found in section 3.11. A corresponding chemical mass transport surface diffusion coefficient can also be defined. Another complication in comparing data from different techniques may arise from the possibility that several surface diffusion mechanisms may be operative. Evidence for different surface diffusion mechanisms may be revealed by large differences in measured activation energies and by large differences in absolute values of measured surface diffusion coefficients at the same temperature. Hence experimental data, especially if they originate from different techniques, need to be be compared systematically in order to decide whether the effective rates of diffusion (at the same or at different temperatures) may be indicative of different diffusion mechanisms. Rates of surface diffusion of CO adsorbed on Ni(110) and Ni(111), for example, were investigated by several rather different techniques: second harmonic diffraction (SHG)[88Zhu, 91Xia] and linear optical diffraction [93Xia, 95Xia, 97Xia] from CO "gratings", quasi-elastic He atom scattering [96Ber], and by field emission fluctuations from CO layers at different coverages on a field emitter tip [90Lin]. It is interesting to compare the various data sets obtained for Ni(110) but also those for Ni(110) with the ones for Ni(111) [88Zhu, 90Lin]. Table1 summarizes the former in terms of pre-exponential factor, ν0, and activation energy of surface diffusion, Edif, according to the phenomenological Arrhenius expression:  E  DS = ν 0 exp − dif  .  kT 

(31)

As expected, surface diffusion of CO is anisotropic on the (110) surface, characterized by a lower activation energy in the close-packed [1 1 0] direction than perpendicular to it. The measured activation energies for CO on clean Ni(110) are in the range of 1-4.8 kcal/mol and pre-exponential factors vary over many decades. Additional measurements on the effect of surface impurities have shown that a small amount of coadsorbed sulfur (θ = 0.05) leads to an increase in the activation energy to 6-8 kcal/mol [97Xia]. This effect is attributed to the prediminant adsorption of impurities at steps thus increasing the apparent activation energy of CO surface diffusion. Figure 15 shows a plot of surface diffusion coefficients of CO versus 1/T for clean Ni(110) calculated on the basis of the data in Table 1 by using Eq. (31). Two well separated data groups can be recognized, one with high diffusion coefficients near 10–5 cm2/s, the other in a range between 10–9 and 10–14 cm2/s, located at lower temperatures. The diffusion coefficients of data set (a) obtained by He atom scattering [96Ber] at a CO coverage of 0.15 are larger by a factor of more than 104 relative to the other group. Also, the activation energies are low for both diffusion directions, with the [001] direction still having a lower activation energy than the [1 1 0] direction, opposite to all measurements in the other data group. Since He atom scattering is a very local probe of diffusional motion, it has been argued that the activation energies are truly representing barriers between adjacent adsorption sites, i.e. independent of the presence of steps on the surface [98Gra]. On the other hand, if CO diffusion along steps is faster than on terraces, the activation energies could also be characteristic of the step mode of surface diffusion. In any case, the physical meaning of data group (a) is not well understood at this time. With regard to coverage dependence, low activation energies are found at near saturation coverage of CO, as shown by the data sets (b) and (c) [91Xia, 93Xia]. An increase in activation energies for both diffusion directions if found at lower CO coverages, as seen by the example (d) [93Xia]. By comparison, surface diffusion of CO on clean Ni(111) is characterized by an activation energy of 6.8-6.9 kcal/mol which is higher than on Ni(110). The calculated diffusion coefficients fall into the same range as those of

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[Ref. p. 59

the lower group in Fig. 15 [88Zhu, 90Lin]. It is interesting to note that two very different techniques, one of them also a local probe of diffusion [90Lin], have produced a fairly consistent set of data for CO/Ni(111). Hence the apparent discrepancy displayed in Fig. 15 for Ni(110) can not easily be associated with local versus non-local measurements of surface diffusion. –4

10

CO/Ni (110)

a –6

2 –1

Diff.coeff. Ds [cm s ]

10

[110] [001] Fig. 15. Surface diffusion data of CO adsorbed on Ni(110) obtained by various authors, techniques and coverages. (a) θCO = 0.15 [96Ber]; (b) θCO near saturation [91Xia]; (c) θCO = 0.98 [93Xia]; (d) θCO = 0.5 [93Xia]. Each data set consists of two lines, corresponding to the [1 1 0] and [001] diffusion directions, respectively.

–8

10

d

–10

10

b

c

–12

10

–14

10

2.5

3.5

4.5

5.5

6.5

–1

–3 –1

7.5

8.5

9.5

Inv. temperature T [10 K ]

Diffusion coefficients of CO adsorbed on Ni(110) and Ni(111) at room temperature are about 10–9 cm2/s [88Zhu, 90Lin, 91Xia, 93Xia], corresponding to a mean diffusion path of 0.63 µm in the time of 1 s. This means that a large area can be sampled in 1 s allowing an equilibrated layer to be established, i.e. ordering of the CO molecules to occur if this is compatible with energy minimization. Indeed, long range ordered adsorbate structures are frequently encountered in the case of adsorbed CO (compare section 3.7.1). Table 1. Survey of surface diffusion data for CO on Ni(110) surface. Edif [kcal/mol]

Range ∆T [K]

Coverage

Ref.

3.8 × 10–9

1.1

105-182

unspec.

[91Xia]

[001]

4.8 × 10

3.1

110-182

[1 1 0]

2 × 10–8

2.1

140-204

0.98

[93Xia]

[001]

2 × 10–8

Direction

ν0 [cm2/s]

[1 1 0]

–6

2.8

140-204

0.98

[1 1 0]

4.5 × 10

–6

4.05

150-220

0.5

[001]

1.5 × 10–6

4.75

180-244

0.5

[1 1 0]

1 × 10–4

6

180-230

0.5 + S

[001]

1 × 10–3

8

180-230

0.5 + S

[1 1 0]

1.8 × 10

–4

1.31

200-360

0.15

[001]

7.3 × 10–5

0.81

240-360

0.15

[93Xia]

[95Xia, 97Xia]

[96Ber]

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1.4.5 Long-range order Lateral interactions between adsorbed species on single crystal surfaces lead frequently to well ordered arrays. The ordered layer may sometimes include substrate atoms, equivalent to a reconstruction of the original surface, or may only consist of the adsorbed species. If the order is of sufficient long range character, diffraction patterns from elastically scattered low-energy (LEED) or high energy (RHEED) electrons, x-rays at grazing incidence, or atoms (such as thermal energy He atom scattering, TEAS) will result. The kinematic features of the diffraction patterns allow to propose a unit cell of the ordered array, and if the coverage is known, also a corresponding structure model. Quantitative analysis of the diffracted intensities versus energy may lead, if the unit cell is not too large, to quantitative structural information of the surface-adsorbate complex, i.e. the adsorbate itself and the adsorption site (compare 1.4.7). Most recently, it has become possible to image adsorbed molecules directly by scanning tunneling microscopy (STM) and to see long range order in the adlayer. Although the area covered in those images is small (about 40×40 Å2) there is no doubt that some layers are excellently ordered over much larger distances. We will illustrate here the long range order effect by qualitative LEED [85Beh], XPD [98Emu] and real space STM images [95Spr] for CO adsorbed on Ni(110). The observations with LEED show that three ordered CO arrays can be noted with increasing coverage at 130 K, with the notations c(8×2), c(4×2) and (2×1)p2mg. Schematic LEED patterns are shown in Fig. 16, together with corresponding structure models [85Beh]. The latter are based on measured CO coverages and the conversion of the unit cell from reciprocal to real space. The corresponding ideal coverages are 2/3, 3/4 and 1.0, respectively. The (2×1)p2mg pattern at unity coverage is sharper than the others, indicative of good long range order. The diffraction spots ( n + 12 , 0) are missing at normal incidence of the electrons. This behavior is consistent with a glide plane along the [1 1 0] surface direction and a mirror plane along the [001] direction, hence the symmetry notation p2mg of the unit cell. Since the unit cell of the (2×1)p2mg structure contains two CO molecules, which must be structurally inequivalent, a tilt of these CO molecules in opposite directions is suggested [82Ban]. The corresponding (2×1)p2mg structure model based on LEED, STM and other experimental work is shown schematically in Fig. 17. The long range order of the (2×1)p2mg-CO layer has also been verified by He atom diffraction [91Par] which probes the outer most atoms at the surface, in this case the oxygen atoms of the adsorbed CO.

Fig. 16a - c. Structure models and schematic LEED patterns for CO on Ni(110) observed at the coverages of (a) θ = 0.67, (b) θ = 0.75 and (c) θ = 1.0 [85Beh]. The unit cell is indicated in each case.

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[Ref. p. 59

Fig. 17a, b. (a) Structure model and unit cell of (2×1)p2mg CO layer on a fcc (110) surface; (b) corresponding 2D Brillouin zone.

Fig. 19a, b. STM images of CO adsorbed on Ni(110) at 300 K in the (2×1)p2mg configuration. The (2×1)p2mg unit cell is indicated in the lower figure. Image sizes are 60×60 Å (upper part) and 30×30 Å (lower part) [95Spr]. Fig. 18a, b. Large solid angle XPD intensity patterns for CO/Ni(110) in the (2×1)p2mg configuration. Azimuthal surface orientation same as in fig. 17. (a) upper part: experimental data, 2-fold averaged, (b) lower part: single scattering calculation [98Emu].

Angle-resolved XPD measurements of C1s intensities from the well ordered (2×1)p2mg-CO layer over a large solid angle are in good agreement with the structure model [75Lam]. Figure 14 showed already four C1s peaks for the [001] azimuth in a single polar angle scan. If the C1s intensity is recorded for the same layer over a large solid angle, other forward scattering peaks arising from intermolecular

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forward scattering can be detected outside the [001] azimuth, such as shown in Fig. 18a by the stereographic plot of C1s intensity. The result of model calculations of elastic photoelectron scattering for an unsupported (2×1)p2mg-CO layer, illustrated in Fig. 17 for CO molecules tilted by 20° relative to normal, is shown in Fig. 18b as a stereographic projection. Excellent agreement between the experimental and theoretical C1s forward scattering peaks is found in position and relative intensity which fully supports the structure model of the (2×1)p2mg CO layer [98Emu]. A real space verification of the long range ordered CO structure on Ni(110) at the coverage of unity was obtained by STM [95Spr]. This coverage was achieved at room temperature by maintaining a background pressure of CO of 1×10–6 mbar in the vacuum chamber (compare the isotherm in Fig. 11). Figure 19 shows two images of the (2×1)p2mg-CO layer, taken at two different bias voltages. The (2×1) unit cell is indicated and it can be clearly seen that there are two CO molecules per unit cell. The CO molecules show a zig-zag arrangement along the [1 1 0] glide direction and a mirror plane perpendicular to it. These are exactly the characteristic features of the (2×1)p2mg unit cell. Refinements of this model, such as quantitative structural data, tilt angle of CO, adsorption site, etc. are based on other techniques (compare 1.4.3 and 1.4.6). The STM images of adsorbed CO in Fig. 19 are only possible because of the high CO coverage which does not permit a diffusional motion of CO across the surface. The packing density of CO is so high that even vibrational motions are hindered to some extent, a fact which explains the sharpness of these images.

1.4.6 Vibrational frequencies Vibrational frequencies of molecules adsorbed on single crystals can be measured by infra-red absorption spectroscopy (IRAS) in reflection, Raman spectroscopy, or by energy loss spectroscopy of scattered lowenergy electrons or He atoms. The vibrational eigenmodes of the adsorbates are characteristic of their bonding to the substrate and their internal structure and bond strengths. Measured vibrational frequencies are always compared to known frequencies of equivalent gaseous species as a reference. Frequency shifts relative to the gas phase species can be interpreted in terms of bond and even structural or chemical changes. The number of observed modes as well as their group symmetries are important guides to structural changes and the orientation of the adsorbate relative to the surface. Depending on the technique, specific selection rules for the excitation of vibrational modes have to be considered. More detail about this aspect can be found in chapter 2.

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[Ref. p. 59

Fig. 21. Dispersion of CO vibrational frequencies for the main directions of the surface Brillouin zone, measured under non-specular conditions for the well ordered (2×1)p2mg CO structure [90Voi]. Fig. 20a, b. Electron energy loss spectra of CO on Ni(110) in (2×1)p2mg structure. The scattering geometry is specular and the energy resolution is 15.5 and 28 cm–1 for (a) and (b), respectively [90Voi].

Since the accessible frequency range is largest in electron energy loss spectroscopy (EELS) of adsorbates, as compared to infra-red absorption spectroscopy (IRAS), a sample EELS spectrum for CO adsorbed on Ni(110) is shown in Fig. 20 [90Voi]. The coverage of CO is at saturation, such that an ordered (2×1)p2mg structure results [75Lam, 85Beh, 85Gur]. The intra-molecular vibration of the C–O stretch is found at 1984 cm–1, indicative of a weakened C–O bond compared to the gas phase molecule which has a stretch frequency of 2143 cm–1. Vibrations characterizing the Ni–C adsorption bond are observed at 114 cm–1 and 421 cm–1, corresponding to the "frustrated" translation/rotation and the Ni–CO stretch modes, respectively. The detected frequency values are not fixed but dependent on the parallel component of the wave vector of the scattering electrons and on the orientation of the scattering plane. This dependence has been investigated, and Fig. 21 shows the dispersion of the CO related frequencies for the two main directions of the unit cell of the (2×1)p2mg structure. The degree of dispersion is a direct measure of the repulsive CO–CO interactions within the adsorbed layer. Measured vibrational frequencies of adsorbed CO contain also information on the adsorption site. Considering the scattering geometry and the group specific selection rules for observing particular modes, it should in principle be possible to elucidate the site [79Ric]. For CO adsorbed on Ni(110), both atop and bridge adsorption sites have been proposed on the basis of EELS data [82Ban, 90Voi]. Bandy et al. deduced a mixture of CO bonding to a single (atop) and two adjacent Ni surface atoms (bridge site) at low CO coverage and exclusively to bridge sites at high CO coverage. Voigtländer et al. favored the atop site Landolt-Börnstein New Series III/42A

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at high coverage. Structural investigations proved the bridge site to be correct at the high CO coverage of the ordered CO (2×1)p2mg layer [88Han, 93Hua, 93Pan1, 93Pan2].

2058

0.545

2055

~ 0,57

2049

1905

1908 1912

1905

T = 90 K (annealed to 240 K) θCO = ~ 0.57

1914

CO/Ni (111)

1902

0.525

0.35 0.33

2049

0.405

2052

2055

Absorbance A

0.435

2054

1887

0.50

1831

0.175 0.14 0.11 0.07 0.03 0.015

1816

1818

0.3

1800

1850

1900 1950 –1 Wavenumber ν [cm ]

2020

0.003 A

resolution = 7 cm

2060

–1

Fig. 22. Infra-red absorption spectra of CO adsorbed on Ni(111) for CO coverages between 0.015 and 0.57. All peaks correspond to C–O stretch vibrations [88Sur].

2100

The correlation between adsorbate eigenfrequencies and adsorption site assignment is in general not unambiguous. The problem is further demonstrated by the example of CO on Ni(111) which has been studied by IRAS [88Sur, 89Che] as well as EELS [79Erl1, 81Ber]. Figure 22 shows a sequence of IRA spectra of adsorbed CO for increasing coverages at 90 K and annealed at 240 K [88Sur]. Two main bands are observed, one at low frequencies of 1816-1914 cm–1, the other at about 2050 cm–1. The low frequency band shifts significantly with increasing coverage. This band was assigned to 3-fold hollow and 2-fold bridge sites, the latter being occupied at higher coverages. The high frequency band was attributed to atop adsorption sites. A well ordered CO layer of c(4×2) symmetry appeared at a coverage of 0.5 at which only one kind of CO was observed, at the time associated with CO in 2-fold bridge sites [79Erl1, 88Sur]. Landolt-Börnstein New Series III/42A

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It was shown later by quantitative photoelectron diffraction work that this site assignment was incorrect [93Sch, 96Dav]. Instead CO was found to be adsorbed in 3-fold hollow sites, both fcc and hcp, at low and intermediate coverages up to 0.5, which is the coverage of the c(4×2)-CO structure. The observed frequency shifts are believed to be largely caused by lateral CO–CO interactions. This example shows that the frequency of an internal mode of an adsorbate is not necessarily a reliable guide to the adsorption site [93Sch].

1.4.7 Structure and adsorption site Quantitative structure investigations of the adsorbate/substrate complex are possible by a number of techniques, such as LEED, photoelectron diffraction, x-ray diffraction and x-ray absorption spectroscopy, to name the most frequently used ones. Quantitative LEED in the form of recorded beam intensities versus energy requires long range ordered adsorbate structures. Photoelectron diffraction and x-ray absorption, on the other hand, are typical short range order techniques. A new variant of LEED rests on the holographic interpretation of elastic electron scattering [90Sal, 95Sal] where the primary scattering event generates the reference wave and the secondary scattering events at neighboring atoms represent the object waves. Superposition of both, reference and object waves, causes interference and produces a diffuse intensity distribution in space (hologram). A suitable Fourier transform of the intensity pattern yields the three-dimensional atomic structure around the primary scattering atom, adsorbed randomly on the surface. This holographic approach works for single atom adsorption in an ordered array, whereby this atom serves as the beam splitter [97Reu]. However, holographic LEED does not work for adsorbed molecules. We stay with the example of CO adsorbed on Ni(110) and present results of a quantitative LEED intensity investigation of the structure of the adsorbed CO [88Han]. In fitting the experimental data of beam intensity versus electron energy to theoretical profiles, a large number of trial structures were considered. Five structural parameters, such as the C–O and the Ni–C bond lengths, the Ni–Ni interlayer spacing, the surface-C and the C–O tilt angles, and the adsorption site (atop, 2-fold short and long bridge) were varied. The results were: CO is adsorbed in the short bridge site, the C–O and Ni–C bond length are 1.12 Å and 1.95 Å, respectively, and the Ni–C and C–O tilt angles in the [001] directions are 27°±3° and 17°±3°, respectively [88Han]. The optimum values are found by the usual R-factor (residual) analysis. For example, Fig. 23 shows the R-factor contour plot for the C–O bond length versus Ni–C bond length, assuming a common Ni–C–O tilt of 20°. A rather shallow broad minimum is achieved.

Fig. 23. LEED R-factor plot for the variables C–O bond length and CO tilt angle. A minimum is found near 22° and 1.9 Å bond length [88Han].

A second quantitative structure determination for the same system is based on energy scanned C1s photoelectron intensities of the adsorbed CO for several directions and a kinetic energy range of 60-400 eV [93Hua]. The data were evaluated by Fourier analysis as well as by fitting to theoretical

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intensity versus energy profiles, based on a multiple scattering spherical wave approach. The results were that CO is adsorbed in the short bridge site, tilted along the [001] azimuth. The tilt angle for the direction between the center of the Ni–Ni bridge and the C-atom is 16°±2°, and the tilt angle for the C–O bond is 19°. The interlayer spacing between the first and second layer is 1.27 Å, and the Ni–C and C–O bond lengths are 1.94 Å and 1.16 Å, respectively [93Hua]. A comparison of best fit experimental and theoretical C1s intensity, in the form of the modulation amplitude, χ(k) = [I(k)–I0(k)]/I0(k), where I0(k) is atomiclike diffractionless C 1s intensity, versus electron momentum, for three measured directions is shown in Fig. 24 for the short brige site and atop site, respectively. The bridge site is clearly favored in this comparison.

Fig. 24a, b. Energy dependent C1s photoemission fine structure for (2×1)p2mg-CO on Ni(110) taken at three polar angles. Comparison of experiment (solid) and theory (dashed; multiple scattering calculation) for two different CO adsorption sites, (a) 2-fold short-bridge and (b) atop [93Hua].

X-ray absorption studies of CO adsorbed on Ni(110) yield the position of the oxygen atom of CO relative to the nearest neighbor Ni atoms (SEXAFS) as well as the inclination of CO relative to the Ni surface (NEXAFS) [93Pan1]. The results are that CO is bonded to the short bridge and tilted by 21°±5° along the [001] azimuth. Finally, we quote a theoretical study of tilted CO on Pt(110) and Ni(110) surfaces [85Bau]. An interesting material dependence is found in that CO tilts 20° along the [001] azimuth for Ni(110), but 35°- 40° in a completely different direction, namely the [433] azimuth, for Pt(110). The latter case would be consistent with a p1g1 symmetry of the unit cell [82Hof1, 82Hof2, 87Wes]. The case CO adsorbed on Pt(110) is from an experimental point of view still controversial since a p1g1 as well as a p2mg symmetry have been reported [84Rie] [92Win]. Table 2 summarizes and compares the quantitative structural data collected so far by various techniques for the (2×1)p2mg CO layer adsorbed on Ni(110).

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[Ref. p. 59

Table 2. Structure data for the (2×1)p2mg CO layer adsorbed on Ni(110). Ref.

[85Rie] [86Alv] [88Han] [88Wes1] [92Kna, 98Emu] [93Hua] [93Pan1] [85Bau]

Adsorption site Bond length Bond length

[001] tilt

[001] tilt

d12 [Å]

of CO

C–O [Å]

Ni–O [Å]

Ni–C

C–O

Ni–Ni

short bridge short bridge short bridge (theory)

1.12 1.16 (1.138)

1.95 1.94 (1.852)

27° 16° -

19° 19° 17° 21° 20° 19° 21° 20°

1.25 1.27 -

1.4.8 Molecular orbital energies, dispersion and 2d band structure Molecular orbital (MO) energies of adsorbed species, detectable by photoelectron spectroscopy, are dependent on the type and strength of bonding to the substrate surface and on the intermolecular interactions within the layer. Angle-resolved measurements of photoemission using linearly polarized ultra-violet light (ARUPS) allows to detect the energetic positions of the orbitals and to determine their symmetry character, provided the adsorbed species have a unique orientation in space. It is also possible to measure the dispersion of MO-states with electron wavevector, provided there is long range order in the layer. Structural details of the layer can be derived in connection with a model calculation of the 2d band structure. The well ordered (2×1)p2mg structure of CO adsorbed on Ni(110) was subject of a detailed ARUPS study [86Kuh] which may serve as an example. The 2d Brillouin zone for the (2×1)p2mg unit cell is shown in Fig. 17b. A single CO species bonded perpendicularly to a high symmetry site on a surface is characterized by three occupied MOs, called the 4σ, 1π and 5σ (in order of decreasing binding energy). Since the symmetry of CO adsorbed on Ni(110) is only 2-fold, the 1π orbital is split into an x- and ycomponent. Furthermore, there are two CO molecules per unit cell (compare 1.4.4), which doubles the number of molecular orbitals compared to the that of an isolated adsorbed CO. Hence a total of eight MOs are expected. Depending on the geometry of the photoemission experiment and the polarization of the incident photons, excitation from different orbitals is enhanced. This effect is illustrated, for example, in Fig. 25 by a series of spectra recorded for different polar angles in the ΓΧ azimuth and for a photon energy of 35 eV. A systematic variation of the kinetic energy of the photoelectron, via the variation of the photon energy, and its detection angle relative to normal, the dispersion of the MO states versus the parallel component of the electron wave vector, kII, has been mapped out for the two high symmetry directions ΓΧ ( [1 1 0] direction) and ΓΥ ( [001] direction) of the 2d Brillouin zone [86Kuh]. Here kII is given by k II =

2mE kin sin ϑ . h2

(32)

The results are summarized in Fig. 26 as a 2d band structure plot of all 8 molecular orbital states of adsorbed CO on Ni(110). A large dispersion of molecular orbitals, in particular of the 1πx and 4σ states, is observed at Γ along the [1 1 0] glide plane. The full lines in Fig. 26 represent the results of a tight binding calculation [79Hor, 83Gre] for an unsupported CO layer of (2×1)p2mg symmetry where some metal–CO bonding was accounted for by renormalized CO wavefunctions. The agreement between experiment and theory has been optimized by choosing a value of the CO tilt angle. The best agreement is

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achieved for a tilt of 17° (error ±2°) and supports the assumed real space structure of Fig. 17a. Larger tilts tend to decrease the dispersion while a zero tilt would cause an unrealistically large dispersion of 4.2 eV for the 1πx states. Geometrically, the tilt of CO minimizes the intermolecular separation between all CO molecules in this ordered structure. In simple terms, a chemisorption bond involves the hybridization of substrate and adsorbate orbitals (electron states), i.e. there are new bonding and antibonding states, some of which may be empty. The empty states are normally not seen by photoemission spectroscopy. They can be analyzed by inverse photoemission spectroscopy (IPES) in a manner analogous to PES. Angle, energy and polarization dependent measurements can be carried out to determine the 2d electron band structure of unoccupied states [86Fre, 89Mem].

CO (2×1) p2mg/Ni (110) ΓX

ϑ = 80° 70° 60°

50°

40°

Intensity I

30°

20°

10° 0° –10°

Fig. 25. Photoemission spectra of CO on Ni(110) taken at several polar angles ϑ in the ΓΧ azimuth, photon energy at 35 eV [86Kuh]. 5

6

Landolt-Börnstein New Series III/42A

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9 8 10 Binding energy Eb [eV]

11

12

13

1 Introduction

34 5.5 6.0

CO (2×1) p2mg/Ni (110)

6.5

1

7.5

Binding energy Eb [eV]

+

1p  x 1

7.0

5

8.0

[Ref. p. 59

1

+ y – y

– – x

8.5 9.0

5

+

9.5 10.0

4

–

10.5 11.0 11.5 Y 

4

Fig. 26. Experimental (filled circles) and theoretical (lines) 2d electron band structure of (2×1)p2mg-CO on Ni(110) along the ΓΧ and ΓΥ directions [86Kuh].

+

Wavevector k

X

1.4.9 Core level binding energies The electron binding energies of core levels are a sensitive indicator of intra-molecular as well as surface bonding. Depending on the chemical environment of an atom, its element-specific core level binding energy can vary significantly mainly because of changes in the local valence electron charge. Hence the core level binding energies of an atom within a molecule will change with the surface-molecule bonding and also with different chemical neighbors of an adsorbed molecule. Furthermore, the core level binding energy of a specific atom within a molecule depends on its immediate neighbors, e.g. the O1s binding energy is expected to be different for O2, CO, NO, H2O, etc. Therefore, measurements of core level binding energies by photoemission are the basis of a surface sensitive chemical analysis of adsorbed layers, atoms and molecules, known as electron spectroscopy for chemical analysis (ESCA) [67Sie]. Also, a molecularly adsorbed state (e.g. N2) can be clearly distinguished from a dissociated state (atomic N) of the same species. Beyond chemical analysis, even subtle structural distinctions can be made, e.g. between physisorption and chemisorption of the same molecule, or between different adsorption sites of the same molecule. However, an effect interfering with this useful correlation between core electron binding energy and chemical/physical state of the adsorbed species is the electronic screening of the hole generated by the photoemission process [82Sie]. The hole screening effects the kinetic energy of the departing photoelectron and hence its apparent binding energy. This final state effect therefore influences the measured electron binding energy in a way that is not straightforwardly associated with the local substrate-adsorbate bond.

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To give an example for subtle distinctions of several adsorbed molecular states and also between molecular and atomic adsorbed states, we present O1s core level data for molecular and atomic oxygen adsorbed on Pt(111) in Fig. 27. Four spectra are shown in this figure, one for the physisorbed molecular O2 state at 25 K, two for chemisorbed molecular O2 at 90 K and 138 K, respectively, and one for the dissociated atomic O state at > 150 K [95Pug]. The two chemisorbed molecular states are associated with superoxo and peroxo configurations, respectively [82Ste]. The characteristic O1s binding energies and structural parameters are summarized in Table 3. The physisorbed O2 state is very similar to the gas phase oxygen state, as judged by valence photoelectron spectra [95Pug]. It is not clear whether this state is equivalent to an intrinsic precursor state for O2 chemisorption or not.

O2/Pt(111)

O1s

hν = 1487 eV

atomic phase

Intensity I

chemisorbed phase II

chemisorbed phase I

Fig. 27. O1s core level spectra of molecular O2 and atomic O adsorbed on Pt(111). Different phases exist at different temperatures: Physisorbed oxygen at 25 K; chemisorbed O2 at 90 K; second chemisorbed O2 phase at 138 K; atomic oxygen at > 150 K. All spectra excited with monophysisorbed phase

540

538

Landolt-Börnstein New Series III/42A

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534 532 Binding energy Eb [eV]

chromatized Al K α 1487 eV [95Pug]. 530

528

526

radiation at

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36

CO/Pt(111)

O1s

[Ref. p. 59

C1s

c(5× 3) θ = 0.6 on top 0.4 bridge 0.2

Intensity I

c(4×2) θ = 0.5 on top 0.25 bridge 0.25

(4×4) θ = 0.2

Fig. 28. C1s and O1s core level spectra of three ordered CO layers at different coverages of 0.2, 0.5 and 0.6 adsorbed on Pt(111). Excited with monochromatized

on top 0.2

Al K α

radiation at 1487 eV

[94Bjö].

536

534

532

530 528 290 Binding energy Eb [eV]

288

286

284

Table 3. Characteristic data of various adsorbed oxygen states on Pt(111).

Chemical state O–O bond order Adsorption T [K] O–O bond length [Å] O1s EB [eV] O–O stretch, ν [cm–1]

Physisorbed O2

Chemisorbed O2

Chemisorbed O2

Chemisorbed O

gas like 2 25-30 (1.208) *) 536.88; 535.80 (1556) *)

superoxo 1.5 90 1.37 530.54 -

peroxo 1 135-150 1.43 529.63 700-875

atomic 0 > 150 529.83 Pt–O: 470

*) Gas phase O2 values. Another illustration concerns the change of binding energy of an adsorbate core level with the adsorption site. Although there is no general correlation between binding energy and site, it appears that a decrease in binding energy is associated with increased coordination of the adsorption site [78Plu]. The example is shown in Fig. 28 for CO on Pt(111) at three different coverages of 0.2, 0.5 and 0.6 [79Nor, 83Kis, 94Bjö]. All layers are well ordered and exhibit a (4×4), c(4×2) and c(5× 3 )rect LEED pattern, respectively. Single O1s and C1s peaks are recorded for the (4×4) phase in which CO adsorbs only in atop sites [87Tüs]. Double O1s and C1s peaks are seen for the other two phases for which both atop and bridge sites are occupied [87Tüs]. Hence it is clear in this case that the higher and lower binding energy peaks correspond to the atop and bridge adsorbed CO, respectively. The quantitative intensities seem to correlate well with the relative site occupations known from the structure models. Another example is CO Landolt-Börnstein New Series III/42A

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adsorbed on a partially hydrogen covered Ni(100) surface [92Til]. For the ordered c(2 2 × 2 )R45°CO/H structure two well separated O1s and C1s peaks of CO are seen which are attributed to CO adsorption in atop and 4-fold coordinated sites. The effect of coadsorbed hydrogen is minor in this case. Table 4 summarizes CO core level binding energies correlated with different adsorption sites. Table 4. Core level binding energies of CO in different adsorption sites. System

Structure

Site

O1s EB [eV]

C1s EB [eV]

Ref.

CO/Ni(100)

c(4×2) p(3 2 × 2 )R45° c(2×2) c(2 2 × 2 )R45°

atop

532.2

285.9

[92Til]

bridge atop

531.3 532.9

285.5 286.3

[92Til]

atop 4-fold bridge atop atop atop

532.8 530.3 531.2 533.0 532.7 532.7

286.2 285.1 285.4 286.3 286.7 286.7

bridge

531.0

286.0

CO/H/Ni(100)

CO/Cu(100) CO/Pt(111)

disordered c(2×2) (4×4) c(4×2) c(5× 3 )rect

[90Ant] [94Bjö]

A detailed study of core level line shapes, satellites, peak splitting and peak shifts is a wide subfield in photoelectron spectroscopy. For example, CO bonds to transition metal surfaces via electron donation and back-donation, involving the anti-bonding CO 2π orbital which becomes partially occupied. Photoexcitation of an O1s or C1s core level creates a positive hole which needs to be screened. Screening may involve charge transfer from metal states to the CO 2π orbital or an intra-molecular 1π→2π transition. The latter occurs also with gas phase CO and is seen as a satellite of the main core level line. It is found at 3.9 eV higher binding energy and therefore called a shake-up peak. A systematic comparison of core level and shake-up peaks for adsorbed CO and carbonyl compounds has been carried out to understand the bonding of CO to transition metals [78Plu, 83Fre2]. Quantitative core line intensities can be used to measure relative coverages of adsorbed species. To get reliable intensities one should integrate the electron emission over a larger solid angle to become insensitive towards effects of angle dependence. Also, a spectrum should be recorded over a sufficiently large energy range, such that all possible satellite peaks are included in the integration. Angle dependent measurements yield information on the orientation of intra-molecular bonds (compare 1.4.3).

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1.4.10 Two-dimensional phase diagrams and order-disorder transitions The study of ordered adsorbate layers on single crystal surfaces is a subfield of adsorption on surfaces. Depending on the relative magnitude of inter-molecular interaction to adsorbate-substrate interaction, a sequence of ordered two-dimensional structures can be formed with increasing coverage. Important are competing nearest and next-nearest neighbor pairwise as well as three-body interactions within the adsorbate layer. Perfectly ordered regions (commensurate structures) may be separated by anti-phase domain boundaries which by themselves may exhibit order (incommensurate structures). Each ordered phase has a limited temperature range of stability. A 2d phase diagram, i.e. a plot of temperature versus coverage, describes the stability regions of all involved phases. Order-disorder as well as order-order transitions may occur at the phase boundaries. Many adsorbate phases are "floating" on the substrate surface, in the sense that the adsorbate-substrate interaction is sufficient to cause commensurability, but insufficient to cause a significant structural change at the surface, such as a reconstruction. However, adsorbate induced surface reconstructions are also known to occur (compare 1.5.1 and 5.1). Such a phase may be part of a complex phase diagram, e.g. for H adsorbed on Ni(110) [81Eng, 84Pen]. The subject will be briefly discussed by the example of H adsorbed on Fe(110) [77Boz, 82Imb, 83Sel]. Two well ordered surface structures of H, (2×1) and (3×1), have been found at 140 K by LEED at the coverages of about 0.5 and 0.67, respectively. Less sharp streaky patterns were seen for intermediate coverages. Recording the intensities of the fractional order (i.e. superstructure) LEED spots versus temperature in the range 150-300 K, an order-disorder transition was monitored at nearly constant H coverages. The critical temperatures were determined from the inflection points of the intensity versus temperature curves. A plot of these transition temperatures versus coverage is shown in Fig. 29a as a phase diagram, complemented by hypothetical two-phase regions (dashed) with anti-phase boundaries [82Imb]. These (2×1) and (3×1) H superstructures apparently do not involve a surface reconstruction. A theoretical modelling of the H/Fe(110) system was carried out by Monte Carlo and transfer matrix techniques [83Sel]. The best agreement with experiment, shown in Fig. 29b, was obtained by including repulsive first and second nearest neighbor (pairwise) and also attractive three-body (nearest neighbor) interactions between adsorbed H. An additional (3×1) H structure at a coverage of 0.33 is found theoretically which was not detected in the experiment. The observation of multiple ordered phases of adsorbates at submonolayer coverages is no rare event. Adsorbed species with large dipole moments, such as alkali metals, CO, H or O atoms, have a particularly strong tendency to order. A second example of a rather complex 2d phase diagram is given in Fig. 30 for CO on Pt(111) [84Bib, 89Per, 90Per]. This somewhat schematic phase diagram is the result of experimental and theoretical studies. Experimental LEED work had shown a series of ordered patterns [77Ert, 82Ste, 90Per] with increasing coverage: ( 3 × 3 ) R 30° = c ( 3 × 5)rect at a CO coverage of 0.33, c(4×2) = ( 3 × 2)rect at 0.5, ( 3 × 5)rect at 0.6, ( 3 × 3)rect at 0.67 and ( 3 × 7)rect at 0.71 coverage. Monte Carlo simulations reproduce all of the observed ordered structures at the ideal coverages of 1/3, 1/2, 3/5, 2/3 and 5/7, respectively. The adsorption sites of CO are close to the ideal atop and 2-fold bridge sites in all cases. This theoretical result is also in good agreement with vibrational studies showing C–O stretch frequencies at 2100 cm–1 and 1840-1887 cm–1 for atop and bridge adsorbed CO, respectively, for the whole coverage range [82Ste, 90Per]. At intermediate coverages incommensurate domain wall structures exist which are equivalent to two-phase regions in the phase diagram in Fig. 30. The critical temperatures for order-disorder transitions, experimentally not yet determined, rise with increasing coverage.

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2.5

Tc = 265 K Tc = 245 K

250

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225

lattice gas

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Temperature T [K]

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175

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0.3

0.4

0.5 0.6 H coverage θ

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Fig. 29a, b. Experimental (a) and theoretical (b) 2d phase diagram of adsorbed H on Fe(110). The low coverage 3×1 phase was not observed experimentally [82Imb, 83Sel]. 400

CO/Pt(111)

350 fluid

250 200 150

( 3× 3)R30°

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I

II

III

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Fig. 30. Proposed 2d phase diagram for adsorbed CO on Pt(111). Phases I, II and III correspond to ordered structures ( 3 × 5) rect at coverage 0.6,

( 3 × 3) rect at 0.67 and

( 3 × 7) rect at 0.71, respectively. Shaded areas in between correspond to incommensurate phases [84Bib, 90Per].

50 0 0.3

multi-layer-growth

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1.4.11 Chemical state One of the important issues in analyzing an adsorbed molecular species, also from a more technical point of view, is the question of its chemical state. Does the molecule stay intact when it adsorbs or does it dissociate into fragments? Which bonds fracture under what conditions? Processes such as bond fracture, dissociation or molecule fragmentation are a direct link to possible surface reactions involving those fragments, formed in the adsorption step, and other coadsorbed molecular or radical species. Therefore, studying adsorption and the chemical state of an adsorbed species, also as a function of temperature, is Landolt-Börnstein New Series III/42A

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always a study of surface reactivity, and hence of direct relevance to the technical field of heterogeneous catalysis. A simple example is the adsorption and dissociation of CO on metal surfaces. Various systematic studies have indicated that the noble metals Cu, Ag and Au and their neighbors in the periodic table do not dissociate CO, while Fe, Mo and W and the elements to their left in the periodic table easily dissociate CO [76Bro]. Metals, such as Co, Ru and Re, seem to be "border line" cases where CO is molecularly adsorbed on some low-index surfaces (at room temperature) while it dissociates on others. Obviously, for these metals the surface structure becomes important for the dissociation of CO, in addition to the electronic structure of the substrate. Similar systematics have been noticed for N2 and NO [76Bro]. Simple theoretical and thermodynamic arguments have been forwarded to explain this material dependence [80Ben, 80Miy, 80Ros]. Another interesting example is the adsorption of ethylene (C2H4, ethene) on Pt(111). This molecule adsorbs intact at 90 K in a di-sigma configuration, i.e. with its C–C axis parallel to the surface [77Iba, 78Iba, 81Bar]. At temperatures around 270 K it partially desorbs and partially dehydrogenates to a species that has a single C-bond to the surface and a concomitant structural reorientation of the C–C axis to perpendicular. The species was later shown to be ethylidyne (–C–CH3) [78Kes, 79Kes] which is stable to about 440 K. Above that temperature it further decomposes and dehydrogenates to –CH radicals. The same ethylidyne species can be obtained by adsorbing acetylene (C2H2) at 120 K and warming this adlayer to 270 K [78Iba, 78Kes, 79Kes]. Under those conditions some molecules dehydrogenate, others react with the adsorbed hydrogen to ethylidyne which is stable up to 440 K. These adsorption/decomposition reactions are element and structure specific as a comparison of Ni, Cu, Pd and Pt surfaces has shown [83Gat, 93Bao]. The foremost spectroscopic techniques that yield information on the chemical state of adsorbates are optical (IRS, Raman, SFG, SHG), electron (EELS, XPS, UPS) and ion (SIMS) spectroscopies. Quantitative structural techniques such as LEED and XPD have also contributed to solving the question of the chemical state of the primary and secondary intermediate species. In this context, sections 1.4.3, 1.4.5-1.4.8 should also be consulted.

1.4.12 Influence of surface structural defects The important fundamental concept of structure sensitivity in heterogeneous catalysis has been proposed on the basis of a supposedly inhomogeneous surface of the active catalyst [25Tay, 29Bal]. So called active centers of either crystallographic [25Tay] or compositional character were believed to be responsible for an increased rate and the selectivity of the reaction. These hypotheses have found support by numerous more or less well defined experiments. For example, the rate of ethylene hydrogenation was found to be more active on preferentially oriented Ni thin films than on unoriented Ni films [40Bee]. Numerous experiments on supported metal catalysts produced evidence of structure sensitive reactions [70Cla, 73Sin]. Therefore it had long been suspected that the adsorption of gases on metals, alloys and semiconductors was structure sensitive, in the sense, that differently coordinated surface atoms of a substrate exhibited a different adsorption energy of a particular species. Along with such a difference, the kinetics of adsorption and also the final adsorbed state may be influenced by surface defects. Dissociation of the molecule may or may not occur, depending on whether the adsorption site is a high coordination defect or a low coordination terrace site. Experimental work on flat single crystal surfaces, either highly oriented or slightly misoriented relative to a low-index orientation, proved to be an excellent way to check the ideas about structure sensitivity at low pressures. Misoriented crystals were prepared to exhibit surfaces with a known defect structure, such as step and kink sites, and with a known density of these defects [77Som, 81Som]. Furthermore, the structural dependence of adsorbate properties, once established by well defined single crystal experiments, is being used to characterize the structure of small metal particles supported on an oxide support [96Rai, 97Rai]. Infra-red spectroscopy of adsorbed CO as a probe molecule yields information on the heterogeneity of the surface via the frequencies of the stretch vibration, for example. This information is very useful in relationship to realistic supported catalysts used in commercial catalytic processes [94Xu].

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The first experiments with adsorption on stepped single crystal surfaces were carried out in 1971/72 for Cu and Pt [71Per, 72Lan]. It was found that dissociative adsorption of H2 and O2, for example, occurred with higher rates at 300 K on stepped Pt(111) and Pt(100) surfaces than on their smooth counterparts. A similar observation was made for the adsorption of oxygen on stepped Si surfaces [73Iba]. A clear demonstration for the influence of step sites on adsorption and reactivity was given for CO on a stepped Ni(111) surface. Experimental results are summarized in Fig. 31 [78Erl]. Thermal desorption spectra of CO from a flat Ni(111) crystal show a single desorption peak at 433 K [74Chr, 78Erl]. For CO desorption from a stepped Ni[5(111)×( 1 1 0 )] crystal, however, a second peak is observed at 820 K which is attributed to associative desorption from C and O atoms. These atoms are originally formed by CO dissociation occurring exclusively at step sites during increasing of the temperature. The fact that they remain located at the step sites was concluded from an additional observation [78Erl]. If CO adsorbed at low temperature was dissociated by electron bombardment and then thermally desorbed, the associative desorption from C and O gives rise to a peak at 620 K, Fig. 31, which must be assigned to C and O atoms located on terrace sites. Hence the desorption peak at 820 K was clearly differentiated from the peak at 620 K due to associative desorption from C and O adsorbed on terrace sites. Additional vibrational spectroscopy showed step-adsorbed CO molecules at 150 K to be characterized by a very low C–O stretch frequency of 1520 cm–1 [79Erl2]. Such a low stretch frequency is indicative of substantial C–O bond weakening and thus consistent with the high propensity of this CO to dissociate on heating. Raising the temperature to 300 K led to a considerable lowering of the intensity of this 1520 cm–1 peak relative to those at higher frequencies characteristic of CO adsorbed on regular terrace sites. This could have already indicated the dissociation of this CO.

Fig. 31a - d. Thermal desorption spectra of CO from a smooth Ni(111) (a-b) and a stepped Ni[5(111)×( 1 1 0 )] crystal (c-d). The α-peak corresponds to molecular CO adsorption. (b) Electron irradiation of the CO layer on Ni(111) causes a new desorption peak β1 due to dissociated CO. (c) Observed β2-peak from stepped Ni[5(111)×( 1 1 0 )] is attributed to thermally dissociated CO at step sites. (d) Electron irradiation of the CO layer on stepped Ni[5(111)×( 1 1 0 )] causes both desorption peaks β1 and β2, due to dissociated CO on Ni(111) terrace sites and step sites, respectively, to appear [78Erl].

Numerous other examples dealing with adsorbed CO or other gases are known where surface defects are special adsorption sites in the sense that the adsorption energy is higher there than on terrace sites [81Som, 89Cam]. Related to this energy difference, step sites are preferentially occupied, and the reactivity of these sites is generally higher, often leading to localized dissociation of adsorbed species. Landolt-Börnstein New Series III/42A

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It is now widely recognized that this important result of systematic surface research constitutes a firm base of Taylor's idea, expressed in 1925, of active sites and structure sensitivity in heterogeneous catalysis [25Tay]. Moreover, atomic steps are not only crystallographic features but also electronic defects since their local electronic structure, characterized by the local electron charge density, differs from that of terrace sites. This was experimentally demonstrated by work function measurements of stepped surfaces which led to the assignment of a dipole moment to the step [77Bes]. In this context the so-called structural effect of adsorption (and catalysis) is at the same time also an electronic effect. Another kind of varying the surface structure is by imposing a lateral stress, such as encountered for thin epitaxial films on a single crystalline substrate. Depending on the lattice mismatch between film and substrate surface, the film may be strained relative to its normal bulk state. Positive as well as negative strain can occur. Due to the strain, the surface stress will also be changed. Investigations of adsorption on such strained (stressed) surfaces of thin films have shown [92Rod, 94Kam, 98Gse] that the properties of the adsorbed species are altered more or less significantly. The variation of the C–O stretch frequence, for example, of CO adsorbed on a number of differently strained surface films shows a linear correlation between frequency shift and strain [94Kam]. Self-consistent density functional calculations of the effect of strain on the reactivity of surfaces has shown by the example of oxygen and CO adsorption on Ru(001) that the heats of adsorption of both species increase with increasing strain in a range from –2.5 to +2.5% [98Mra]. A corresponding decrease was found for the activation energy of CO dissociation. Overall, the imposed stress causes strain, which changes the surface structure (e.g. via slight expansion or compression), and furthermore the surface electronic structure, such as the width and center position of the d-band of transition metals, for example. Mavrikakis et al. demonstrate that the changes in the energetic adsorbate properties can also be correlated with changes of the center position of the d-band [98Mra]. Summarizing the influence of crystallographic surface orientation, surface structural defects, surfacs strain on reactivity, one can argue qualitatively that the more "open" the surface (in the sense of a lower bond order of surface atoms), the more reactive it will be.

1.4.13 Influence of chemical surface additives ("promotors") Modyfying surface properties by alloying or simply by adding second surface components, sometimes called the "promotor" of a reaction, to a clean surface is an issue that is aimed at probing the electronic factor in heterogeneous catalysis. The general idea is to change the local electron concentration at the surface and to thereby influence its reactivity. The prime example in catalysis is the addition of alkali metal species in various forms [83Mro]. This idea has been carried over to theory and experiments of adsorption, where single crystal surfaces have been modified by adsorbing atomic species, such as alkali metals or other species, to investigate induced changes in the properties of subsequently added adsorbates. The study of the mutual influence of two (or more) different adsorbates constitutes the field of coadsorption. Obviously, two groups of additives may be distinguished, electron donors and electron acceptors. While alkali metals are typical electron donors, lowering the work function of a metal substrate [23Lan], species such as C, O, P, S, Se etc. are considered to be electron acceptors, associated with an increase in the work function of the substrate. As a rule, the electron donating species enhance the propensity of adsorption, the electron accepting species retard adsorption (and reactions), i.e. they act as "poisons" to a surface reaction. Early electron band theories of this effect were aimed at explaining the electronic factor in catalysis [38Wag]. Numerous systematic studies of the alkali metal promoter effect on well defined single crystal surfaces have been reported. Although coadsorption phenomena in general shall not be elaborated on in this volume of LANDOLT-BÖRNSTEIN, two examples will be mentioned that illustrate the effect. These are the K promoted adsorption of CO and N2 on Fe single crystal surfaces [79Bro, 79Ert]. The first bears some relevance to the Fischer-Tropsch synthesis of hydrocarbons from CO and H2 [56And, 72Dry, 82Bon1], and the second to the synthesis of NH3 from N2 and H2 [75Emm, 80Ert], both on K promoted Fe-based catalysts. For example, adsorbed K on Fe(110) enhances the propensity for CO dissociation at 310 K and low pressure, as shown in Fig. 32. While the total coverage of C and O increases with increasing K coverage, the ratio of dissociated to molecular CO rises from about 0.2 to 1 at a monolayer Landolt-Börnstein New Series III/42A

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of K. The initial sticking coefficient of CO, on the other hand, decreases with increasing K coverage. This behavior has been explained in terms of an increased adsorption energy of CO/K compared to CO on clean Fe(110) and a concomitant decrease in the activation barrier of dissociation [79Bro]. An analogous result and interpretation was found for the K-promoted adsorption and dissociation of N2 on Fe(110) [79Ert]. Further studies by vibrational spectroscopies at 150 K have demonstrated the C–O bond weakening of K coadsorbed CO [92Zhu], a feature that parallels an increased backdonation of electrons into the anti-bonding 2π* molecular orbital of CO and hence an increased metal–CO bond strength [81Kis, 87Bon1].

Fig. 32a - c. Effect of K-induced dissociation of CO on Fe(110) at 310 K. (a) Increase in total C,O coverage with increasing K coverage. (b) Initial sticking coefficient of CO vs. K coverage. (c) Fraction of dissociated over molecular CO, determined by photoemission spectroscopy, vs. K coverage [79Bro].

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1.5 Adsorbate-induced changes of substrate properties The adsorption of atoms and molecules on crystalline surfaces implies some degree of physical and/or chemical interaction with the substrate. A pure physical van der Waals-type interaction is relatively weak and will not change the structural environment near the adsorption site to any significant extent. However, apparent electronic changes of the substrate, such as electron work function or core and valence level binding energies, may be expected. On the other hand, when chemical bonding between certain adsorbate orbitals and localized or delocalized electron orbitals of surface atoms occurs, the redistribution of valence charges near the adsorption site may be substantial and thus effect nearest and next nearest neighbor bonds in the substrate (as well as in the adsorbate). In that case it is evident that structural, electronic and vibrational changes in the substrate, usually in the local environment of the adsorbed species, will occur, effecting surface energy and surface stress as well. These effects are generally summarized as adsorbate-induced changes of substrate properties. A systematic investigation of such changes yields information on the adsorbate and also on the adsorbate-substrate interaction. The most important adsorbate-induced changes of substrate properties will be briefly introduced in this section.

1.5.1 Changes of structure: surface relaxation and surface reconstruction The structure of clean single crystal surfaces is frequently not equal to the structure of an equivalent cut through a bulk crystal [78Mül, 84Est]. Quantitative structural studies have shown that the separation between atomic layers near the surface is often smaller (seldom larger) than in the bulk ("relaxation"). In some cases also the lateral structure deviates from the bulk terminated structure, equivalent to a change in the structural unit cell. These surfaces are then called "reconstructed". Examples of reconstructed surfaces were found at first on low-index semiconductor surfaces [59Sch] and later on metal surfaces [65Hag, 66Fed, 67Fed1, 67Lyo]. A large number of structural data is now available on relaxation and reconstruction phenomena of clean surfaces [88Jon, 93Fas]. Adsorbate-induced changes of clean surface structures are divided into three categories: (1) Changes in surface relaxation, i.e. in interlayer separations vertical to the surface. (2) Surface reconstruction, i.e. changes in interatomic bond lengths parallel (and perpendicular) to the surface, causing a periodic lateral shifting of atoms or a density change of surface atoms, connected with a superstructure different from that of the clean surface. Two examples of reconstructed fcc (110) surfaces are shown schematically in Fig. 33, the missing row and the pairing row structures, respectively. Both exist in nature, as we will see below. (3) Surface faceting, i.e. breakup of a flat surface of a certain crystallographic orientation into a rough hill and valley structure, consisting of two or more new surface orientations ("facets") appearing in a more or less irregular fashion. There are also cases where the reconstruction of a clean surface is destabilized ("lifted") by adsorption, e.g. the missing row (1×2) reconstruction of Pt(110) by adsorbed CO [73Bon, 76Com]. The structural transformation (1×2) → (1×1)-CO → (2×1)p1g1-CO is driven by a change in total surface free energy which is lower for (1×2) in the clean state but lower for the non-reconstructed surface in the CO covered state [82Bon2, 82Fer]. That is equivalent to the adsorption energy of CO being lower on the reconstructed than on the non-reconstructed surface [83Beh, 84Bar, 88Imb]. The adsorbate-induced destabilization of a reconstructed surface requires a certain minimum temperature because structural changes are thermally activated. Thus the (1×2) → (1×1)-CO transition occurs at T > 240 K [82Fer] while below this temperature the adsorption of CO on the stable (1×2) surface can be studied. Historically, the phenomenon of surface reconstruction was closely related to adsorption, which occurred unintentionally in the sense of contamination. The principal question, whether reconstruction could be a genuine phenomenon of a clean surface or be due to impurities on that surface, was, at least for metals, a matter of serious debate [67Fed2, 67Som]. It was later clarified that surface reconstruction was indeed a rather common phenomenon, both for clean and adsorbate covered surfaces [89Som, 94Sta]. However, even the adsorbate-induced reconstruction of surfaces was a controversial issue in the beginning, best illustrated by early investigations of H2 and O2 adsorption on Ni(110) [62Ger]. A (2×1)-H superstructure had been observed by LEED, and it was argued by Germer that the extra LEED beams were indicative of a reconstructed Ni surface since H-atoms were known to be poor electron scatterers Landolt-Börnstein New Series III/42A

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and not capable of causing intense extra beams [66Ger]. This was questioned by Bauer [66Bau]. On the other hand, adsorbed oxygen caused a (1×2)-O LEED pattern which Germer attributed to an ordered array of O-atoms on the surface [62Ger]. Years later it was shown that the (2×1)-H superstructure is indeed due to H ordering on the non-reconstructed Ni(110) surface [81Eng, 83Rie, 84Pen, 87Rei] while the (1×2)-O LEED pattern is due to a reconstructed Ni(110) surface with an ordered array of O-atoms [81Nie, 81Sme, 90Kle, 90Voi].

Fig. 33a - c. Perspective view of fcc (110) surfaces. (a) non-reconstructed surface; (b) reconstructed (1×2) missing row surface; (c) reconstructed (1×2) pairing row surface [74Chr].

The system H/Ni(110) is most interesting from another point of view. More than five H-related superstructures were later detected by elastic He scattering and LEED [83Rie, 84Pen]. The one with the highest H-coverage of 1.5 was a (1×2)-H structure on a reconstructed Ni surface which involved a pairing of atomic Ni rows in the first layer, such as illustrated in Fig. 33c, and additional changes in interlayer spacings beneath the surface [87Kle]. Whereas the interlayer spacing between the first and second layer of the clean Ni(110) surface is contracted by 8.5% [87Rei], it is slightly expanded for the (1×2)-H structure [87Kle]. This behavior is typical for adsorbate-induced changes of relaxation in that the interlayer bond distances at the surface increase in the presence of an adsorbate, tending to assume a nearbulk value [89Som]. This tendency is also visible for the non-reconstructed (2×1)-H superstructure where the change in interlayer spacing goes from 8.5% contraction (clean) to 4.5% contraction for the H covered surface [87Rei]. Overall, the adsorbate-induced reduction of the clean surface interlayer relaxation seems to be a general phenomenon, at least for surfaces where the first-to-second interlayer spacing exhibits a contraction [89Som]. The interplay between adsorption, in particular chemisorption, and surface structural changes is of principal importance in heterogeneous catalysis [72Som1, 95Som]. Since many catalytic reactions are structure sensitive, it is of great interest to know the most active surface orientation for a particular reaction. This knowledge is in general very difficult to obtain because comprehensive structural investigations during an ongoing reaction are not possible. The third kind of structural change, faceting, is much more violent and involves a massive lateral transport of matter. Adsorption of alkali metals on some fcc (110) surfaces causes the missing row structure of Fig. 33b. This structure is characterized by (111) oriented nanoscale facets. Thus reconstruction can in some cases be viewed as a nucleus to faceting. Facets of µm dimension are often Landolt-Börnstein New Series III/42A

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seen after oxygen or chlorine treatment or after surface reactions involving oxygenates or halogenated molecules [79Fly]. Furthermore, monolayer coverages of a deposited metal, such as Rh, Pd, Au, Pt, on W(111) or Mo(111) surfaces may cause a complete breakup of the surface into small {211} and {110} facets when heated to more than 800 K [97Nie, 99Mad]. This behavior is possibly significant in relationship to heterogeneous reactions on bimetallic catalysts. One of the critical questions concerns the connection between coverage and faceting. Is there a critical coverage of an adsorbate beyond which faceting of a surface will occur? The basic reason for larger scale faceting is a change in the anisotropy of the substrate's surface free energy caused by adsorption. However, quantitative information on this dependence is scarce. This topic will be dealt with in section 1.5.4.

1.5.2 Changes of electron work function The electron work function of a crystal is the difference between bulk chemical potential (Fermi level), µ , and the total electrostatic potential barrier at the surface. Adsorption of atoms or molecules on the surface can not change the bulk chemical potential but certainly the surface barrier if the adsorbed species develops a dipole moment in the process of adsorption or has a permanent dipole moment which becomes oriented in the electrostatic field at the surface. The work function change, ∆φ, is therefore equal to the electrostatic surface potential barrier connected with a dipole moment via the classic Helmholtz equation: ∞

∆φ = − µ + 4πe ∫ dz z δn( z) .

(33)

−∞

Here δn( z ) is the local redistribution of (valence) charge density that accompanies adsorption. The concomitant formation of an adsorbate dipole moment with adsorption can occur via charge transfer between this species and the surface or by charge polarization in the surface-adsorbate complex. The former is common for more strongly chemisorbed species while the latter is important for physisorption. The classic example of a work function change in context with physisorption is the adsorption of noble gases, e.g. xenon on a metal surface. Theoretically the interaction can be described as van der Waals (long range) or, in the framework of local density theory, as due to electron correlation forces between the valence electrons of Xe and those of the metal [82Lan]. In the latter, an exchange-correlation potential outside the surface was calculated which is of longer range than the electrostatic (image) potential of the surface, shown in Fig. 34. The adsorbed Xe atom is localized entirely in the field of the exchange-correlation potential where it is polarized. The resulting dipole moment of adsorbed Xe is then responsible for the heat of adsorption and for a change in work function measurable outside the surface. Work function changes of up to 0.8-1.0 eV may result from Xe adsorption [79Küp, 82Jac]. Furthermore, electrons bound in valence and core levels of adsorbed Xe may experience binding energy shifts which depend on the total magnitude of the potential [82Lan]. Numerous measurements of the 5p1/2 level binding energy of adsorbed Xe atoms on various clean metal substrates indicate that the observed shifts in this binding energy agree closely with the measured work function differences of these surfaces [80Hul, 84Wan]. A similar study for stepped surfaces shows two well separated Xe 5p1/2 levels which can be correlated with Xe adsorption on terrace and step sites, respectively [81Wan]. The binding energy difference was interpreted in terms of a corresponding local difference in electrostatic potential ("local work function") of step sites and terrace sites. Thus photoemission measurements of adsorbed Xe (PAX) were proposed to be a technique to study local work function differences due to crystallographic defects or pre-adsorbed foreign atoms. It should be mentioned, however, that the correlation between local work function and Xe 5p1/2 binding energy has been discussed controversially in the literature [80Kai, 86Wan, 87Kai, 87Ste]. The chemisorption of atoms or molecules, on the other hand, is generally characterized by chemical bond formation between adsorbate and substrate surface atoms, i.e. some degree of hybridization between electronic states of both partners is involved. The direction of the charge transfer determines in many cases the sign of the work function change and the orientation of the surface dipole. For example, Fig. 35 shows measured work function changes for adsorbed Cl and Cs atoms on a Cu(111) surface, respectively [77God, 80Lin]. Since the electronegative Cl accepts charge from Cu, the work function increases, and vice versa for Cs. The behavior for Cs is typical of adsorbed alkali metals on metal surfaces in that there Landolt-Börnstein New Series III/42A

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is a strong initial decrease in work function followed by a shallow minimum and a small rise near a saturated monolayer [89Lan]. The latter features are due to depolarization of closely packed dipoles. The final work function denotes a metallic alkali metal overlayer. The strong initial decrease indicates a substantial charge transfer from the alkali metal to the substrate, equivalent to a large dipole moment of the adsorbed alkali species. Dipole moments of single adsorbed species can be evaluated from the slope of ∆φ versus coverage in the limit of vanishing coverage.

Fig. 35a, b. Electron work function changes due to (a) chlorine and (b) cesium adsorption on a Cu(111) surface, respectively [77God, 80Lin].

Fig. 34a-c. Results of a model calculation of a Xe atom adsorbed on a high electron density jellium surface (e.g. aluminium). (a) Contours of constant electron density in a cut perpendicular to the surface through the center of the Xe atom. (b) Xe valence p-electron density vs. distance (difference density between metal-adatom system and sum of clean metal plus single Xe atom except 5p level). (c) Effective single particle potential energy contributions due to electrostatic dipole, Ves, and the exchange-correlation interaction, Vxc, respectively, [82Lan].

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1.5.3 Electron binding energy changes, core and valence levels The adsorption of atoms and molecules on surfaces can not only be studied by analyzing their valence and core level spectra (sections 1.4.7/1.4.8) but also by evaluating changes in substrate levels although these are more subtle and not so easy to recognize. For example, core level spectra of clean semiconductor and metal single crystal surfaces consist of (at least) two contributions, one due to surface atoms and the other due to bulk atoms. The energetic difference is called a surface core level shift, ∆Es,b, defined as the difference EB(surface atom) – EB(bulk atom). This difference can be positive or negative. When there is more than one kind of surface atom, such as for fcc (110) or bcc (111) oriented surfaces, separate surface contributions can be attributed to surface atoms of different local coordination. The separation of a surface peak from the bulk core level peak can be achieved by comparing spectra taken at normal and grazing (more surface sensitive) emission angles, particularly for low kinetic photoelectron energies. When atoms or molecules are adsorbed on a single crystal surface, the energetic situation of surface atoms involved in the adsorption bond changes and so does the core level binding energy of that atom. Thus there is a new surface core level shift for surface atoms bonding to an adsorbate, ∆Es,ad, defined as EB(surface atom with adsorbate) – EB(clean surface atom). The adsorbate-induced surface core level shifts can be as large as 1.4 eV. The well studied system of CO on Pt(111) shall serve as an example [82Apa, 86Düc, 94Bjö]. Figure 36 illustrates the results for the Pt 4f7/2 core level studied with monochromatized synchrotron radiation of 125 eV [94Bjö]. This low photon energy, which is equivalent to a low kinetic energy of about 50 eV for a Pt 4f7/2 photoelectron, enhances the surface sensitivity, such that for clean Pt(111) the surface and bulk contributions are readily detected at binding energies of 70.50 and 70.90 eV, respectively, corresponding to ∆Es,b = –0.40 eV [94Bjö]. This is in good agreement with previous reports [82Apa, 83Apa, 86Düc]. Adsorption of CO at a coverage of 0.2, causing a (4×4) LEED pattern, reduces the intensity of the clean surface peak and causes a new CO-related peak at 71.9 eV, corresponding to a surface core level shift of ∆Es,CO = 1.4 eV. Increasing the CO coverage to 0.5 and 0.6 produces sequentially two more ordered CO arrays with both atop and bridge adsorbed CO. The clean surface peak has become quite small under these conditions but now two CO-related surface peaks at 71.2 and 71.9 eV binding energy are needed to fit the measured spectrum. Those peaks are attributed to atop and bridge adsorbed CO, with resolved shifts of 1.4 and 0.7 eV, respectively. Previous studies had not resolved the adsorption-site-specific core level shifts, and therefore "average" values of ∆Es,CO = 1.3 eV [83Apa] and 1.0 eV [86Düc] had been reported. The relatively large magnitude of > 1 eV for a CO-induced surface core level shift, i.e. for a shift beyond the position of the bulk Pt peak, is not easily explained by the charge distribution in this Pt–CO surface complex. Instead, details of the photoemission process have to be invoked to rationalize this number. A phenomenological way of understanding the magnitude is by means of a Born-Haber energy cycle which at the same time shows the relationship of surface core level measurements to thermodynamic surface properties. The principal of the cycle is illustrated in Fig. 37 [83Ege]. CO adsorbed on Pt(111) is shown in the lower left corner. Desorption of CO costs 1.38 eV [84Poe]. Removing an electron from the 4f7/2 core level of the clean and CO covered surface costs 70.5 and 71.9 eV (atop CO), respectively, leaving a Au surface atom behind provided the core hole is fully screened (so-called Z → Z+1 approximation). Finally, desorbing a CO molecule from a Au surface atom embedded in a Pt surface costs approximately the desorption energy of CO from Au. At the end we have a relationship for estimating this desorption energy: E ad , CO ( Au ) = ∆Es, CO − E ad , CO ( Pt ) .

(34)

Inserting the measured values (e.g. for atop CO) the estimate for the adsorption energy of CO on Au is 0.02 eV which is a little too low compared to literature data [76Mce]. If we take the average value of ∆Es,CO = 1.05 eV for a mixture of atop and bridge CO, we find a more reasonable desorption energy of CO from Au of 0.33 eV. Another useful relationship, based on a Born-Haber cycle similar to the one illustrated in Fig. 37, connects surface core level shifts with the energy of surface segregation (section 3.6) [80Joh, 83Ros]. Emitting a 4f7/2 core electron from a surface and bulk Pt atom, for example, creates a Au surface and Au Landolt-Börnstein New Series III/42A

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bulk atom in a Pt matrix. Moving the Au dissolved "impurity" atom to the Pt surface requires the energy of segregation of Au to the Pt surface. Hence we have Esegr(Au,Pt) = ∆Es,b(Pt). Of course, such a simple relationship holds only for neighboring elements in the periodic table, since the Z → Z+1 approximation is used. This relationship between surface core level shifts and energies of surface segregation has been critically discussed by Feibelman [83Fei]. It is also known that the energy of segregation of a Z+1 element in a Z matrix is related to the energy of solution of Z+1 in Z and the difference in surface free energies of the clean Z and Z+1 materials [77Wyn, 78Mie, 83Fei]. Thus there exists a connection between surface core level shifts ∆Es,b(Z) and surface free energies [87Bon2]. Feibelman points out that differences in the energy of adsorption of a species "ad" on surfaces of Z and Z+1 can be related to the work function change due to adsorption on Z, ∆φ ad , and the adsorbate induced surface core level shift [83Fei]:

[

]

∆Ead ( Z, Z + 1) = κ ∆φad ( Z ) + ∆Es, ad ( Z ) ,

(35)

where κ is a constant. These various equations show how adsorption induced changes of substrate properties, such as the work function, surface core level binding energies and surface energies, are connected to energies of adsorption.

Fig. 37. Born-Haber energy cycle depicting CO desorption from Pt and Au surface atoms (vertical arrows) and core level photoemission from a clean and CO covered Pt(111) surface (horizontal arrows) [83Ege, 86Düc].

Fig. 36. High resolution Pt 4f7/2 photoemission spectra (photon energy of 125 eV) of a clean and CO covered Pt(111) surface at several CO coverages of 0.2, 0.5 and 0.6. Note the shifted Pt surface atom peak at 70.9 eV (clean) due to adsorbed CO. Compare also fig. 28 [94Bjö].

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[Ref. p. 59

1.5.4 Changes of surface free energy and surface stress The most simple and fundamental thermodynamic relationship governing surface energetics is Gibbs' adsorption equation (9) in section 1.2. Accordingly, adsorption always causes a decrease in the surface free energy of a clean crystalline surface. The rate of change in surface energy with the change in chemical potential in the gas phase is a means to determine the surface excess, i.e. the amount of material adsorbed:  ∂γ  1  ∂γ  = = − Γ2 .     ∂µ kT  2  T, µ1  ∂ ln p 2  T, µ1

(12)

Measurements to prove Eq. (12) and to determine the surface excess have been made before the times of routine surface analysis by modern spectroscopies. For example, the absolute value of the surface energy of Cu (predominantly of (100) orientation) and its changes with O2 chemical potential at a high temperature of 1200 K, have been determined quantitatively under equilibrium conditions by the zero creep technique [70Hon1]. The results are shown in Fig. 38. There is a plateau at 1410 erg/cm2 for very low partial O2 pressures, representative of the clean surface, and a sharp decrease by about 600 erg/cm2 in a range of 10–23 to 10–18 bar O2 pressure. Here oxygen adsorption takes place causing the decrease according to Eq. (12). A quantitative evaluation of the surface excess yields 4 × 1014 oxygen atoms/cm2 which is a coverage of 0.25 on the Cu(100) surface. These results have been well reproduced by Bauer et al. [76Bau]. A further increase in O2 chemical potential leads to a sudden rise in surface energy between about 10–16 to 10–14 bar. This increase is associated with a surface phase change: beginning of oxidation of Cu and severe surface faceting. Evaluation of this data by Eq. (12) is no longer sensible. 16

O2/Cu(100)

2

–2

Surface energy Es [10 erg cm ]

14

12

10

bulk oxide

8

6 –30 10

10

–26

–22

–18

–14

10 10 10 10 O2 partial pressure p [bar]

–10

10

–6

10

–2

Fig. 38. Change of absolute surface free energy of Cu(100) vs. logarithm of oxygen partial pressure at 1200 K under equilibrium conditions [70Hon2].

Hondros and McLean have also studied the relative anisotropy of the free surface energy (γ-plot) of Cu in the clean and oxygen covered state by evaluating grain boundary groove angles [70Hon2]. Figure 39 shows a selection of their results as contours of constant surface energy plotted in a unit triangle of a stereographic projection. The surface energy values, obtained at T = 1200 K, are normalized to unity at the (100) orientation. Two γ-plots are shown, one for the clean surface at 2.5 × 10–24 mbar of O2 and the other for an O-covered surface at 1 × 10–14 mbar of O2. The total anisotropy of surface energy for the clean surface is about 2.1% with a minimum at the most densely packed (111) orientation. For the O-covered surface the total anisotropy has risen to 3.25%, and the absolute minimum is now at the (100) orientation; even the (110) orientation has a lower surface free energy than (111). Thus (111) as well as (110) oriented surfaces are expected to facet under the influence of oxygen adsorption, exposing

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preferentially (100) facets. This is indeed observed [70Hon2]. The change in anisotropy of the surface free energy by adsorption is due to different adsorption energies of the same species on differently oriented faces. For example, if the adsorption energy on the (111) surface is lower than on the (100), the corresponding coverage and hence the decrease in surface energy is lower for that orientation, such that the surface energy of the covered (100) may now be smaller than that of the covered (111) orientation. The adsorbate-induced change in surface energy is related to the energy of adsorption in a non-linear way. The relationship can be obtained, for the simple case of non-activated Langmuir adsorption (Ead = Ed), for example, by inserting Eq. (28) into Eq. (12):  ∂γ  p , = − kT Γ2 = − kTN 0   p + κ ( T)  ∂ ln p 2  T, µ

(36)

 E  12 with κ ( T) = νd N 0 (2πmkT) exp − ad  .  kT 

(37)

1

Integration yields for the adsorption-induced change in surface energy:  p  ∆γ( p, T) = − kTN 0 ln 1 +  . κ ( T)  

(38)

The ratio p/κ(T) can become very large compared to 1 for typical values in a vacuum chemisorption experiment, e.g. for p = 10–7 mbar, νd = 1012 s–1, Ead = 1 eV, and T = 300 K. Under these conditions p/κ(T) = 1890, and we recover a simple linear relationship between ∆γ and the energy of adsorption:   p ∆γ( p, T) = − N 0  kT ln + E ad  . 1/ 2 νd N 0 ( 2πmkT)  

(39)

This equation depends weakly on temperature and pressure, i.e. it holds for the saturation limit of an adsorbate's isotherm. One obtains under the above mentioned conditions ∆γ = 313 erg/cm2. At 10–5 mbar the decrease would amount to 500 erg/cm2. Higher values of p are unrealistic at the low temperature of 300 K and the chosen high adsorption energy, in particular since Eqs.(38) and (39) do not give an asymptotic limit of ∆γ. Adsorbate-induced changes in surface energy are also related to changes in surface stress via the Shuttleworth Eq. (13). In a qualitative comparison to the data of Fig. 39, changes of surface stress due to oxygen adsorption on a Ni(100) surface have been measured by the single crystal cantilever bending technique [92San, 97Iba]. The results, obtained at room temperature and in a coverage range up to 0.5, are shown in Fig. 40, exhibiting large values of ∆τ up to –5400 erg/cm2 at the maximum oxygen coverage. Compared to the intrinsic (tensile) surface stress of 1440 erg/cm2 for clean Ni(100) [91Gum], this is a very large change. In fact, the adsorption of oxygen changes the absolute surface stress from tensile to a high compressive stress (τ < 0). Unfortunately, a more quantitative comparison of changes of the surface energy and the surface stress for a certain oxygen coverage and a possible evaluation of the gradient term ∆(dγ/dε) in the spirit of the Shuttleworth Eq. (13) is not possible since measurements of both quantities for the same adsorbate/substrate system are not available. High values of adsorbate-induced changes in surface stress, such as measured for adsorbed carbon, oxygen and sulfur on Ni(100) [97Iba], may lead to surface reconstruction. In fact, it is noteworthy that under the conditions of an adsorbed layer only changes in surface stress will cause reconstruction. The reason is that changes in surface energy due to adsorption are always negative, i.e. reducing the surface energy of the clean surface. However, the latter is already minimized from a structural point of view, and a further reduction, beyond that caused by the adsorbate, does not seem physically possible, as long as the Landolt-Börnstein New Series III/42A

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0 -1

∆ τ (10

-2

Surface stress

3

erg/cm

2)

coverage stays below a value needed for faceting. On the other hand, a high compressive surface stress is equivalent to a weakening of lateral surface bonds favoring a lateral surface expansion. This bond weakening has been directly detected by a softening of certain surface phonon modes [83Sze, 86Mül]. As a response to this driving force, the surface tries to increase the nearest neighbor bond distances in the first layer, either by a surface reconstruction in which the original density of surface atoms is maintained, or by reducing the surface density, in that a certain number of atoms is kicked out. These types of reconstruction are then driven by a relief of surface stress and not by a lowering of the surface free energy. Famous examples are the carbon-induced reconstructions on Ni(100) [79Onu] and Ni(111) [93Gar]. In the case of oxygen on Ni(100), although the maximum change in surface stress is very large (Fig. 40), a surface reconstruction does apparently not take place.

-4

-3

-5 0.0

O/Ni(100) 0.1

0.2

0.3

0.4

0.5

Oxygen coverage θ Fig. 40. Changes in the surface stress of Ni(100) induced by oxygen adsorption at room temperature [92San, 97Iba]. Reference state is the clean surface at ∆τ = 0.

Fig. 39a, b. Contour plot of relative surface free energy of Cu measured at T = 1200 K. Data are shown as a stereographic projection in the unit triangle of low-index orientations. All values are normalized to unity at the (100) orientation. (a) Clean Cu surfaces; (b) oxygen covered Cu surfaces at a O2 partial pressure of 10–14 mbar [70Hon2].

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1.5.5 Changes of surface phonon dispersion

Frequency

The dispersion of surface phonons of clean solid surfaces has been measured for a large number of materials [91Kre]. The technique is quasi-elastic scattering of either He atoms at energies of 30-50 meV or of low-energy electrons at 100-300 eV from single crystal surfaces. The scattered particles are energy analyzed with highest resolution to determine the phonon frequencies. The scattering occurs under nonspecular conditions to obtain the variation of phonon frequency as a function of parallel momentum transfer, with the scattering plane located in a high symmetry surface direction [82Iba, 92Iba, 94Ben]. Surface phonons are quantized vibrational eigenstates of surface atoms and exhibit a well defined energy versus momentum dependence. In many cases the dispersion curves of surface phonons are separated from the continuum of bulk phonon states. Depending on the wave vector, the decay length of a surface phonon amplitude into the bulk can be extremely short (couple of layers), i.e. it is localized at the surface, whereas the decay length for surface resonances is infinite by definition but with a large amplitude at the surface [92Iba]. The dispersion of surface resonances is fully embedded in the projected dispersion of bulk phonons. In general, the dispersion of surface phonons depends sensitively on the interatomic bond strengths of atoms in the surface layer and the interaction between first and second layer. In the presence of adsorbed species the bonding of surface atoms to all its neighbors is changed, i.e. the bond strength within the first layer and also between first and second (less to the third etc.) layer is altered. Accordingly, all the interatomic separations at the surface may change, an effect that is measurable as a change in the amount of surface relaxation and also surface stress (compare 1.5.4). Sometimes the energetic changes are so large that the surface will reconstruct. Of course, the dispersion of surface phonons is altered as well. One of the prominent surface phonon modes is the Rayleigh phonon, a vibration of surface atoms in a plane normal to the surface (sagittal plane) and with a k-vector parallel to the surface. This typical surface vibration depends sensitively on the lateral and vertical bonding of surface atoms, and hence changes with the presence of adsorbed species. To illustrate the expected changes, a phonon dispersion diagram is shown schematically in Fig. 41 where the bulk phonon bands are indicated as a projected area (hatched) and the Rayleigh surface phonon is drawn as a line starting from the Γ -point to the zone boundary X [97Iba].

Bulk phonon band ∆τ > 0 clean surface ∆τ < 0

Surface phonon 0.0

Γ

0.2

0.4

0.6

q-vector

0.8

1.0

Fig. 41. Schematic plot of the dispersion of a Rayleigh surface phonon (solid line) and of a bulk phonon band (hatched area). Atoms or molecules adsorbed on the surface can change the surface phonon dispersion, visible as an increase or decrease of the corresponding frequencies relative to those of the clean surface. These shifts are equivalent to a strengthening or weakening of the interatomic surface bonds, respectively, and correspond also to a change in surface stress, being tensile (∆τ > 0) or compressive (∆τ < 0), respectively [97Iba].

X

The surface phonon has a certain frequency at this boundary for the clean surface, related to the intrinsic stress of that surface. Adsorbing atoms or molecules may now strengthen or weaken the intra-layer surface bonds (depending e.g. on the direction of charge transfer between surface and adsorbate). Accordingly, there is a force for the intra-layer bond length to shorten or elongate, or in other words, the surface wants to laterally compress or dilate, respectively. Normally neither of this can happen since the surface layer stays in registry with the bulk, as long as we do not consider surface reconstruction. Hence these forces are equivalent to a change in surface stress, ∆τ, which is positive (tensile) or negative (compressive), respectively, corresponding to either stronger or weaker interatomic bonds relative to the clean surface. The restoring force for the vibrational motion of surface atoms (e.g. vertical to the surface) will increase (stiffen) or decrease (relax) leading to an increase or decrease in the frequency of the Rayleigh mode, as schematically indicated in the figure. Landolt-Börnstein New Series III/42A

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[Ref. p. 59

c(2×2)O/Ni(100)

450 400 350

–1

Frequency ν [cm ]

300 250 200

Fig. 42. Comparison of experimental and theoretical (solid lines) surface phonon dispersion data (frequency vs. parallel component of wave vector) for an ordered c(2×2)-O Ni(100) surface. The calculations are based on the position of O-atoms at 0.9 Å above the surface and the inclusion of lateral dipole-dipole interactions. For comparison, the experimental data for the clean surface Rayleigh phonon (solid points) are also included [83Leh, 84Rah].

150 clean surface

100 50 0 Γ

0.2

0.4

0.6 0.8 1.0 –1 Wave vector qII [Å ]

1.2

X

An interesting example for the change in surface phonon dispersion due to an adsorbate is presented in Fig. 42 for the system oxygen on Ni(100) characterized by a c(2×2) LEED pattern [83Sze, 84Rah]. Dispersion curves for several surface phonon modes are shown for the oxygen covered surface. The branch of the Rayleigh phonon dispersing from zero energy at Γ to a high value at X , is compared to that measured for the clean Ni(100) surface [83Leh, 86Roc]. The Rayleigh phonon for the c(2×2)-O surface is clearly shifted to lower frequencies over the whole range, at the zone boundary ( X -point) from 132 cm–1 down to 80 cm–1. Such a big change is indicative of substantially weakened intermolecular Ni–Ni surface bonds and a corresponding decrease in surface stress, such as measured independently by Sander et al. [92San] and displayed in Fig. 40. A theoretical simulation of the oxygen induced change in surface phonon dispersion yields quantitative values for the position of the oxygen atom above the surface and changes in lateral and vertical bond strength [84Rah]. These results are qualitatively consistent with changes in the interlayer separation between the first and second Ni layer of the c(2×2)-O-Ni(100) surface. The surface was found to expand relative to the bulk for the oxygen covered surface, in contrast to a contraction determined for the clean Ni(100) surface [83Fre1]. The total change of 8.4% is very substantial and indicative of a large change in the Ni–Ni force constant. Other examples of adsorbate induced changes in surface phonon dispersion show even stronger effects, such as soft phonon modes, Kohn anomalies and surface reconstructions.

1.5.6 Changes of surface optical properties The scattering of light at surfaces (in a range of near visible and low uv frequencies) has been used in a large variety of experimental approaches to probe surfaces and interfaces [95Mcg], in particular also changes of surfaces due to the adsorption of atoms and molecules. One of the main interests in pursuing optical techniques is the advantage that they do not require vacuum environment. Hence they are applicable in a wider range of technologically relevant situations, such as material processing steps, e.g. during molecular beam epitaxial growth of semiconductor thin films, or in electrochemistry. The Landolt-Börnstein New Series III/42A

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penetration depth of light into the solid is large (could be an advantage for studying burried interfaces) and therefore the techniques have in general a poor surface sensitivity. The low surface sensitivity is at least valid for linear optical scattering experiments whereas non-linear second order scattering, such as important in second harmonic (SHG) and sum frequency generation (SFG) spectroscopies, can be highly surface sensitive [84She, 86She, 89Lie]. In general, the optical response of a solid to an electromagnetic field of optical frequency depends on the first, second, and higher order dielectric susceptibilities. If the bulk of the solid is centrosymmetric, the bulk second order dipole response is zero, and the dominant second order contribution originates from the surface (or a nearby interface) where the inversion symmetry is broken. Therefore the study of second harmonic generated intensity is sensitive to the electronic properties (expressed e.g. by the charge density profile) of the outermost layer [92Urb, 95Wol] and intrinsically surface sensitive. It is useful for the study of adsorbing species on the surface or of clean surface structural changes induced by varying the temperature, for example. Most light scattering techniques, however, depend on the first order dielectric response which is measured through the reflectivity of (linearly) polarized monochromatic light. Here the surface sensitivity is enhanced by subtracting the dominant isotropic bulk contribution. Relatively simple techniques are the differential reflectance (DRS) [71Chi] and reflectance anisotropy (RAS) [85Asp, 87Asp] spectroscopies. In the first the reflectance is measured as a function of frequency for two different surface conditions, clean and adsorbate covered, for example. Taking the difference between both signals removes the bulk contribution, with the remainder being characteristic of changes at the surface. In the second, the reflectance is measured for linearly polarized light at near normal incidence for optically anisotropic surfaces, with the E-vector oriented in two orthogonal high symmetry surface directions a and b. The normalized difference, ∆r / r = ( ra − rb ) / ( ra + rb ) [85Asp], is then recorded either as a function of time, to monitor changes at the surface, or versus frequency, in the sense of a true spectroscopy. Another similar but older technique is spectroscopic ellipsometry where the reflection induced changes in the state of polarization of a linearly polarized incident light is measured [68Arc, 71Mey, 83Gij]. The ratio of reflectivity, measured with the polarization parallel and perpendicular to the plane of incidence, can be expressed as a function of two parameters, ∆ and Ψ, the phase shift and relative attenuation of the field vectors parallel and perpendicular to the plane of incidence. Through Maxwell's theory, these parameters are related to the refractive index of the ambient and the optical constants of the reflecting system. For a clean isotropic surface these are the real and imaginary parts of the refractive index. In the case of an adsorbed layer, the changes in ∆ and Ψ are related in a complex way to the optical constants of both the film and the substrate as well as the thickness of the film. It is common to nearly all optical techniques that the physical interpretation of measured signals and even of the changes of physical parameters evaluated from the primary signal is difficult. As far as adsorption induced changes of clean surface properties are concerned, the information obtained from optical techniques is therefore rather indirect. In some cases spectral resonance features associated with the surface (interface) may be detected, and their changes with adsorbing atoms or molecules may be useful to follow the kinetics of this process but fundamental information on the properties of the adsorbed species is rarely obtained. To illustrate the information extracted from some of the more frequently used techniques, we present examples for adsorbates on Cu(110) analyzed by ellipsometry [79Hab, 82Han], RAS [95Hof] and SHG [95Wol]. Due to the two-fold symmetry of Cu(110), the surface optical properties are anisotropic. The results for the ellipsometric investigation are shown in Figs. 43a and b. The data in Fig. 43a correspond to differences of ∆ and Ψ, each measured for the two azimuth [1 1 0] and [001] at three temperatures, respectively, that characterize the clean Cu(110) surface. Obviously δ∆ = ∆( [1 1 0] ) – ∆( [001] ) and, to a lesser extent, δΨ show a "resonance" near 600 nm (2 eV). In Fig. 43b the dependence of the relative oxygen Auger peak intensity (ratio of the oxygen 510 eV peak to the Cu 920 eV peak) versus δ∆ (measured at a wavelength of 632.8 nm) is presented for oxygen covered Cu(110) and Cu(111) surfaces at 296 K and on removal of adsorbed oxygen at 473 K [79Hab]. There is a linear relationship between both quantities which shows that δ∆ can be used under non-vacuum conditions to monitor the oxygen coverage. The absolute coverage of oxygen or surface structural information is not readily obtained from the optical data.

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0.6

3.0

2.5

Photon energy hν [eV] 2.0

[Ref. p. 59

1.5

Cu(110)

0.5 0.4

δ∆ [deg]

0.3 0.2 0.1 0 – 0.1 – 0.2 400

0.2

450 500 550 600 650 700 750 800 850 Wavelength λ [nm] Photon energy hν [eV] 3.0 2.5 2.0 1.5

0.6

O/Cu

0.1

δΨ [deg]

0 – 0.1 – 0.2 – 0.3 – 0.4

T = 295 K 520 K 600 K

Auger peak ratio O510 eV/Cu920 eV

0.5

– 0.5 – 0.6 400

a

450 500 550 600 650 700 750 800 850 Wavelength λ [nm] b

0.4 0.3 0.2

Cu(110) T = 296 K Cu(111) 520 K Cu(111) 600 K

0.1

0

0.1

0.2

0.3 0.4 δ∆ [deg]

0.5

0.6

0.7

Fig. 43a, b. (a) Spectral ellipsometry from clean Cu(110) showing the differences δψ and δ∆ vs. wavelength of light at three different temperatures [82Han]. (b) Dependence of the relative oxygen Auger peak intensity (ratio of the oxygen 510 eV peak to the Cu 920 eV peak) vs. ellipsometric parameter δ∆ measured at a wavelength of 632.8 nm. Data are plotted for oxygen covered Cu(110) and Cu(111) surfaces at 296 K and on removal of adsorbed oxygen from Cu(111) at 473 K [79Hab].

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Reflectance Re(∆r/ r )

Cu(110)

(2×1)-O/Cu(110)

5 × 10

–3

(2×1)-CO/Cu(110)

1.5

2.0

2.5

3.0

3.5

4.0

Photon energy E [eV]

4.5

5.0

5.5

6.0

Fig. 44. Real part of the optical reflectance anisotropy spectra for clean Cu(110), oxygen covered (2×1)-O-Cu(110) and CO covered (2×1)-CO-Cu(110) surface. Horizontal lines indicate zeros of each spectrum [95Hof] .

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Fig. 45. Dependence of the s- and p-polarized SHG intensity vs. oxygen exposure for a Cu(110) surface. SHG radiation generated by a fundamental wave at 630 nm at normal incidence in a plane parallel to the

Γ X [1 1 0] azimuth [95Wol].

The second example in Fig. 44 shows the real part of the reflectance anisotropy versus photon energy for the clean, oxygen and CO covered Cu(110) surfaces, respectively [95Hof]. Substantial differences in the spectra are obvious. The resonance at 2.1 eV of the clean surface is nearly quenched by adsorbed oxygen. It is totally quenched by adsorbed CO and a large peak near 4.4 eV emerges for that case. The big changes at 2.1 eV allow time resolved (exposure dependent) measurements of the adsorption kinetics to be made. The resonance at 2.1 eV is explained by a transition involving electronic surface states of Cu(110) [91Jia, 95Hof]. Thirdly, the SHG study of the same system also showed the same resonance at 2.06 eV for clean Cu(110) and a shifted resonance at 2.09 eV for the oxygen covered Cu surface [95Wol]. The resonance at 2.06 eV was identified as a surface state transition at the Y point of the surface Brillouin zone (compare also [92Urb]). The occupied surface state is strongly attenuated with increasing oxygen coverage, thus effecting the intensity of the SHG resonance. The dependence of the SHG intensity versus oxygen exposure is illustrated in Fig. 45 for s- and p-polarized light, incident at the fundamental wavelength of 630 nm (1.97 eV) along the [1 1 0] azimuth. The drastic change in intensity for the s-polarized case can be correlated with the known structural changes of the Cu(110) surface during oxygen exposure. The steep decrease up to 1 L exposure corresponds to the loss of inward relaxation (–8.5%) and changes of the electronic surface structure while the smaller increase for higher exposures is related to the formation of the (2×1)-O surface reconstruction and outward relaxation of 17% [95Wol]. Note that this detailed interpretation would not be possible without referring to the results of extensive studies carried out with other quantitative spectroscopies and structural techniques. In comparing the spectral features of all three optical experiments dealing with the Cu(110) surface it is obvious that the resonance at 2.1 eV is present and dominant in all data sets. The sensitivity of electronic surface states (of clean Cu(110)) to adsorbed oxygen (and probably other adsorbates) causes in this case the optical techniques to be quite sensitive to adsorbates, enabling their use to monitor the kinetics of adsorption/desorption kinetics, for example. Since electronic surface states are quite common for a number of semiconductor surfaces, it is understandable that optical response investigations are sensitive to adsorbates especially on these surfaces. Hence they are frequently employed to study kinetic phenomena involving adsorption or thin film growth.

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References for 1 1876 1878 1879 13Lan 15Knu 18Lan 21Vol 23Lan 25Tay 27Dav 28Len 28Str 29Bal 29Ste 30Cla 31Str 32Len 36Len 37Dev 37Len 38Bru 38Wag 39Fow 39Mit 39Vol 40Bee 47Bar 50Shu 51Kin 52Her

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83Ege 83Fei 83Fre1 83Fre2 83Gat 83Gij 83Gom 83Gre 83Kis 83Leh 83Mro 83Pfn 83Rie

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Imbihl, R., Ladas, S., Ertl, G.: Surf. Sci. 206 (1988) L903. Jona, F., Marcus, P.M., in: Structure of Surfaces II. Springer Series in Surf. Sci., Vol. 11, Berlin: Springer-Verlag, 1988, p. 90. 88See Seebauer, E.G., Kong, A.C.F., Schmidt, L.D.: Surf. Sci. 193 (1988) 417. 88Stu Stulen, R.H., Knotek, M.L.: "Desorption Induced by Electronic Transitions - DIET III", in: Springer Series in Surf. Sci., Vol. 13. Ertl, G., Gomer, R. (eds.), Berlin: Springer-Verlag, 1988. 88Sur Surnev, L., Xu, Z., Yates jr., J.T.: Surf. Sci. 201 (1988) 1; 14. 88Wes1 Wesner, D.A., Coenen, F.P., Bonzel, H.P.: Surf. Sci. 199 (1988) L419. 88Wes2 Wesner, D.A., Coenen, F.P., Bonzel, H.P.: Phys. Rev. Lett. 60 (1988) 1045. 88Zhu Zhu, X.D., Rasing, T., Shen, Y.R.: Phys. Rev. Lett. 61 (1988) 2883. 89Cam Campbell, C.T.: Adv. Catalysis 36 (1989) 1-54. 89Che Chen, J.G., Erley, W., Ibach, H.: Surf. Sci. 223 (1989) L891. 89Lan Lang, N.D.: "Theory of Alkali Adsorption on Metal Surfaces", in: Physics and Chemistry of Alkali Metal Adsorption. Bonzel, H.P., Bradshaw, A.M., Ertl, G. (eds.), Amsterdam: Elsevier, 1989, p. 11-24. 89Lie Liebsch, A., Schaich, W.L.: Phys. Rev. B 40 (1989) 5401. 89Mem Memmel, N., Rangelov, G., Bertel, E., Dose, V., Kometer, K., Rösch, N.: Phys. Rev. Lett. 63 (1989) 1884. 89Per Persson, B.N.J.: Solid State Commun. 70 (1989) 211. 89Som Somorjai, G.A., Hove, M.A. v.: Progr. Surf. Sci. 30 (1989) 201. 89Wes Wesner, D.A., Coenen, F.P., Bonzel, H.P.: Phys. Rev. B 39 (1989) 10770. 90Ant Antonsson, H., Nilsson, A., Martensson, N., Panas, I., Siegbahn, P.E.M.: J. Electron Spectrosc. Relat. Phenom. 54/55 (1990) 601. 90Ber Berger, H.F., Leisch, M., Winkler, A., Rendulic, K.D.: Chem. Phys. Lett. 175 (1990) 425. 90Bet Betz, G., Varga, P.: "Desorption Induced by Electronic Transitions - DIET IV." Springer Series in Surf. Sci., Ertl, G., Gomer, R. (eds.), Berlin: Springer-Verlag, 1990. 90Fei Feigerle, C.S., Desai, S.R., Overbury, S.H.: J. Chem. Phys. 93 (1990) 787. 90Gom Gomer, R.: Rep. Progr. Phys. 53 (1990) 917. 90Kle Kleinle, G., Wintterlin, J., Ertl, G., Behm, R.J., Jona, F., Moritz, W.: Surf. Sci. 225 (1990) 171. 90Lin Lin, T.S., Lu, H.J., Gomer, R.: Surf. Sci. 234 (1990) 251. 90Per Persson, B.N.J., Tüshaus, M., Bradshaw, A.M.: J. Chem. Phys. 92 (1990) 5034. 90Sal Saldin, D.K., Andres, P.L. d.: Phys. Rev. Lett. 64 (1990) 1270. 90Voi Voigtländer, B., Bruchmann, D., Lehwald, S., Ibach, H.: Surf. Sci. 225 (1990) 151. 91Bor Borroni-Bird, C.E., Al-Sarraf, N., Andersson, S., King, D.A.: Chem. Phys. Lett. 183 (1991) 516. 91Gum Gumbsch, P., Daw, M.: Phys. Rev. B 44 (1991) 3943. 91Jia Jiang, M.Y., Pajer, G., Burstein, E.: Surf. Sci. 242 (1991) 306. 91Kre Kress, W., Wette, F.W. d.: "Surface Phonons", in: Springer Series in Surf. Sci. Vol. 21. Ertl, G., Gomer, R. (eds.), Berlin: Springer-Verlag, 1991. 91Par Parschau, G., Rieder, K.H.: Surf. Sci. 257 (1991) L628. 91Xia Xiao, X.D., Xu, X.D., Daum, W., Shen, Y.R.: Phys. Rev. Lett. 66 (1991) 2352. 92Dea DeAngelis, M.A., Glines, A.M., Anton, A.B.: J. Chem. Phys. 96 (1992) 8582. 92Iba Ibach, H.: Phys. Blätter 9 (1992) 705. 92Kna Knauff, O., Grosche, U., Bonzel, H.P., Fritzsche, V.: Mol. Phys. 76 (1992) 787. 92Rod Rodriguez, J.A., Goodman, D.W.: Science 257 (1992) 897. 92San Sander, D., Linke, U., Ibach, H.: Surf. Sci. 272 (1992) 318. 92Til Tillborg, H., Nilsson, A., Martensson, N.: Surf. Sci. 273 (1992) 47. 92Urb Urbach, L.E., Percival, K.L., Hicks, J.M., Plummer, E.W., Dai, H.L.: Phys. Rev. Lett. 45 (1992) 3769. 92Win Wintterlin, J., Behm, R.J., in: Scanning Tunneling Microscopy I. Springer Series in Surf. Sci. 20. Güntherodt, H.H., Wiesendanger, R.(eds.), Berlin: Springer-Verlag, 1992, p. 39-81. 92Zhu Zhu, L., Bao, S., Xu, C.Y., Xu, Y.B.: Surf. Sci. 260 (1992) 267. 93Bao Bao, S., Schindler, K.M., Hofmann, P., Fritzsche, V., Bradshaw, A.M., Woodruff, D.P.: Surf. Sci. 291 (1993) 295. Lando lt -Börnst ein New Ser ies III/42A

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93Stu 93Xia 94Ben 94Bjö 94Fri 94Gat 94Kam 94Sta 94Xu 95Fei 95Hof 95Mcg 95Pug 95Sal 95See 95Som 95Spr 95Wol 95Xia 96Ber 96Dav 96Des 96Rai 97Iba 97Nie 97Rai 97Reu 97Xia 97Yeo

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Bonzel, H.P.: "Surface Diffusion on Metals", in: Diffusion in Solid Metals and Alloys. Landolt-Börnstein (New Series) III/26. Mehrer, H. (ed.), Berlin: Springer-Verlag, 1993, p. 717747. Burns, A.R., Stechel, E.B., Jennison, D.R.: "Desorption Induced by Electronic Transitions DIET V." Springer Series in Surf. Sci., Ertl, G., Gomer, R. (eds.), Berlin: Springer-Verlag, 1993. Fasolino, A., Selloni, A., Shkrebtii, A.: "Surface reconstruction and relaxation", in: Physics of Solid Surfaces: Structure. Landolt-Börnstein (New Series) III/24a. Chiarotti, G. (ed.), Berlin: Springer-Verlag, 1993, p. 125-224. Gardin, D.E., Batteas, J.D., Hove, M.A. v., Somorjai, G.A.: Surf. Sci. 296 (1993) 25. Huang, Z., Hussain, Z., Huff, W.T., Moler, E.J., Shirley, D.A.: Phys. Rev. B 48 (1993) 1696. Pangher, N., Haase, J.: Surf. Sci. 292 (1993) L791. Pangher, N., Haase, J.: Surf. Sci. 293 (1993) L908. Schindler, K.M., Hofmann, P., Weiss, K.U., Dippel, R., Gardner, P., Fritzsche, V., Bradshaw, A.M., Woodruff, D.P., Davila, M.E., Asensio, M.C., Conesa, J.C., González-Elipe, A.R.: J. Electron Spectrosc. Relat. Phenom. 64/65 (1993) 75. Stuckless, J.T., Al-Sarraf, N., Wartnaby, C., King, D.A.: J. Chem. Phys. 99 (1993) 2202. Xiao, X.D., Xie, Y., Shen, Y.R.: Phys. Rev. B 48 (1993) 17452. Benedek, G., Toennies, J.P.: Surf. Sci. 299/300 (1994) 587-611. Björneholm, O., Nilsson, A., Tillborg, H., Bennich, P., Sandell, A., Hernnäs, B., Puglia, C., Martensson, N.: Surf. Sci. 315 (1994) L983. Fritzsche, V., Knauff, O., Bonzel, H.P.: Phys. Rev. B 49 (1994) 10643. Gatos, H.C.: Surf. Sci. 299/300 (1994) 1. Kampshoff, E., Hahn, E., Kern, K.: Phys. Rev. Lett. 73 (1994) 704. Starke, U., Hove, M.A. v., Somorjai, G.A.: Progr. Surf. Sci. 46 (1994) 305. Xu, X., Szanyi, J., Xu, Q., Goodman, D.W.: Catal. Today 21 (1994) 57. Feibelman, P.J.: Phys. Rev. B 51 (1995) 17867. Hofmann, P., Rose, K.C., Fernandez, V., Bradshaw, A.M., Richter, W.: Phys. Rev. Lett. 75 (1995) 2039. McGilp, J.F.: "Optical Characterization of Semiconductor Surfaces and Interfaces." Progr. Surf. Sci. 49 (1995) 1-106. Puglia, C., Nilsson, A., Hernnäs, B., Karis, O., Bennich, P., Martensson, N.: Surf. Sci. 342 (1995) 119. Saldin, D.K., Chen, X.: Phys. Rev. B 52 (1995) 2941. Seebauer, E.G., Allen, C.E.: Progr. Surf. Sci. 49 (1995) 265-330. Somorjai, G.A., Hove, M.A. v.: Acta Crystallogr. B 51 (1995) 502. Sprunger, P., Besenbacher, F., Steensgaard, I.: Surf. Sci. 324 (1995) L321. Woll, J., Meister, G., Barjenbruch, U., Goldmann, A.: Appl. Phys. A 60 (1995) 173. Xiao, X.D., Xie, Y., Jakobsen, C., Galloway, H., Salmeron, M., and Shen, Y.R.: Phys. Rev. Lett. 74 (1995) 3860. Bertino, M.F., Hofmann, F., Steinhögl, W., Toennies, J.P.: J. Chem. Phys. 105 (1996) 11297. Davis, R., Woodruff, D.P., Hofmann, P., Schaff, O., Fernandez, V., Schindler, K. M., Fritzsche, V., Bradshaw, A.M.: J. Phys. Condens. Matter 8 (1996) 1367. Desjonquères, M.C., Spanjaard, D.: Concepts in Surface Physics. Berlin: Springer-Verlag, 1996. Rainer, D.R., Wu, M.C., Mahon, D., Goodman, D.W.: J. Vac. Sci. Technol. A 14 (1996) 1184. Ibach, H.: Surf. Sci. Rep. 29 (1997) 193-264. Nien, C.H., Madey, T.E.: Surf. Sci. 380 (1997) L527. Rainer, D.R., Xu, C., Holmblad, P.M., Goodman, D.W.: J. Vac. Sci. Technol. A 15 (1997) 1653. Reuter, K., Bernhardt, J., Wedler, H., Schardt, J., Starke, U., Heinz, K.: Phys. Rev. Lett. 79 (1997) 4818. Xiao, X.D., Xie, Y., Jakobsen, C., Shen, Y.R.: Phys. Rev. B 56 (1997) 12529. Yeo, Y.Y., Vattuone, L., King, D.A.: J. Chem. Phys. 106 (1997) 1990.

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1 Introduction Brown, W.A., Kose, R., King, D.A.: "Femtomole Adsorption Calorimetry on Single-Crystal Surfaces." Chem. Rev. 98 (1998) 797-832. Emundts, A., Pirug, G., Werner, J., Bonzel, H.P.: Surf. Sci. 410 (1998) L727. Graham, A.P., Toennies, J.P.: "Determination of the Lateral Potential Energy Surface of Single Adsorbed Atoms and Molecules on Single Crystal Surfaces Using Helium Atom Scattering", in: Int. Conf. on Vibrations at Surfaces. Tokyo, Japan, 1998. Gsell, M., Jakob, P., Menzel, D.: Science 280 (1998) 717. Mravikakis, M., Hammer, B., Norskov, J.K.: Phys. Rev. Lett. 81 (1998) 2819. Madey, T.E., Nien, C.H., Pelhos, K., Kolodziej, J.J., Abdelrehim, I.M., Tao, H.S.: Surf. Sci. 438 (1999) 191.

2 Characterization of adsorbate overlayers: measuring techniques (CH. WÖLL) See subvolume III/42 A2

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3 Data: Adsorbate properties

3.1 Adsorption of noble gases

3.1.1 Noble gases on metals and semiconductors P. ZEPPENFELD

3.1.1.1 Introduction 3.1.1.1.1 General remarks After 30 years of continuing investigation, the adsorption properties of the noble gases on metal and semiconductor surfaces have recently attracted renewed interest. On the one hand, some fundamental aspects have come within the reach of modern experimental and theoretical techniques, such as the very nature of physisorption and the noble gas - substrate interaction, the possibility to study growth and surface kinetics at the atomic scale, and the recent interest in nanoscale surface friction and related tribological issues, where noble gas adlayers serve as model systems [99P]. On the other hand, noble gas adsorption is being used as a non-destructive and quantitative surface analytical tool as, for instance, in photoemission of adsorbed xenon (PAX) [97W] and for titration analysis of heterogeneous surfaces based on the site specificity of the interaction strength [96S, 98W]. Hence, it may be expected that the noble gases will continue to serve as model systems for solving fundamental issues in surface science as well as to provide a powerful analytical probe for surface characterization. 3.1.1.1.2 The interaction of noble gases at surfaces The surface potential energy V can be decomposed into the contribution of the substrate holding potential VAS (i.e., the interaction of an isolated noble gas atom with the surface) and the effective lateral interaction VAA between the adsorbed atoms. The holding potential is a function of the lateral position x,y of the adsorbate and of its height z above the surface. The interaction between the noble gases and metal surfaces is attractive at larger distances (van der Waals attraction) and thus proportional to -z-3 (-z-4 at very large distances, where retardation effects have to be taken into account). Close to the surface, the interaction becomes strongly repulsive (Pauli repulsion) and can be described by an exponential or algebraic decay. The combination of both the repulsive and the attractive part gives rise to a shallow physisorption well in the holding potential whose depth ranges from a few meV for He up to about 300 meV for Xe. The potential minimum determines the binding distance z0 as well as the adsorption site (x0,y0). The lateral variation of the well depth VAS(x ,y,z0) reflects the atomic and electronic structure of the substrate lattice; its peak-to-peak amplitude ∆VAS is called the surface corrugation. Various theoretical models have been proposed to describe the atom-surface interactions for the noble gases [91V1]. In the simplest approach, the holding potential is obtained as the pairwise sum of atomic

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pair-potentials, e.g., of the Lennard-Jones or Morse type. Alternatively, the potential may be expanded into a Fourier series with the first few terms (V0(z) and VG(z)) being taken into account. Recently, a more sophisticated type of potential has been constructed by Barker [91B] for the case of Xe/Pt(111) in which non-central terms are added to the usual pairwise contributions in order to mimic the repulsive interaction with the delocalized metal electrons. In this case, the potential minimum and, hence, the Xe adsorption site is located on top of the Pt surface atom in contrast to the high coordination (hollow sites) obtained with pair potentials. The lateral interaction between the adsorbed noble gas atoms is, to a large extend, determined by the dispersion-repulsion usually described by the well known gas phase potentials. However, significant contributions may also arise from surface induced dipole repulsions, many-body and substrate mediated interactions as discussed in detail in Ref. [97B2]. These contributions tend to weaken the attractive interactions with respect to the gas phase value. For instance, according to the gas phase Xe Lennard-Jones potential, the lateral interaction in a hexagonal close packed 2D solid phase would be 72 meV per Xe atom, whereas a value of 43 meV has been reported for Xe/Pt(111) [88K2]. In a few but notable cases, the repulsive terms may even outweigh the attractive van der Waals potential, resulting in an overall repulsive lateral interaction, as observed for Xe on the strongly binding substrates Pd, W and Ni. Such strong repulsions have been attributed to surface induced dipole-dipole interactions and initiated further investigations on the precise nature of the noble gas - metal interaction (see below). Modifications of the electron density distribution within the metal were revealed in LDA calculations of Xe adsorped on a Pt25 cluster [90M] and have been interpreted in terms of hybridization of atomic orbitals. This has led to an ongoing debate on the ‘chemical contributions’ in the noble gas - metal interaction (which, by the way, were already suggested in the early work of Xe adsorption on W and Ni in the 1970s). Further support on the role of hybridization of the noble atom orbitals with the substrate electronic states have been obtained from the experimental evidence of ‘anticorrugation’ effects in He vs. Ne scattering from surfaces [93R] and related density functional calculations [84A, 96P]. Furthermore, intrinsic surface electronic states have been suggested to play an important role in the binding of the noble gases on metals affecting both VAS and VAA [96B]. 3.1.1.1.3 Sticking and accommodation A large number of studies has dealt with the scattering (adsorption-desorption) of noble gas atoms from surfaces as a function of kinetic energy, incident angle, and surface temperature. From a fit to these data, noble gas - surface potentials have been derived, such as the aforementioned Xe-Pt(111) potential [91B]. In the present context, we will limit ourselves to those experiments which are relevant to the adsorption properties, i.e., we will address the sticking probabilities for noble gas atoms incident with thermal energies, but not the angular and energetic distributions of the backscattered atoms. For an overview of the latter issues we refer to [91R]. At thermal kinetic energies and low enough surface temperature, the heavier noble gases (Xe, Kr, Ar) usually have a sticking probability close to unity although on some surfaces such as Ru(0001) [92S2] and Cu(110) [94Z2] values as low as 20% have been reported. These small values are due to the high elastic reflection probability which is a consequence of the inefficient energy transfer (phonon mismatch) and the phonon quantization [92S2]. The situation is most dramatic for the lighter noble gases which exhibit pronounced quantum behaviour. For instance, Ne on Ru(0001) has an initial sticking probability below 1% at low incident kinetic energy [88S]. The sticking coefficient generally depends on the surface coverage θ. Especially in those cases, where the initial sticking coefficient s0 = s(θ→0) is significantly smaller than one, surface areas already covered with the noble gas allow a more efficient trapping of the incident noble gas atoms due to the more efficient energy transfer on these areas [91H]. The trapping efficiency of the noble gas covered areas strongly depends on the surface temperature as well as on the adlayer morphology. If, e.g., 2D islands are formed on the surface during the adsorption process, noble gas atoms impinging on these islands may be either trapped on top of an island and become incorporated at the island edge, or they may desorb from the island before reaching the island edge, if the surface temperature is too high for the bilayer to be stable and if the islands have grown sufficiently large. In this case a more complex variation of the Lando lt Bö rnst ein New Ser ies III/42A1

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sticking coefficient is observed (Fig. 4) [94Z2]. In addition, the presence of surface defects or impurities as well as the ‘transient’ mobility of a noble gas atom upon adsorption [85T, 94Z2] may strongly affect the sticking coefficient. 3.1.1.1.4 Adsorption energies Experimentally, adsorption energies can be inferred from adsorption isotherms in which the surface coverage is recorded as a function of the equilibrium pressure and temperature. The surface coverage θ can be monitored in various ways, such as by the appearance of adlayer diffraction spots (or, alternatively, the intensity decrease of the substrate related spots) using low energy electron, X-ray or thermal He atom diffraction; the height of the noble gas Auger peaks; the photoemission signal, or the work function change ∆φ upon adsorption. For a quantitative evaluation, the isosteric heat Qiso, which is the difference between the enthalpies of the adsorbed and the 3D gas phase, is evaluated from the Clausius-Clapeyron equation as described in chapter 1.2. It should be noted that in most experiments the 3D gas and the physisorbed adlayer are not in true thermodynamic equilibrium since the temperature of the 3D gas (usually at room temperature) and the surface temperature (typically between 20 and 100 K) are not the same. The corresponding corrections, however, are small and usually disregarded. In many experiments, the isosteric heat of adsorption (latent heat) is determined for adsorption into the 2D solid monolayer phase. This value denoted by Q1, can be assumed to be constant over the coverage range of coexistence between a 2D solid and a 2D gas phase, and before any phase transition or compression of the monolayer solid phase takes place. At low coverage, where only a dilute phase (2D gas) is formed, the isosteric heat may increase or decrease with coverage depending on whether the lateral interactions between the adsorbed noble gas atoms are attractive or repulsive. In this context the isosteric heat of adsorption approaching zero coverage Q0 = Qiso(θ → 0) is another important quantity. Its experimental determination is more delicate and may be obscured by the fact that the initial adsorption may preferentially occur at surface defects (steps) or impurities due to a stronger binding of the noble gas atoms to these defects. In fact, the increase of Qiso at very low coverage observed, e.g., on stepped or high index surfaces allows to extract the adsorption energy of the defect sites and can even be used as a quantitative measure to determine the defect concentration. The isosteric heat of adsorption Qiso(θ) is related to the (differential) potential energy V(θ) of the adsorbate on the surface and the (temperature dependent) kinetic degrees of freedom f in the adsorbed and the 3D gas phase, respectively: Qiso (θ ) = H ads (θ ) − H 3 D ≈ U ads (θ ) − H 3 D = V (θ ) + [ f ads − ( f 3 D + 2)] kT / 2 . Assuming an ideal, mono-atomic gas, the kinetic correction becomes −kT / 2 for adsorption into an (ideal) 2D gas phase and + kT / 2 for adsorption into a 2D solid. A detailed account of the thermodynamics of adsorption can be found in [97B2]. The individual contributions to the binding energy V are not all independently accessible to the experiment. Nevertheless, the lateral interaction energy VAA can be inferred from the variation of the isosteric heat with coverage or simply from Q1 – Q0. It can also be measured directly by determining the critical coverage θc at which the transition from the 2D dilute into the 2D solid phase occurs. The 2D condensation can be detected, e.g., in a helium scattering experiment due to different effective cross sections for diffuse scattering from the 2D dilute and the 2D solid phase, respectively [83P, 88K2]. The 2D heat of condensation Q2D is then deduced from the 2D analogon of the Clausius-Clapeyron equation, where the 2D spreading pressure p2D is related to the critical coverage θc by p 2 D = N 0θ c kT (assuming an ideal 2D gas). Taking into account the kinetic contributions, the lateral interaction is given by VAA = Q2D − kT.

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3.1.1.1.5 Desorption energies and desorption kinetics Aside from isothermal adsorption experiments, the binding energy of the noble gases can also be inferred from thermal desorption measurements. The desorption rate is recorded as a function of time during a linear temperature ramp (temperature programmed desorption, TPD) or at constant temperature (isothermal desorption). If the adlayer remains in quasi 2D-equilibrium during the desorption process the rate can be expressed by the Polanyi-Wigner equation (see Eq. 24):  E  rd (θ , T ) = ν d (T )θ n N 0 exp − d  .  kT  The exponent n denotes the order of desorption, related to the nature and the statistics of the desorption pathway, and Ed is the desorption energy. In accordance with the shape of the holding potential (see 3.1.1.1.2), the desorption of the noble gases is not activated and Ed is a direct measure of the binding energy. More precisely, it is the difference between the differential enthalpy of an atom in the adsorbed phase and in the 3D gas phase (generally not in thermodynamic equilibrium with the adsorbed phase). Up to kinetic corrections of the order of kT the desorption energy Ed is thus identical to the isosteric heat of adsorption Qiso defined above. Therefore, in the tables in section 3.1.1.2.2 no distinction between adsorption and desorption energies is made, but the experimental method is indicated. The prefactor νd appearing in the Polanyi-Wigner equation is related to the entropy term in the relevant free enthalpy balance ∆G = µ = ∆H - T∆S, i.e., νd = exp(∆S/k). For the adsorbed noble gases the prefactor is usually of the order of 1012 to 1013 s−1and can be interpreted as an ‘attempt frequency’ for desorption associated with the (perpendicular) atom-surface vibration frequency. As far as the desorption kinetics is concerned, desorption orders of zero and one have been observed for the noble gases on different surfaces and in different coverage regimes. In the case of phase coexistence (2D equilibrium) between a 2D dilute (gas) and a 2D solid phase as well as for noble gas multilayers zero order desorption is expected, i.e., the desorption rate is independent of coverage and follows a simple exponential increase with temperature. This implies that in a series of TPD curves recorded for different initial coverages the leading edges of these curves will coincide. The TPD curves are, therefore, conveniently plotted in an Arrhenius type diagram in which the desorption energy and the prefactor are readily obtained from the slope and offset of the common leading edge [92S1]. First order desorption kinetics is observed if the noble gas adlayer is in a single phase. In particular, this situation occurs at low coverage (or high desorption temperature) where a pure 2D gas phase is stable. An extended coverage regime of first order desorption (even up to monolayer completion) has been observed in those cases where repulsive lateral interactions between the adsorbed noble gas atoms prohibit the condensation of the dilute phase into a 2D solid phase, such as for Xe on Pd, W and Ni surfaces. In most other cases the regime of first order desorption and, hence, the stability of a 2D gas phase is limited to a small fraction of a monolayer. Finally, the presence of surface defects (steps or impurities) may significantly alter the desorption kinetics, affecting the desorption order as well as the desorption energy and prefactor [90B]. 3.1.1.1.6 Structure and phase diagram Noble gas monolayers are often considered as model systems in the study of two-dimensional phases and phase transitions. As in bulk matter the analog of a gas, fluid and solid phase also exist in purely two dimensional ‘floating’ adlayers, although the translational ordering of a floating solid is not of long range order - with important consequences on the nature of the 2D solid-fluid (melting) transition. The adsorption on corrugated crystalline substrates differs from the ideal 2D case, e.g., by the appearance of lattice gas and fluid phases due to the discrete spacing of the adatoms on preferred lattice sites located at the potential minima of the holding potential. In addition, several solid phases may exist beside the floating 2D incommensurate phase, such as commensurate or high-order commensurate phases in registry with the 2D substrate lattice. Which type of solid phase is formed depends on the relative size of the lateral interaction VAA between adsorbed atoms and the corrugation Vc = ∆VAS of the holding potential as Lando lt Bö rnst ein New Ser ies III/42A1

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well as on the natural misfit m between the 2D floating adlayer and the substrate lattice. Perfectly commensurate (C) monolayer solids are expected for strongly corrugated substrates, weak lateral interactions (Vc/VAA ≥ 1) and small lattice misfit. On the other hand, incommensurate (I) structures are favored for (Vc/VAA « 1) or large lattice mismatch. For intermediate cases, high-order commensurate (HOC) phases characterized by a commensurate superstructure whose unit cell contains several atoms on different lattice sites can be obtained. Experimentally, all these cases have actually been observed (see Table 7). On a few close packed substrates, namely Pt(111), Pd(111) and Cu(111), Xe may form perfectly commensurate phases with a ( 3 × 3 ) R30° structure and for Xe on W(100) a c(2×2) structure was reported. On most other surfaces with hexagonal or square lattice symmetry, such as Ag(111), Al(111), Ni(100), Pd(100), etc., the noble gases form purely incommensurate, hexagonal close packed structures with an interatomic spacing close to the corresponding bulk value. Nevertheless, these adlayers are usually orientationally aligned along a high symmetry direction of the substrate. This has led to the conclusion in the early literature, that ‘the substrate may influence the orientation but not the structure and internal spacing of physisorbed adlayers’ [75P]. The (111) faces of various fcc metals can stabilize uniaxially commensurate (UC) phases due to the high corrugation along the [001] direction, i.e., the adsorbate may be localized within the potential troughs parallel to the [1 1 0] direction. The noble gas atoms are then arranged in a quasi-hexagonal c(α×2) structure with a more or less significant distortion between the interatomic spacings along (a) and across (b) the troughs. In some cases, such as Kr and Xe on Cu(110), α can be a rational number giving rise to (n×2) HOC phases. Another frequent observation is the occurence of azimuthally broadened ‘sickle-like’ diffraction spots or, in some cases, a finite azimuthal rotation angle. Such a ‘Novaco-McTague’ rotation out of the high symmetry direction can occur as a result of strain energy minimization. The rotation seems to be quite susceptible to the presence of structural imperfections (steps) or impurities (such as K in the case of Ag(111) [97L]). As another example, Kr and Ar adlayers on Pt(111) can be prepared in both R0° and R30° orientation depending on whether the substrate steps, involved in the 2D island nucleation and growth, are clean or pre-covered with, e.g., H or CO [86K3, 88K2]. Transitions between the various 2D phases can occur as a function of surface temperature and coverage, giving rise to rather complex structural phase diagrams. For instance, the variation of the lattice misfit m with temperature (thermal expansion) or coverage (lateral compression) can induce a change of the equilibrium structure among the various I, C, UC and HOC phases. As an example, the phase diagram for the Xe monolayer on Pt(111) presented in Fig. 11 includes a ( 3 × 3 ) R30° commensurate (C), an incommensurate (I) phase, their transition to a uniaxially compressed (striped incommensurate - SI) phase, a hexagonal incommensurate (HI) compressed phase and a Novaco-McTague R(30°±3.3°) rotated phase [87K1, 87K2]. This phase diagram and the sequence of the observed 2D phase transitions are in agreement with theoretical predictions [79B]. 3.1.1.1.7 Adsorption site In the earlier literature the preferential adsorption sites for noble gas atoms on surfaces were generally assumed to be those with highest coordination (i.e., hollow sites on terraces and bottom sites at the substrate steps). Only recently, theory [90M, 90G] and experiment [92W, 94Z3, 98S] have pointed out the possibility of an on-top adsorption site. In particular, Xe adsorbed on the fcc(111) surfaces of Pt, Pd, Cu [98S] as well as Xe on Ru(0001) [97N] were shown to be most strongly bound atop of the substrate atoms and at the upper edge of the substrate steps [94Z3]. This feature has been ascribed to the peculiar interaction of the noble gas atoms to the metal substrate which obviously cannot be described in terms of a simple sum of pair potentials which, instead, would predict high coordination sites. Both the on top adsorption site and the increased repulsion between the adsorbed noble gas atoms have been correlated with the strength of the holding potential VAS [86J]. Strongly binding substrates like Pd or adsorption sites with enhanced binding energy (such as the step edges on Pt(111)) seem to promote on-top adsorption and repulsive interactions between neighboring adatoms. A recent DFT study [96P] reveals that the nature of the interaction of the noble gases (He, Ne) is determined by the subtle interplay between electron Lando lt Börnst ein New Ser ies III/42A1

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polarization and hybridization [96P]. In addition, the contribution of intrinsic surface states to the binding of the noble gases on metals has been proposed to explain the stronger binding of Xe on Pd(111) than on Pt(111), the different lateral interactions of Xe on the two surfaces and the preferential decoration of the upper step edge on the Pt(111) surface. Nevertheless, a quantitative understanding of the noble gas substrate interaction and of the relation between binding strength, adsorption site and lateral repulsive interactions is still lacking. Quantitative results on the adsorption geometry have been obtained from LEED I-V curves for the aforementioned cases. The best agreement in all these cases is found for an on-top adsorption geometry (see Table 8). 3.1.1.1.8 Electronic structure Early work has shown that upon noble gas adsorption the surface potential (work function) of the substrate is lowered by as much as 1 eV (Table 9). These large values can be ascribed to the large polarizability α of the noble gas atoms (in particular Xe) and possible chemical contributions to the surface bond. The work function change ∆φ has also been used to measure the surface coverage, e.g., in isothermal adsorption experiments. An analytic relation, accounting for dipole-dipole interactions and mutual depolarization effects, is given by the Topping formula: ∆φ =

4πµ 0 n ad 3/2 1 + 9αn ad

,

where µ0 is the adsorption induced atomic dipole moment which is related to the work function change via 4πµ 0 = ∂ (∆φ ) / ∂n ad . For noble gas adsorption, the Topping formula has been checked to hold in several (but not in all) cases. The initial Xe dipole moment on the low index Pd (fcc) planes has been found to increase in the order µ0(110) < µ0(100) < µ0(111) and, hence, to exhibit the reverse face specificity as the initial desorption energies [84W3]. This observation was explained in the framework of the ‘s-resonance model’ [84W2]. The electronic structure of the adsorbed noble gases is determined in the valence band by the occupied np1/2 and np3/2 atomic orbitals (n = 3, 4, 5 for Ar, Kr and Xe, respectively) and by the unoccupied (n+1)s orbitals which are usually located far above the Fermi level. Due to the coupling with the substrate and the Xe-Xe lateral interactions, the original atomic states are broadened and the np3/2 photoemission peak is split into two peaks due to the lifting of the degeneracy of the mj = ±1/2 and ± 3/2 states. It has been argued that the binding energy for a given bound electronic state of an adsorbed noble gas atom is ‘pinned’ to the vacuum level [84W1, 90W]. In the case of Xe adsorption this would imply that EV(5p1/2) = EF(5p1/2) + φ, where the superscripts V and F denote the vacuum and the Fermi reference levels, respectively. The photoemission derived binding energies, however, are smaller (by about 1.1 eV) than those of the corresponding atomic states, which has been attributed to final state relaxation (electron hole screening). For a large number of substrates (mainly transition metals) the relaxation effect was found to be essentially substrate independent [90W], whereas on the sp-metal Pb(111), for instance, layerdependent shifts of the photoemission peaks attributed to changes in the final state relaxation have been reported [88J]. It has further been argued that the photoemission derived binding energies depend on the local surface potential of the immediate adsorption site i = (xi,yi) [97W]. Hence, the electron energy difference between two unlike sites i and j reflects the difference in the local work function., i.e., for Xe: ∆EF(5p1/2) (i,j) = ∆φ(i,j). This ‘local work function concept’ together with the site specificity of the noble gas adsorption is the basis of the Photoemission-spectroscopy of Adsorbed Xe (PAX), which has become a powerful tool for the characterization of heterogeneous surfaces, such as stepped surfaces or surface alloys [90W, 97W]. In Table 10 we have listed the values for the measured binding energies EF(np) for flat and homogeneous surfaces, only. Upon 2D island formation, the noble gas np derived states develop a 2D band structure (Table 12) with typical dispersion amplitudes (band widths) ∆ε of the order of 0.1 to 0.5 eV, related to the strength

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of the lateral interaction [80H]. At step edges or on anisotropic surfaces, such as Pt(110)-(1×2), the noble gas atoms aggregate into chain-like structures exhibiting a 1D band-structure [95W, 97T]. Finally, noble gas multilayers have been shown to exhibit quantized electronic states depending on the layer thickness [95S, 95P1]. Their number and energies can be explained within a simple potential well model [99G2]. 3.1.1.1.9 Diffusion kinetics Surface diffusion data for the noble gases on surfaces are scarce and microscopic studies (using FEM and STM) on the diffusion processes, if they exist, are not always quantitative. The experimental determination of the surface mobility is complicated by two effects: (i) noble gas atoms may exhibit an initial hyperthermal mobility related to the binding energy gained by the noble gas atom upon adsorption and the inefficient energy dissipation via lateral adsorbate-substrate phonon coupling [85T]. This ‘transient mobility’ must be separated from the ‘true’ thermal mobility of the thermalized noble gas atom. (ii) Surface defects act as efficient traps or nucleation sites for the diffusing noble gas atoms. They have to be included in calculating the diffusion constants from macroscopic measurements or from an analysis of the island density or size distribution in adsorption experiments. (iii) The diffusion process may be complicated by the discrete nature of the vibrational levels within the shallow diffusion potential, especially for the lighter noble gases. Laser induced desorption experiments for Xe and Kr on Pt(111) which probe the diffusion on a length scale of a few hundred µm, reveal a significant coverage dependence (adatom diffusion vs. chemical diffusion) yielding diffusion constants which vary by an order of magnitude between 5% and 25% of the monolayer saturation coverage [93M2]. The diffusion barrier extracted from these experiments (Edif = 52(±9) meV for Xe/Pt(111) in the intermediate coverage range) was assigned to the detachment of Xe atoms from island edges and, therefore, involves the corrugation energy of the holding potential as well as the lateral interaction between the noble gas atoms. This value is consistent with thermodynamic data of adsorption [88K1]. A similar value (48(±12) meV) was found for Xe diffusion on W(110) using the field emission current fluctuation method [80C]. STM data for Xe/Pt(111) at 4 K [92W] show a preferential decoration of the step edges during adsorption and, at the same time, very small thermal mobility of isolated thermalized Xe adatoms. This observation has been interpreted in terms of a large transient mobility and a sizeable surface corrugation amplitude. From STM experiments at variable temperature, the corrugation amplitude (diffusion barrier for a Xe adatom) and the activation energy for detachment from a 2D island edge can be estimated to be of the order of 31 and 64 meV, respectively, at low temperatures [95H2]. In contrast, recent quasi-elastic He scattering experiments performed on the Xe 2D-gas phase on Pt(111) at surface temperatures around 105 K [99E] seem to indicate an almost vanishing barrier for adatom diffusion. It should be noted, however, that the effective or ‘dynamic’ barrier probed at these large thermal energies is smaller than the ‘static’ diffusion barrier or surface corrugation [99G1], which has been estimated to be < 9.6 meV. 3.1.1.1.10 Lattice dynamics The lattice dynamics (phonon spectrum) of a physisorbed noble gas adlayer is characterized by three vibration modes, one perpendicular to the surface with no or very weak dispersion (Einstein mode) and two other modes polarized within the surface plane. The vibration energy of the Einstein mode is related to the second derivative of the surface holding potential (perpendicular force constant). In the harmonic approximation the only lateral coupling is due to the stress within the noble gas monolayer (first derivative of VAA) which may be non-zero but is usually quite small. This explains the weak energy variation of this mode with wavevector parallel to the surface. As a consequence, sharp multiple phonon losses can be observed for this mode [99S2]. Experimentally, the surface phonon spectrum of noble gas monolayers has been investigated on several systems using high resolution inelastic He atom scattering. Although the cross section is largest for the perpendicular vibration mode, longitudinally and transversely polarized modes have also been detected, namely on the Cu(100), (110) and (111) surfaces and on Pt(111) [00B]. The vibration energy for the perpendicular mode ranges between 2.5 meV for the heaviest species (Xe) and 5 meV for Ar and is expected to increase with the strength of the holding potential. The Lando lt Börnst ein New Ser ies III/42A1

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vibration energies can be used to fit the holding potential VAS (perpendicular mode), the interatomic potential VAA (longitudinal mode) as well as the surface stress [94Z1]. The phonon modes may couple to the substrate phonons where they overlap with the substrate bulk phonons and where the perpendicular adlayer mode crosses the edges of the projected bulk phonon bands or the surface Rayleigh mode of the substrate [85H]. A linewidth broadening in the overlap region could first be detected for the noble gases on Ag(111) [88G1] and later for the noble gases on Pt(111). In the latter case, the hybridization between the substrate Rayleigh wave and the noble gas Einstein-mode [89H, 90Z1] as well as the coupling to the longitudinal bulk band edge (Van Hove anomaly) [90Z2] has also been evidenced. With increasing thickness, the phonon spectrum continuously evolves towards the one expected for a semi-infinite noble gas crystal in a layer-by-layer fashion [88G2, 90Z1]. The phonon signal can thus be used to characterize the adsorption and growth of noble gas multilayers.

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3.1.1.2 Data In the tables heats of adsorption and desorption energies are given in meV (per atom). Translation into other commonly used units is achieved with the following conversion table: 1 kJ/mol 1 kcal/mol 1000 K

= = =

10.36427 meV 43.38484 meV 86.17386 meV

The following standard acronyms are used to denote the experimental techniques: AES: ARUPS: FE: FEM: ICISS: LEED: LEED-IV: PES: SEXAFS: SPLEED: TEAS: TPD: UPS: XPS: XRD: ∆φ:

Auger Electron Spectroscopy Angularly Resolved UPS Field Emission Field Emission Microscopy Impact Collision Ion Scattering Spectroscopy Low Energy Electron Diffraction LEED I (intensity) vs. V (voltage, energy) profiles PhotoEmission Spectroscopy (used here in connection with synchrotron radiation) Surface Extended X-ray Absorption Fine Structure Spin Polarized LEED Thermal Energy (He) Atom Scattering Temperature Programmed Desorption UV-light PES X-ray PES X-ray Diffraction Workfunction measurements

The following tables are intended to provide a complete as possible compilation of the literature data, whereas the figures only serve as an illustration of some of the characteristic properties.

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3.1.1.2.1 Sticking coefficients of the noble gases See Figs. 1 – 5. Table 1. Initial sticking coefficient s0 of the noble gases (for thermal incident energies and surface temperatures typical for adsorption experiments). Abbreviations used: Tg: gas temperature, Ts: surface temperature during adsorption, : coverage in monolayer units. (Ad. = adsorbate) Substrate

Ad.

Initial sticking coefficient s0

Remarks

Ref.

Ag(111) Cu(100) Cu(110)

Ni(111)

Xe Xe Ar Kr Xe Ar Kr Xe Xe Ar Kr Xe Xe

Pd(100) Pd(110) Pt(111)

Xe Xe Ar

~1 ~ 0.9 ... 1 0.15 ± 0.06 0.24 ± 0.1 0.37 ± 0.15 0.052 0.15 0.20 ~1 0.23 0.30 0.46 0.35 0.6 > 0.9 ~1 0.9

86B 79G 94Z2 94Z2 94Z2 93F 93F 93F 82C2 87M 87M 87M 96W 91W 71P 79K1 90R2

Xe

0.90 ± 0.03

TPD, XPS, Ts = 30 K AES TEAS, Tg = 300 K, Ts = 30 K TEAS, Tg = 300 K, Ts = 43 K TEAS, Tg = 300 K, Ts = 55 K TPD, Tg = 300 K, Ts = 6.5 K TPD, Tg = 300 K, Ts = 6.5 K TPD, Tg = 300 K, Ts = 6.5 K decreasing with  TPD, Tg = 295 K, Ts = 25 K TPD, Tg = 295 K, Ts = 25 K TPD, Tg = 295 K, Ts = 25 K optical differential reflectance, Ts = 38 K TPD,  ”  ∆φ, AES, at Ts = 77 K  ”  trapping probability, Ts = 80 K, low incident energy for Ts = 95 K, low incident energy (smaller and coverage dependent at higher incident energies) Ts = 87 K, coverage dependent trapping probability, Ts = 80 K, low incident energy for thermal beams, significant angular and energy dependence TPD, Tg = 300 K, Ts = 6.5 K TPD, Tg = 300 K, Ts = 6.5 K TPD, Tg = 300 K, Ts = 6.5 K TPD, Tg = 300 K, Ts = 6.5 K Tg = 110 ... 300 K; Ts = 60 ... 65 K trapping probability, Ts = 80 K, low incident energy Tg = 105 K, Ts = 62 K Tg = 110 K, Ts = 20 K 0 ”  ”  Ts = 104 K

K1)

Ni(100) Ni(111)

0.48 1 Pt(110)-(1x2) Xe

≥ 0.9

Ru(0001)

W(100) W(100)-2H

Ne Ar Kr Xe Xe Ar

0.0042 0.13 0.25 0.71 0.95 ± 0.05 0.9

W(110)

Xe

W(111)

Xe

0.9 ± 0.1 1 ~ 0.5

1

90A, 91A

90S2 90R2 93S3 92S2 92S2 92S2 92S2 80W2 90R2 79W 80W2 74D

) K multilayers (about 10 ML thick) deposited on a Ru(0001) substrate.

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3.1.1.2.2 Binding energies, thermodynamic quantities and phase diagrams See Figs. 6 – 10. Table 2. Heats of adsorption and desorption energies of the noble gases in the low coverage limit. The values correspond to either a 2D gas phase (on terraces) or the initial binding strength to surface defects (step edges). Abbreviations used: T: surface temperature during adsorption, : coverage in monolayer units. Percentage values: maximum 2D-gas density in units of the density of the monolayer solid. (Ad. = adsorbate) Substrate

Ad.

Energy [meV]

Remark

Ref.

Ag(111)

Ar Kr Xe

74 ± 7 110 ± 10 215 ± 15

Al(110) Cu(100) Cu(110) Cu(111) K

Xe Xe Xe Xe Ar Kr Xe Xe Xe Kr Xe

190

LEED, 1 ... 11% LEED, 1 ... 9% LEED, 1 ... 7% UPS, 6% at T = 58 K TPD, 1 ... 10%, νd = 5×1013 s−1 AES, ~ 10% at T ~ 80 K TEAS, from Q1 – Q2D UPS, 11% at T = 58 K TPD,  → 0, nonwetting TPD,  → 0, nonwetting TPD,  → 0, nonwetting TPD, 1st order, νd = 1012 s−1 TPD,  ”  st order regime) LEED,  → 0 LEED, 0 ”  ”  ∆φ, LEED,  → 0 TPD,  → 0, using νd = 1015 s−1 UPS, 100% at T = 58 K TPD, 1st order, using νd = 1013 s−1 TPD,  → 0, using νd = 1015 s−1 TPD,  → 0, using νd = 1015 s−1 AES, θ = 0 ... 1 (terraces) AES, θ = 0 ... 1 (step edges)

82U 82U 82U 86E 91S 79G 94R 86E 93F 93F 93F 82C2 91C1 84M3 84M3 71P 84W3 86E 79K1 84W3 84W3 83M2

Ni(100) NiAl(110) Pd(100)

Pd(110)

Xe

Pd(111) Pd(810)

Xe Xe

Pt(110)-(1×2) Pt(111)

Xe Xe

Pt(112) Pt(557) Pt(997) Ru(0001) 1

Xe Xe Xe Xe

180 ± 10 28 56 83 226 200 ~200 273 ± 5 ~330 408 > 425 442 360 356 ± 13 443 ± 13 347 277 278 245 ± 15 1) 410 ± 40 239 250 293 249 ± 22 373 ± 22 369 ± 22 370

TEAS TEAS, νd = 2.95×1013 s−1, θ ”  on terrace, TPD, νd = 1.4×1012 s−1 at defects, TPD, νd = 9×1015 s−1 TPD, on terraces TPD, at defects TPD, νd = 1012.5± 0.9 s−1 TPD, νd = 1014.2±1 s−1 at steps (θ = 0.04) TPD, νd = 1014.1±0.9 s−1 at steps (θ = 0.04) TPD, at step edges (θ < 0.16) UPS, 14% at T = 58 K ~ 5% at T = 20 K

83K 86K2 85P 90R1 83K 98W 90S2 90S2 90S2 98W 86E 97N

) Obtained from an Arrhenius plot. In a subsequent analysis [90B] the true holding potential minimum was suggested to be 255 meV (due to the temperature dependence of the desorption prefactor νd ).

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Table 3. Heats of adsorption and desorption energies for (unconstrained) monolayers of the noble gases. The values are characteristic of the monolayer latent heat in the 2D gas-solid coexistence regime, Q1, for systems with attractive adsorbate-adsorbate interactions and for a dense 2D gas phase in the case of repulsive interactions. In the first case the 2D heat of condensation, Q2D, is indicated if known. In the second case (‘rep.’) the coverage or coverage range of the measurement is specified. Abbreviations used: T: surface temperature during adsorption, : coverage in monolayer units. (Ad. = adsorbate) Substrate

Ad.

Energy [meV]

Ag(111)

Ar Kr Xe

99 ± 7 151 ± 5 225 ± 5 187 ± 21 224

Al(110) Au(100)-rec Cu(100) Cu(110)

Xe Xe Xe Kr Kr Xe

Cu(110)-(2×1)O Xe Cu(211) Cu(311) Cu(610)

Xe Xe Xe

Ge(100)-(2×1)

Xe

Ge(111)-c(2×8) Ir(100) Ir(110) Ir(111) Ir(210) Ir(321) Ir(511) Ir(531)-(731)

Kr Xe Xe Xe Xe Xe Xe Xe

Ni(100)

Xe

207 ± 4 190 ± 3 180 224 ± 10 ... 236 ± 8 270 ± 2 130 ± 5 114 ± 10 226 ± 6 218 ± 6

Ref. Q2D [meV] 81U 81U 79U 76R 86B 88G2 98I 91S 76M 79G 81G 00S 47 ± 9 94R 98P

256 ± 9 ... 174 ± 5

89B

200 ± 5

81G

223 ± 6 174 ± 6 197 ± 21 197 ± 21 278 ± 13 282 ± 4 233 ± 8 175 ± 8 166 ± 10, 163, 118 325 ... 282 304 ... 273 325 ... 282 312 ... 291 338 ... 304 312 ... 282 312 ... 291 248 ± 10, 232, 164 226

98P 76R 75P 80B 93S2

rep. ?

88P 74N2 74N2 74N2 74N2 74N2 74N2 74N2 88P 82C2

Remark LEED LEED LEED ∆φ TPD, 0th order, νd = 3×1015 s−1 TEAS, isothermal desorption ellipsometry TPD ∆φ AES LEED, AES,  ~ 1 LEED isobars,  ~ 0.5 TEAS TPD, 0th order, νd = 1013± 1 s−1 LEED, decrease upon monolayer compression AES, LEED, c(2x2) high temperature, low density phase. TPD, A-sites TPD, B-sites, νd = 4⋅1011± 1 s−1 ∆φ ∆φ AES,  < 0.4 AES, 0.4 <  < 0.8 two steps in LEED isotherms, T < 77 K LEED, three substeps FEM FEM FEM FEM FEM FEM FEM LEED, three substeps ∆φ, 0.1 <  < 0.5, TPD: 1st order

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3.1.1 Noble gases on metals and semiconductors Ref. Q2D [meV]

Substrate

Ad.

Energy [meV]

Ni(111)

Xe

191 ± 8

96W

Xe

317 ± 26

Xe Xe

217 ... 270 228 ... 259 259 ... 155 ~200 ... ~250 ~330 ... ~280 408 ... 364

89F, 83D2 87M 90C, 91C1 84M3 71P 84W3

NiAl(110) Pd(100)

Kr Xe

273 ± 5 Pd(110)

Xe

Pd(111)

Xe

Pd(810)

Xe

Pt(100) Pt(110)-(1×2)

Xe Xe

Pt(110)-(1×2)H Xe Pt(111)

Ar Kr

Xe

Pt(210) Pt(321) Pt(997)

Xe Xe Xe

Ru(0001)

Ne Ar Kr Xe

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rep. rep. rep. core

84M3

Remark optical differential reflectance, isothermal desorption, νd = 3.4⋅1011 s−1 UPS isotherms, 80 K ≤ T ≤ 90 K TPD, νd = 1011 ... 1014, θ = 0.2 ... 1 TPD, state 1, θ = 0.3 ... 0.5 TPD, state 2, θ = 0.5 ... 1 LEED, θ = 0 ... 0.7 ∆φ, LEED, θ = 0 ... 1 TPD, θ = 0 ... 0.35, using νd = 1015 s−1 LEED, 0 <  < 0.8

TPD, 1st order, using νd = 1013 s−1 TPD, θ = 0 ... 1, using νd = 1015 s−1 360 ... 334 84W3 TPD, θ = 0 ... 0.7, using νd = 1015 s−1 2 356 ± 13 ... 295 ± 13 rep. 83M2 ) AES, θ = 0 ... 1 (terraces) 443 ± 13 ... 356 ± 13 rep. AES, θ = 0 ... 1 (step edges) 325 ... 278 74N1 FEM 338 88D TPD, A-sites 208 TPD, B-sites 310 99W TPD, A-sites 190 TPD, B-sites 95 17 91K, TEAS 88K2 154 26 91K, TEAS 88K2 161 ± 9 93M2 TPD, νd = 4.4⋅1011± 0.4 s−1 310 43 91K, TEAS 88K2 336 ± 4 48 ± 4 85P, 83P TEAS 284 ± 22 90S2 TPD, νd = 1012.5± 0.9 s−1 270 ... 280 98W TPD, νd = 2 ... 8⋅1012 s−1, θ = 0.1 ... 0.7 286 ± 9 93M1 TPD, νd = 1.3⋅1013± 0.4 s−1 330 ... 273 74N1 FEM 312 ... 295 74N1 FEM 338 ... 299 74N+1 FEM 370 98W TPD, at step edges (θ ”  on terraces 280 28 92S1 TPD 103 92S1 TPD 152 92S1 TPD 233 92S1 TPD

> 425 ... 373 442 ... 399

79K1 84W3

79

80

3.1.1 Noble gases on metals and semiconductors

Substrate

Ad.

Ru(0001)-sk

Xe

Energy [meV]

Ref. Q2D [meV] 81W

Si(100)-(2×1)

Xe

Si(111)-(7×7)

Kr

369 ... 321 252 ... 174 202 (site 1) 175 (site 2) ~ 300 ... ~ 250

Xe

~ 330 ... ~ 280

83C

W(100)

Ar Kr Xe

W(110)

Ar Kr Xe

W(111)

Ar Kr Xe

82 1) 236 1) 255 1) 269 1) 94 1) 319 1) 399 1) 230 187 ... 174 83 1) 220 1) 255 1) ~350 217 402 ± 2

70E 70E 70E 80W2 70E 70E 70E 80W2 81O 70E 70E 70E 59E 62R 74D

W(210)

Ar Kr Xe Ar Kr Xe Xe

93 1) 246 1) 279 1) 82 1) 239 1) 283 1) 325

70E 70E 70E 70E 70E 70E 62R

W(211)

W(411)

92M 83C

[Ref. p. 111

Remark TPD, using νd = 1013 s−1 kink and step sites terraces TPD, using νd = 1011 s−1 AES - Fowler isotherms, small  (strongest binding sites) AES - Fowler isotherms, small  (strongest binding sites) FEM FEM FEM ∆φ(T) FEM FEM FEM ∆φ(T) TPD FEM FEM FEM FEM FEM TPD, 1st order, νd = 1015 s−1, absolute accuracy ± 56 meV FEM FEM FEM FEM FEM FEM FEM

1

) The values obtained in [70E] are model dependent and possibly erroneous [80W2]. In fact, the results in [80W2] and [74D] suggest that the adsorption energies on the low index planes of bcc W decrease in the order (111) > (100) > (110) in agreement with the coordination argument in [84W3]. 2 ) In a subsequent paper [84M2] coverage independent values were given: 438 meV (at step edges) and 347 ± 9 meV (on terraces).

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Table 4. Heats of adsorption and desorption energies for bilayers of the noble gases. The values are characteristic of the bilayer latent heat in the 2D gas-solid coexistence regime, Q2 (adsorbate-adsorbate interactions in the second layer are always attractive). Abbreviations used: T: surface temperature during adsorption, : coverage in monolayer units. Substrate

Adsorbate

Binding energy [meV]

Ref.

Remark

Ag(111)

Ar Kr Xe

Cu(110) Pd(100) Pd(810)

Xe Kr Xe Xe

81U 81U 79U 86B 88G2 98I 88Q 98P 84M3 84M3 83M2 84M2

Pt(111)

Xe

Pt(997) Ru(0001)

Xe Ne Ar Kr Xe

89 ± 4 118 ± 4 173 ± 5 187 153 ± 6 171 ± 3 186 182 ± 6 122 ± 5 145 ± 15 252 ± 13 243 221 205 ± 12 170 170 22 85 122 173

LEED LEED LEED TPD, 0th order, νd = 9×1013 s−1 TEAS, isothermal desorption ellipsometry surface plasmon resonance TPD, νd = 1015± 1 s−1 LEED, isosteres LEED, isosteres AES step edges terraces TEAS TPD, νd ~ 1013 s−1 TPD, νd ~ 1013 s−1 TPD TPD TPD TPD

86K2 98W 98W 92S1 92S1 92S1 92S1

Table 5. Heats of adsorption and desorption energies for multilayer (≥ 3ML) noble gas films. At the top of the table the heats of sublimation for the bulk crystals of Ne, Ar, Kr, and Xe are given as a reference. (Ad. = adsorbate) Substrate

Ad.

Binding energy [meV]

Layer thickness Ref. [ML]

Remark

Ne Ar Kr Xe

21.5 81.3 115.0 163.3

∞ ∞ ∞ ∞

93S1 93S1 93S1 93S1

T = 7.5 K T = 28 K T = 38 K T = 52 K

Ag(111) Ag(111) Cu(110) Pd(810)

Xe Xe Xe Xe

TEAS, isothermal desorption ellipsometry TPD, νd = 5⋅1013± 1 s−1 AES step edges terraces

Xe Ne Ar Kr Xe

3 3 ≥3 ≥3 3 3 ≥4 >3 ≥5 ≥5 ≥5 ≥5

88G2 98I 98P 83M2 84M2

Pt(111) Ru(0001)

115 ± 10 174 ± 3 167 ± 6 165 ± 13 200 187 156 171 20 77 112 162

Lando lt Börnst ein New Ser ies III/42A1

84M2 86K2 92S1, 90S1 92S1, 90S1 92S1, 90S1 92S1, 90S1

TEAS TPD, νd TPD, νd TPD, νd TPD, νd

= 1⋅1012 s−1 = 5⋅1012 s−1 = 1⋅1013 s−1 = 2⋅1013 s−1

82

3.1.1 Noble gases on metals and semiconductors

[Ref. p. 111

Table 6. Other thermodynamic quantities of noble gas monolayers. Abbreviations used: T: surface temperature, : coverage in monolayer units, d: nearest neighbor adsorbate spacing. (Ad. = adsorbate) Substrate Ad.

Ag(111) Ar Kr Xe

thermal expansion coefficient α [10–4 K–1] 22 ± 4 8±1 4.4 ± 5 (above 60 K)

thermal expansion coefficient γ [10–3 K–1]

2.0 ± 2 (ML step) 1.3 ± 2 (BL step)

Cu(100) Xe

Cu(110) Xe Pt(111)

Xe

Substrate Ad.

Cu(100) Xe Pd(810) Xe Pt(111)

Xe

~ 1 ... 8 (25 K ... 60 K)

isothermal compressibility

Ref.

KT [10–3 Å2/K] 81U 81U 1.68 ± 0.02, unconstrained ML 79U (d = 4.515 Å, T = 76 K) 0.97 ± 0.16, compressed ML (d = 4.366 Å, T = 56 K) 1.8 ± 7 97B1, (d = 4.41 ... 4.50 Å, 00B T = 62 ... 78 K) 1.5 ± 2 84G (d = 4.56 Å, T = 71.5 K) ~ 2.0 ... 3.8 88K1 (d = 4.45 ... 4.57 Å, T = 88 K)

roughening Remark critical temperature triple point Ttr temperature [K] TR [K] [meV/K] Tc [K] 0.26 ± 0.04 T = 77 ... 111 K 0.61 ± 0.09 66.4 (2. ML) 68.2 ± 0.7 67.3 (3. ML) ~ 1.4 ... 0.65 120 98 Entropy

Ref.

79G 84M2 85P, 88K1

3.1.1.2.3 Monolayer structures and phase diagrams See Fig. 11 Table 7. Structure of the 2D solid phase of noble gas adlayers in the monolayer coverage regime ( ≤ 1). Abbreviations used: T: surface temperature, p: 3D equilibrium pressure in mbar, : coverage in monolayer units, θs: coverage in substrate atom units; C: commensurate phase, HI: hexagonal incommensurate phase, SI: striped incommensurate phase, UC: uniaxially commensurate phase, HOC: high-order commensurate phase; R denotes the adlayer azimuthal orientation with respect to the substrate surface lattice; a, (b): adsorbate nearest neighbor spacings. If not stated otherwise, the structures were obtained from LEED. (Ad. = adsorbate) Substrate

Ad. Structure

unit cell dimensions atomic area Remark [Å] [Å2]

Ag(110)

Xe

UC-R0°

Ag(111)

Ar

HI-R0°

c(α×2) α ≈ 1.53 a = 4.42 ± 0.05 (b = 4.65 ± 0.05) a = 3.78...3.93 a = 3.79 ± 0.02

18.0

Ref.

T = 77 K, p > 10−6

73C

T = 34...45 K, p ~ 4×10−6 T = 21 K

82U 88G2

Lando lt Bö rnst ein New Ser ies III/42A1

Ref. p. 111] Substrate

Ad. Structure

unit cell dimensions atomic area Remark [Å] [Å2]

Ref.

Kr

a = 4.04 ... 4.15 a = 4.19 ± 0.05 a = 4.02 ± 0.02 a = 4.50 ± 0.03 a = 4.38 ± 0.02 a = 4.42...4.54 a = 4.529

17.5 ± 0.1

82U 76R 88G2 73C 88G2 79U 87G

a = 4.42 ± 0.05 a = 4.41, b = 4.61 a = 4.38 ± 0.03

16.9 ± 0.5 17.9 16.6 ± 0.2

Xe

HI-R0°

HI-R0° HI-R0° HI-R0°

Ag(211) Al(110) Al(111) Al(332)facetted Au(100)-rec Cr(110)

83

3.1.1 Noble gases on metals and semiconductors

Xe HI-R0° Xe UC-R0° Xe HI-R0° Xe Xe Xe C

p(2×2) a = 4.99 b = 5.76 Cu(100) Xe HI-R0° a = 4.5 ± 0.1 a = 4.52 ± 0.01 a = 4.40 ± 0.01 Cu(110) Ar I (R~4°?) a = 3.90 ± 0.07 b = 3.88 ± 0.07 Kr UC-R0° a > 4.08, b > 4.15 HOC (8×2), a = 4.08, b = 4.15 HI-R0° a = 4.03 ± 0.05 Xe UC, HOC-R0° (α×2) α ≥ 12/7 a ≥ 4.37, b ≥ 4.22 HOC (26×2), a = 4.42, b = 4.23 HOC (12×2), a = 4.37, b = 4.15 C (?) c(2×2) a = 5.1, b = 4.42 Cu(110)Xe UC (2×α) (2×1)O a = 5.1, b ≥ 4.33 HOC (2×3) ( 3 × 3 )R30° Cu(111) Xe C a = 4.42 I a = 4.3 ... 4.4 Cu(211) Xe HI-R0° a = 4.42 ± 0.05 Kr HI-R0° a = 4.18 ± 0.05 Cu(311) Xe HI-R0° a = 4.45 ± 0.05 Cu(610) Xe HOC-R45° (2×6), a ≈ 4.33 ( 3 × 3 )R30° Cu3Pt(111) Xe C a = 4.52 HI ?

Lando lt Börnst ein New Ser ies III/42A1

15.2 ± 4

16.9...17.9 17.762

23.5

17.5 ± 0.8

13.1 ± 0.2

T = 5...60 K T = 55 K, p = 6.5×10−4 T = 22 K T = 77 K, p > 10−6 T = 24 K T = 5...85 K XRD, at melting point TM = 131.8 K, p = 1.5 torr T = 77 K, p > 10−6 T = 45 K, θ > 0.1 T ≥ 40 K aligned R0° (step direction) no new LEED spots T = 80 K, p > 2×10−6 T = 77 K, p > 10−6 TEAS, T = 77 K TEAS, T < 65 K T = 24 K

73C 91S 85M 90H 76M 89K

71C, 79G 97G 82H

> 14.7 14.7

T = 53 K, p < 3×10−5

81G 81G, 82H

14.1 15.8...17.5 ≥ 15.8

T = 42 K LEED, TEAS, T = 20...70 K

82H 73C, 89B, 81G, 96Z

16

θ = 0.1...1, T ≤ 61 K

96Z

15.8 18.4

T < 45 K, θ → 1 T ≥ 70 K, p ~ 10−7... 10−6 small θ only TEAS, θs ≤ 0.42

96Z, 89B 73C, 81G

> 22.1 13.8 16.9

16.9 15.2 17.1 ± 0.4 17.7 < 17.7

θs = 0.67 T = 77 K, p > 10−6 T = 50 K SEXAFS, T = 18 ... 47 K T = 77 K, p = 3×10−6 T = 55 K, p = 6.5×10−4 T = 77 K, p = 3×10−6 T = 84 K, p = 3.9×10−7 T = 50 K, θ = 0.1...1.0 T = 50 K, θ = 0.2...0.6 T = 50 K, θ > 0.6

98P

73C 98S 90J 76R 76R 75P 80B 94S 92S3

84

3.1.1 Noble gases on metals and semiconductors

[Ref. p. 111

Substrate

Ad. Structure

unit cell dimensions atomic area Remark (Å) (Å2)

Ref.

Ge(100)(2×1) Ge(111)c(2×8) InSb(100)rec Ir(100)(1×1) Ir(100)(1×5)

Xe

C

(2×1)

no extra LEED spots

93S2

Xe

C

c(2×8)

88P

Xe

C

Xe

HI-R45° UC –R45°(?) HOC

sequential population of three different sites In registry with ×4 reconstructed surface T = 55 K, θ ≥ 1 T = 55 K, θ = 0.2

72I

T = 55 K, θ ≥ 1 thick Ar films T = 30 K, 2.5 L, diffuse ring T = 65...84 K Transient during heating, only in coexistence with HI-R30° T = 38 K, saturation coverage no extra spots in LEED T = 45 K, θ > 0.5 sickle shaped spots θ = 0.4...1, diffuse ring T = 13 K, θ = 0.7...0.9 θ = 0.6...1, diffuse ring T = 77 K T ~ 100 K, p >10−7 T ~ 100 K, p >10−6 saturation at T = 80 K 3.8 L at 70 K T = 50 K

72I 70D 82C2

84M3 71P 79K1, 84W3 84W3 91V2 95H1, 92H2 91V2, 92H2

4.6 L at 55 K

95H1, 92H2

Xe

Nb(100) Ni(100)

HI-R90° Ar UC Xe HI

Ni(111)

Xe

Xe Ni(hkl) NiAl(110)

Xe Xe

Pd(100)

Kr

HI-R30° C (?)

a = 4.44 ± 0.01 a = 4.48, b = 4.64 a ~ 4.4 ... 4.02 a ~ 4.06 a = 4.8 ... 4.35 a = 4.48 a = 4.49 ( 3 × 3 )R30° a = 4.76

17.1 ± 1

HI-R33.8° C HI-R0°, 30° Pt(100)-hex Xe C I Xe

Xe

16.8 ± 0.2 p(2×2)

HI-R0±8° UC (?) HI

HI UC-R45° (?) Xe UC-R0° Xe C

Kr

17.7 ± 0.2

16.1

C

Pt(110)(1×2)

a = 4.35 c(α×2) a = 4.52 ± 0.03

( 3 × 3 )R30° a = 4.31

C

Pd(810)

a = 4.36 a = 4.42 (3×5)

C

Xe

Pd(110) Pd(111)

13.9

UC

HOC

20...16.5 17.4 17.5 19.6

( 7 × 7 )R19.2° 15.3 a = 4.20 ( 19 × 19 )R23.4° 17.8 a = 4.53 a ~ 4.25 15.6 (2×1)-1D a = 4.48 17.4 ( 3 × 3 )R30°

(α×2), α ≈ 10/7 a ≈ 3.95 a = 3.93 ± 0.15 (8×2) (3×2)

28.9 16.3

at step edges on terraces, T = 73 K θ < 0.8 θ ≥ 0.8 C-I transition similar to Xe/Pt(111) LEED, 0.3 ≤ θ ≤ 1 ARUPS, two different Kr-species T ≤ 97 K T ≤ 77K, θ = 1

88M 72I

89F

96W 92F 91C1 90C 84M3

92H2 83M2 99G2

95W 95W 88D, 95W

Lando lt Bö rnst ein New Ser ies III/42A1

Ref. p. 111] Substrate

Ad. Structure UC

Pt(111)

Ar

Kr

HOC HOC, HI-R0° HI(?)-R30° HI-R30° HOC

unit cell dimensions atomic area Remark (Å) (Å2) (α×2) a = 4.5 ... 4.2 (4×4) (n×n), n = 7,11,18, ...

11.9 ≥ 12.6

a = 4.10 ... 4.14 14.6...14.8 (5×5) – with R30° 13.9 layer orientation

HI-R0° 1) ( 3 × 3 )R30° a = 4.80 a = 4.79...4.50 b = 4.80 a = 4.49...4.45 a = 4.44...4.33

19.9

HOC-R33.3° HI-R0°

a = 4.33

16.2

HI-R0° HI-R0° C-R0° (steps)

a = 4.43 a = 4.4 a = 5.54 (1D)

16.8

I-R0°

a = 4.1, b = 4.4

15.9

Ar Kr

HOC HOC

Xe

C

(4×3) (3×3) a = 4.07 ( 3 × 3 )R30° a = 4.69

Xe

C SI HI-R30° HI-R30°±α

Xe Pt(332) Pt(997)

Ru(0001)

Xe Xe

Xe Xe

...

95W

TEAS, T < 33 K T ≥ 33 K

92Z

after step decoration with 88K2 CO (< 0.01 ML), TEAS 87K3 T = 25 ... 55 K, θ ≤ 0.8 T < 50 K, θ ≥ 0.9 TEAS after step decoration with H 86K3 or CO (< 0.01 ML) 83P, 85P, TEAS, 91K T ≥ 62 K, θs ≤ 0.33 θs ≤ 0.37 (if not C) 87K2 0.37 ≤ θs ≤ 0.38 0.38 ≤ θs ≤ 0.40, α = 0 ... 3.3° θs = 0.40 only at high dosing pressures (10−6 mbar) T < 70 K, θ → 1 T = 25 K, θs = 0.40 (sat.) step decoration, θ ” 

86K1 88C

12.7 14.3

89C2 98W (see also 97P2, 92W) T = 45 K, ML completion, 97P2 row-by-row growth 98N, 00N2 annealed to 55 K 97N, 98N

19.1

annealed to 77 K at 1 K/s

98N, 92S1

(7×7) ? HI-R45°

18.2 23.8 ( 2 × 2 )R45°

Ref.

θ = 0.3 ... 1

16.4

HI-R0°, HOC(?) Si(111)(7×7) W(100)

85

3.1.1 Noble gases on metals and semiconductors

90S1 84D, 89M 79W

(measured: 22.2 at 66 K, 80W2 imperfections) 79E W(110) Xe C p(2x2) 28 T = 77 ... 90 K, p ~ 10−7 T ~ 20 K 80C 79E UC, I, a = 6.32 ... 5.53 20.2 ... 17.6 T = 77 ... 90 K, p > 10−6 HOC (?) b = 4.49 ... 4.22 18.2 saturation at T = 62 K 79W 1 ) A rotation of the Kr adlayer by 5-6° out of the R30° orientation have been observed by Zeppenfeld and [00B] and could be due to the influence of residual defects or impurities on the surface. C (?)

Lando lt Börnst ein New Ser ies III/42A1

20

3 different states (local adsorption sites) T ~ 60 K T ~ 65 K

87K1, 91K

86

3.1.1 Noble gases on metals and semiconductors

[Ref. p. 111

Table 8. Details of noble gas 2D monolayer structures. Abbreviations used: T: surface temperature, HI: hexagonal incommensurate phase. If not stated otherwise, the structures were obtained from LEED. < u ⊥2 >1/2 denotes the vertical mean square displacement of the noble gas atom. (Ad. = adsorbate) adsorption site adlayer-substrate < u ⊥2 >1/2 spacing d [Å] [Å]

Substrate

Ad.

Ag(111)

Kr

3.3 ± 0.1

Xe

3.55 ± 0.1

Cu(110) Cu(111)

Ir(100)-(1×1) Ir(100)-(1×5) Ni(100) Pd(111)

Pt(111)

Ru(0001)

Kr Xe

2

3.36 ± 0.07 3.60 ± 0.08

Xe

3.45 ± 0.1

Xe Xe Ar Kr Xe

on top

2.95 ± 0.03 3.16 ± 0.03 1.6 ± 0.5 3.5 ± 0.8 3.4 ± 0.1

on top

3.5 ± 0.1

fcc and hcp hollow 1) on top

4.0 ± 0.1

Xe

Kr Xe

1

top of rows on top

3.4 ± 0.2

fcc and hcp 4.2 ± 0.1 hollow 1) preference for 3.70 ± 0.03 2) on top sites (average height) 3.54 ± 0.06

Remark

Ref.

0.08 ± 0.01 LEED-IV, T = 30 K HI phase 0.11 ± 0.01 LEED-IV, T = 45 K HI phase 0.67 LEED-IV, T = 25 K 0.22 ± 0.11 LEED-IV, T = 50 K ( 3 × 3 )R30° phase SEXAFS HI phase LEED-IV LEED-IV ICISS ICISS LEED-IV, T= 80K, 110 K ( 3 × 3 )R30° phase SPLEED, T = 55 K dilute phase SPLEED, T = 70K ( 3 × 3 )R30° phase 0.3 ± 0.1 LEED-IV, T = 80 K, 110K ( 3 × 3 )R30° phase SPLEED, T = 75 K ( 3 × 3 )R30° phase LEED-IV, T = 25 K (3×3) HOC phase 0.28 LEED-IV, T = 25 K ( 3 × 3 )R30° phase

81U 81U 00S 98S 90J 72I 72I 93S4 93S4 99S1 93H, 95H1 93H, 95H1 99S1

95P2 97N, 98N 97N, 98N

) In contrast, the more recent LEED-IV experiments seem to rule out the hollow sites. ) Closest approach to the metal is found for atoms closest to on top sites.

Lando lt Bö rnst ein New Ser ies III/42A1

Ref. p. 111]

87

3.1.1 Noble gases on metals and semiconductors

3.1.1.2.4 Electronic structure See Figs. 12 – 18. Table 9. Substrate work function changes ∆φ induced by noble gas monolayers. The initial dipole moment µ 0 per atom and the polarizability α were obtain from the intitial slope ∂ (∆φ ) / ∂θ and from a fit to the Topping formula, respectively. (Ad. = adsorbate) Substrate

Ad.

∆φ [V]

µ0 [D]

α Remark [10−24 cm3]

Ref.

Al(111)

Ar Kr Xe Xe Xe Xe

0.143 ± 0.015 0.185 ± 0.015 0.290 ± 0.015 0.1 ... 0.2 0.45 0.44 0.45 0.48 ± 0.01 0.5 0.29 0.45

0.096 0.134 0.235

2.66 2.76 3.20

82C1 82C1 82C1 90H 73C 73C 76R 86B, 86J, 85J 87F 76R 73C 76R 76M 71C, 73C 99G2 73C, 82M1 73C 86E 76R 76R 75P 82L 88P 74N2 74N2 74N2 74N1 74N1 82C2 92F

Al(332) Ag(110) Ag(111)

Ag(211)

Kr Xe

Au(100)-rec Cu(100)

Xe

Cu(110) Cu(111)

Xe Xe

Cu(211) Cu(211) Cu(311) Gd(0001) Ge(111)-(2×8) Ir(100) Ir(110) Ir(111) Ir(210) Ir(321) Ni(100)

Kr Xe Xe Xe Xe Xe Xe Xe Xe Xe Xe

0.45 0.47 0.33 0.61 ± 0.02 0.48 0.58 0.35 0.53 0.58 0.60 ± 0.03 0.22 ± 0.01 1.6 0.8 1.8 1.3 1.0 0.376

Ni(110) Pb(111)

Kr Ar Xe Ar Kr Xe

0.25 0.165 1.00 0.085 0.100 0.130

Lando lt Börnst ein New Ser ies III/42A1

∆φ ∆φ UPS Inverse PES ∆φ ∆φ ∆φ ∆φ ∆φ

0.20

0.24

0.53 0.14

0.29 0.2

XPS XPS XPS UPS

3.67

∆φ, ARUPS ∆φ UPS ∆φ ∆φ ∆φ PES secondary electron cutoff FEM FEM FEM FEM FEM ∆φ per step atom on Ni(h10) vicinal surfaces, UPS

ARUPS ARUPS ARUPS ARUPS

82C2 82C2 82J2 88J 88J 88J

88

3.1.1 Noble gases on metals and semiconductors

Substrate

Ad.

∆φ [V]

µ0 [D]

α Remark [10−24 cm3]

Pd(100)

Kr Xe

0.36 ± 0.05 0.94

0.17 ± 0.05 0.95

1.7 ± 0.08 8.2

0.86 ± 0.02

0.61

8.4

0.45 ± 0.03 0.44 0.42 0.70

3.6 ± 0.08

Pd(110)

Xe

Pd(111)

Xe

Pd(810)

Xe

Pt(100) Pt(111) Pt(111)

Xe Xe Xe

Pt(210) Pt(311) Pt(321) Pt(997)

Xe Xe Xe Xe

Ru(0001)

Xe

0.65 0.70 ± 0.02 0.96 ± 0.02 0.92 ± 0.01 0.85 ± 0.02 0.60 0.27 ± 0.02 1.03 ± 0.02 1.0 0.6 0.29 0.26 1.1 0.9 0.9 0.47 0.32 0.72 ± 0.02

1.12 0.49 0.53 0.3 ± 0.1

1.4 0.34 0.30 1.0

∆φ ∆φ, µ 0 at steps ? see [83M2] ∆φ µ ave = 0.36 D initial slope (small ) ∆φ UPS ∆φ ARUPS UPS, step edges full monolayer FEM full monolayer ( 3 × 3 )R30° phase hex-R33.3° phase FEM FEM FEM step decoration terrace saturation on terraces at step edges

[Ref. p. 111 Ref. 84M3 71P 84W3 86E 80K 84M3 84W3 79K1 84W3 88C 83M2 74N1 86S, 98W 96O 74N1 74N1 74N1 98W 86J, 86E 81W 99G2 70E 70E 70E 75W 80W2 70E 70E 70E 80W2 80C 83O 70E 70E 70E 74D 70E 70E 70E 70E, 62R 70E 70E

0.62 FE 0.46 ... 0.60 0.31 1) FE 0.83 0.38 1) FE 1.35 0.97 1) 0.99 ± 0.05 UPS 1.05 ± 0.02 0.98 ~6 ∆φ FE W(110) Ar 0.85 ... 1.05 0.29 1) FE Kr 1.97 1.93 1) FE Xe 2.4 1.67 1), 2) 0.45 ± 0.02 0.35 6.6 ∆φ 2.0 FE 2.1 FE FE W(111) Ar 0.40 0.16 1) FE Kr 0.83 0.50 1) FE Xe 1.13 0.41 1) 1.1 ± 0.01 0.66 ... 0.75 3.5 ... 4.9 retarding potential FE W(120) Ar 0.70 0.40 1) FE Kr 0.95 0.43 1) FE Xe 1.4 0.60 1) FE W(211) Ar 0.34 0.29 1) FE Kr 0.58 0.44 1) FE Xe 0.92 0.81 1) 1 ) Assuming monolayer densities [1014 atoms/cm2] of 7.9 (Ar), 7.2 (Kr) and 6.0 (Xe). 2 ) Based on Fowler-Nordheim equation which was later noted to break down for Xe/W(110) [80W2]. W(100)

Ar Kr Xe

Lando lt Bö rnst ein New Ser ies III/42A1

Ref. p. 111]

89

3.1.1 Noble gases on metals and semiconductors

Table 10. Energetic positions of the 5p orbital states of adsorbed Xe as derived from photoemission. If not stated otherwise, the values are for the low coverage limit. The energies are referred to the Fermi level but the workfunction values for the clean substrates, φC , are also given. Abbreviations used: T: surface temperature, : coverage in monolayer units, Γ: center of the Brillouin zone (electron emission normal to the surface plane)- see also Table 12. Substrate

φC [eV] 1)

Ag(100) Ag(111)

4.65 4.72

E(5p3/2) [eV]

Al(110) Al(111)

4.45 4.48 4.30 Al(332)-facetted 4.4 Au(111) Cu(100) Cu(110)

5.68 4.59 4.74 4.48 4.5

Cu(111)

4.90

Cu3Pt(111)

5.4 5.65

6.1 ~ 6.02 5.7 (mj = ± 3/2) 6.1 (mj = ± ½)

5.7 2) 5.8 3) 6.6 (mj = ± 3/2) 7.2 (mj = ± ½)

Co(0001) Fe(110) GaAs(110)

5.56

Gd(0001) Ir(100) Ir(100)-(1×1) Ir(100)-(1×5) Ir(110) Ir(111) Ir(210) Ir(321) Ir(531)-(731) Ni(100)

3.3 ± 0.1 5.67 ± 0.05 6.15 6.00 5.0 5.79 ± 0.05 5.0 5.4 4.9 5.30 5.56 5.2 ± 0.1 5.1 ± 0.1

5.5 ± 0.1 5.75 ± 0.1

Ni(310) Ni(410) Ni(810) Ni(110)

Lando lt Börnst ein New Ser ies III/42A1

4.55 4.55

6.4 ~ 6.2

E(5p1/2) [eV] 7.68 7.62 7.27 7.56 ... 7.76 7.74 7.55 7.5 7.8 6.72 7.3 ~ 7.15 7.80 7.3 7.30 7.10 6.9 6.65 6.9 2) 7.0 3) 8.1

Remarks

2D-solid 2D-gas θ = 0 ... 1, T = 45K ARUPS at Γ terrace and steps or (111) and (221) facets UPS ARUPS at Γ, θ = 1 ARUPS at Γ, θ = 1 2D-solid 2D-gas ordered surface disordered surface ARUPS at Γ, θ = 1 ARUPS at Γ, θ = 1 PES

PES FEM UPS 6.24 4) UPS 6.38 4) FEM FEM FEM FEM FEM 6.83 (6.90) PES, θ = 1 but coverage independent 6.75 ± 0.1 UPS 7.00 ± 0.1 UPS θ = 0.1 7.5 ± 0.1 θ > 0.1 7.4 ± 0.1 7.6 ± 0.1 at step edges, θ = 0.4 7.45 ± 0.1 θ = 0.89 7.5 ± 0.1 at step edges, θ = 0.11 on terraces, θ ≥ 0.17 6.8 ± 0.1 7.75 UPS ~ 7.5 ARUPS at Γ

Ref. 90W 86J 91S 90W 85M 90H 90W 97W 99G2 90W 82M1 86E 92S3 93G 93G 92H1 82L 74N2 90W, 79K3 90W, 79K3 74N2 74N2 74N2 74N2 74N2 82C2 92F 76T 92F 92F 92F 82J1 82J2

90 Substrate

φC [eV] 1)

Ni(111)

5.40 5.3 ± 0.1

NiAl(100) Pb(111)

4.05 ± 0.02

3.1.1 Noble gases on metals and semiconductors

[Ref. p. 111

E(5p3/2) [eV]

Ref.

5.2 ± 0.1 5.3, 5.7 5.55 ± 0.1 6.05 6.4

Pd(100) Pd(110)

5.65 5.65 5.20

Pd(111)

5.95

Pd(810)

5.55

Pt(100)-(1×1) Pt(100)-hex

5.77 5.80 5.72 5.7 5.8

Pt(100) Pt(110)-(1×2) Pt(110)-(1×2)H Pt(111)

6.40

5.9

5.85 Pt(210)

Pt(311) Pt(321) Pt(332) Pt(997) Re(0001) Ru(0001)

5.83 ... 6.21 5.82 ... 6.18 5.27 ... 5.62 6.0 splitting: < 0.1 0.40 ± 0.03 0.58 ± 0.03

4.9 ~ 4.9 4.7-4.8 5.5 4.7 (mj = ± 3/2) 4.1 (mj = ± ½) 5.1

E(5p1/2) [eV] 6.80 6.6 ± 0.1 6.9 6.80 ± 0.1 7.27 7.60 7.65 6.75 ... 6.98 6.2 7.03 ... 7.36 6.97 ... 7.33 6.47... 6.82 7.2

6.88 ... 6.99 6.88 ... 7.25 6.08 6.10 6.1 ~ 6.1 5.9-6.0 6.8 5.8 5.90 6.88 6.03

~ 4.15 (mj = ± 3/2) ~ 4.75 (mj = ± ½) 4.2, 4.70 5.95 6.2 6.95

5.2 5.5 5.4 ~ 5.0 5.4 6.65 5.52

5.4 6.4 ~ 5.22

6.22 ... 6.28 6.80 6.8 5.40 6.76 7.6 6.48

Remarks

UPS, low coverage ARUPS at 30°, θ = 1 UPS UPS, θ = 0 ... 1 ARUPS at Γ, θ = 1 ARUPS, no dispersion, low coverage (< 0.3L) UPS, θ = 0 ... 1 ARUPS at Γ UPS, θ = 0 ... 1 UPS, θ = 0 ... 1 UPS, θ = 0 ... 1 at step edges dilute phase ( 3 × 3 )R30° ( 7 × 7 )R19.2° on terraces at step edges ARUPS at Γ ARUPS at Γ UPS ARUPS at Γ, θ = 1 FEM UPS, ARUPS at Γ 2 sites even for θ → 0 ARUPS at Γ on terraces at step edges θ →0 FEM spin resolved ARUPS at Γ, θ = 1 ARUPS at Γ on terraces at step edges FEM FEM FEM UPS, on terraces at step edges 5) ARUPS at Γ on terraces at step edges ARUPS at Γ, θ = 1

90W 89F 76T 90C 88J 88J 84W3 90W 84W3 79K2 84W3 80W1 91V2

83M2 90W 97W 95S 74N1 88D, 95W 97T, 99W 83D1 89A 74N1 85S 88C 97W 74N1 74N1 74N1 89C2 97T 90W 85J 80W1, 81W 99G2

Lando lt Bö rnst ein New Ser ies III/42A1

Ref. p. 111]

91

3.1.1 Noble gases on metals and semiconductors

φC [eV] 1)

Substrate

E(5p3/2) [eV]

E(5p1/2) [eV]

Remarks

Ref.

5.0 (mj = ± 3/2) 5.4 (mj = ± 1/2)

6.65

ARUPS at Γ, ( 3 × 3 )R30°

00W

Rh(111) 5.6 n-Si(100) 4.60 n-Si(111)-(7×7)

6.7 7.70 7.40 7.70 7.53 7.70

4.5 p-Si(111)-(7×7)

5.95 6.05 5.6 5.4 4.50 4.65 ± 0.03 6.8 5.10

W(100) W(110)

corner holes, θ = 0...0.05 terrace sites, θ = 0.05...0.7 adatoms, θ = 0.7...1 UPS, T = 60 K site 1, θ = 0...0.04 site 2, θ = 0.04...0.8 site 3, θ = 0.8...1 UPS, T = 60 K

6.75 7.90 8.1 7.15

UPS, 5L at 80 K

94J 90W 89M

97P1 84

97P1 90W 75W 90W

1

) If not given in the indicated reference, values were taken from Table 1 in [90W]. ) Thin and magnetized Co film on W(110). Spin resolved measurements reveal a magnetic splitting of ∆E(5p1/2) = 0.05 ± 0.03 eV and ∆E(5p3/2) = 0.10 ± 0.03 eV. 3 ) Thin and magnetized Fe film on W(110). Spin resolved measurements reveal a magnetic splitting of ∆E(5p1/2) = 0.18 ± 0.03 eV and ∆E(5p3/2) = 0.24 ± 0.03 eV. 4 ) The peak positions which can be extracted from the spectra in [79K3] differ considerably from those listed in [90W]. 5 ) Adsorption at step edges can be suppressed after pre-adsorption of CO or H2 2

Table 11. Energetic positions of the np orbital states of adsorbed Kr (n = 4), Ar (n = 3) and Ne(n=2) as derived from photoemission. If not stated otherwise, the values are for the low coverage limit. The energies are referred to the Fermi level but the workfunction values for the clean substrates, φC , are also given. Abbreviations used: : coverage in monolayer units, Γ: center of the Brillouin zone (electron emission normal to the surface plane). (Ad. = adsorbate) – see also Table 12. Substrate

Ad.

φC [eV] E(5p3/2) ) [eV]

1

Ni(110)

Ne Ar

Remark

15.05 15.05 UPS, no splitting 9.15 9.6 UPS ~ 9.2 ~ 9.2 ARUPS at Γ, no splitting at low θ Kr 7.85 8.5 UPS ~ 7.65 ~ 8.35 ARUPS at Γ 6.9 ARUPS Pt(110)-(1×2) Kr 5.9 (mj = ± 3/2) 6.3 (mj = ± 1/2) spin resolved Pt(111) Ar ~ 7.75 (mj = ± 3/2) ARUPS at Γ, θ = 1 ~ 7.65 (mj = ± 1/2) spin resolved Kr ~ 5.80 (mj = ± 3/2) ~ 6.95 ARUPS at Γ, θ = 1 ~ 6.15 (mj = ± 1/2) Rh(111) Ar 5.6 8.7 UPS, no splitting at low θ Kr 5.6 7.7 UPS 1 ) If not given in the indicated reference, values were taken from Table 1 in [90W].

Lando lt Börnst ein New Ser ies III/42A1

4.55 4.55 4.55 4.55 4.55

E(5p1/2) [eV]

Ref. 82J1 82J1 82J2 82J1 82J2 95W 86S 85S, 86S 94J 94J

92

3.1.1 Noble gases on metals and semiconductors

[Ref. p. 111

Table 12. Band structure (dispersion) of the p valence levels of the noble gas monolayers obtained in angular resolved photoemission. The energies at Γ are referred to the Fermi level. If not explicitly given in the indicated reference, the positions EF and band widths ∆ε were extracted from graphs of the dispersion curves. In this case the values are given with a ~ sign. Abbreviations used: : coverage in monolayer units, Γ: center of the Brillouin zone (electron emission normal to the surface plane). (Ad. = adsorbate) EF [eV] at Γ

Substrate

Ad.

Al(111)

Xe 1) ~ 5.8 ~ 6.3 ~ 7.55 Ar ~ 9.2 ~ 9.7 Kr ~ 7.2 ~ 7.5 ~ 8.4 Xe 2) ~ 5.4

Cu(110)

~ 5.95

Cr(110)

Xe

Pb(111)

Ar

Kr

Xe

Pd(100)

Ar Kr

Xe

7.3 5.7 7.0 ~ 9.1 ~ 9.15 ~ 9.70 ~ 7.75 ~ 8.1 8.83 ~ 5.9 ~ 6.35 7.60 8.50 8.90 6.35 6.7 7.55 4.6 5.1 6.4

Derived from Orbital ∆ε [eV]

Remarks

Ref.

0.44 4p3/2, mj = ± 3/2 0.40 4p3/2, mj = ± 1/2 0.36 4p1/2, mj = ± 1/2 3p3/2, mj = ± 1/2, ± 3/2 0.35 3p1/2, mj = ± 1/2 4p3/2, mj = ± 3/2 4p3/2, mj = ± 1/2 0.37 4p1/2, mj = ± 1/2 0.57 5p3/2, mj = ± 3/2 0.80 5p3/2, mj = ± 1/2 0.55 0.60 5p1/2, mj = ± 1/2 0.40 3p3/2, mj = ± 1/2, ± 3/2 ~ 0.2 ~ 0.2 3p1/2, mj = ± 1/2 ~ 0.4 3p3/2, mj = ± 3/2 ~ 0.4 3p3/2, mj = ± 1/2 ~ 0.3 3p1/2, mj = ± 1/2 ~ 0.5 4p3/2, mj = ± 3/2 ~ 0.45 4p3/2, mj = ± 1/2 ~ 0.4 4p1/2, mj = ± 1/2 ~ 0.6 5p3/2, mj = ± 3/2 ~ 0.5 5p3/2, mj = ± 1/2 ~ 0.5 5p1/2, mj = ± 1/2 3p3/2, mj = ± 1/2, ± 3/2 3p1/2, mj = ± 1/2 4p3/2, mj = ± 3/2 4p3/2, mj = ± 1/2 0.4 4p1/2, mj = ± 1/2 0.51 5p3/2, mj = ± 3/2 0.72 5p3/2, mj = ± 1/2 0.55 0.60 5p1/2, mj = ± 1/2 0.43 0.45

along ΓM along ΓM along ΓM along ΓM, ΓK along ΓM, ΓK along ΓM, ΓK along ΓM, ΓK along ΓM, ΓK along ΓM along ΓK along ΓM along ΓK along ΓM, ΓK

85M

82H 82H

82M1

89K along ΓH along ΓH along ΓH along ΓH along ΓH along ΓH along ΓH along ΓH along ΓH along ΓH along ΓH along ΓH along ΓH along ΓH along ΓM along ΓK along ΓM along ΓK along ΓM along ΓK

88J

88J

88J

80H 80H

78H

Lando lt Bö rnst ein New Ser ies III/42A1

Ref. p. 111]

93

3.1.1 Noble gases on metals and semiconductors

Substrate

Ad.

EF [eV] at Γ

Derived from Orbital ∆ε [eV]

Remark

Ref.

Pt(110)(1×2)

Kr

5.9 6.3 6.9 ~ 4.7 ~ 5.9 4.7 4.1 5.8 4.2

4p3/2, mj = ± 3/2 4p3/2, mj = ± 1/2 4p1/2, mj = ± 1/2 5p3/2 5p1/2 5p3/2, mj = ± 3/2 5p3/2, mj = ± ½ 5p1/2, mj = ± 1/2 5p3/2, mj = ± 3/2

dilute layer, θ = 0.4 3)

95W

4.70

5p3/2, mj = ± ½

5.95

5p1/2, mj = ± 1/2

5.4 6.8

5p3/2 5p1/2

Xe Pt(110)(1×2)H

Xe

Pt(111)

Xe

Pt(997)

Xe

0.20 0.25 0.80 0.24 0.22 0.33 0.65 0.35 0.41 0.32 0.35 ~0 ~0

along ΓX dilute layer, θ = 0.34 3) along ΓX dilute layer, θ = 0.45 3, 4 ) along ΓX ~ along ΓM ~ along ΓK ~ along ΓM ~ along ΓK ~ along ΓM ~ along ΓK dilute layer, θ = 0.15 5) along ΓK (and ΓM)

95W 97T, 99W

88C

97T

) Using EF = EV - φ with φ = 4.05 eV such that E(5p1/2) = 7.55 eV according to private communication cited in [88C]. The values for ∆ε were evaluated from Fig. 4 in [85M] and are smaller than those given in Tab. 2 of [88C]. 2 ) A broadening of the band width upon uniaxial compression is observed - here the values for ‘full coverage’ are given. 3 ) Under these conditions, Kr and Xe form quasi 1D structures along the Pt-[11 0] direction. Indeed, no dispersion is observed in the orthogonal ΓY-direction. 4 ) Note that the energetic position of the mj = ± 1/2 and mj = ± 3/2 subbands of the 5p3/2 level at the Γ-point is reversed as compared to the usual energetic ordering of the subbands in 2D. 5 ) In this case, a single Xe chain decorates the (111)-step edge with a large spacing between neighboring atoms being 2aPt = 5.56 Å. No splitting of the 5p3/2 subbands and no dispersion is observed along the chain direction. 1

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94

3.1.1 Noble gases on metals and semiconductors

[Ref. p. 111

3.1.1.2.5 Surface diffusion coefficients

See Fig. 19.

Table 13. Diffusion barriers Edif for the noble gases on various metal surfaces. The prefactor D0, if indicated, is related to the measured diffusion coefficient D via D = D0 exp(-Edif /kT). Abbreviations used: T: surface temperature, : coverage in monolayer units, θs: coverage in substrate atom units. (Ad. = adsobate) Substrate

Ad.

Edif [meV] D0 [cm2/s]

Ni(111)

Xe

14 ± 1 17 ± 2

Pt(111)

Kr Xe

~ 48 52 ± 9 56 ± 4 31 64 < 9.6 48 ± 13 48 ± 13

7×10−8 10−8 ... 10−9

W(110)-vicinals Xe

239 252 108

6×102 2×103 2×10−6

W(111) W(310)-(100)

65 ... 148 < 39 > 48 ~ 167

Xe

W(110)

Xe Xe

Xe Ar Kr Xe

2×10−9±0.2 3×10−8±0.3 3.4×10−4±0.5 1.1×10−4±0.2

Remarks

Ref.

θs = 0.04 θs = 0.16 first order linear optical diffraction θ = 1, assuming D0 = 10−9 cm2/s θ = 0.25 θ =1 adatom diffusion (θ → 0) + detachment from 2D islands 2D gas (θ = 0.017), T = 105 K θ = 0.3, T = 54 ... 72 K θ = 0.9, T = 67 ... 83 K FE current fluctation method θ = 0.3 θ = 0.5 θ = 0.7 FE current fluctation method FEM FEM FEM FEM

00N1

93M2 93M1, 93M2 95H2 99E 80C

83O

59E 59E 59E 59E

Lando lt Bö rnst ein New Ser ies III/42A1

Ref. p. 111]

95

3.1.1 Noble gases on metals and semiconductors

3.1.1.2.6 Vibration frequencies and phonon dispersion See Figs. 20 – 23. Table 13. Perpendicular vibration frequencies !ω⊥ and characteristics of the phonon dispersion curves for the noble gas monolayers. The sound velocities cl and ct were obtained from the initial slope of the dispersion curves for the longitudinal (L) and shear-horizontal (SH) modes, respectively. Where complete or partial dispersion curves are available, only the value at the boundary of the surface Brillouin zone is indicated. Abbreviations used: Γ, M, K: high symmetry points of the 2D adlayer Brillouin zone (BZ); [001] , [1 1 0] and [112 ] : crystallographic directions of the substrate surface. All data were obtained using inelastic He-atom scattering. (Ad. = adsorbate) Substrate

Ad.

!ω⊥ (meV)

Ag(110)

Kr Xe Ar Kr Xe Ar Kr Xe Kr Xe Xe Kr Xe Xe

~ 2.7 ~ 2.3 3.67 ± 0.15 2.92 ± 0.14 2.79 ± 0.15 3.9 ... 4.1 3.3 ... 3.5 2.8 ... 2.9 ~3 ~ 2.5 2.62 ~ 2.8 ~ 2.5 2.55 ± 0.05 0.7 2.71 0.4 4.70 ± 0.05 (Γ) 5.00 ± 0.05 (M) 5.00 ± 0.05 (K)

Ag(111)

Au(111)

Cu(100)

Cu(110)

Cu(111)

Xe

Pt(111)

Ar

Kr

Xe

Lando lt Börnst ein New Ser ies III/42A1

cl (m/s)

ct (m/s)

Ref. 84M1 84M1 88G1 88G1 88G1 86M 86M 86M 82M2 81M, 82M2 97G, 99S2 83M1 83M1, 94Z1 94Z1, 97R

along [001] 99S2 98B 00B, 90Z2 1400 ± 50 1460 ± 60

880 ± 50 900 ± 60

4.05 ± 0.05 (Γ) 3.85 ± 0.05 (M) 3.85 ± 0.05 (K)

1100 ± 50 1170 ± 60

620 ± 50 670 ± 30

3.80 ± 0.05 (Γ) 3.40 ± 0.05 (M) 3.40 ± 0.05 (K)

1230 ± 50 1280 ± 50

750 ± 30 780 ± 30

Remark

at BZ boundary

at BZ boundary gap energy (L) at BZ boundary gap energy (SH)

[112] [1 1 0] 00B, 89H

[1 1 0] [112] 00B, 89H

[1 1 0] [112]

3.1.1 Nobel gases on metals and semiconductors

96

[Ref. p. 111

Figures for 3.1.1 1.0

Sticking coeff. s0

0.8 Ne Ar Kr Xe

0.6

0.4

0.2

100

200 300 400 Gas temperature Tg [K]

500

600

1.0

5

0.8

4

Sticking coeff. s0 [10–3]

Sticking coeff. s0

0

Fig. 1. Initial sticking coefficient s0 of Ne, Ar, Kr and Xe on Ru(0001) as a function of the gas temperature Tg (surface temperature during adsorption Ts = 6.5 K) [92S2].

0.6

0.4

Ar Kr Xe

0.2

0 0

15

30 45 Surface temperature Ts [K]

60

3

2

Ne

1

75

0

5

6

7 8 9 Surface temperature Ts [K]

10

11

Fig. 2. Initial sticking coefficient s0 of Ne, Ar, Kr and Xe on Ru(0001) as a function of the surface temperature Ts (gas temperature Tg = 300 K). The usable temperature range is limited by the thermal desorption rate [92S2].

Lando lt -Börnst ein New Ser ies III/42A1

Ref. p. 111]

3.1.1 Nobel gases on metals and semiconductors

1.0

1.0

Ne/Ru (0001)

Ar/Ru (0001) 0.8

Sticking coeff. s

Sticking coeff. s

0.8

0.6

0.4

0.2

a

0

0.6

0.4

0.2

0.5

1.0 1.5 Coverage θ [ML]

2.0

2.5

b

1.2

0

1.0

0.8

0.8

Sticking coeff. s

Sticking coeff. s

1.0 1.5 Coverage θ [ML]

2.0

2.5

2.0

2.5

Xe/Ru (0001)

1.0

0.6

0.6

0.4

0.4

0.2

0.2

0

0.5

1.2

Kr/Ru (0001)

c

97

0.5

1.0 1.5 Coverage θ [ML]

2.0

2.5

d

0

0.5

1.0 1.5 Coverage θ [ML]

Fig. 3. Coverage dependence of the sticking coefficient s() of Ne, Ar, Kr and Xe on Ru(0001) at a surface temperature Ts = 6.5 K and gas temperature Tg = 300 K. Measurements for adsorption at 6.5 K (filled circles) and for adsorption onto an annealed monolayer of the noble gas (open circles) are shown [90S1].

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3.1.1 Nobel gases on metals and semiconductors

98 1.0

1.0

Ar/Cu (110)

Kr/Cu (110) 0.8

Sticking coeff. s

Sticking coeff. s

0.8

0.6

0.4

0.2

0

[Ref. p. 111

0.6

0.4

0.2

0.2

0.4 0.6 Coverage θ [ML]

0.8

1.0

0.4 0.6 Coverage θ [ML]

0.8

1.0

0

0.2

0.4 0.6 Coverage θ [ML]

0.8

1.0

1.0

Xe/Cu (110)

Sticking coeff. s

0.8

0.6

0.4

0.2

0

0.2

Fig. 4. Coverage dependence of the sticking coefficient s() of Ar, Kr and Xe gas on Cu(110) at a surface temperatures Ts of 30, 43 and 55 K, respectively; gas temperature Tg = 300 K [94Z2].

Lando lt -Börnst ein New Ser ies III/42A1

Ref. p. 111]

3.1.1 Nobel gases on metals and semiconductors

1.0

1.0

Pt (111)

Pt (557)

Rel.sticking coeff. s/sm

0.8

Rel.sticking coeff. s/sm

0.8

0.6

0.4

0.2

0

99

0.6

0.4

0.2

0.2

0.4 0.6 Coverage θ [ML]

0.8

1.0

0.4 0.6 Coverage θ [ML]

0.8

1.0

0

0.2

0.4 0.6 Coverage θ [ML]

0.8

1.0

1.0

Pt (112)

Rel.sticking coeff. s/sm

0.8

0.6

0.4

0.2

0

0.2

Fig. 5. Relative sticking coefficient of Xe on Pt(111), Pt(557) and Pt(112) as a function of coverage at a surface temperature Ts = 87 K [90S2].

Lando lt -Bö rnst ein New Ser ies III/42A1

3.1.1 Nobel gases on metals and semiconductors

100 7

10

2D solid [( 3× 3)R30°] + 2D gas

Xe coverage θ [%]

5

2D liquid + 2D gas

8

Thermal expansion α [10–4 K–1]

6

4 3 Ttr

2

2D gas

1

Tc

0 80

85

90

95 100 105 110 Surface temperature T [K]

115

320

Xe/Pt(111)

6 Xe/Ag(111)

4 bulk Xe

2

0 15

120

Fig. 6. 2D triple point Ttr, critical temperature Tc and phase coexistence lines for monolayer Xe on Pt(111) [85P]. Further details (2D solid phases) of the phase diagram are shown in Fig. 11.

25

35 45 Surface temperature T [K]

55

65

Fig. 7. Linear thermal expansion coefficient α of the unconstrained monolayer for Xe/Pt(111), Xe/Ag(111) and bulk Xe [88K1].

1.50

Molar adsorption entropy Sad [meV K–1]

1.25

Adsorption heat Qiso [meV]

310

1.00

300

0.75

290

0.50

280

270

[Ref. p. 111

0.25

0

0.1

0.2 Coverage θs

0.3

0.4

Fig. 8. Isosteric heat of adsorption Qiso of the Xe adlayer on Pt(111) as a function of Xe coverage θs [88K1]. The coverage is given in substrate atom units, i.e., θs = 1/3 corresponds

to

saturation

of

the ( 3 × 3 )R30°

commensurate phase corresponds to θs = 1/3.

0

0.1

0.2 Coverage θs

0.3

0.4

Fig. 9. Differential molar entropy of the Xe adlayer on Pt(111) as a function of Xe coverage. Data points (circles) and theoretical curves assuming a completely mobile 2D ideal gas (solid line), a completely mobile Volmer gas (dashed line) and a localized adlayer (dashdotted line) [88K1]. The coverage is given in substrate atom units, i.e., saturation of the ( 3 × 3 )R30° commensurate phase corresponds to θs = 1/3.

Lando lt -Börnst ein New Ser ies III/42A1

Ref. p. 111]

3.1.1 Nobel gases on metals and semiconductors

–4

–3

10 8

10 8

6 4

6 4

2

2 –4

–5

bulk Argon

6 4 2

–5

10 8

bilayer

6 4

2D solid

2 –6 6 4

2 –6 10 8 6 4

20

bilayer 2D solid

2

2D gas

2

–7

a

6 4

–7 10 8 6 4

10 8 2

bulk Krypton

10 8

Vapor pressure p [Torr]

Vapor pressure p [Torr]

10 8

10

101

2D gas

–8

22

–5

10 8

24 26 28 30 –1 –3 –1 Inv. temperature T [10 K ]

32

10

34

b

14

16

18 20 22 24 –1 –3 –1 Inv. temperature T [10 K ]

26

28

6 4

Vapor pressure p [Torr]

2 –6 10 8 6 4

bulk Xenon

2 –7 10 8 6 4

bilayer 2D solid

2 –8

10 8 6 4

2D gas

2 –9

10

8

10

c

12 14 16 18 –1 –3 –1 Inv. temperature T [10 K ]

20

22

Fig. 10. (a) Phase diagram of Ar on Ag(111) [81U]. The dashed line is the vapour pressure of bulk Ar. Circles, triangles and squares mark the onset of formation of the first, second and third layer, respectively. From the slope of the coexistence lines (solid lines through the symbols) the latent heats of adsorption (Tables 3–5) were determined. (b) Phase diagram of Kr on Ag(111) [81U]. Lines and symbols: same meaning as in (a). (c) Phase diagram of Xe on Ag(111) [79U]. Lines and symbols: same meaning as in (a).

Lando lt -Bö rnst ein New Ser ies III/42A1

3.1.1 Nobel gases on metals and semiconductors

102

130

0.90

G L

unrelaxed

0.75

~3%

90

6.5%

( 3× 3)R30°

70

Workfunction change ∆φ [eV]

Temperature T [K]

1.05

Tc

110

7.2%

0.60

HI

C

(4.49... 4.45 Å)

(4.8 Å)

0.45

HIR

(4.44... 4.33 Å)

50

SI

0.1

0.30

HOC

relaxed

(4.79 ... 4.5 Å)

30 0

[Ref. p. 111

0.15

9.6%

0.2 0.3 Coverage θs

0.4

0.5

Fig. 11. Structural phase diagram of monolayer Xe on Pt(111) (schematic) [91K]. C, SI, HI and HIR denote the commensurate ( 3 × 3 )R30° structure, the striped incommensurate, the hexagonal incommensurate and the hexagonal incommensurate rotated 2D solid phases. G and L denote the 2D gas and liquid phases, respectively.

HOC denote the high-order commensurate phase. Percentages indicate the lattice misfit defined as m = (a0-a)/a0 with a0 = 4.80 Å being the commensurate lattice spacing.

0

0.15

0.30

0.45 0.60 0.75 Coverage θ [ML]

0.90

1.05

Fig. 13. Comparison of the work function change for Xe on Pd(100) as a function of Xe coverage from different experiments [84M3]. Open symbols: Moog and Webb [84M3] with fit to Topping formula (solid line); dashed line: Wandelt and Hulse [84W3]; dotted line: stepped surface, Miranda et al. [83M2]; dash-dotted line: Palmberg [71P]. The work function change found by Kaindl et al. [80K] for monolayer coverage is also indicated (filled circle).

For Fig. 12 see next page 4.0 5p3/2, mj = ± 3/2

Binding energy Eb [eV]

4.5

F

5.0 5p3/2, mj = ± 1/2

5.5 6.0

Fig. 14. Dispersion curves for the 5p Xenon levels along the ΓKMΓ direction of the surface Brillouin zone of a Xe layer adsorbed on Pt(111). Circles refer to the

5p1/2

6.5 H K K'

7.0

0

0.25

0.50

M M'

0.75 1.00 1.25 –1 Wavevector kII [Å ]

1.50

1.75

( 3 × 3 )R30° commensurate layer with a Xe-Xe distance of 4.8 Å, triangles refer to an incommensurate rotated phase with a Xe-Xe distance of 4.38 Å. Data from [88C], figure from [90W].

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Ref. p. 111]

3.1.1 Nobel gases on metals and semiconductors

0

0

Al(111)

– 0.025

Ar dφ = – 0.30(3) eV dθ 0

Workfunction change ∆φ [eV]

Workfunction change ∆φ [eV]

– 0.025 – 0.050 – 0.075 – 0.100 – 0.125 – 0.150 – 0.175 0

103

Kr dφ = – 0.36(4) eV dθ 0

– 0.050 – 0.075 – 0.100 – 0.125 – 0.150 – 0.175

0.25

0

0.50 0.75 1.00 1.25 Coverage θ [ML]

1.50

1.75

– 0.200 0

0.25

0.50

0.75

1.00

1.25

1.50

1.75

Workfunction change ∆φ [eV]

– 0.05 Xe dφ = – 0.54(4) eV dθ 0

– 0.10 – 0.15 – 0.20 – 0.25 – 0.30 0

0.25

0.50 0.75 1.00 1.25 Coverage θ [ML]

1.50

1.75

Fig. 12. Measured work function changes as a function of coverage θ for Ar, Kr and Xe adsorbed on Al(111) at 40 K. The solid and dashed lines are theoretical curves based on the Topping model [82C1].

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3.1.1 Nobel gases on metals and semiconductors

104 9.0

K

Ar/Pb(111)

H

3p

Binding energy Eb [eV]

9.2

F

[Ref. p. 111

K M

Γ

9.4

9.6

5.8

9.8

6.0

10.0 0

0.25

7.6

0.50 0.75 1.00 –1 Wave vector kII [Å ]

1.25

Xe/Pb(111) 5p

6.2

1.50

6.4

5p3/2, mj = ± 3/2

Kr/Pb(111) 4p

7.8

6.6

8.0

Binding energy Eb [eV]

6.8

F

mj = ± 1/2

8.2

F

Binding energy Eb [eV]

7.0

7.2

8.4

8.6

7.4

8.8

7.6

9.0

7.8

9.2 0

0.25

0.50 0.75 1.00 –1 Wave vector kII [Å ]

1.25

1.50

8.0 0

5p1/2

0.25

0.50 0.75 1.00 –1 Wave vector kII [Å ]

1.25

1.50

Fig. 15. Band dispersion (along the ΓH direction) of the valence p-levels of Ar, Kr and Xe at monolayer coverage on Pb(111) [88J].

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Ref. p. 111]

3.1.1 Nobel gases on metals and semiconductors

Γ – 9.5

Γ – 9.5

M

105 M

–10.0

–10.0

–10.5

Binding energy Eb rel. to Evac [eV]

Binding energy Eb rel. to Evac [eV]

j = 3/2

–11.0 Γ

M

1st layer 2nd layer indirect transitions

–11.5

–10.5

–11.0

–11.5

j = 1/2

–12.0

–12.0

–12.5 0 0.2 a Monolayer

0.4

0.6 0.8 1.0 1.2 –1 Wave vector kII [Å ]

1.4

1.6

–12.5 0 b Bilayer

0.2

0.4

0.6 0.8 1.0 1.2 –1 Wave vector kII [Å ]

1.4

1.6

Fig. 16. Band dispersion along ΓM for monolayer and bilayer Xe on Al(111). Solid and dashed lines represent the theoretical single layer band dispersion curves [80H] displaced by layer dependent binding energy shifts [85M].

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3.1.1 Nobel gases on metals and semiconductors

106

4.25

4.25

4.50

4.50

5p3/2 mj = ± 1/2

Binding energy Eb [eV]

4.00

Binding energy Eb [eV]

4.00

4.75

5p3/2 mj = ± 3/2

F

F

4.75 5.00

5.00

5.25

5.25

kII along ΓX

5.50

5.75

6.00

6.00 2.0

1.5 1.0 –1 Wave vector kII [Å ]

0.5

kII along ΓY

5.50

5.75

6.25 2.5

[Ref. p. 111

6.25

0

5p1/2 mj = ± 1/2

0

0.5

1.5 1.0 –1 Wave vector kII [Å ]

2.0

2.5

Fig. 17. Band dispersion (along the ΓX and ΓY directions) of Xe adsorbed on a hydrogen modified Pt(110)-(1×2) surface (Xe coverage θ = 0.45 ML). The symbols correspond to experimental data derived from ARUPS spectra with different photon energies (26 and 30 eV) and different directions of light incidence (normal and 45° off-normal). The solid lines are the results of a fully relativistic Korringa-Kohn-Rostocker (KKR) calculation for freestanding Xe chains [99W].

For Fig. 18 see next page. 2.5 T = 45 K

Xe/Pt(111)

T = 80 K

2.0

1.2

2 –1

0.8

0.4

0

a

Kr/Pt(111)

Diff. coeff. D [10–6 cm s ]

2 –1

Diff. coeff. D [10–7 cm s ]

1.6

1.5

1.0

0.5

0.2

0.4 0.6 Coverage θ [ML]

0.8

1.0

0

b

0.2

0.4 0.6 Coverage θ [ML]

0.8

1.0

Fig. 19. Surface diffusion coefficient D for Kr (at 45 K) and Xe (at 80 K) on Pt(111) as a function of coverage. Symbols: data extracted from experiment, solid line: prediction based on the quasi-chemical approximation [93M2].

Lando lt -Börnst ein New Ser ies III/42A1

Ref. p. 111] 10

3.1.1 Nobel gases on metals and semiconductors 10

Xe/Cu(100)

Xe/Ru(0001)

8 Xe coverage θ [ML]

Xe coverage θ [ML]

8

107

6

4

2

6

4

2

0 4.4 10

5.2

6.0

6.8 7.6 F Binding energy Eb [eV]

0 4.4

8.4

5.2

6.0

6.8 F

Binding energy Eb [eV]

7.6

8.4

Xe/Pt(100)-hex

Xe coverage θ [ML]

8

6

4

Fig. 18. Quantum well electronic states of Xe multilayer films adsorbed on Cu(100), Ru(0001) and Pt(100)-hex as a function of the film thickness. Dots and triangles are the experimental results, the vertical bars are theoretical predictions of a tight binding calculation [99G2].

2

0 4.4

5

5.2

6.0

6.8

Binding energy EbF [eV]

7.6

8.4

Γ

K

Phonon energy hω [meV]

4 ML

3 BL

2

1

0

Fig. 20. Phonon dispersion curves for monolayer (ML), bilayer (BL), trilayer (TL) and 25 ML Xe on Pt(111) along the adlayer ΓK direction (substrate

TL

[112] direction). Beside the evolution of the mode dispersion with increasing film thickness the hybridization between the adlayer mode and the surface Rayleigh wave (solid line) is apparent [90Z1].

25ML

0.2

Lando lt -Bö rnst ein New Ser ies III/42A1

0.4 0.6 –1 Wave vector q [Å ]

0.8

1.0

3.1.1 Nobel gases on metals and semiconductors

108 8.0 R

LR

8.0

Ar/Pt(111) [110]

SH

6.0

7.0

5.0

Phonon energy hω [meV]

Phonon energy hω [meV]

7.0

S

4.0 LA

LA

3.0 2.0

SH

0

0.5

1.0 1.5 –1 Wave vector q [Å ]

8.0

[110]

R

LR

4.0

SH

2.0

0

0.5

8.0

1.0 1.5 –1 Wave vector q [Å ]

0.5

1.0 1.5 –1 Wave vector q [Å ]

2.0

2.5 [112]

R

LR

5.0 S

4.0

SH

LA

3.0 2.0

0

2.5

7.0

[110] LA

5.0 4.0

S

3.0 2.0 SH

0.5

2.0

2.5

1.0 1.5 –1 Wave vector q [Å ]

2.0 [112]

R

L

2.5

6.0 5.0

LA

4.0 S

3.0 2.0 1.0

1.0 1.5 –1 Wave vector q [Å ]

0.5

8.0

Xe/Pt(111)

R

L

2.0

6.0

0

2.0

1.0

Phonon energy hω [meV]

Phonon energy hω [meV]

c

SH

3.0

6.0

S

LA

3.0

1.0

S

4.0

7.0

5.0

7.0

5.0

8.0

1.0

b

LA

6.0

0

2.5

Phonon energy hω [meV]

Phonon energy hω [meV]

2.0

Kr/Pt(111)

7.0 6.0

[112]

R

LR

1.0

1.0

a

[Ref. p. 111

0

SH

0.5

1.0 1.5 –1 Wave vector q [Å ]

2.0

2.5

Fig. 21. For caption see next page.

Lando lt -Börnst ein New Ser ies III/42A1

Ref. p. 111]

3.1.1 Nobel gases on metals and semiconductors

109

Fig. 21. (a) Phonon dispersion curves for a HI-R0° Ar monolayer on Pt(111) along the substrate [1 1 0] and [112] directions at T = 23 K. (b) Phonon dispersion curves for a HI-R30±523° Kr monolayer on Pt(111) along the substrate [1 1 0] and [112] directions at T = 50 K. (c) Phonon dispersion curves for a hexagonal incommensurate rotated (HI-R30±2.6°) Xe monolayer on Pt(111) along the substrate [1 1 0] and [112] directions at T = 50 K. Notations used: R, L: Pt(111) surface Rayleigh wave and longitudinal resonance, respectively; S, LA and SH: perpendicular, longitudinal and shear horizontal Xe adlayer modes, respectively. The lines are calculations based on McLachlan modified HFD-B2 gas-phase potentials (solid lines) [00B].

10

Γ

K

X

10

R 6

4

⊥2 H1

Γ

Y

8

⊥3

Phonon energy [meV]

Phonon energy [meV]

8

M

L

⊥3 R

6

4

⊥2 L*

H

⊥ 2

a

⊥ 2

H2

0

G 0.4

0.8 1.2 –1 Wave vector q [Å ]

1.6

0

b

0.2

0.4 0.6 –1 Wave vector q [Å ]

0.8

1.0

Fig. 22. Phonon dispersion curves for the (26×2) HOC monolayer of Xe on Cu(110) along the ΓX (a) and ΓY (b) directions. Notations used: R: Cu(110) surface Rayleigh wave; ⊥, ⊥2, ⊥3: single and multiple excitation of the perpendicular Xe vibration mode; H, H1, H2: branches of the hybridized ⊥ and R modes. L, L*: longitudinal Xe modes, G: gap mode. Dashed lines are the result of a lattice dynamics calculation [97R].

Lando lt -Bö rnst ein New Ser ies III/42A1

3.1.1 Nobel gases on metals and semiconductors

110

[Ref. p. 111

4.0 3.5

R

Phonon energy [meV]

3.0

⊥

2.5

Fig. 23. Phonon dispersion curves for a Xe monolayer on Cu(100) along the [100] substrate direction (after [97G]). Notations used: R: Cu(100) surface Rayleigh wave; ⊥ and SH: perpendicular and shear horizontal Xe adlayer modes, respectively. The SH mode was first explained by assigning it to the longitudinal branch [97G,99S2], which required a large softening of the inplane Xe-Xe force constant. Later it was suggested [97B1,00B] that it should be assigned to the SHpolarized mode.

2.0 SH

1.5 1.0 0.5 0

0.2

0.4 0.6 –1 Wave vector q [Å ]

0.8

1.0

Lando lt -Börnst ein New Ser ies III/42A1

3.1.1 Nobel gases on metals and semiconductors

References for 3.1.1 59E 62R 70D 70E 71C 71P 72I 73C 74D 74N1 74N2 75P 75W 76M 76R 76T 77K 78H 79B 79E 79G 79K1 79K2 79K3 79U 79W 80B 80C 80H 80K 80W1 80W2 81G 81M 81O 81U 81W 82C1 82C2 82H 82J1 82J2 82L 82M1 82M2 82U 83C 83D1

Ehrlich, G., Hudda, F.G.: J. Chem. Phys. 30 (1959) 493. Rootsaert, W.J.M., van Reijen, L.L., Sachtler, W.M.H.: J. Catalysis 1 (1962) 416. Dickey, J.M., Farrell, H.H., Strongin, M.: Surf. Sci. 23 (1970) 448. Engel, T, Gomer, R.: J. Chem. Phys. 52 (1970) 5572. Chesters, M.A., Pritchard, J.: Surf. Sci. 28 (1971) 460. Palmberg, P.W.: Surf. Sci. 25 (1971) 598. Ignatiev, A., Jones, A.V., Rhodin, T.N.: Surf. Sci. 30 (1972) 573. Chesters, M.A., Hussain, M., Pritchard, J.: Surf. Sci. 35 (1973) 161. Dresser, M.J., Madey, T.E., Yates jr., J.T.: Surf. Sci. 42 (1974) 533. Nieuwenhuys, B.E., Meijer, D.Th., Sachtler, W.M.H.: Phys. Status Solidi A 24 (1974) 115. Nieuwenhuys, B.E., Sachtler, W.M.H.: Surf. Sci. 45 (1974) 513. Papp, H., Pritchard, J.: Surf. Sci. 53 (1975) 371. Waclawski, B.J., Herbst, J.F.: Phys. Rev. Lett. 35 (1975) 1594. McElhiney, G., Pritchard, J.: Surf. Sci. 60 (1976) 397. Roberts, R.H., Pritchard, J.: Surf. Sci. 54 (1976) 687. Tapping, R.L., Norton, P.R.: Chem. Phys. Lett. 41 (1976) 252. Klein, M.L., Venables, J.A. (eds.): Rare Gas Solids, Vol. II. London: Academic 1977. Horn, K., Schefffler, M., Bradshaw, A.M.: Phys. Rev. Lett. 41 (1978) 822. Bak, P., Mukamel, D., Villain, J., Wentowska, K.: Phys. Rev. B 19 (1979) 1610. Engel, T., Bornemann, P., Bauer, E.: Surf. Sci. 81 (1979) 252. Glachant, A., Bardi, U.: Surf. Sci. 87 (1979) 187. Küppers, J., Nitschké, F., Wandelt, K., Ertl, G.: Surf. Sci. 87 (1979) 295. Küppers, J., Nitschké, F., Wandelt, K., Ertl, G.: Surf. Sci. 88 (1979) 1. Küppers, J., Michel, H., Nitschké, F., Wandelt, K., Ertl, G.: Surf. Sci. 89 (1979) 361. Unguris, J., Bruch, L.W., Moog, E.R., Webb, M.B.: Surf. Sci. 87 (1979) 415. Wang, C., Gomer, R.: Surf. Sci. 84 (1979) 329. Bardi, U., Glachant, A., Bienfait, M.: Surf. Sci. 97 (1980) 137. Chen, J.-R., Gomer, R.: Surf. Sci. 94 (1980) 456. Hermann, K., Noffke, J., Horn, K.: Phys. Rev B 22 (1980) 1022. Kaindl, G., Chiang, T.-C., Eastman, D.E., Himpsel, F.J.: Phys. Rev. Lett. 45 (1980) 1808. Wandelt, K., Hulse, J., Küppers, J., Ertl, G.: Proc. IV ICSS and III ECOSS (Le Vide, Les Couches Minces, 1980), Vol. 1, p. 104. Wang, C., Gomer, R.: Surf. Sci. 91 (1980) 533. Glachant, A., Jaubert, M., Bienfait, M., Boato, G.: Surf. Sci. 115 (1981) 219. Mason, B.F., Williams, B.R.: Phys. Rev. Lett. 46 (1981) 1138; Surf. Sci. 111 (1981) 609. Opila, R., Gomer, R.: Surf. Sci. 112 (1981) 1. Unguris, J., Bruch, L.W., Moog, E.R., Webb, M.B.: Surf. Sci. 109 (1981) 522. Wandelt, K., Hulse, J, Küppers, J.: Surf. Sci. 104 (1981) 212. Chiang, T.C., Kaindl, G., Eastman, D.E.: Solid State Commun. 41 (1982) 661. Christmann, K., Demuth, J.E.: Surf. Sci. 120 (1982) 291. Horn, K., Mariani, C., Cramer, L.: Surf. Sci. 117 (1982) 376. Jacobi, K., Hsu, Y.-P., Rotermund, H.H.: Surf. Sci. 114 (1982) 683. Jacobi, K., Rotermund, H.H.: Surf. Sci. 116 (1982) 453. Lang, N.D., Williams, A.R., Himpsel, F.J., Reihl, B., Eastman, D.E.: Phys. Rev. B 26 (1982) 1728. Mariani, C., Horn, K., Bradshaw, A.M.: Phys. Rev. B 25 (1982) 7798. Mason, B.F., Caudano, R., Williams, B.R.: J. Chem. Phys. 77 (1982) 562. Unguris, J., Bruch, L.W., Webb, M.B., Phillips, J.M.: Surf. Sci. 114 (1982) 219. Conrad, E., Webb, M.B.: Surf. Sci. 129 (1983) 37. Daiser, S., Wandelt. K.: Surf. Sci. 128 (1983) L213.

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111

112 83D2 83M1 83M2 83K 83O 83P 84A 84D 84G 84M1 84M2 84M3 84W1 84W2 84W3 85H 85J 85M 85P 85S 85T 86B 86E 86J 86K1 86K2 86K3 86M 86S 87F 87G 87K1 87K2 87K3 87M 88C 88D 88G1 88G2 88J 88K1 88K2 88M 88P 88S 88Q

3.1.1 Nobel gases on metals and semiconductors Dolle, P., Alnot, M., Ehrhardt, J.J., Thomy, A., Cassuto, A.: C. R. Acad. Sci. (Paris) 296 (1983) 529. Mason, B.F., Williams, B.R.: Surf. Sci. 130 (1983) 295. Miranda, R., Daiser, S., Wandelt, K., Ertl, G.: Surf. Sci. 131 (1983) 61. Küppers, J., Seip, U.: Appl. Surf. Sci. 16 (1983) 313. Okano, T.: Jpn. J. Appl. Phys. 22 (1983) 1496. Poelsema, B., Verheij, L.K., Comsa, G.: Phys. Rev. Lett. 51 (1983) 2410. Annett, J.F., Haydock, R.: Phys. Rev. Lett. 53 (1984) 838. Demuth, J.E., Shell-Sorokin, A.J.: J. Vac. Sci. Technol. A 2 (1984) 808. Glachant, A., Bienfait, M., Jaubert, M.: Surf. Sci. 148 (1984) L665. Mason, B.F., Williams, B.R.: Surf. Sci. 139 (1984) 173. Miranda, R., Albano, V.E., Daiser, S., Wandelt, K., Ertl, G.: J. Chem. Phys. 80 (1984) 2931. Moog, E.R., Webb, M.B.: Surf. Sci. 148 (1984) 338. Wandelt, K.: J. Vac. Sci. Technol. A 2 (1984) 802. Wandelt, K., Gumhalter, B.: Surf. Sci. 140 (1984) 355. Wandelt, K., Hulse, J.E.: J. Chem. Phys. 80 (1984) 1340. Hall, B., Mills, D.L., Black, J.E.: Phys. Rev. B 32 (1985) 4932. Jablonski, A., Eder, S., Wandelt, K.: Appl. Surf. Sci. 22/23 (1985) 309. Mandel, T., Kaindl, G., Domke, M., Fischer, W., Schneider, W.D.: Phys. Rev. Lett. 55 (1985) 1638. Poelsema, B., Verheij, L.K., Comsa, G.: Surf. Sci. 152/153 (1985) 851. Schönhense, G., Eyers, A., Friess, U., Schäfers, F., Heinzmann, U.: Phys. Rev. Lett. 54 (1985) 547. Tully, J.D.: Faraday Discuss. Chem. Soc. 80 (1985) 291. Behm, R.J., Brundle, C.R., Wandelt, K.: J. Chem. Phys. 85 (1986) 1061. Eder, S., Markert, K., Jablonski, A., K., Wandelt, K.: Ber. Bunsenges. Phys. Chem. 90 (1986) 225. Jablonski, A., Eder, S., Markert, K., Wandelt, K.: J. Vac. Sci. Technol. A 4 (1986) 1510. Kern, K., David, R., Palmer, R.L., Comsa, G.: Phys. Rev. Lett. 56 (1986) 620. Kern, K., David, R., Palmer, R.L., Comsa, G.: Surf. Sci. 175 (1986) L669. Kern, K., Zeppenfeld, P., David, R., Palmer, R.L., Comsa, G.: Phys. Rev. Lett. 57 (1986) 3187. Mason, B.F., Williams, B.R.: Surf. Sci. 177 (1986) L925. Schönhense, G.: Appl. Phys. A 41 (1986) 39. Frank, K.H., Horn, K., Wilder, J., Koch, E.E.: Appl. Phys. A 44 (1987) 97. Greiser, N., Held, G.A., Frahm, R., Greene, R.L., Horn, P.M., Suter, R.M.: Phys. Rev. Lett. 59 (1987) 1706. Kern, K.: Phys. Rev. B 35 (1987) 8265. Kern, K., David, R., Zeppenfeld, P., Palmer, R.L., Comsa, G.: Solid State Commun. 62 (1987) 391. Kern, K., Zeppenfeld, P., David, R., Comsa, G.: Phys. Rev. Lett. 59 (1987) 79. Menzel, D.: Kinetics of Interface Reactions, Springer Series in Surface Sciences Vol. 8. Berlin: Springer Verlag 1987, p. 1. Cassuto, A., Ehrhardt, J.J., Cousty, J., Riwan, R.: Surf. Sci. 194 (1988) 579. Ducros, R., Ehrhardt, J.J., Fusy, J., Mutafschiev, B.: Phys. Rev. B 38 (1988) 10035. Gibson, K.D., Sibener, S.J.: J. Chem. Phys. 88 (1988) 7862. Gibson, K.D., Sibener, S.J.: J. Chem. Phys. 88 (1988) 7893. Jacobi, K.: Phys. Rev. B 38 (1988) 5869. Kern, K., David, R., Zeppenfeld, P., Comsa, G.: Surf. Sci. 195 (1988) 353. Kern, K., Zeppenfeld, P., David, R., Comsa, G.: J. Vac. Sci. Technol. A 6 (1988) 639. Mason, B.F., Williams, B.R.: Z. Phys. D 10 (1988) 369. Packard, W.E., Webb, M.B.: Surf. Sci. 195 (1988) 371. Schlichting, H., Menzel, D., Brunner, T, Brenig, W., Tully, J.C.: Phys. Rev. Lett. 60 (1988) 2515. Qian, X., Betz, M.: Phys. Rev. Lett. 61 (1988) 1497. Lando lt Bö rnst ein New Ser ies III/42A1

3.1.1 Nobel gases on metals and semiconductors 89A 89B 89F 89H 89K 89M 90A 90B 90C 90G 90H 90J 90M 90R1 90R2 90S1 90S2 90W 90Z1 90Z2 91A 91B 91C1 91C2 91E 91K 91H 91R 91S 91V1 91V2 91W 92F 92H1 92H2 92M 92S1 92S2 92S3 92W 92Z 93F

113

Alnot, A., Ehrhardt, J.J., Barnard, J.A.: Surf. Sci. 208 (1989) 285. Berndt, W.: Surf. Sci. 219 (1989) 161. Fargues, D., Dolle, P., Alnot, M., Ehrhardt, J.J: Surf. Sci. 214 (1989) 187. Hall, B., Mills, D.L., Zeppenfeld, P., Kern, K., Becher, U., Comsa, G.: Phys. Rev. B 40 (1989) 6326. Komeda, T., Sakisaka, Y., Onchi, M., Kato, H., Suzuki, S., Edamoto, K., Aiura, Y.: Phys. Rev. B 40 (1989) 3344. Markert, K., Pervan, P., Heichler, W., Wandelt, K.: Surf. Sci. 211/212 (1989) 611. Arumainayagam, Ch., Madix, R.J., McMaster, M.C., Suzawa, V.M., Tully, J.C.: Surf. Sci. 226 (1990) 180. Bethune, D.S., Barker, J.A., Rettner, C.T.: J. Chem. Phys. 92 (1990) 6847. Castro, G.R., Isern, H., Schneider, U., Stöcker, M., Wandelt, K.: Vacuum 41 (1990) 393. Gottlieb, J.M.: Phys. Rev. B 42 (1990) 5377. Hinch, B.J., Lock, A., Madden, H.H., Toennies, J.P., Witte, G.: J. Electron. Spectrosc. 51 (1990) 673. Jupille, J., Ehrhardt, J.-J., Fargues, D., Cassuto, A.: Faraday Discuss. Chem. Soc. 89 (1990) 323. Müller, J.E.: Phys. Rev. Lett. 65 (1990) 3021. Rettner, C.T., Bethune, D.S., Schweizer, E.K.: J. Chem. Phys. 92 (1990) 1442. Rettner, C.T., Mullins, C.B., Bethune, D.S., Auerbach, D.J., Schweizer, E.K., Weinberg, W.H.: J. Vac. Sci. Technol. A 8 (1990) 2699. Schlichting, H.: Dissertation, Technical University Munich (1990). Siddiqui, H.R., Chen, P.J., Guo, X., Yates, J.T.: J. Chem. Phys. 92 (1990) 7690. Wandelt, K.: Chemistry and Physics of Solid Surfaces VIII, Springer Series in Surface Sciences Vol. 22. Berlin: Springer Verlag 1990, p. 289. Zeppenfeld, P., Becher, U., Kern, K., Comsa, G.: J. Electron Spectrosc. 54/55 (1990) 265. Zeppenfeld, P., Becher, U., Kern, K., David, R., Comsa, G.: Phys. Rev. B 41 (1990) 8549. Arumainayagam, Ch., Stinnett, J.A., McMaster, M.C., Madix, R.J.: J. Chem. Phys. 95 (1991) 5437. Barker, J.A., Rettner, C.T., Bethune, D.S.: Chem. Phys. Lett. 188 (1991) 471. Castro, G.R., Isern, H., Schneider, U., Stöcker, M., Wandelt, K.: J. Vac. Sci. Technol. A 9 (1991) 1676. Cathrine, B., Fargues, D., Alnot, M., Ehrhardt, J.J.: Surf. Sci. 259 (1989) 162. Eigler, D.M., Weiss, P.S., Schweizer, E.K., Lang, N.D.: Phys. Rev. Lett. 66 (1991) 1189. Kern, K., Comsa, G.: Phase Transitions in Surface Films, NATO ASI Series 261. New York: Plenum Press, 1991, p. 41. Head-Gordon, M., Tully, J.C., Schlichting, H., Menzel, D.: J. Chem. Phys. 95 (1991) 9266. Rettner, C.T., Ashfold, M.N.R. (eds.): Dynamics of Gas-Surface Interactions, Advances in GasPhase Photochemistry and Kinetics. Cambridge: The Royal Society of Chemistry, 1991. Schneider, U., Castro, G.R., Isern, H., Janssens, T., Wandelt, K.: Surf. Sci. 251/252 (1991) 551. Vidali, G., Ihm, G., Kim, H.-Y., Cole, M.W.: Surf. Sci. Rep. 12 (1991) 133. Vogt, B., Kessler, B., Müller, N., Schönhense, G., Schmiedeskamp, B., Heinzmann, U.: Phys. Rev. Lett. 67 (1991) 1318. Weiss, W., Umbach, E.: Surf. Sci. 249 (1991) L333. Fargues, D., Dolle, P., Ehrhardt, J.J., Sotto, M., Bouillard, J.C.: Surf. Sci. 274 (1992) L494. Haugstad, G., Raisanen, A., Yu, X., Vanzetti, L., Franciosi, A.: Phys. Rev. B 46 (1992) 4102. Hilgers, G.: Dissertation, University Bielefeld, 1992. Michel, E.G., Pervan, P., Castro, G.R., Miranda, R., Wandelt, K.: Phys. Rev. B 45 (1992) 11811. Schlichting, H., Menzel, D.: Surf. Sci. 272 (1992) 27. Schlichting, H., Menzel, D., Brunner, T, Brenig, W.: J. Chem. Phys. 97 (1992) 4453. Schneider, U., Castro, G.R., Busse, H., Janssens, T., Wesemann, J., Wandelt, K.: Surf. Sci. 269/270 (1992) 316. Weiss, P.S., Eigler, D.M.: Phys. Rev. Lett. 69 (1992) 2240. Zeppenfeld, P., Becher, U., Kern, K., Comsa, G.: Phys. Rev. B 45 (1992) 5179. Friess, W., Steinacker, E., Brunner, T., Menzel, D.: Surf. Sci. 298 (1993) L173.

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114 93G 93H 93M1 93M2 93M3 93R 93S1 93S2 93S3 93S4 94J 94R 94S 94Z1 94Z2 94Z3 95H1 95H2 95P1 95P2 95S 95W 96B 96O 96P 96S 96W 96Z 97B1 97B2 97G 97L 97N 97P1 97P2 97R 97T 97W 98B

3.1.1 Nobel gases on metals and semiconductors Getzlaff, M., Bansmann, J., Schönhense, G.: Phys. Rev. Lett. 71 (1993) 793. Hilgers, G., Potthoff, M., Müller, N., Heinzmann, U.: Surf. Sci. 287/288 (1993) 414. Meixner, D.L., George, S.: J. Chem. Phys. 98 (1993) 9115. Meixner, D.L., George, S.: Surf. Sci. 297 (1993) 27. Menzel, D., Brenig, W., Brunner, T., Frieß, W., Schlichting, H.: J. Electron Spectrosc. 64/65 (1993) 583. Rieder, K.H., Parschau, G., Burg, B.: Phys. Rev. Lett. 71 (1993) 1059. Schlichting, H., Menzel, D.: Rev. Sci. Instrum. 64 (1993) 2013. Schwennicke, C., Schimmelpfennig, J., Pfnür, H.: Phys. Rev. B 48 (1993) 8928. Schroeder, S., McMaster, M.C., Stinnett, J.A., Madix, R.J.: Surf. Sci. 297 (1993) L148. Soszka, W.: Surf. Sci. 287/288 (1993) 69. Janssens, T.V.W., Castro, G.R., Wandelt, K., Niemantsverdriet, J.W.: Phys. Rev. B 49 (1994) 14599. Ramseyer, C., Girardet, C., Zeppenfeld, P., Goerge, J., Büchel, M., Comsa, G.: Surf. Sci. 313 (1994) 251. Schneider, U., Busse, H., Linke, R., Castro, G.R., Wandelt, K.: J. Vac. Sci. Technol. A 12 (1994) 2069. Zeppenfeld, P., Büchel, M., David, R., Comsa, G., Ramseyer, C., Girardet, C.: Phys. Rev. B 50 (1994) 14667. Zeppenfeld, P., Goerge, J., Büchel, M., David, R., Comsa, G.: Surf. Sci. 318 (1994) L1187. Zeppenfeld, P., Horch, S., Comsa, G.: Phys. Rev. Lett. 73 (1994) 1259. Hilgers, G., Potthoff, M., Müller, N., Heinzmann, U.: Surf. Sci. 322 (1995) 207. Horch, S., Zeppenfeld, P., Comsa, G.: Surf. Sci. 331-333 (1995) 908. Paniago, R., Matzdorf, R., Meister, G., Goldmann, A.: Surf. Sci. 325 (1995) 336. Potthoff, M., Hilgers, G., Müller, N., Heinzmann, U., Hauner, L., Braun, J., Borstel, G.: Surf. Sci. 322 (1995) 193. Schmitz-Hübsch, T., Oster, K., Radnik, J., Wandelt, K.: Phys. Rev. Lett. 74 (1995) 2595. Weinelt, M., Trischberger, P., Widdra, W., Eberle, K., Zebisch, P., Gokhale, S., Menzel, D., Henk, J., Feder, R., Dröge, H., Steinrück, H.-P.: Phys. Rev. B 52 (1995) R17048. Bertel, E.: Surf. Sci. 367 (1996) L61. Ostertag, Ch., Oelsner, A., Schicketanz, M., Schmidt, O., Fecher, G.H., Schönhense, G.: Surf. Sci. 352-354 (1996) 179. Petersen, M., Wilke, S., Ruggerone, P., Kohler, B., Scheffler, M.: Phys. Rev. Lett. 76 (1996) 995. Stichler, M., Zebisch, P., Weinelt, M., Steinrück, H.-P.: Surf. Sci. 348 (1996) 370. Wong, A., Zhu, X.D.: Appl. Phys. A 63 (1996) 1. Zeppenfeld, P., Büchel, M., Goerge, J., David, R., Comsa, G., Ramseyer, Ch., Girardet, C.: Surf. Sci. 366 (1996) 1. Bruch, L.W.: J. Chem. Phys. 107 (1997) 4443. Bruch, L.W., Cole, M.W., Zaremba, E.: Physical Adsorption: Forces and Phenomena, Oxford: Clarendon Press, 1997. Graham, A.P., Bertino, M.F., Hofmann, F., Toennies, J.P., Wöll, Ch.: J. Chem. Phys. 106 (1997) 6194. Leatherman, G.S., Diehl, R.D., Karimi, M., Vidali, G.: Phys. Rev. B 56 (1997) 6970. Narloch, B., Menzel, D.: Chem. Phys. Lett. 270 (1997) 163. Pervan, P., Markert, K., Wandelt, K.: Appl. Surf. Sci. 108 (1997) 307. Pouthier, V., Ramseyer, C., Girardet, C., Kuhnke, K., Marsico, V., Blanc, M., Schuster, R., Kern, K.: Phys. Rev. B 56 (1997) 4211. Ramseyer, C., Pouthier, V., Girardet, C., Zeppenfeld, P., Büchel, M., Diercks, V., Comsa, G.: Phys. Rev. B 55 (1997) 13203. Trischberger, P., Dröge, H., Gokhale, S., Henk, J., Steinrück, H.-P., Widdra, W., Menzel, D.: Surf. Sci. 377-379 (1997) 155. Wandelt, K.: Appl. Surf. Sci. 111 (1997) 1. Braun, J., Fuhrmann, D., Siber, A., Gumhalter, B., Wöll, Ch.: Phys. Rev. Lett. 80 (1998) 125. Lando lt Bö rnst ein New Ser ies III/42A1

3.1.1 Nobel gases on metals and semiconductors 98I 98N 98P 98S 98W 99E 99G1 99G2 99P 99S1 99S2 99W 00B 00N1 00N2 00S 00W

115

Igarashi, S., Abe, Y., Irie, Y., Hirayama, T., Arakawa, I.: J. Vac. Sci. Technol. A 16 (1998) 974. Narloch, B., Menzel, D.: Surf. Sci. 412-413 (1998) 562. Pouthier, V., Ramseyer, C., Girardet, C., Diercks, V., Halmer, R., David, R., Zeppenfeld, P.: Phys. Rev. B 57 (1998) 13149. Seyller, Th., Caragiu, M., Diehl, R.D., Kaukasoina, P., Lindroos, M.: Chem. Phys. Lett. 291 (1998) 567. Widdra, W., Trischberger, P., Frieß, W., Menzel, D., Payne, S.H., Kreuzer, H.J.: Phys. Rev. B 57 (1998) 4111. Ellis, J., Graham, A.P., Toennies, J.P.: Phys. Rev. Lett. 82 (1999) 5072. Graham, A.P., Toennies, J.P.: Surf. Sci. 427-428 (1999) 1. Grüne, M., Pelzer, T., Wandelt, K., Steinberger, I.T.: J. Electron Spectrosc. 98-99 (1999) 121. Persson, B.N.J.: Surf. Sci. Rep. 33 (1999) 83. Seyller, Th., Caragiu, M., Diehl, R.D., Kaukasoina, P., Lindroos, M.: Phys. Rev. B 60 (1999) 11084. Siber, A., Gumhalter, B., Braun, J., Graham, A.P., Bertino, M.F., Toennies, J.P., Fuhrmann, D., Wöll, Ch.: Phys. Rev. B 59 (1998) 5898. Widdra, W., Trischberger, P., Henk, J.: Phys. Rev. B 60 (1999) R5161. Bruch, L.W., Graham, A.P., Toennies, J.P.: J. Chem. Phys. 112 (2000) 3314. Nabighian, E., Zhu, X.D.: Chem. Phys. Lett. 316 (2000) 177. Narloch, B.: Dissertation, Technical University Munich (1996) and in preparation. Seyller, Th., Caragiu, M., Diehl, R.D.: Surf. Sci. 454-456 (2000) 55. Widdra, W., Fink, A., Menzel, D.: Appl. Phys. A, in preparation.

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3.1.2 Noble gases on graphite, lamellar halides, MgO and NaCl M. BIENFAIT The experimental studies of the adsorption of monolayers of rare gases on graphite, BN, MgO and lamellar halides have been very active during the last 30 years. These adsorbed monolayers were thought to be physical realizations of two-dimensional matter. Experimentalists wanted to determine to which extend the physical properties and the phase transitions in two dimensions were comparable to their bulk counterparts. The obtained results could be tested against theoretical predictions on the influence of reduced dimensionality on the physical behaviour of matter. In addition, the influence of the surface potential on the structure, dynamics and phase transitions could be comprehensily studied. A lot of results have been obtained so far and the major part of them have been reviewed or collected in proceedings [1-10]. This chapter reviews the thermodynamics, the structure, the thermal vibrations and the kinetics of adsorption of the noble gases condensed in the monolayer range on the basal planes of graphite, BN and lamellar halides, and on the (100) surface of MgO and NaCl.

3.1.2.1 Thermodynamics The measurements have been performed on uniform powders by adsorption volumetry [6], or calorimetry [1], or on single crystal surfaces by Auger spectroscopy [11], LEED [9,12] and ellipsometry [13]. 3.1.2.1.1 Rare gases adsorbed on graphite (0001) 3.1.2.1.1.1 Xenon on graphite The two-dimensional phase diagram of the monolayer of Xe adsorbed on graphite is displayed in Figs. 1 [6,8,14] and 2 [11,15,16] in two usual representations, coverage θ vs. pressure and pressure vs. T−1. Fig. 2 extends the data of Fig. 1 to lower pressures and temperatures and allows the presentation of the second layer formation and of the bulk sublimation curve, as well. The phase diagram exhibits 2D gas, liquid and solid phase coexistence, i.e. first order phase transitions between gas ↔ solid, gas ↔ liquid, and liquid ↔ solid. The corresponding triple point Tt and critical temperature Tc are Tt = 99 ± 1K and Tc = 117 ± 1K, respectively (see Table I). The liquid-solid phase transition study has been extended to higher temperatures [17-21]. There is still a debate to know whether the first order transition becomes continuous above a tricritical temperature located between 125 and 150K. From the Arrhenius plots (Fig. 2), the isosteric heats of adsorption can be measured. Their values can be found in Ref. 14 and 15 and in Table II. 3.1.2.1.1.2 Krypton on graphite Many papers and discussions [14,22-36] were devoted to determination of the phase diagram of the first monolayer of Kr adsorbed on graphite. It is now well accepted that there is no liquid-gas coexistence domain in this diagram. The surface corrugation of graphite with respect to krypton has such a large effect that it stabilizes the 2D solid to high temperatures and does not allow any clear distinction between gas and liquid. It is said that the system has an incipient triple point. The phase diagram is represented in Figs. 3 and 4. It also exhibits a tricritical point at about 115K. The surface corrugation also induces structural effect like the commensurate-incommensurate transition and rotational epitaxy (see paragraph II). The values of the isosteric heats of adsorption for this system can be found in Ref. 14 and in Table II.

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3.1.2.1.1.3 Argon on graphite The phase diagram of the adsorbed monolayer of Ar/graphite is displayed in Fig. 5 and 6 in the coverage temperature and log p – T−1 variables respectively. It has been drawn from the combinaison of thermodynamics and scattering experiments [37-47] ; it has 2D gas, liquid and incommensurate hexagonal solid phases. There is a triple point at Tt = 49.7K according to Ref. 45 or at 47K according to Ref. 42, and a critical point at Tc = 59 or 55K according to Ref. 22 and 42, respectively. The melting is either weakly first order [42] or continuous [44] ; the liquid phase is a strongly correlated fluid close to the melting temperature ; it becomes an isotropic liquid at higher T [46].

3.1.2.1.1.4 Neon on graphite A phase diagram collecting all the thermodynamic information on the neon/graphite system [48-57] is shown in Fig. 7. Coexistence in the monolayer range between liquid-solid, liquid-gas and solid-gas has been observed ; the triple point Tt is 13.6K and the critical temperature Tc is 15.8K. 3.1.2.1.1.5 Rare gas mixtures on graphite A few studies have been devoted to the co-adsorption of different rare gases on graphite. They are reported in paragraph II.5 below.

3.1.2.1.1.6 Helium on graphite The monolayer adsorption of 4He and 3He on graphite has been reviewed comprehensibly in several monographs [1,10].

3.1.2.1.2 Rare gases on BN The hexagonal boron nitride has been used as a substrate for the adsorption of Kr and Xe. The surface of its basal plane displays the same hexagonal structure than graphite with a lattice parameter difference of 2%. The published data are scarce [58,59] ; they were obtained by volumetric adsorption isotherm measurements. The critical temperatures for Kr and Xe and the triple point for Xe are reported in Table I. The heat of adsorption can be found in Ref. 59 and in Table II.

3.1.2.1.3 Rare gases on lamellar halide surfaces One of the major questions raised in the study of two-dimensional phase transitions in adsorbed layers was to check the validity of the corresponding state law for van der Waals, i.e. rare gases interactions. This law is fairly well obeyed for rare gases adsorbed on graphite [22]. It was tempting to determine the influence on the reduced 2D critical temperatures of the corrugation potential and of the lattice parameter of the surface, as well. A set of measurements have been carried out on the (111) surface of lamellar halides like CoCl2, CoBr2, FeCl2, NiCl2, CdCl2 [60-63]. They are reported in Fig. 8. The results show that the localization of the inert gases on the substrate potential wells (dimensional incompatibility zero) stabilizes the layer above the theoretical reduced critical temperature T2c/T3c = 0.38. Conversely the corresponding state law is well obeyed when the lattice misfit is large or small. In that case, the rare gas atoms can experience an "average" interaction potential.

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3.1.2.1.4 Rare gases on MgO(100) and NaCl(100) A major stimulus to recent studies of physical adsorption on ionic crystals has been the desire to examine the frustration resulting from the competition between the square symmetry of their (100) surface and the natural hexagonal packing of the rare gases ; new universality classes could be accessible for the square two-dimensional lattice [64]. The phase diagram of the first layer of Xe, Kr and Ar adsorbed on MgO(100) has been measured by adsorption volumetry [64,65]. Phase coexistence has been observed and the corresponding triple points and critical temperatures have been determined. They are collected in Table I. The phase diagram are represented in Fig. 9, 10, 11 for Xe, Kr and Ar/MgO, respectively. The heat of adsorption can be found in Ref. 64-68 and in Table II. A first order two-dimensional gas

→ ←

solid phase transition has also been observed in the monolayer of

the Xe/NaCl(100) system [69].

3.1.2.2 Structure Physical adsorption includes a range of phenomena in the monolayer regime which arise from the competition between the adsorbate-adsorbate and adsorbate-substrate interactions. Depending on the relative strength of these interactions and on temperature and chemical potential, the rare gases structure can be either commensurate or incommensurate with the graphite substrate. The incommensurate solid can be a floating 2D crystal, or a striped or hexagonal phase ; it can exhibit either static distortion waves and orientational epitaxy at small misfit or domain-walls at larger dimensional incompatibility. There are examples where the domain-walls are mobile ; they stabilize a domain-wall fluid, also called a reentrant fluid. At high temperature, the substrate induces strong correlation in the adsorbate fluid. More details on the theory of these fascinating surface phase can be found, for instance, in Ref. 10 (see also "Zeppenfeld" for the incommensurate-commensurate transition in rare gas layers adsorbed on metals).

3.1.2.2.1 Xenon on graphite The various hexagonal structures measured by different diffraction techniques [16,20,34,70-79] have been reviewed in Ref. 10 (p. 218-220). In brief, the monolayer of Xe/graphite condenses in the major part of the solid phase diagram in a hexagonal incommensurate structure exhibiting an orientational alignment depending on lattice misfit (Fig. 12) ; the commensurate ¥[¥ ODWWLFH LV UHDFKHG MXVW EHIRUH WKH VHFRQG layer condensation. At melting, the dense fluid exhibits strong orientational and positional correlations.

3.1.2.2.2 Krypton on graphite The structure of the adsorbed monolayer is dominated by effects of the substrate corrugation which imposes a commensurate solid in a large part of the phase diagram. A commensurate-incommensurate transition is observed ; it is associated at low and medium temperature to an orientational epitaxy of the layer (see Fig. 12). At higher temperature, the commensurate and incommensurate regions are separated by a domain-wall fluid [25-30, 80-81].

3.1.2.2.3 Argon on graphite The monolayer of solid argon is hexagonal incommensurate. Its lattice parameter varies with temperature and coverage ; furthermore, the layer exhibits an epitaxial alignment which depends on lattice misfit as represented in Fig. 12. This was the first example in which the predicted Novaco-McTague orientational alignment [83] was observed for the first time [47]. Just above the monolayer melting, the liquid is a strongly correlated fluid [41,43-45,47,82]. Landolt-Börnstein New Series III/42A1

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3.1.2.2.4 Neon on graphite The solid layer at low temperature has a ¥[¥ 5ƒ KLJKHU RUGHU an important (12-13°) orientational alignment is observed [54-56].

VXSHUODWWLFH $W KLJKHU WHPSHUDWXUH

3.1.2.2.5 Rare gas mixtures on graphite The introduction of Xe in a layer of Kr stabilizes the ¥[¥ FRPPHQVXUDWH VWUXFWXUH >@ 7KH DQDO\VLV RI the corresponding binary phase diagram shows a first order transition between the commensurate and incommensurate solids [85,86]. Mixtures of Ar and Xe exhibit a large tendency to form commensurate alloys [87]. A first order commensurate-incommensurate phase transition is also observed in that case. Although outside the scope of this review, interesting features have been found in the study of mixed layers of one rare gas and another gas. For instance, Ar + CO [88,89] and Ar + N2 [89] mixtures exhibit pinwheel and herringbone structures; on the other hand, displacement transitions have been observed in Kr + SF6 [90], Xe + SF6 [91], Kr + C6H12 [92,93,95], Kr + CCl4 [94,95], Kr + CH4 [96], Xe + CH2Cl2 [97], Kr + CH2Cl2 [98] mixtures. 3.1.2.2.6 Rare gas on lamellar halides A few diffraction studies have been performed on the rare gas monolayers adsorbed on graphite ; they are devoted to the Kr/NiCl2 and Xe/NiCl2 systems [62]. The observed structure is hexagonal incommensurate.

3.1.2.2.7 Rare gases on MgO(100) and NaCl(100) The argon and krypton monolayers adsorbed on MgO(100) exhibit typical frustration phenomenon induced by the troughs along the [110] Mg ions rows on the MgO surface [67]. This frustration leads for argon to a 2x3 lattice which evolves to a pseudo-hexagonal incommensurate structure at monolayer completion [65-67]. An interesting feature is observed for the 2x3 structure when its temperature is raised; a unidirectional order-disorder transition is measured both by neutron diffraction [65] and quasielastic neutron scattering [99]. The krypton layer displays a coexistence between a 2xn and a hexagonal incommensurate phase [67,68,100]. The solid layer of Xe/NaCl(100) is hexagonal incommensurate [101].

3.1.2.3 Influence of structural defects 3.1.2.3.1 Thermodynamics and phase transitions The shape of adsorption isotherms measured on lamellar halides [102], on graphite [103] and on NaCl [101] strongly depends on surface homogeneity. Poor substrates exhibit broad distributions of adsorption energies whereas uniform surfaces allow the observation of step wise isotherms. The steps are clear signatures of first order two-dimensional phase transitions [6,8,14].

3.1.2.3.2 Structure Few adsorption studies have been devoted to surface with controlled defects. A typical example relates the influence of atomic steps on the adsorbate structure [101]. Vicinal (610) NaCl surfaces have been used as a substrate. Heterogeneities do not modify the lateral structure of the two-dimensional solid xenon which remains hexagonal close-packed, but they reduce the size of the two-dimensional crystallites.

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3.1.2.4 Vibrations Only a few lattice dynamics studies have been carried out on rare gases adsorbed on lamellar compounds or on MgO. To our best knowledge, the only adsorbate studied so far was Ar. The experiments took advantage of the large neutron cross section of the 36Ar isotope. The phonon density of states of Ar adsorbed on graphite has been measured by inelastic neutron scattering [43,54]. Transverse and longitudinal in-plane modes and one out-of-plane mode were observed. The same kind of experiments was performed for the two structures (2x3 and hexagonal) of 36Ar adsorbed on MgO(100) [99]. The measured density of states is different for the two atomic arrangements as shown in Fig. 13 and 14 ; they correspond to in-plane and out-of-plane modes. The all set of experimental results has been used to test the accuracy of the interaction potentials [43,54,99].

3.1.2.5 Kinetics of adsorption and desorption Three regimes of condensation, previously observed in thermodynamics measurements (paragraph I.1.1), have been measured in the adsorption of a submonolayer of xenon adsorbed on graphite [104]. The first one corresponds to the condensation or evaporation of a two-dimensional (2D) "gas", the second one to the growth of 2D crystal in the presence of the 2D gas, and the third one to the completion of the 2D crystal on the (0001) graphite face. Zero order kinetics for both adsorption and desorption is found in the large range of coverage (0.3 < 0 < 0.9) where the two phases coexist on the surface. The activation energy of desorption of the 2D crystal is measured ; its value (~ 6 kcal mole−1) is in fair agreement with the value of the latent heat of evaporation of this phase (5.5 or 5.7 kcal mole−1) determined previously. The interpretation of this zeroth order surface kinetics can be understood as due to the coexistence of twodimensional gas and islands and to a very rapid exchange between the atoms in the gas and those of the island edges [105,106]. Table I. Twodimensional triple points Tt and critical temperatures Tc of the first layer of noble gases adsorbed on graphite, BN and MgO.

Tt Tc

Tt Tc

Xe/graphite

Kr/graphite

Ar/graphite

Ne/graphite

99 ± 1 117 ± 1

incipient triple point

47 - 50K 55 - 59K

13.6 15.8

Xe/BN

Kr/BN

Xe/MgO

Kr/MgO

Ar/MgO

87

101 ± 1 119 ± 2

67 ± 1 87 ± 2

38 ± 2 63 ± 2

102 119

Table II Isosteric heat of adsorption in kcal mole−1 of rare gases adsorbed on graphite, BN and MgO in the monolayer range.

solid-gas liquid-gas

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Kr/BN

Xe/Mgo

5.5 5.1

3.4

3.67 (65) 2.74 (65) 2.0

(15) (14)

4.0

Kr/MgO

Ar/MgO

(59) 4.4

(59)

(59)

(65)

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Figures for 3.1.2

Xe/graphite

B1

1.0

D'1

D'1

L

Coverage θ

0.8

+S

S A'1

L

D1

0.6 G +S

0.4

G

0.2

8 10

–4

+L G

A1

0 –5 4⋅10 6

Fig. 1. Phase diagram showing the evolution of xenon adsorption isotherms between 97 and 117 K on a homogeneous graphite surface (from Ref. 6). G: twodimensional gas; L: twodimensional liquid; S: twodimensional solid.

A1 2

4

6

–3

8 10 2 4 6 Vapor pressure p [Torr]

–2 8 10

2

4

6

–1 810

–3

10

"liquid 2D" 1st layer

crystal 3D

–4

10

transition

1st layer

2nd layer

–5

Vapor pressure pXe [Torr]

10

crystal 2D 1st layer

–6

10

"gas 2D" 1st layer

–7

10

Fig. 2. Logarithm of the threedimensional pressure of xenon of the first and second layer adsorbed graphite vs. reciprocal temperature (from Ref. 15).

–8

10

–9

10

9

11

13 15 –1 –3 –1 Inv. temperature T [10 K ]

17

19

Landolt-Börnstein New Series III/42A1

3.1.2 Noble gases on graphite, lamellar halides, MgO and NaCl

2.00 1.75 1.50 Fractional coverage θ

2c

IC

A2

2b

1.25

A1

1.00

2a

C2

–16

C1

–17

B7

C

F

IC

L

–22

70

80

1.2

90 100 110 Temperature T [K]

120

130

140

–23 70

F

G 80

90

100 110 120 Temperature T [K]

130

140

150

Fig. 4. Reentrant fluid of Kr/graphite. High T region of the Kr/graphite phase diagram (from Ref. 30). The reentrant fluid (RF) phase is a domain wall fluid bounded by commensurate (C) and incommensurate (IC) regimes. S(23D) and L(3D) are the bulk solid and liquid phases. Solid lines denote first-order transitions and dashed lines denote continuous transitions.

S

1.0

Fractional coverage θ

RF

C

–21

Fig. 3. Phase diagram of Kr/graphite, in the monolayer regime, in terms of fractional coverage and temperature (from Ref. 24). C, F and IC denote commensurate, fluid, and incommensurate phases, respectively. Dashes indicate paths of specific heat scans. There is a tricritical point at the extrapolated intersection of the IC to C + F and C to F boundaries and a multicritical point at C1.

0.8 S+V

L+V

0.6 F

0.4 0.2 0 40

IC-A

–20

C+F

L(3D)

IC-R

–19

B6

0.25 0 60

S(3D)

–18

0.75 0.50

123

–15

2d

Chemical potential µ [102 K]

Ref. p. 128]

45

Landolt-Börnstein New Series III/42A1

50 55 60 Temperature T [K]

65

70

Fig. 5. Proposed phase diagram of Ar on graphite. S, L, V and F represent, respectively, solid, liquid, vapor and fluid phases. Solid circles near 55 K at submonolayer coverages correspond to positions of heat-capacity anomaly arising from liquid-vapor transition. Other circles are signatures of melting. Dashed lines are speculative. At submonolayer coverages, Ar solid melts via a weak first-order transition at a triple-point temperature (47.2 K) to a liquid-vapor coexistence region. The liquid phase appears to be orientationally ordered below 54 K. The positions of the broad anomalies centering near 49.5 K, due to the gradual decrease of this order, are not shown. Unless indicated otherwise, the uncertainty in the peak position of the heat-capacity anomalies is comparable to or smaller than the size of the circles (from Ref. 42).

124

3.1.2 Noble gases on graphite, lamellar halides, MgO and NaCl

2

10

[Ref. p. 128

0.55

two or more layers

10

0.50

d

c

–2

Crit. temperature ratio T2C / T3C

Vapor pressure p [Torr]

1

b a

–4

10

0.45

2D solid monolayer

2D gas

–6

10

3.78 Å

Ar Kr Xe

0.40

–8

10

12

16

20 24 28 –1 –3 –1 Inv. temperature T [10 K ]

0.20 – 0.25

32

4

10

Temperature T [K] 22 18 20

26 25 24 3D liquid

Tt

16

1.5

0.25

15

Neon/graphite

3D solid

Parameter: coverage in ml

2

10

– 0.05 0.0.5 0.15 Dimensional incompatibility

Fig. 8. 2D critical temperatures as a function of misfit. Ratio of 2D to 3D critical temperatures for Ar, Kr and Xe on various lamellar halide surfaces (from Ref. 63). The dimensional incompatibility is the excess above one of the ratio of the spacing between neighboring anions of the substrate and the interatomic spacing of the (111) plane of the bulk adsorbate.

Fig. 6. Phase diagram of Ar/graphite (from Ref. 41).

30 28

– 0.15

2D critical point in second layer

1.0

Vapor pressure p [Torr]

10 0.75 0.88

–2

10

1.0

1.5

0.5 0.813

–4

10

2D hypercritical fluid

2D rotated incommensurate solid

–6

10

0.767

2D –8

10

3.0

3.5

4.0

Tc = 15.80 K Tt = 13.57 K

4.5 5.0 5.5 6.0 –1 –2 –1 Inv. temperature T [10 K ]

6.5

7.0

Fig. 7. Phase diagram of Ne/graphite (from Ref. 56). Not shown are the ¥ RUGHUHG SKDVH DW lower T and the 2D critical and triple points, which occur at pressures that are too low to measure; the corresponding temperatures are indicated, however.

Landolt-Börnstein New Series III/42A1

Ref. p. 128]

3.1.2 Noble gases on graphite, lamellar halides, MgO and NaCl

2

10

60 40

Xe/MgO

20 6 4

bulk

2

fluid

18

Tc(2D)

6 4 2

sub vapor

–1

10

Vapor pressure p [Torr]

Vapor pressure p [Torr]

8 6 4

Kr/MgO

2

10

10 8

8 6 4

second solid

first

75

85 90 95 100 –1 –4 –1 Inv. temperature T [10 K ]

105

Fig. 9. Arrhenius plot diagram showing features for vapor pressure of 3D Xe. Various monolayer critical and triple points are shown (from Ref. 64).

1 (2D) dense phase A

10–1

bulk

2

1

8 6 4

fluid

Tc(2D)

sub solid

vapor first

10 –3 6⋅10 10

Tt(2D)

11

15

13 14 12 –1 –3 –1 Inv. temperature T [10 K ]

Fig. 10. P vs 1/T diagram for Kr/MgO and vapor pressure of 3D Kr. The monolayer critical and triple points and various adsorbed phases are indicated (from Ref. 64).

3.0°

Ar/MgO

2.5°

(2D) dense phase B

Ar

2.0°

Rotation angle ϕ

h.c.p. solid

10–2

second

2 –2

Tt(2D) 80

8 6 4

2 –1 10 8 6 4

–2

2⋅10

Vapor pressure p [Torr]

125

1.5°

–3

10

Kr

1.0°

10–4 10–5 14

Xe

(2D) gas 0.5°

16

18 20 22 24 –1 –3 –1 Inv. temperature T [10 K ]

26

28

Fig.11. Clapeyron lines representing the pressure dependence of the two (2d) transitions, (2d) gas ⇔ (2d) dense phase A and (2d) dense phase A ⇔ (2d) dense phase B, vs. 1/T. The intersection of the two lines defines the triple point temperature T2t ; T2t = 38 ± 2 K (neutron diffraction results show that the dense phases A and B are, respectively, a (2d) "liquid crystal" like phase and a h.c.p. (2d) solid) (from Ref. 65).

Landolt-Börnstein New Series III/42A1

0°

2

3

4

5 Misfit [%]

6

7

8

Fig. 12. Epitaxial orientation. Rotation angle as a function of fractional misfit for Ar, Kr and Xe on graphite (from Ref. 10). The angle shown is the increment from the 30° axis of the graphite. The misfits are negative for Ar and Kr and positive for Xe.

126

3.1.2 Noble gases on graphite, lamellar halides, MgO and NaCl

[Ref. p. 128

500 450 400

INS intensity [counts]

350 300 b

250 200 150 × 0.1

100 50 a

0 – 6.0

– 4.5

– 3.0

–1.5

0 1.5 Energy [meV]

3.0

4.5

6.0

Fig. 13. Inelastic neutron-scattering spectra of 36Ar/MgO(100) at 10 K. (a) Experimental spectra at incident energy of 7 meV for a 1.16 layer (hexagonal structure); the vertical bars and the triangle represent experimental errors and the experimental broadening (reduced by a factor of 1/10), respectively; (b) calculated spectrum for the hexagonal incommensurate structure after convoluting with the instrumental line shape of 0.3 meV at a neutron gain of 5 meV. Units are arbitrary and the baseline is shifted with respect to curve (a) (from Ref. 99).

Landolt-Börnstein New Series III/42A1

Ref. p. 128]

3.1.2 Noble gases on graphite, lamellar halides, MgO and NaCl

1000.0 937.5 875.0 812.5 750.0 687.5

INS intensity [counts]

625.0 562.5 c

500.0 437.5 375.0 312.5

b

250.0 187.5 125.0 62.5

a

× 0.03

0 – 6.0

– 4.5

– 3.0

–1.5

0 1.5 Energy E [meV]

3.0

4.5

6.0

Fig. 14. Inelastic neutron-scattering spectra of 36Ar/MgO(100) at 10 K. (a) Experimental spectra at incident energy of 7 meV for a 0.8 layer 2x3 structure; note the difference between the experimental errors (vertical bars) in the gain and the loss energy ranges; the triangle represents the experimental line shape reduced by a factor of 1/30. (b) Calculated spectrum for the 2x3 structure, in arbitrary units, after convoluting with the instrumental resolution of 0.3 meV at a neutron gain of 5 meV. (c) Calculated spectrum without broadening. The width of the peaks is due to the numerical step in the calculation of the dispersion branches. Baselines of curves (b) and (c) are shifted with respect to curve (a) (from Ref. 99).

Landolt-Börnstein New Series III/42A1

127

128

3.1.2 Noble gases on graphite, lamellar halides, MgO and NaCl

References for 3.1.2 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40

Dash, J.G.: Films on Solid Surfaces. New York: Academic Press, 1975. Phases bidimensionnelles adsorbées. Bienfait, M., Suzanne, J. (eds.): J. Phys. (Paris) Colloq. 10 C4 (1977). Phase transitions in Surface Films, NATO-ASI-BSI. Dash, J.G., Ruvalds, J. (eds.), New York: Plenum, 1980. Bienfait, M., in: Current Topics in Materials Science, Vol. 4. Kaldis, E. (ed:), Amsterdam: North-Holland, 1980, p. 361. Proceedings of the Intern. Conf. on Ordering in Two Dimensions, Lake Geneva, Wisconsin. Sinha, S.K. (ed.), Amsterdam: North-Holland, 1980. Thomy, A., Duval, X., Regnier, J.: Surf. Sci. Rep. 1, 1 (1981). Phase transitions in Surface Films 2, NATO-ASI, Vol. 267. Taub, H., Torzo, G., Lauter, H.J., Fain, S. (eds.), New York: Plenum, 1991. Thomy, A., Duval, X.: Surf. Sci. 299/300 (1994) 415. Suzanne, J., Gay, J.M.: The structure of physically adsorbed phases in Handbook of Surface Science, Vol. 1, chap. 10. Unertl, W.N. (ed.), Elsevier, 1996, p. 503. Bruch, L.W., Cole, M.W., Zaremba, E.: Physical Adsorption: Forces and Phenomena, Oxford Science Publ. 1997. Suzanne, J., Coulomb, J.P., Bienfait, M.: Surf. Sci. 40 (1973) 414; 44 (1974) 141. Calisti, S., Suzanne, J., Venables, J.A.: Surf. Sci. 115 (1982) 455. Quentel, G., Rickard, J.M., Kern, R.: Surf. Sci. 50 (1975) 343. Thomy, A., Duval, X.J.: Chim. Phys. 67 (1970) 1101. Suzanne, J., Coulomb, J.P., Bienfait, M.: Surf. Sci. 47 (1975) 204. Hamichi, M., Faisal, A.Q.D., Venables, J.A., Kariotis, R.: Phys. Rev. B 39 (1989) 415. Colella, N.J., Suter, R.M.: Phys. Rev. B 34 (1986) 2052. Gangwar, R., Colella, N.J., Suter, R.M.: Phys. Rev. B 39 (1989) 2459. Jin, A.J., Bjurstrom, M.R., Chan, M.H.W.: Phys. Rev. Lett. 62 (1989) 1372. Dimon, P., Horn, P.M., Sutton, M., Birgeneau, R.J., Moncton, D.E.: Phys. Rev. B 31 (1985) 437. Nuttal, W.J., Noh, D.Y., Wells, B.O., Birgeneau, R.J.: J. Phys. Condens. Matter 7 (1995) 4337. Larher, Y., Gilquin, B.: Phys. Rev. A 20 (1979) 1599. Larher, Y.: J. Chem. Soc. Faraday Trans. I 70 (1974) 320. Butler, D.M., Litzinger, J.A., Stewart, G.A., Griffiths, R.B.: Phys. Rev. Lett. 42 (1979) 1289; Butler, D.M., Litzinger, J.M., Stewart, G.A.: Phys. Rev. Lett. 44 (1980) 466. Kramer, H.M., Suzanne, J.: Surf. Sci. 54 (1976) 659. Chinn, M.D., Fain, S.C.: Phys. Rev. Lett. 39 (1977) 146. Price, G.L., Venables, J.A.: Surf. Sci. 59 (1976) 509. Fain, S.C., Chinn, M.D., Diehl, R.D.: Phys. Rev. B 21 (1980) 4170. Suter, R.M., Colella, N.J., Gangwar, R.: Phys. Rev. B 31 (1985) 627. Specht, E.D., Mak, A., Peters, C., Sutton, M., Birgeneau, R.J., D'Amico, K.L., Moncton, D.E., Nagler, S.E., Horn, P.M.: Z. Phys. 69 (1987) 346. Migone, A.D., Chan, M.H.W., Niskanen, K.J., Griffiths, R.B.: Journal of Physics 16 (1983) L.1115. Niskanen, K.J., Griffiths, R.B.: Phys. Rev. B 32 (1985) 5858. Larher, Y., Terlain, A.: J. Chem. Phys. 72 (1980) 1052. Schabes-Retchkiman, P.S., Venables, J.A.: Surf. Sci. 105 (1981) 536. Guryan, C.A., Lee, K.B., Stephens, P.W., Goldman, A.I., Larese, J.Z., Heiney P.A., Fontes, E.: Phys. Rev. B 37 (1988) 3461. Chung, S., Kara, A., Larese, J.Z., Leung, W.Y., Frankl, D.R.: Phys. Rev. B 35 (1987) 4870. Rouquerol, J., Partyka, J., Rouquerol, F.: J. Chem. Soc. Faraday Trans. I 73 (1977) 306. Lahrer, Y.: J. Chem. Phys. 68 (1978) 2257; Surf. Sci. 134 (1983) 469. Prenzlow, C.F., Halsey, G.D.: J. Phys. Chem. 61 (1957) 1158. Millot, F.: J. Phys. (Paris) Lett. 40 (1979) L 9.

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3.1.2 Noble gases on graphite, lamellar halides, MgO and NaCl 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74

75 76 77 78 79 80 81 82

129

Shaw, C.G., Fain, S.C.: Surf. Sci. 83 (1979) 1; Surf. Sci 91 (1980) L 1. Migone, A.D., Li, Z.R., Chan, M.H.W.: Phys. Rev. Lett. 53 (1984) 810. Taub, H., Carneiro, K., Kjems, J.K., Passell, L., McTague, J.P.: Phys. Rev. B 16 (1977) 4551. Nielsen, M., Als-Nielsen, J., Bohr, J., McTague, J.P., Moncton, D.E., Stephens, P.W.: Phys. Rev. B 35 (1987) 1419. D'Amico, K.L., Bohr, J., Moncton, D.E., Gibbs, D.: Phys. Rev. B 41 (1990) 4368. Zhang, Q.M., Larese, J.Z.: Phys. Rev. B 43 (1991) 938. Shaw, C.G., Fain, S.C., Chinn, M.D.: Phys. Rev. Lett. 41 (1978) 955. Thomy, A., Duval, X., Regnier, J.: C. R. Acad. Sci. (Paris) C268 (1969) 1416. Lerner, E., Hedge, S.G., Daunt, J.G.: Phys. Lett. 41A (1972) 239. Huff, G.B., Dash, J.G. J.: Low Temp. Phys. 24 (1976) 155. Antoniou, A.A.: J. Chem. Phys. 64 (1976) 4901. Lerner, E., Hanono, F.: J. Low Temp. Phys. 35 (1979) 363. Rapp, R.E., de Souza, E.P., Lerner, E.: Phys. Rev. B 24 (1981) 2196. Tiby C., Lauter, H.J.: Surf. Sci. 117 (1982) 277. Calisti, S., Suzanne, J.: Surf. Sci. 105 (1981) L255. Calisti, S., Suzanne, J., Venables, J.A.: Surf. Sci. 115 (1982) 68. Demetrio de Souza, J.L.M., Rapp., R.E., de Souza, E.P., Lerner, E.: J. Low Temp. Phys. 55 (1984) 273. Régnier, J., Thomy, A., Duval, X.: J. Colloid Interface Sci. 70 (1979) 105. Dupont-Pavlovsky, N., Bockel, C., Thomy, A.: Surf. Sci. 160 (1985) 12. Teissier, C., Larher, Y., in: Ordering in Two-dimensions. Sinha, S.K. (ed.), New-York: NorthHolland, 1980, p. 163. Nardon, Y., Larher, Y.: Surf. Sci. 42 (1974) 299. Morishige, K., Hanayama, M., Kittaka, S.: J. Chem. Phys. 88 (1988) 451. Millot, F., Larher, Y., Tessier, C.: J. Chem. Phys. 76 (1982) 3327. Coulomb, J.P., Sullivan, T.S., Vilches, O.E.: Phys. Rev. B 30 (1984) 4753. Coulomb, J.P.: in Ref. 7, p. 113. Meichel, T., Suzanne, J., Gay, J.M.: C. R. Acad. Sci. Paris 303 (1986) 989. Meichel, T., Suzanne, J., Girard, C., Girardet, C.: Phys. Rev. B 38 (1988) 3781. Angot, T., Suzanne, J., in: The Structure of Surfaces III. Tong, S.Y., Van Hove, M.A., Takayanagi, K., Xie, X.D. (eds.), Springer Series Surf. Sci. 24. Berlin: Springer-Verlag, p. 671. Glachant, A., Bardi, U.: Surf. Sci. 87 (1979) 187. Hong, H., Peters, C.J., Mak, A., Birgeneau, R.J., Horn, P.M., Suematsu, H.: Phys. Rev.B 40 (1989) 4797. Nuttall, W.J., Fahey, K.P., Young, M.J., Keimer, B., Birgeneau, R.J., Suematsu, H.: J. Phys. Condens. Matter 5 (1993) 8159. Faisal, A.Q.D., Hamichi, M., Raynerd, G., Venables, J.A.: Phys. Rev. B 34 (1986) 7440. Hammonds, E.M., Heiney, P.A., Stephens, P.W., Birgeneau, R.J., Horn, P.M.: J. Phys. C 13 (1980) L 301. Heiney, P.A., Stephens, P.W., Birgeneau, R.J., Horn, P.M., Moncton, D.E.: Phys. Rev.B 28 (1983) 6416; Nagler, S.E., Horn, P.M., Rosenbaum, T.F., Birgeneau, R.J., Sutton, M., Mochrie, S.G.J., Moncton, D.E., Clarke, R.: Phys. Rev. B 32 (1985) 7373. Zerrouk, T.E.A., Hamichi, M., Pilkington, J.D.H., Venables, J.A.: Phys. Rev. B 50 (1994) 8946. Nuttall, W.J., Noh, D.Y., Wells, B.O., Birgeneau, R.J.: Surf. Sci. 307-309 (1994) 768. Mowforth, C.W., Rayment, T., Thomas, R.K.: Faraday Symp. Chem. Soc. 20 (1985). Ellis, T.H., Iannotta, S., Scoles, G., Valbusa, U.: Phys. Rev. B 24 (1981) 2307; Bracco, G., Cantini, P., Glachant, A., Tatarek, R.: Surf. Sci. 125 (1983) L 81. Grimm, B., Hövel, H., Pollmann, M., Reihl, B.: Phys. Rev. Lett. 83 (1999) 991. D'Amico, K.L., Moncton, D.E., Specht, E.D., Birgeneau, R.J., Nagler, S.E., Horn, P.M.: Phys. Rev. Lett. 53 (1984) 2250. Stephens, P.M., Heiney, P.A., Birgeneau, R.J., Horn, P.M., Moncton, D.E., Brown, G.S.: Phys. Rev. B 29 (1984) 3512. Tiby, C., Lauter, H.J.: Surf. Sci. 117 (1982) 277.

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130 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106

3.1.2 Noble gases on graphite, lamellar halides, MgO and NaCl Novaco, A.D., McTague, J.P.: Phys. Rev. Lett. 38 (1977) 1286; J. Phys. (Paris) Colloq. 38 C4-116. Régnier, J., Bockel, C., Dupont-Pavlovsky, N.: Surf. Sci. 112 (1981) L770. Ceva, T., Goldmann, M., Marti, C.: J. Phys. (Paris) 47 (1986) 1527. Stephens, P.W., Goldman, A.I., Heiney, P.A., Bancel, P.A.: Phys. Rev. B 33 (1986) 655. Bohr, J., Nielsen, M., Als-Nielsen, J., Kjaer, K., McTague, J.P.: Surf. Sci. 125 (1983) 181. You, H., Fain, S.C.: Phys. Rev. B 34 (1986) 2840. You, H., Fain, S.C., Satija, S., Passell, L.: Phys. Rev. Lett. 56 (1986) 244. Bouchdoug, M., Menaucourt, J., Thomy, A.: J. Phys. (Paris) 47 (1986) 1797. Menaucourt, J., Bockel, C.: J. Phys. (Paris) 51 (1990) 1987. Razafitianamaharavo, A., Convert, P., Coulomb, J.P., Croset, B., Dupont-Pavlovsky, N.: J. Phys. (Paris) 51 (1990) 1961. Razafitianamaharavo, A., Dupont-Pavlovsky, N., Thomy, A.: J. Phys. (Paris) 51 (1990) 91. Abdelmoula, M., Ceva, T., Croset, B., Dupont-Pavlovsky, N.: Surf. Sci. 272 (1992) 167. Dupont-Pavlovsky, N., Abdelmoula, M., Rakotozafy, S., Coulomb, J.P., Croset, B., Ressouche, E.: Surf. Sci. 317 (1994) 388. Hamdi-Alaoui, M.A., Coulomb, J.P., Dupont-Pavlovsky, N., Mirebeau, I., Mutaftschiev, B.: Surf. Sci. 295 (1993) L1031. Rakotozafy, S., Dupont-Pavlovsky, N., Croset, B., Duval, X.: Surf. Sci. 350 (1996) 206. Madih-Ayadi, K., Dupont-Pavlovsky, N., Ceva, T., Convert, P., Croset, B., Ayadi, A.: Surf. Sci. 405 (1998) 192. Layet, J.M., Bienfait, M., Ramseyer, C., Hoang, P.N.M., Girardet, C., Coddens, C.: Phys. Rev. B 48 (1993) 9045. Jordan, J.L., McTague, J.P., Hastings, J.B., Passell, L.: Surf. Sci. 150 (1985) L 82. Bardi, U., Glachant, A., Bienfait, M.: Surf. Sci. 97 (1980) 137. Bonnetain, L., Duval, X., Letort, M.: C. R. Acad. Sci. Paris 234 (1952) 1363. Duval, X., Thomy, A.: C. R. Acad. Sci. Paris 259 (1964) 4007. Bienfait, M., Venables, J.A.: Surf. Sci. 64 (1977) 425. Venables, J.A., Bienfait, M.: Surf. Sci. 61 (1976) 667. Opila, R., Gomer, R.: Surf. Sci. 112 (1981) 1.

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3.2.1 Alkali metals on metals

131

3.2 Adsorption of alkali metals

3.2.1 Alkali metals on metals R.D. DIEHL, R. McGRATH

3.2.1.1 Introduction The study of alkali metal adsorption on metal surfaces has been of interest in surface science for nearly 70 years, and there have been many reviews and monographs addressing different aspects of the subject [77B1, 82B1, 84N1, 84N2, 86B1, 89A1, 89B2, 89M1, 90C1, 91D1, 92K3, 93B1, 93N1, 93P2, 94B1, 94N1, 94N3, 94P1, 95A1, 95D1, 95F1, 95O1, 95S1, 96D1, 97D1, 98O2, 98T1, 99G2]. The interest in this topic is partly due to the importance of technological applications (promotion of catalytic reactions, enhancement of oxidation, increases in electron and ion emission rates, electrochemistry and battery production), but also due to the fundamental interest in how these “simple” adsorbates interact with each other, with coadsorbates and with the surface itself. Alkali atoms have a simple valence electronic structure (one single s electron) and hence are attractive systems to model using quantum mechanical calculations. The following table indicates some physical parameters for the alkali metals. Physical properties of alkali metals: Ionic radii Rion and metallic radii Rmet of alkali metals, in Å, their melting temperatures Tm, their ionization potentials (IP) and their nearest-neighbor (NN) distances in the bulk metals [86K1]. Metal

Rmet [Å]

Rion [Å]

Tm [K]

IP [eV]

NN [Å]

Li Na K Rb Cs

0.68 0.97 1.33 1.48 1.67

1.56 1.91 2.38 2.55 2.73

453.7 371.0 336.3 312.6 301.6

5.39 5.14 4.34 4.18 3.89

3.02 3.66 4.53 4.84 5.24

In this compilation we address several quantifiable aspects of alkali adsorption on metal surfaces encompassing electronic, thermodynamic, and structural results. After listing known physical properties of the bulk alkalis for reference, we start with one of the classic manifestations of alkali adsorption: the adsorbate-induced change in system work function. We tabulate the large number of studies of changes in work function as a function of adsorbed alkali coverage. We then tabulate the coverage dependence of energy losses due to alkali valence electron excitation measured using electronic energy loss spectroscopy (EELS). Finally, we list studies of occupied and unoccupied states close to the Fermi level. Next we turn to quantification of characteristic heats of adsorption of alkali atoms. In general these are coverage dependent so we list mainly the heat of adsorption at zero coverage. We then list coveragedependent values for alkali adatom vibrational mode energies which have been obtained using HREELS, HAS and LEED. Structural aspects of alkali adsorption account for the remainder of the chapter. Much excitement was generated in the early 1990's by the discovery of unexpected adsorption sites for alkalis on metal surfaces [96D1, 97D1]. After tabulating the known adsorption sites for simple structures we address several structural phenomena which have been observed with alkali adsorption systems: incommensurate overlayer rotation, monolayer compression relative to the bulk and condensation transitions at low coverages. Known temperature-coverage and isothermal phase diagrams are then presented. In recent

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132

[Ref. p. 169

years several alkali systems have been discovered where the alkali adatoms intermix with the substrate top layers. These are listed in the last section. Coadsorption of alkali atoms with other species, on which there is a vast literature (e.g. [86B1, 92K3, 93B1] and references therein), will not be considered in this chapter. The results of DFT calculations will not be considered here either. Throughout this chapter we consider the alkali coverage θalkali as the ratio of the number of alkali atoms to the number of substrate atoms in the first substrate layer, rather than considering the coverage in units of a saturated monolayer of alkali atoms. Acronyms used in the text DFT: ESDIAD: FE(M): HAS: (HR)EELS: IPES: IRAS: LEED: MDS: MEIS: NEXAFS: (NI)SXW: PhD: RHEED: SCLS: SEC(E/P): SEXAFS: STM: SXRD: TDS: UPS: VC:

Density-functional theory Electron-stimulated desorption ion-angular distribution Field emission (microscopy) Helium-atom scattering (High-resolution) electron energy-loss spectroscopy Inverse photoemission spectroscopy Infrared reflection absorption spectroscopy Low-energy electron diffraction Metastable deexcitation spectroscopy Medium-energy ion scattering Near-edge extended x-ray absorption fine structure (Normal incidence) standing x-ray wavefield absorption Photoelectron diffraction Reflection high-energy electron diffraction Surface core-level spectroscopy Secondary electron method (electron/photon) Surface extended x-ray-absorption fine structure Scanning tunneling microscopy Surface x-ray diffraction Thermal desorption spectroscopy Ultraviolet photoemission spectroscopy Vibrating capacitor

3.2.1.2 Adsorbed alkali metals: Data 3.2.1.2.1 Adsorption bonds The nature of the chemisorption bond formed when alkali metal atoms adsorb on metals has been a point of contention and much discussion [97D1]. The earliest measurements of alkali metal adsorption were of the large work function decrease which occurs when alkali metals are adsorbed on metal surfaces [23L1, 25L1, 29L1, 31L1, 32L1]. The early models of alkali metal chemisorption invoked some element of charge transfer from the alkali adatom to the metal substrate in order to explain this large decrease in work function [32L1, 35G1], although they did not quantitatively reproduce the experimental results. Later proposals were made to suggest that the decrease in work function might also be consistent with covalent bonding [88I1, 90R1, 94W3]. Many of these later discussions were based on the results of core-level photoemission studies. Some confusion in determining the nature of the alkali chemisorption bond arose from the difficulty in interpreting the core-level shifts which can be observed using high-resolution photoemission. It has now been established [93A2] that core-level photoemission cannot be used to directly probe the amount of charge transfer between the adsorbed alkali atoms and the substrate. The reason for this that the initial state and final state effects are entangled in core-level photoemission; there is no simple way to disentangle them to get the information on the initial-state properties. There are comparisons of the core-

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3.2.1 Alkali metals on metals

133

level shifts observed for the different alkali on the same substrate, notably for adsorption on Al(111) [93A2], but little if any quantitative information on the chemisorption bond itself has been obtained from these measurements. For these reasons we have not attempted to tabulate the results of core-level shift experiments in this work. Core-level photoemission results have provided extremely useful qualitative information regarding the adsorption geometries of adatoms, and much of this work is summarized in two reviews [93A2, 95A1]. The ensuing discussion of the issue of charge transfer provoked many experimental and theoretical studies of alkali metal adsorption. In the aftermath of this discussion, it is recognized that the picture of charge transfer is useful when discussing alkali metal adsorption, but that the terms "ionic" and “covalent” as used in molecular bonding may not be appropriate. Recent first-principles calculations have been carried out which quantitatively reproduce the work function measurements for Na adsorption on Al(100) and Al(111) [91S1, 94B2], and while they do indicate some degree of charge transfer, it is not possible to quantify the amount of charge transfer, nor to measure it directly. Work function measurements, however, give some quantitative comparison of the polarization induced in the different adsorption systems, while electron energy loss measurements provide information on how the chemisorption bond affects the electron states within the adatoms. 3.2.1.2.2 Work function changes Because they are highly electropositive, the adsorption of alkali metals causes large decreases in the work functions of surfaces. The adsorption of alkali metals onto metal surfaces causes a characteristic work function change: at low alkali coverage there is a sharp decrease in the system work-function, which goes through a minimum and then reaches a saturation value. This behavior is interpreted generally as being due to the large charge transfer per adatom at low coverages where the adatoms are essentially isolated from each other (thus decreasing the work function at low coverages), and a counteracting continual decrease in adatom polarization due to their mutual interaction as the density increases (thus increasing the work function at higher coverages) [89B2]. There has been a debate on whether the dipole moment reflects transfer of charge from the alkali to the metal surface or merely polarization within the alkali atom [93N2]. The characteristic work-function curve is illustrated in Fig. 1, which also defines the measured parameters. The initial dipole moment µ 0 can be evaluated from the work function curve. Defining the dipole moment as µ = q2d, where we approximate the dipole as point charges, 2d being the distance between the center of alkali charge and its image charge in the metal, then the change in work function is given by the Helmholtz equation: ∆φ = 2πµ(θ)θ where θ is the alkali coverage. Then µ 0 can be determined either by evaluating the initial slope of the curve:

µ=

1  d (∆φ )    2Œ  dθ  θ → 0

or by fitting the curve to the Topping/Miller formula [27T1, 46M1] ∆φ = 2πθ

µ0 1 + 9αθ 3 / 2

where α is the polarizability. Studies where the results have been analyzed using both methods show only very small variations in the numerical values obtained. The unit of µ 0 is the Debye (1 D = 3.33564x10−30 coulomb meter).

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134

[Ref. p. 169

As discussed by several authors [79H1, 89A1, 89W1] there is an inconsistency in the literature in the usage of µ. Some authors have defined µ = qd which leads to a difference of a factor of 2 in µ 0 from that considered here. The values presented in the following table have been corrected where necessary to satisfy the definition µ = q2d. The technique of photoemission of adsorbed xenon (PAX) has been used in a number of cases [86M1], [85M1, 89W1, 92J2] to address the question of the extent of the lateral electronic perturbation of the substrate around an absorbed alkali atom. By measuring Xe 5p1/2 core-level shifts of Xe atoms at, close to, or removed from the alkali adsorbate, the local change in surface potential (not local change in work function, see discussion in [89A1]) can be measured at these locations. These studies indicate a strong short-range variation in surface potential as a function of distance from the alkali. These results have not been tabulated in this chapter. The following tables summarize the results of experimental work function data. Tsub is the substrate temperature in K during deposition. RT denotes room temperature. The methods of work function measurement are: VC: Vibrating capacitor method; RP: Retarding potential method; SEC(E) and SEC(P): Electron- and photon-induced secondary electron method respectively; FE: Field emission method. ∆φmin is the work function change at the minimum, ∆φML is the work function change at one saturated monolayer. µ 0 is the initial dipole moment. Where * appears in the table, a minimum was not observed. The tables are adapted and updated from [89A1]. Experimental work function data for lithium. Substrate

T [K]

Method

∆φmin [eV]

∆φML [eV]

Ag(111) Al(111) Cu(001) Cu(111) Mo(211) Ni(100) Ru(0001) W(110) W(110) W(110) W(211) W(211) W(100) W(111)

RT 140 180 160 77 308

VC VC SEC(E) RP RP RP VC RP RP FE VC RP/FE VC VC

−1.86 * −2.1 −2.4 * −2.8 −3.5 −2.9 −2.8 −3.0 * * * *

−1.76 −3.22 −1.7 −1.85 −1.5 −2.5 −2.5 −1.9 −2.1 −2.3 −1.5 −1.5 −1.4 −1.4

300 77 77 300 77/300 300 300

µ0 [D]

2.0

4.9

Ref. [86P1] [89H2] [94M2] [96L1] [79G1] [88G1] [96E1, 98E1] [74M1] [74M1] [74M1] [74M1] [73M1] [74M1] [74M1]

Experimental work function data for sodium. Substrate

T [K]

Method

∆φmin [eV]

∆φML [eV]

Ag(100) Ag(110) Al(111) Al(111) Al(111) Al(100) Al(100) Al(100)

300

SEC(P) SEC(P) SEC(E) VC VC SEC(E) SEC(E) SEC(E)

* * * −2.85 −2.85 * −2.0 *

−2.4 −2.0 −1.6 −2.55 −2.77 −1.6 −1.6 −1.6

RT 300 140 RT 100 350

µ0 [D]

6.8 3.6 4.2 6.4 6.4

Ref. [85G1] [77B2] [74P1] [89H2] [89H2] [74P1] [87P1] [87P1]

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3.2.1 Alkali metals on metals

Substrate

T [K]

Method

∆φmin [eV]

∆φML [eV]

Au(100) Au(100) Cu(111)

300 130 RT

VC VC RP

* −2.8 −3.4

−2.6 −2.6 −3.0

Cu(111) Cu(111) Cu(111) Cu(110) Cu(100) Cu(001) Mo(211) Ni(111) Ni(111) Ni(100) Ni(100) Ni(100) Ni(110) Pt(111) Ru(0001) Ru(0001) Ru(0001) Ru(0001) Ru(1010) Ta(110) W(110) W(110) W(110) W(100) W(112)

RT RT RT RT 100 180 77 RT RT RT RT 323 RT

RP SEC(E) RP/SEC(P) SEC(P)/RP RP SEC(E) RP VC RP/SEC(P) VC RP RP VC SEC(P) SEC(P) SEC(E) RP RP RP RP RP RP RP SEC(P) RP

−2.4 −2.75 −2.3 −2.15 −2.2 −2.5 −1.9 −3.1 −3.25 −3.1 −3.3 −3.2 −2.1 −4.0 −3.5 −3.5 −3.6 −3.23 −3.1 −2.65 −3.4 −3.5 −2.9 −3.0 −2.2

−2.0 −2.25

120 300 300 •

300 300 77 300 300 RT 200

−1.9 −1.8 −2.15 −1.8 −2.2 −2.5 −2.5 −2.6 −2.4 −2.0 −3.0 −3.0 −2.7 −2.8

135 µ0 [D]

22.6

7.4 7.2 6.8 3.2 7.2 6.8 8.6 6.9

−2.8 −2.48 −2.6 −2.6 −2.6 −2.7 −2.1

2.9 8.5±0.6

µ0 [D]

Ref. [95N2] [95N2] [80L1] [91T1] [93S2, 93S4] [91D2] [93S3] [83W2] [94M2] [80G1] [69G1] [93S2, 93S4] [69G1] [74A1, 75A2] [88G1] [69G1] [91B2] [91P1] [87R1] [85K1] [89D1] [87K2] [71F1] [70M1] [70M1] [89M2] [85C2] [71C1]

Experimental work function data for potassium. Substrate

T [K]

Method

∆φmin [eV]

∆φML [eV]

Au(100) Au(100) Au(100) Ag(111) Ag(100) Al(111) Al(111) Al(100) Al(100) C(0001) Co(0001) Cu(100) Cu(100) Cu(100)

300/100 300 130

SEC(E) VC VC RP SEC(P) SEC(P)/RP VC SEC(E) SEC(E) RP SEC(P) SEC(E)

* * -3.4 -2.9 -2.5 * -2.61 -2.8 * * -3.3±0.1 -3.0 -3.6 -2.85

-3.1 -3.1 -3.1 -2.4 -2.4 -2.2 -2.07 -2.3 -2.3 -1.8 -2.8±.1 -2.5 -2.3 -2.0

RT 140 100 350 90 200 330 120 RT

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VC

8.2 9.2 9.2 12±2 11±1 15.7

Ref. [92O1] [95N2, 95S3] [95N2, 95S3] [82F1] [90N1] [86P1] [89H2] [87P1] [87P1] [93H2] [79H1] [86A1] [87D1] [92A3]

3.2.1 Alkali metals on metals

136 Substrate

T [K]

Method

∆φmin [eV]

∆φML [eV]

Cu(110) Fe(110) Fe(110) Fe(100) Fe(111) Mo(110) Mo(100) Mo(211) Mo(111) Ni(111) Ni(111) Ni(100) Ni(100) Ni(100) Ni(100) Ni(110) Pd(100) Pt(111) Pt(111) Pt(111) Pt(111) Re(001) Rh(111) Ru(0001) Ru(0001) Ru(0001) Ru(0001) Ru(0001) Ru(0001) Ru(0001) Ru(0001) Ru(0001) Ru( 10 10 )

RT RT RT RT RT 77 77 77 77 80 90 RT 120 100 323 RT 300

SEC(P) SEC(P) VC VC VC FE FE FE FE SEC SEC(P) RP SEC(P) SEC(P) RP VC

-3.1 -3.7 -3.5 -2.4 -2.5 -3.1 -2.4 -2.5 -2.1 * -4.0 -3.5 -3.6 -3.5 -3.7 -2.7 -4.15 -4.7 -4.6 -4.6 -4.5 -4.35 -3.8 -4.3 -4.0 -4.4 -3.9 -4.0 -3.9 4.0 -3.9 -3.76 -2.6

-2.1 -2.8 -3.0 -2.1 -2.4 -2.3 -2.1 -2.1 -1.7 -4.2 -3.5 -2.8 -2.9 -2.9 -3.3 -3.2 -4.0 -4.1 -4.0 -3.7 -3.0 -3.2 -2.4 -3.3 -2.4 -3.0 -3.1 -3.2 -3.4 -3.2 -3.2 -2.4

Ru( 10 10 ) Ta(110) Ta(100) Ta(211) Ta(111) W(110) W(110) W(100) W(100) W(100) W(100) W(211) W(211) W(211) W(111) W(111)

300 300 77 77 77 RT 77 300 RT RT

-3.3 -3.02 -2.3 -2.1 -1.6

-2.9 -2.68 -2.1 -1.8 -1.3

300 300 <140 RT 80 60-80 85 120
RT 245 77 RT 77

SEC(P) SEC(P) SEC(P) RP VC SEC(P)-

SEC(P) SEC(P) SEC(P) RP SEC(P) SEC(E) RP RP RP RP FE FE FE FE FE RP FE SEC(P) FE FE

-2.77

-2.64

-3.1

-2.7

µ0 [D] 12.0 14.0 8.8 7.8

7.4 13.5

5.3 12.8 15.0 18.8 18.8

13.8 7.3 14.6 15.6 13.6 7.8 13±0.8

15.7 17.2 13.5±0.7 9.5 9.7 13.6

-2.9 FE FE FE

[Ref. p. 169

-2.7 8.2 11.5 6.2

Ref. [85W1] [79B1] [81L1] [81L1] [81L1] [76B1] [76B1] [76B1] [76B1] [85L2] [86U1] [74A1, 75A2] [84L1] [84S1] [88G1] [69G1] [87B3] [91B2] [83K1] [85L1] [96L4] [97V1] [92C1] [85D1] [85M1] [87D2] [91P1] [86U2] [88S2] [85W3] [87R1] [88D1] [86H2] [88S2] [71F1] [75B1] [75B1] [75B1] [66S1] [76B1] [71F1] [66S1] [85C2] [75B1] [66S1] [74M1] [75B1] [66S1] [75B1]

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3.2.1 Alkali metals on metals

137

Experimental work function data for rubidium. Substrate

T [K]

Method

∆φmin [eV]

∆φML [eV]

µ0 [D]

Ref.

Al(111)

140

VC

−2.52

−1.99

8.2

[89H2]

µ0 [D]

Ref.

Experimental work function data for cesium. Substrate

T [K]

Method

∆φmin [eV]

∆φML [eV]

Ag(110) Al(111) Al(111) C(0001) Cu(111) Cu(100) Cu(110) Fe(110) Mo(100) Mo(110) Mo(211) Ni(100) Ni(100) Ni(100) Ni(110) Ru(0001) Ru(0001) Ru(0001) Ru(0001)

300 140 RT 80 RT RT 300 RT

SEC(P) VC SEC(E)/RP RP RP RP RP SEC(P)

77 77 RT RT 323 RT 120 300 300

RP RP SEC(P) RP VC SEC(P) SEC(E) RP SEC(E)

−2.5 −2.44 −2.6 −2.44 −3.4 −2.9 −3.1 −4.1 −3.6 −3.6 −2.8 −3.0 * −3.8 * −4.0 −4.1 −4.1 −4.1

−2.4 −1.8 −2.3 −2.2 −3.0 −2.5 −2.6 −3.4 −3.4 −3 −2.7 −2.6 −3.1 −3.3 −3.1 −3.6 −3.4 −3.4 −2.9

RP RP FE RP SEC(P) RP VC VC VC RP RP SEC(E) RP VC FE FE FE RP FE FE

−3.4 −3.18±0.03 −2.8 −3.7 −3.9 −3.6 −3.85 −2.9 −3.13 −3.1 −2.88 −3.1 −3.1 −3.04 −2.9 −3.9 −3.2 −3.0 * *

−3.1 −2.94 −2.7 −3.2

Ru( 10 10 ) Ta(110) W(111) W(110) W(110) W(110) W(110) W(100) W(110) W(100) W(100) W(100) W(100) W(100) W(100) W(110) W(211) W(211) W(103) W(115)

300 300 77 77 300 250 RT RT RT 300 RT RT 300 77 77 77 RT 77 77

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−3.2 −3.1 −2.88 −3.03 −2.4 −2.83 −2.4 −2.6 −2.82 −2.8 −3.6 −3.1 −2.9 −2.95 −2.5

8.2 18±0.8 19.2

8.8

28.2 7.0 13.8 22.0

15.3±0.7 17.4

15.8±0.8 19.9±1 15.0±0.8

18.1 34 23 17.8 15.8

[83H1] [87H1, 89H2] [86P1] [86H1] [78L1, 80L1] [82P1] [97A1] [99S1] [82S1] [94G1] [81G1] [75P1] [77K1] [88G1] [69G1] [91P1] [87R1] [88S2] [85H1] [88S2] [71F1] [69S1] [70F1] [97P1] [89M2] [80D1] [71L1] [71L1] [73P1, 73P2] [71F1] [69M1] [72V1] [73D1] [69S1] [69S1] [69S1] [71P1] [69S1] [69S1]

3.2.1 Alkali metals on metals

138

[Ref. p. 169

3.2.1.2.3 Electronic structure of adatoms In order to understand the mechanism of the alkali-metal-induced work-function variation, it is necessary to know the valence electronic structure of the adatoms. When low-energy electrons impinge on a solid surface, some of them undergo characteristic energy losses due to inelastic scattering in the solid. Some of these are due to the excitation of valence electrons. The energy losses for single-particle excitations are generally in the range 1-20 eV. For alkali metal adsorption, it is generally found that these loss peaks appear at very low coverages and shift to lower energies with increasing coverage, up to the work function minimum. At higher coverages, the losses shift back to higher energies. In the following table we have tabulated the results of many EELS studies for alkali metal adsorption, including the energy loss at very low coverage ( E10 ), at the work function minimum ( E1min ) and at the completion of the monolayer ( E1ML ). There are some general features of these results. First, the energy losses extrapolated to zero coverage lie in the range of 3-4 eV. Second, the minimum energy losses are close to the excitation from the ns level to the np level in a free alkali atom. This suggests that at this point, the ns resonance of the adsorbed alkali-metal atom is filled with almost one electron, a fact which has relevance to the condensation transitions observed for some systems. Third, with the exception of Cs/Al(111), the coverages corresponding to the minimum energy loss correspond closely to those of the work function minimum. And fourth, the loss energies shift to higher energies at higher coverages. This shift is most prominent for Na and decreases for the heavier alkali metals. EELS Results for alkali-metal covered surfaces. The experimental numbers indicate the energy loss at very low coverage ( E10 ), at the work function minimum ( E1min ) and at the completion of the monolayer ( E1ML ). Alkali

Substrate

E10 [eV]

E1min [eV]

E1ML [eV]

Ref.

Na Na Na Na Na Na Na Na Na Na K K K K K K K K K Rb Cs Cs Cs Cs Cs Cs Cs

Al(111) Al(111) Al(111) Cu(111) Mo(100) Ni(100) Ni(100) Pt(111) Ru(0001) W(100) Al(111) Ag(111) Ag(100) Cu(100) Ni(100) Ni(100) Pd(100) W(100) W(100) W(100) Al(111) Ag(100) Cu(111) Mo(100) Mo(110) W(100) W(100)

2.6-3.1

2.0

3.0 2.8

2.5 3.2 3.2 3.4

2.0 2.3 2.8 2.1

4.0 3.6 3.2

2.0 3.0 2.8 1.5 1.5

3.7 3.5

1.7 1.5

2.8

2.1

1.8

0.95

3.1 2.9

1.25 1.6 2.2

2.9

1.5

[87K1] [89H2] [91G2] [80L1] [96L3] [75A1, 75A2, 79J1] [73A1] [88H1] [87R1, 87S1] [85C2] [91G2] [82F1] [91M1] [86A1] [75A1, 75A2, 77S1, 79J1] [73A1] [87B3] [85C2] [72T1] [72T1] [87H1] [91M1] [78L1, 80L1] [82S1, 83S1, 85S1] [94G1] [69M1] [83S1, 85C2, 85S1]

3.2 3.1 3.7 3.5 3.7 3.7 1.65 2.3 1.8 2.25 2.3 2.5 2.6 2.3 2.0 1.8 0.95 1.3 1.55 1.7 1.5 1.5

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3.2.1 Alkali metals on metals

139

Further results on the electronic structure of the adatom–substrate complex have been obtained using other spectroscopic techniques. These techniques probe the occupied and unoccupied alkali-induced states near the Fermi level. We have tabulated the results of UPS and MDS experiments probing the occupied density of states. In these studies, evidence for an occupied ns resonance is observed. In many of these studies, this resonance has only been observed at coverages close to or above the work-function minimum and some workers have inferred that this is evidence for an ionic-to-metallic phase transition of the alkali layer. However in other work, this resonance has been observed at very low alkali coverages. It appears that the width of the resonance and experimental resolution considerations must be taken into account in considering these results in the context of alkali metal bonding [88H2, 89H3, 89I1]. States observed in UPS and MDS experiments for alkali metal covered surfaces. θ is the coverage range over which the adsorbate-induced occupied state is reported.

Alkali

Substrate

Technique

θ

Assignment Ref.

Li Na K K K K Cs

Cu(111) Cu(111) Al(111) Al(111) Ag(110) Cu(110) Cu(111)

UPS UPS UPS UPS UPS MDS UPS

•

2s 3s 4s 4s 4s 4s 5s

• • • • • •

[93D1] [93D1] [88H2] [89F1] [90N1] [85W1] [93D1]

Complementary to these studies are results obtained with IPES and two-photon photoemission, which probe the unoccupied density of states above the Fermi level. Interpretation of these studies is somewhat complicated by the presence of image charge states, but in general for the lighter alkalis Li, Na and K the unoccupied density of states for adsorbed layers is derived primarily from np orbitals. For Cs, the unoccupied electronic states have been variously assigned to 6p [89F1, 93C2, 93D1] or 5d orbital character [97A1]. The general behavior of adsorbate induced unoccupied p and d states is a continuous shift towards the Fermi level as a function of alkali coverage. The results are presented below. Some workers do not assign the adsorbate-induced features to specific atomically-derived orbitals [91M2, 93F1, 94F1, 94S5, 94W1] and these results have been omitted. States observed in IPES experiments for alkali metal covered surfaces. θ is the coverage range over which the adsorbate-induced occupied state is reported. Alkali

Substrate

θ

Assignment Reference

Li Na Na Na Na Na K K K Cs Cs Cs Cs

Cu(111) Al(111) Cu(111) Cu(111) Cu(110) Ni(111) Al(111) Ag(110) Cu(111) Al(111) Cu(111) Cu(111) Cu(100)

0.25 >0.09 0.15-0.25 0.25

2p 3p 3p 3s 3p 3p 4p 4p 4p 6p 6p 5d 5d

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• • •

0.08-0.34 0.25 •

0.25 • •

[93D1] [88H1] [93D1] [91D2, 93D1] [93T2] [93T1] [89F1] [87J1] [93D1] [89F1] [93D1] [97A1] [97A1]

3.2.1 Alkali metals on metals

140

[Ref. p. 169

3.2.1.2.4 Heats of adsorption/desorption Most of the direct measurements of the adsorption energies of alkali metals adsorbed on metal surfaces are those deduced from thermal desorption measurements. This can be observed directly in the zerocoverage limit using field ion microscopy. Otherwise, families of desorption curves at different starting coverages can be obtained from flat single crystals. The general features observed in families of thermal desorption curves from alkalis adsorbed on metal surfaces are first-layer desorption peaks which shift to lower temperature as the coverage is increased, and frequently peaks at successively lower temperatures due to further adsorbed layers. As discussed in the Section 1.3.1 of the Introduction to this Volume, it is possible to deduce the thermal desorption energy from such curves. In general, desorption energies decrease as the coverage increases for alkali metals on metal surfaces. An example of such measurements for Cs on Ru(0001) are shown in Fig. 2. Desorption energies can also be deduced from trapping measurements. In these measurements, the initial trapping probability of alkali adatoms is measured, along with the temperature dependence of the mean residence time of those trapped adatoms. From those parameters, the zero-coverage desorption energy can be derived [76H1]. An alternative method for determining these energies is to measure a family of adsorption or desorption isotherms and then to extract the heats of adsorption from the slope of the adsorption points on an Arrhenius plot of the isosteres. This is discussed in detail in Section 1.3.2 of the Introduction to this Volume. These measurements are somewhat more complex to carry out since they require an accurate assessment of both the vapor pressure at the surface and the coverage during the measurement. The one reported measurement of this type was carried out using He-atom scattering [94R1]. A list of measured heats of desorption are given in the following table for several alkali metal adsorption systems. Measured heats of adsorption/desorption for alkali metals on metal surfaces. The values given are the zero-coverage limit unless stated otherwise. (FEM) indicates that the measurement was done on an FEM tip. Alkali

Substrate

Method

Coverage

Energy [eV]

Ref.

Li Li Li Li Na Na Na Na Na Na Na Na Na Na Na K K K K K

Ru(0001) Ru(0001) Ru(0001) W(110) Au(100) Ag(110) Ni(111) Ni(100) Ni(110) Ru(0001) Ru(0001) Ru(0001) Ru (10 10) W (FEM) W(110) Cu(100) Au(100) Fe(111) Fe(100) Fe(110)

TPD TPD TPD Trapping TPD TPD TPD TPD TPD TPD TPD TPD TPD TPD Trapping HAS Isotherms TPD TPD TPD TPD

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.26-0.37 0 0 0 0

2.8 2.9 3.2 2.8 2.4 2.0 2.54 2.52 2.18 2.5 2.5 2.8 2.64 2.4 2.6 1.0±0.1 2.6 2.25 2.34 2.47

[96P1] [86D1] [98E1] [76H1] [95N2] [76M1] [70G1] [70G1] [70G1] [83D1] [87R1] [89D1] [88K1] [70G1] [76H1] [94R1] [95N2] [81L1] [81L1] [81L1]

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3.2.1 Alkali metals on metals

141

Alkali

Substrate

Method

Coverage

Energy [eV]

Ref.

K K K K K K K K K K K

Ni(110) Pt(111) Pt(111) Pt(111) Re(001) Ru(0001) Ru(0001) Ru(0001) Ru(0001) Ru(0001) Ru (10 10)

TPD TPD TPD TPD TPD TPD TPD TPD TPD TPD TPD

0 0 0.36 0 0 0 0.33 0 0 0 0

2.56 2.6 1.1 2.6 2.97 2.8 1.1 2.9 3.5 2.8 2.9

[70G1] [82G1] [82G1] [82C1] [97V1] [85D1] [85D1] [87R1] [88D1] [89H5] [86H2]

K K Cs Cs Cs Cs Cs Cs Cs Cs Cs Cs Cs Cs Cs

Ru (10 10) W(110) Ni(110) Ni(FEM) Ru(0001) Ru(0001) Ru(0001) Ru(0001) Ru(0001) Ru (10 10) W(100) W(110) W(110) W(110) W(110)

TPD Trapping TPD TPD TPD TPD TPD TPD TPD TPD TPD TPD TPD TPD TPD

0 0 0 0 0 0 0 0.33 0 0 0 0 0 0 0

2.84 2.1 2.72 3.1 2.9 3.2 2.6 0.82 3.2 3.16 2.8 3.2 3.2 3.06 3.1

[88K1] [76H1] [70G1] [70G1] [90D1] [96P1] [85H1] [85H1] [87R1] [88K1] [67G1] [67G1] [70F1, 72K1] [74T1] [80D1]

3.2.1.2.5 Adatom vibrational frequencies A common method used to obtain information about chemisorption bonds is to measure the vibrational frequencies of adsorbed adatoms. There have been many such studies for adsorbed alkalis, most of them employing either inelastic He-atom scattering or high-resolution electron energy loss spectroscopy. The modes which have been observed have been identified as vibrations of the adatoms either perpendicular or parallel to the surface. In general, the perpendicular vibrations have been found to have higher energies than the parallel vibrations, for on-surface adsorption. In the cases of intermixed alkalis, the situation is more complex because there are many types of intermixed geometries. The following paragraphs summarize the observed trends. The perpendicular vibration modes for on-surface adsorption scale approximately with the inverse square root of the mass of the alkali for any given substrate, indicating that the perpendicular force constant does not vary strongly with alkali (or with the adsorbate-substrate spacing). Because the HREELS measurements of these modes have relied primarily on their high cross-sections for dipole scattering, the numbers given in the following table are zone-center values, and their dispersion has not been measured (apart from the Na-Al(111) system, Reference [95N1, 97N1]). Their coverage dependence has been studied for several systems, and there are a few trends which appear to be common to most of these systems. The characteristic features in the HREELS measurements are a nearly-coverageindependent perpendicular vibration frequency and a strongly-coverage-dependent loss-peak intensity. The intensity grows to a maximum at a relatively low coverage, and then decreases to a very low level for higher coverages, reflecting the changing character of the electronic structure of the adlayer as the coverage changes. The perpendicular vibrational frequency usually remains constant or increases slightly

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[Ref. p. 169

with coverage. This shift is generally at least partially attributed to the change in the dipole-dipole interaction as the coverage increases. The expression which describes this dependence is

ω 2 = ω 02 +

Q2Σ M(1 + α e Σ)

where Q is the dynamic charge, αe is the electronic polarizability and M is the reduced mass. Σ is a lattice sum over the r−3 term in the dipole-dipole interaction, and for a hexagonal lattice is equal to 8.9n3/2, where n is the surface density of atoms. In some cases, this equation appears to not account for the full shift in vibrational frequency, and this has been attributed to a delocalization of the mode and an increasing participation of the substrate atoms in the mode as the coverage increases, but this explanation cannot fully explain all of the observations [96L1]. The parallel vibration modes typically have very low energies which may be difficult to resolve in a HREELS experiment, in addition to having very small dipole moments which would result in low intensities. The lower energy range, however, is ideal for He-atom scattering measurements. Because Heatom scattering does not rely on dipole scattering, the dispersion curves for the parallel modes have been mapped out for many systems using this technique. The modes are usually dispersionless, or nearly so. No clear trends have been observed in the coverage dependence of these modes due to lack of coveragedependent data. At coverages near the saturated monolayer, the energies of the parallel modes for alkalis on graphite have been found to scale with the inverse square root of the mass of the alkali, similar to the case of the perpendicular vibrations. However, for low coverages of alkalis on Cu(100), the energy of the parallel mode is found to decrease more strongly as mass increases. This has been attributed to the difference in the lateral potentials (due to the substrate) experienced by the different adatoms [98S1]. The parallel mode energies can also be extracted from LEED intensity measurements, if the perpendicular mode energy is already known. Such an analysis has been performed for Cs/Ru(0001) [95O2]. The vibration frequencies for the systems studied thus far basically are similar for similar geometries. For example, the following table shows that the perpendicular vibration energy for Li is around 33-43 meV for systems where the adatom are on the surface (on the Cu surfaces), where as it is much less, about 18 meV, for intermixed Li (on Al). Likewise, the perpendicular vibration frequencies for Na are around 18 meV except for the intermixed Na/Al which is about 12 meV, and the parallel vibration frequencies are around 5-6 meV. For K, the perpendicular modes are around 12-14 meV and the parallel vibration frequencies are in the 2-6 meV range, whereas an intermixed species has a perpendicular mode energy of 28 meV. There have been no studies which specifically measure differences in vibrational frequencies due to adsorption geometry, e.g. a site dependence, although small geometrical effects should be expected [92N1]. Fig. 3 shows the on-surface perpendicular and parallel frequencies for adsorbed alkalis plotted against M−1/2.

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3.2.1 Alkali metals on metals

143

Experimental values for alkali adatom vibrational mode energies. Alkali Substrate Li Li Li Li Li Li Na Na Na Na Na Na Na Na Na Na K K K K K K K K K K K Rb Cs Cs Cs Cs Cs Cs

Technique Coverage

Al(111) HREELS Cu(111) HREELS Cu(111) HREELS Cu(110) HREELS Cu(110)-(1x2) HREELS Cu(110)-(1x2) HREELS Al(111) HREELS Al(111) HREELS Cu(111) HREELS Cu(100) HREELS Cu(100) HAS Cu(100) HAS Cu(110) HREELS Cu(110)-(1x2) HREELS Mo(100) HREELS Pt(111) HAS Cu(111) HREELS Cu(111) HREELS Cu(100) HAS Cu(100) HREELS Cu(100) HREELS Cu(110) HREELS Cu(110)-(1x2) HREELS Ni(110) HREELS Pt(111) HREELS Graphite(0001) HAS Graphite(0001) HAS Graphite(0001) HAS Cu(100) HAS Cu(100) HAS Ru(0001) HREELS Ru(0001) HREELS Ru(0001) LEED Graphite(0001) HAS

0.03-1.0 0.025-0.3 0.3-0.5 0.08-0.80 0.04-0.40 0.40-0.80 0.067-0.33 0.5 0.075-0.3 0-0.4 0-0.13 0.18-0.5 0.13 0.6 0-0.45 0.05 0.02-0.27 0.08-0.4 0.07 0.0-0.02 0.02-0.11 0.02-0.32 0.02-0.56 0.2 0.02-0.15 0.04 0.25 0.25 0.08 0.27 0.03-0.19 0.19--0.24 0.25 0.25

Polarization

Energy [meV]

Geometry

Ref.

Perpendicular Perpendicular Perpendicular Perpendicular Perpendicular Perpendicular Perpendicular Perpendicular Perpendicular Perpendicular Parallel Parallel Perpendicular Perpendicular Perpendicular Parallel Perpendicular Perpendicular Parallel Perpendicular Perpendicular Perpendicular Perpendicular Perpendicular Perpendicular Parallel Parallel Parallel Parallel Perpendicular Perpendicular Perpendicular Parallel Parallel

17.6-18.1 38-43 43 35-37 33-36 36-35 11.6-12.6 15 21 18 5.6-6.3 6.3-2.0 18 18 19 5.2 12 13 2.86 10-13 13 14 10-13 14.9 17-22 6.5 4.4 2.8 0.0-0.65 6.8 6.7-9.0 9.0-8.3 1.0-1.3 2.2

Intermixed On-surface On-surface On-surface On-surface On-surface Intermixed Intermixed On-surface On-surface On-surface On-surface On-surface On-surface On-surface On-surface On-surface On-surface On-surface On-surface On-surface On-surface On-surface Reconstructed On-surface On-surface On-surface On-surface On-surface On-surface On-surface On-surface On-surface On-surface

[95N1] [96L1] [96L1] [91R1] [91R1] [91R1] [95N1, 97N1] [95N1, 97N1] [90L1, 93L1] [90A1] [97G1] [97G1] [90R2] [90R2] [96L3] [99G1] [90A1] [93L1] [98S1] [90A1] [90A1] [90R2] [90R2] [85W2] [97H1, 99K1] [93C1] [93C1] [93C1] [98S1] [99S2] [96H1] [96H1] [95O2] [93C1]

3.2.1.2.6 Adsorption sites and bond lengths (commensurate structures) The adsorption sites determined for relatively simple (primitive) commensurate overlayer structures are given in the tables below. The large number of measured structures allows some trends to be observed. First, alkalis adsorbed on the substrates of square and rectangular symmetry are in the high-coordination hollow sites. All available evidence indicates that these are the preferred sites over the whole coverage range [93M1, 93W1, 94M1]. The situation for the hexagonal substrates is more interesting. In some cases the equilibrium adsorption site is the highest-coordination hollow site (either hcp or fcc), while for others it is the lowestcoordination top site. In the LEED studies of the top-site systems where substrate relaxations are included in the analysis, all of them show some degree of rumpling. The main effect of this rumpling is to move the alkali adatoms closer to the surface, thus slightly decreasing their nearest-neighbor distance as well as the next-nearest-neighbor distance. It has been shown using DFT calculations that a necessary component Lando lt -Bö rnst ein New Ser ies III/42A1

144

3.2.1 Alkali metals on metals

[Ref. p. 169

of the top-site structure for K/Al(111) is a small rumpling of the substrate [95S1]. Therefore it has been proposed that whether an atom occupies a top site may depend on how easily the substrate can be deformed to accommodate the rumpling [95O1], and that therefore a substrate which cannot be easily deformed is less likely to exhibit top-site adsorption. DFT calculations have predicted that for K/Al(111) there is a crossover from top site to hollow site as the coverage decreases, and that a single adatom should be in the hollow site [92S1]. It has also been suggested that top-site structures (and rumpling) are related to a possible increased screening effect for certain symmetries [92O2], implying that top site occupation is a collective effect and would not happen for a single adatom. Of the lowest-coverage site determinations for such a system, the NISXW study of Rb/Al(111) [92K2, 93K2], indicates that the top site is still occupied at a coverage of 0.12 in the disordered phase. A PhD experiment for K/Al(111) indicates that the top-site is occupied in the coverage range 0.05-0.40 [95C1]. This is not in agreement with the DFT result [92S1]. At higher coverages, a change in adsorption site with coverage has been observed on three substrates, Ru(0001) [92O2], Ag(111) [97K1] and Rh(111) [96S1]. In the cases of Cs/Ru(0001) and Cs/Rh(111), the site changes from the top site in the p(2x2) structure to the hcp site in the (¥[¥ 5ƒ VWUXFWXUH ,W ZDV proposed [92O2] that for Cs/Ru(0001) this change is due to the screening afforded by the surface geometry of the atop site in the p(2x2) phase but not the atop site in the (¥[¥ 5ƒ SKDVH ,Q WKH FDVHV of K and Rb on Ru(0001), and K, Rb and Cs on Ag(111), the adatoms are adsorbed in the fcc sites in the p(2x2) phase and in the hcp sites in the (¥[¥ 5ƒ SKDVH )RU DGVRUSWLRQ RQ 5X LW ZDV SURSRVHG that the hcp site at higher coverage occurs because the hcp site is the natural "metallic" site on Ru(0001), but this is clearly not the case on Ag(111). Since this site change has been observed now on both an hcp and an fcc substrate, a likely cause of the change may be coordination. In the p(2x2) structure, adatoms in either hollow site effectively increase their coordination when the substrate rumples, and the choice of fcc site may be related to the rumpling energy. In the (¥[¥ 5ƒ VWUXFWXUH KRZHYHU UXPSOLQJ FDQQRW occur by symmetry for either hollow site, therefore the coordination is a maximum when the second-layer substrate atom is directly beneath the adatom. On other surfaces, notably Pt(111), Pd(111) and K on Rh(111), the adsorption site is hcp for both the p(2x2) and the (¥[¥ 5ƒ SKDVHV ,Q WKH FDVH RI 3W  ')7 FDOFXODWLRQV [98M1] have suggested that the origin for the hcp site preference is due to the tilting of the electron density due to the d-states toward the hcp sites, leading to an added attraction in those sites which is not present for the fcc sites. This picture is consistent with the results for alkali adsorption on Rh(111) and Pd(111), where hcp sites are also occupied in the p(2x2) structure. It is also consistent with the observations of fcc-site occupation for the p(2x2) structure in the systems of K and Rb on Ru(0001), and K, Rb and Cs on Ag(111), where the effect of the d-electrons may be significantly less. An issue which has been discussed with respect to the nature of the adsorption bond is the chemisorption bond length. The chemisorption bond length was initially expected to increase as the alkali coverage increases due to large depolarization which occurs as the coverage increases, as similar changes had been observed for Cl and S adsorption [88L1, 88S1, 89W2]. Changes have been observed in the chemisorption bond lengths for alkalis, but only when their coordination to the substrate changes. The data in the tables below show that for any given alkali-substrate combination, when the coordination of the alkali increases, the chemisorption bond length increases. If one corrects for the different radii of the various substrates by subtracting the substrate metallic radius from this number it can be seen that generally this "effective r" increases with coordination, irrespective of the substrate. There are a few notable exceptions, particularly for Cs adsorption. There the difference in the chemisorption bond strength is believed to play a role, as discussed in reference [99K2]. The other surprising adsorption sites for alkali metals are the so-called substitutional sites. At the simplest, these structures involve adatoms which occupy vacancies that are induced by the alkali adsorption [94S3]. For the case of Al(111), DFT calculations have indicated that the reason a substitutional structure is so favorable is that the energy for vacancy formation on Al(111) is so small (0.36 eV) [93P1, 95S1]. It was also suggested that these substitutional structures provide a way for the alkali adatom to form a more ionic bond with the substrate, the evidence of this being the increase of largely-substrate charge density between the alkali adatoms [95S1]. A low vacancy-formation energy was also predicted for Ag(111) (0.67 eV) and Cu(111) (0.92 eV) [93P1], but so far no substitutional sites have been observed on those surfaces except for Li adsorption. Lando lt -Börnst ein New Ser ies III/42A1

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3.2.1 Alkali metals on metals

145

More complex multilayer intermixed structures have also been observed and characterized for alkali adsorption on the (100) surfaces of Cu, Ag, Al, Ni and Au, and the (111) surfaces of Al and Cu [98T1]. The fcc(110) surfaces of many metals also have been observed to undergo significant reconstructions upon alkali adsorption, and the geometries of many of these substrate reconstructions have been measured [96D1, 98T1]. The following tables contain experimentally-determined commensurate structure parameters for alkali metal adsorption systems (only simple structures are listed). The temperatures quoted are the measurement temperature. The bond length quoted is the chemisorption bond length. Effective r (Eff. r) is the chemisorption bond length minus the metallic radius of the substrate atom. Excess r (Exc. r) is the Effective r minus the ionic radius of the alkali metal atom. N is the coordination number of the alkali adatom. A coordination number denoted as * indicates that due to surface reconstruction, an unambiguous assignment cannot be made.

Commensurate structure parameters for lithium adsorption. Surface

Structure

T [K]

Al(100) Cu(100) Ni(100) Ru(0001)

c(2x2) 300/100 c(2x2) 180 c(5¥[¥ 5ƒ 230 (¥[¥ ƒ 50

Site

Method Bond length [Å]

Eff. r [Å]

Exc. r N [Å]

Ref.

subst. hollow hollow hcp

LEED LEED LEED LEED

1.43±0.05 1.39±0.08 1.33±0.05 1.39±0.05

0.76 0.71 0.65 0.71

[99P1] [93M2] [97J3] [95G1]

2.87±0.05 2.67±0.08 2.58±0.05 2.74±0.05

4 4 4 3

Commensurate structure parameters for sodium adsorption. Surface

Structure

T [K]

Site

Method Bond length [Å]

Eff. r [Å]

Exc. r N [Å]

Ref.

Al(111) Al(111) Al(111) Al(100) Al(100) Al(100) Cu(100) Cu(100) Ni(100) Ni(100) Rh(111) Ru(0001) Ru(0001)

(¥[¥ 5ƒ (¥[¥ 5ƒ (¥[¥ 5ƒ c(2x2) c(2x2) c(2x2) c(2x2) c(2x2) c(2x2) c(2x2) (¥[¥ 5ƒ p(2x2) (¥[¥ 5ƒ

100/300 300 170/300 140 100 100/300 100 300 300 320 30 50 50

subst. subst. subst. hollow hollow subst. hollow hollow hollow hollow hcp fcc hcp

LEED 3.21±0.01 SEXAFS3.31±0.03 NISXW 3.10±0.06 SEXAFS3.20±0.03 LEED 3.27±0.01 LEED 3.07±0.01 LEED 2.98±0.03 LEED 3.03±0.04 LEED 2.84±0.08 LEED 2.95±0.04 LEED 2.84±0.09 LEED 2.95±0.04 LEED 2.95±0.04

1.78±0.01 1.88±0.03 1.67±0.06 1.76±0.03 1.83±0.01 1.63±0.01 1.71±0.03 1.76±0.04 1.59±0.08 1.72±0.04 1.49±0.09 1.60±0.04 1.60±0.04

0.81 0.91 0.70 0.79 0.86 0.66 0.74 0.79 0.62 0.75 0.52 0.63 0.63

[94B3] [91S2] [92K1] [92A1] [95B3] [95B3] [99M1] [99M1] [75A1, 75D1] [94N4] [94V1] [94H1] [94H1]

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3.2.1 Alkali metals on metals

146

[Ref. p. 169

Commensurate structure parameters for potassium adsorption.

Surface

Structure

T [K]

Site

Method

Ag(111) Ag(111) Ag(111) Al(111) Al(111) Co(0001) Co (10 10) Cu(111) Cu(110) Fe(100) Ni(111) Ni(111) Ni(111) Ni(111) Ni(100) Pd(111) Pd(111) Pd(100) Pt(111) Pt(111) Rh(111) Rh(111) Ru(0001) Ru(0001)

p(3x3) p(2x2) (¥[¥ 5ƒ (¥[¥ 5ƒ (¥[¥ 5ƒ p(2x2) c(2x2) p(2x2) (1x2) (3x3) p(2x2) p(2x2) p(2x2) p(2x2) c(4x2) p(2x2) (¥[¥ 5ƒ c(2x2) p(2x2) (¥[¥ 5ƒ p(2x2) (¥[¥ 5ƒ (¥[¥ 5ƒ P(2x2)

40/300 40/300 40/300 90 300 160/400 300 65/300 100/300 300 120/400 70/300 130/300 100/300 80 50/604 50/470 300 100 100 50 50 80 80

fcc LEED fcc LEED hcp LEED top LEED subst LEED top LEED hollow LEED top SEXAFS subst. PhD subst. SXW top LEED top SEXAFS top PhD top PhD hollow LEED hcp LEED hcp LEED hollow LEED hcp LEED hcp LEED hcp LEED hcp LEED hcp LEED fcc LEED

Bond length [Å]

Effective r [Å]

Exc. r [Å]

N

Ref.

3.27±0.03 3.27±0.03 3.29±0.02 3.23±0.05 3.58±0.03 2.93±0.11 3.12±0.05 3.05±0.02 3.27±0.27 2.92±0.04 2.82±0.04 2.92±0.02 3.02±0.01 2.86±0.03 3.20±0.05 3.10±0.07 3.10±0.07 3.20±0.05 3.12±0.04 3.15±0.02 3.15±0.05 3.15±0.05 3.29±0.05 3.25±0.05

1.82±0.03 1.82±0.03 1.84±0.02 1.80±0.05 2.10±0.03 1.68±0.11 1.87±0.05 1.77±0.03 1.99±0.27 1.66±0.04 1.57±0.04 1.67±0.03 1.77±0.01 1.62±0.03 1.96±0.05 1.72±0.07 1.72±0.07 1.82±0.05 1.74±0.04 1.77±0.02 1.80±0.05 1.80±0.05 1.98±0.05 1.94±0.05

0.49 0.49 0.51 0.47 0.73 0.35 0.54 0.44 0.66 0.33 0.24 0.34 0.44 0.29 0.62 0.39 0.39 0.49 0.41 0.44 0.46 0.46 0.65 0.61

3 3 3 1 6 1 * 1 * 8 1 1 1 1 4 3 3 4 3 3 3 3 3 3

[97K1] [95L2] [95L2] [92S1] [92S1] [99L1] [91B1] [93A1] [94H2] [97C1] [92F1] [93A1] [93H1] [94D1] [92M1] [99K2] [99K2] [96B1] [98M1] [98M1] [96S1] [96S1] [92G1] [92G1]

Commensurate structure parameters for rubidium adsorption.

Surface

Structure

T [K]

Site

Method

Bond length [Å]

Effective r [Å]

Exc. r [Å]

N

Ref.

Ag(111) Ag (111) Ag(111) Al(111) Al(111) Al(111) Al(111) Al(111) Al(111) Al(111) Cu(111) Rh(111) Ru(0001) Ru(0001)

p(3x3) p(2x2) (¥[¥ 5ƒ p(2x2) p(2x2) (¥[¥ 5ƒ (¥[¥ 5ƒ (¥[¥ 5ƒ (¥[¥ 5ƒ (¥[¥ 5ƒ p(2x2) (¥[¥ 5ƒ p(2x2) (¥[¥ 5ƒ

40/300 40/300 40/300 170 100 170 150 100 300 100/300 300 50 50 50

hcp fcc hcp top top top top top subst. subst. top hcp fcc hcp

LEED LEED LEED SXW LEED SXW SXW LEED SXW LEED SXW LEED LEED LEED

3.43±0.03 3.39±0.03 3.40±0.03 3.13±0.10 3.21±0.26 3.13±0.10 3.23±0.10 3.36±0.03 3.72±0.10 3.74±0.02 3.07±0.01 3.20±0.05 3.41±0.05 3.41±0.05

1.98±0.03 1.94±0.03 1.95±0.03 1.70±0.10 1.78±0.26 1.70±0.10 1.80±0.10 1.93±0.03 2.29±0.10 2.27±0.02 1.79±0.01 1.85±0.05 2.07±0.05 2.07±0.05

0.50 0.46 0.47 0.22 0.30 0.22 0.32 0.45 0.81 0.79 0.31 0.37 0.59 0.59

3 3 3 1 1 1 1 1 6 6 1 3 3 3

[97K1] [95L2] [95L2] [92K2] [99A1] [92K2] [94S2] [94N2] [94S2] [94N2] [94S1] [96S1] [94H3] [94H3]

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3.2.1 Alkali metals on metals

147

Commensurate structure parameters for cesium adsorption.

Surface

Structure

T [K]

Site

Method Bond length [Å]

Effective r [Å]

Exc. r [Å]

N

Ref.

Ag(111) Ag(111) Ag(111) Ag(111) Ag(111) Ag(100) Al(111) C(0001) Cu(111) Pd(111) Pd(111) Rh(111) Rh(111) Rh(100) Ru(0001) Ru(0001)

(2¥[¥ 5ƒ p(3x3) (¥[¥ 5ƒ p(2x2) (¥[¥ 5ƒ c(2x4) (¥[¥ 5ƒ p(2x2) p(2x2) p(2x2) (¥[¥ 5ƒ p(2x2) (¥[¥ 5ƒ c(4x2) p(2x2) (¥[¥ 5ƒ

40/100 40/100 40/200 40/200 40/300 170 100 80 300 50/592 50/445 50 50 120 80 80

fcc fcc fcc fcc hcp hollow top hollow top hcp hcp top hcp hollow top hcp

LEED LEED LEED LEED LEED SXD LEED LEED LEED LEED LEED LEED LEED LEED LEED LEED

2.12±0.03 2.11±0.04 2.07±0.04 2.08±0.03 2.08±0.03 1.78±0.16 2.03±0.03 2.41 1.73±0.05 1.79±0.07 1.81±0.07 1.62±0.05 1.94±0.05 2.10±0.06 1.90±0.08 2.17±0.02

0.45 0.44 0.40 0.41 0.41 0.11 0.36 0.74 0.06 0.12 0.14 -0.05 0.27 0.43 0.23 0.50

3 3 3 3 3 4 1 6 1 3 3 1 3 4 1 3

[99C1] [97K1] [99C1] [97K1] [97K1] [97M1] [98N1] [89H4] [83L1] [99K2] [99K2] [99K2] [99K2] [89V1] [92O2] [92O2]

3.57±0.03 3.55±0.04 3.51±0.04 3.52±0.03 3.52±0.03 3.72±0.16 3.45±0.03 3.1 3.01±0.05 3.17±0.07 3.19±0.07 3.25±0.05 2.95±0.05 3.44±0.06 3.25±0.08 3.52±0.02

3.2.1.2.7 Incommensurate overlayer rotations The rotational epitaxy of incommensurate layers has been studied for many years in a diverse range of systems, and many models have been devised to describe these systems [91G1]. In this section we will describe a few of the models which are possibly applicable to alkali overlayers. A geometrical model developed by Bohr and Grey [91G1] and applied with success to various metal interfaces, proposes that the overlayer will tend to align itself so that its domain walls (which arise from the static distortion of the lattice) are oriented along a symmetry direction of the substrate. Thus various trajectories of rotational angle vs. lattice misfit are predicted for incommensurate overlayers, depending on their symmetry. A second geometrical model, first applied to alkali metals by Doering [85D2], proposes that the overlayer may form higher-order commensurate (HOC) structures, where the repeat distance of the overlayer relative to the substrate is large compared to the lattice spacing. For a finite system, there are several main trajectories of HOC structures in angle-misfit space, which an overlayer might follow quasicontinuously as its density (and misfit) changes. A more extensive theory was developed by Novaco and McTague (NM) [77N1, 79M1] in which the adatom-adatom interactions are explicitly taken into account in the form of elastic constants. This firstorder theory calculates the response of an elastic overlayer to a small-amplitude substrate potential corrugation. Since, in general, transverse overlayer deformations cost less energy than longitudinal ones, the incommensurate overlayer relaxes by rotating relative to the substrate, i.e. the rotation is essentially a static transverse distortion wave in the overlayer. For any given misfit there is at least one minimumenergy overlayer angle. Since elastic properties depend on the details of the adatom-adatom interactions, one might expect different rotation angles for different adatom-adatom interactions. Fig. 4 shows plots of the angle-misfit trajectories for these models. The reason for the correspondence between the geometrical models and the harmonic NM theory is not completely obvious since the models have quite different origins, but in essence, the HOC and domain-wall alignment models pick out low-energy trajectories, just as the NM theory does. However, the NM theory actually selects the lowest-energy trajectory for a given interadsorbate interaction, whereas the geometric models cannot distinguish between the different trajectories.

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[Ref. p. 169

The NM theory and the geometric models are expected to break down close to commensurate structures where the periodic effects of the substrate on the overlayer are more important. For this regime, a domainwall theory was developed by Shiba [79S1, 80S1] which predicts that close to a commensurate structure where domain walls in the overlayer are relatively sharp, the overlayer (and the domain walls) will remain aligned along a substrate direction until a certain critical misfit is reached. The critical misfit occurs at a point where the domain walls become too weak for the overlayer to sustain the alignment. At this point the overlayer crosses over from a “domain wall” to a “modulated” regime, and the equilibrium angle of rotation moves toward that predicted by the NM theory for a “uniform” overlayer. In the geometrical models, this crossover behavior of the overlayer could be accommodated by the jumping from one trajectory to another, but of course there is no way in these models to predict when or how this might occur. The following table indicates which alkali overlayers have been observed to form rotated incommensurate structures and the density range and angle range over which they have been observed. In general all of the systems behave similarly at the same coverages. On the hexagonal substrates the data in most cases qualitatively follow the predictions of the NM theory for a repulsive dipole interaction. There are deviations from this behavior though, and in some cases (notably Li/Ru(0001)), the geometrical theories may provide a better description. It should be noted, however, that a marked temperature dependence was observed in the rotation angle for alkalis on Ag(111) [96L2] and Cu(100) [85A1], and such a change with temperature may make comparisons to the models difficult. It does rule out a simple application of the geometrical models, though, since a continuous off-trajectory change would not be consistent with their predictions. There are fewer data for rotated alkali layers on square-symmetry substrates, but the data which are available indicate that these systems also agree qualitatively with the NM prediction for repulsive dipoles. Rotational parameters for alkali metal overlayers. Alkali

Substrate

Coverage range Angle range [deg]

Ref.

0.16-0.22 0.33-0.59 0.33-0.44 0.33-0.46 0.33-0.53 0.14-0.20 0.14-0.21 0.14-0.23

5-0 30-18 30-20 30-13 30-14 19.1-0 19.1-0 19.1-0

[91W1] [88C2] [88P1] [86D1] [83D1] [96L2] [96L2] [96L2]

0.33-0.37 0.32-0.38 0.33-0.43

3.3-6.0 3.3-6.0 0-12

[85A1] [92F2] [87B2]

hexagonal on hexagonal: Cs Na K Li Na K Rb Cs

C(0001) Pt(111) Pt(111) Ru(0001) Ru(0001) Ag(111) Ag(111) Ag(111)

hexagonal on square: K K Cs

Cu(100) Ni(100) Rh(100)

The temperature dependence of the overlayer rotation angle for alkalis on Ag(111) was studied in some detail [96L2]. For most coverages, the rotation angle decreases toward 0° as the temperature is increased. The move toward alignment with the substrate is a consequence of the loss of adatom-adatom correlations as the temperature increases. The temperature dependence of this rotation angle has been shown to be consistent with the power law behavior predicted by a mean-field theory of epitaxial rotation [92A2]. This theory could not be applied to the data at low coverages, however. Near the (¥[¥ 5ƒ SKDVH the rotation angle was found to increase, possibly toward 30°, but this could not be confirmed because the rotation transition was pre-empted by melting of the overlayer.

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3.2.1.2.8 Monolayer saturation lattice parameters The nearest-neighbor distances of alkali metals in their saturated monolayers are generally smaller than their metallic diameters derived from the bulk solids. The following table shows the lateral nearestneighbor distances at monolayer saturation for many alkali overlayers along with the ratios of the monolayer nearest-neighbor spacing to the bulk metallic alkali diameter. While it has been occasionally suggested that this is due to charge transfer in the chemisorption bond which makes the effective size of the alkali smaller, calculations for a free-standing Cs monolayer indicate that it is due to the strong intralayer metallic bonding [83W1]. Such a compression is a consequence of the reduced coordination of the atoms in the 2D solid, similar to the shorter bond lengths observed for the lower coordination bonds in general [60P1]. It should be noted, however, that for systems which form islands at low coverages, the equilibrium spacing in these “unconstrained” layers below saturation coverage is generally larger than the bulk spacing [97L1]. This is an indication that the adsorbate-substrate interaction is considerably more important at the lower coverages than it is at monolayer saturation. This compression effect at monolayer saturation has been observed in other metallic adsorption systems, for example Pb/Cu(100) [91L1] or Hg/Cu(100) [92L1]. Looking at overlayers which are commensurate at saturation coverage, it is clear that the presence of a commensurate phase can stabilize the structure at a density extraordinarily compressed relative to the normal bulk alkali spacing, or, in some cases, expanded relative to the bulk. However, it is the incommensurate structures which give us a clearer view of the "true" two-dimensional compression effect. There is some scatter in the measured values for the incommensurate lattice spacings, but there do not seem to be any clear trends which depend on either the substrate material or its symmetry, which is consistent with the notion that this compression is more a property of the 2D layer than of the chemisorption bond. However, the heavier alkali metals experience a larger compression than the lighter ones. From the data we have available, the mean measured compressions (for incommensurate monolayers) are 2% for Li, 5% for Na, 8% for K, 7% for Rb and 15% for Cs. The calculated value for the free-standing Cs monolayer was 11% [83W1]. Monolayer-saturation lattice constants for alkali overlayers. C or I denotes whether the monolayer saturation structure is commensurate, incommensurate, or higher-order commensurate. NN denotes the nearest-neighbor distance and dmetallic denotes the metallic diameter. Alkali

Substrate

NN [Å]

NN/dmetallic

C/I/HOC

Ref.

Li Li Na Na Na Na Na Na Na K K K K K K K K K

Cu(100) Ru(0001) Al(111) Cu(100) Cu(111) Ni(111) Ni(100) Ru(0001) W(112) C(0001) Pd(100) Al(111) Cu(111) Cu(100) Cu(110) Fe(110) Ni(111) Ni(100)

2.94 3.06 3.82 3.61 3.78 3.54 3.52 3.67 3.54 4.92 3.89 4.26 4.4 4.57 4.3 4.31 4.47 4.35

0.94 0.98 1.00 0.95 0.99 0.93 0.92 0.94 0.93 1.03 0.82 0.90 0.92 0.96 0.90 0.91 0.94 0.91

C I C C HOC I C I I C C I I I I I I I

[92T1] [95G2] [93A2] [93E1, 97G3] [91T1] [69G1] [69G1] [83D1] [70P1] [91L2] [87B3] [93A2] [88F1] [84A1] [89F2] [99S1] [88C1] [92F2]

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[Ref. p. 169

Alkali

Substrate

NN [Å]

NN/dmetallic

C/I/HOC

Ref.

K K K K K K Rb Rb Rb Rb Rb Cs Cs Cs Cs Cs Cs Cs Cs Cs Cs Cs Cs Cs Cs

Pd(111) Pd(100) Pt(111) Ru( 10 1 0 ) Ag(111) Ag(100) Al(111) Cu(111) C(0001) Ag(111) Ru(0001) Al(111) C(0001) Ag(111) Cu(111) Cu(100) Cu(110) Ir(100) Mo(110) Ni(111) Ni(100) Pt(111) Ru(0001) W(100) W(110)

4.58 4.30 4.16 4.02 4.54 4.08 4.96 5.10 4.92 4.76 4.69 4.95 4.92 5.01 4.86 4.57 4.7 4.04 4.74 4.71 5.0 4.36 4.69 4.81 4.70

0.96 0.90 0.87 0.84 0.95 0.86 0.97 1.00 0.96 0.93 0.97 0.91 0.90 0.92 0.89 0.84 0.86 0.74 0.87 0.86 0.92 0.80 0.89 0.88 0.86

I C I I I C C C C I C C C C I I I I I I I I C I I

[87M1] [87B3] [88P1] [85D1] [96L2] [90M1] [93A2] [94S1] [94W2] [96L2] [94H3] [93A2] [94W2] [96L2] [88F1] [85C1] [89F2] [85H2] [84R1] [89C1] [72A1] [88C2] [92O2] [89M1] [70F1]

3.2.1.2.9 Condensation transition parameters For certain alkali-substrate combinations, the alkali overlayers undergo a condensation transition at a relatively low coverage instead of compressing uniformly as the coverage is increased. This condensation transition is intriguing because it resembles a nonmetal to metal transition such as those observed in other metal adsorption systems [93P2, 94P1]. (It should be noted, however, that "metalization" transitions have also been observed in the absence of condensation in alkali overlayers [96L5, 99F1].) The structural result of the condensation is the formation of 2D islands of alkali metal, presumably in equilibrium with a 2D vapor phase. In all cases but one, these islands are solid at room temperature, and their melting has not been studied. The alkali adsorption systems for which condensation has been observed are shown in the following table. This table neglects any condensation phenomena which might be associated with large reconstructions such as those which occur on fcc (110) surfaces.

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Alkali adsorption systems which undergo condensation. The information given includes the coverages at which they condense, the structure they condense into, and the temperature. LT denotes a low temperature (usually 80-150 K) and RT denotes room temperature. System

Coverage

Structure

Temp

NN[Å]

Ref.

Na/Al(111) Na/Al(111) Na/Al(111) K/Al(111) Rb/Al(111)

0.15 0.06 0.15 0.1 0.08

LT RT RT LT,RT LT

~4.3 4.96 4.96 4.96 5.73

[93A2] [95B2] [93A2] [93A2] [93A2]

Rb/Al(111)

0.1

"3x3" HOC (√3x√3)R30° (√3x√3)R30° (√3x√3)R30° p(2x2) 1 1    HOC 5 − 6

RT

5.5

[93A2]

Na/Al(100) Na/Al(100)

0.25 0.2

RT LT

4.05 4.05

[95B3] [97L1]

K/Al(100)

0.18

c(2x2) c(2x2) 2 0   HOC   1 5/3 

LT

5.56

[97L1]

Li/Be(0001) Na/Cu(111) Li/Cu(100) K/Cu(100) K/C(0001) Rb/C(0001) K/Ag(100)

0.20 0.18 0.25 0.18 0.02 0.02 0.08

(√3x√3)R30° (3x3)HOC c(2x2) ring p(2x2) p(2x2) c(2x2)

RT LT LT RT LT LT RT

3.97 6.01 3.61 5.6 4.92 4.92 4.09

[94W1] [94F1] [92T1] [85A1, 86A1] [91L2] [94W2] [90M1]

The condensation of Na on Al(111) has been studied theoretically using density-functional theory [93N2, 94S3]. This DFT study indicates that at low coverages, the adsorbate-substrate interaction dominates the overlayer, while at higher coverages the attractive, metallic adsorbate-adsorbate bonds are more important and cause the condensation of the overlayer [93N2, 94S3] The reason that condensation occurs for some alkali overlayers and not others is apparently a result of the balance between the adsorbate-adsorbate and adsorbate-substrate interactions. The stronger dipole moments of the heavier alkali atoms upon adsorption and their lower cohesive energies presumably are related to the fact that they have less of a tendency to condense, compared to the lighter ones. In all cases reported here, alkali metals condense into commensurate or higher-order commensurate phases, suggesting that the extra energy gained by forming a commensurate structure may tip the balance in favor of condensation. This energy must be quite large in the case of alkalis on Al(111) at room temperature where the site is substitutional. As discussed in Section 3.2.1.2.8, the alkali-alkali distance is usually expanded relative to the nearest-neighbor distance in the bulk alkali metal, upon condensation into islands [97L1].

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[Ref. p. 169

3.2.1.2.10 Two-dimensional phase diagrams Equilibrium structures Coverage-temperature phase diagrams provide a useful tool for understanding and comparing alkali metal adsorption systems. The usual method for mapping out these phase diagrams is to measure diffraction intensities of the observed overlayer phases as a function of temperature, over the entire submonolayer coverage range (and sometimes above). The inflection points of the curves obtained in this way are used to identify the disordering temperatures, and these temperatures comprise the order-disorder (or melting) phase boundary. The intermixing of alkalis with some substrates, in particular aluminum and graphite, have complicated the mapping of equilibrium phase diagrams of those systems. Since many of the structures formed on these substrates at low temperatures are metastable, isothermal phase diagrams, such as those shown in the next section, provide a useful alternative. Only a few coverage-temperature phase diagrams have been mapped for alkali metal adsorption on reconstructed surfaces and these are rather complex. The systems for which equilibrium phase diagrams have been determined are shown in the following table. Equilibrium phase diagrams. All phase diagrams were determined using LEED. Alkali

Substrate

Figure

Reference

K K Cs K Cs K K Cs K Cs Na K Cs K Rb Cs Cs

Co(0001) Co (10 10) Cu(111) Cu(110) Cu(110) Ni(111) Ni(100) Ni(111) Pt(111) Rh(100) Ru(0001) Ru(0001) Ru(0001) Ag(111) Ag(111) Ag(111) W(100)

5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

[98V1] [92M2] [88F1] [88F3, 89F2] [88F3, 89F2] [93K1] [92F2] [89C1] [88P1] [87B2] [83D1] [85D1] [92O2] [96L2] [96L2] [96L2] [89M1]

The phase diagrams for alkali metal overlayers on flat metal surfaces have several common elements. In the next few paragraphs we will over-generalize slightly in order to describe several aspects which are common to many of these adsorption systems. At coverages significantly lower than monolayer saturation, ordered phases only occur below room temperature. The exceptions to this arise in cases where the adsorption potential is more corrugated, producing a higher degree of site stabilization. At very low coverages the dominant alkali-alkali interaction is repulsive, causing phases with widely-spaced adatoms. Typically, if the temperature is low enough, diffraction rings are observed at low coverages. These rings indicate that there is a reasonably well-defined nearest-neighbor distance but no long-range rotational correlations in these dispersed overlayers. Rings have been observed at very low coverages, even in most cases where the alkali overlayer condenses at some critical coverage into islands. The formation of these uniform-density overlayers depends on a strong repulsive interaction between the alkali adatoms, and rings corresponding to adatom-adatom spacings as large as of 60 Å have been observed [91L2]. All of the available evidence indicates that these dispersed "ring" phases are repulsive fluids except at very low temperatures. The high mobility of the adatoms in these dispersed phases has been the bane of experiments seeking to determine low-coverage adsorption sites on

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fcc (111) surfaces [93A1]. On substrates of somewhat higher corrugation such as fcc(100), some site stabilization has been observed for very low coverages at temperatures near 100 K [93W1]. At intermediate coverages these low-density fluids solidify. In some cases there is a condensation into a dense phase (see section 3.2.1.2.9), but in most cases the overlayer forms a low-density solid phase. The temperature stability of these solids increases rapidly as their density increases, suggesting that if the temperature is lowered sufficiently, these solid phases can be produced at extremely low densities. The symmetry of alkali metal overlayers, even on surfaces having square or rectangular symmetry, is almost always hexagonal or quasi-hexagonal, except in cases of exceptional substrate corrugation. Commensurate structures are usually more stable than incommensurate structures of a similar density. In general, more open substrate surfaces have a larger corrugation for alkali adsorption than closepacked ones, and the larger alkali metal atoms are affected less by any given substrate periodicity than the smaller ones. The refractory metals provide a larger corrugation than the lighter transition metals. The importance of the substrate corrugation for any particular system is evident by the relative stability of the commensurate phases, both to changes in coverage and to increasing temperature. Since the adatom-adatom and adatom-substrate interactions change with the coverage, the corrugation of the chemisorption potential can also change with coverage, even causing the equilibrium adsorption site to change with coverage (see section 3.2.1.2.6). On more corrugated substrates, the coverage-driven transitions between commensurate phases tend to be first-order transitions, in which the intermediate coverage phases consist of coexisting commensurate structures and the diffraction pattern indicates the presence of both commensurate phases. On very smooth substrates such as the fcc(111) surfaces, incommensurate phases tend to dominate the phase diagram, and the stability of these incommensurate phases depends largely on the strength of the adatom-adatom interactions which stabilize them. Intermediate substrate corrugation causes the formation of density modulations, or domain walls in these incommensurate phases, and a further increase in the corrugation can lead eventually to the formation of microscopic domains of two (or more) commensurate structures, and finally to the type of phase coexistence described above [94N1, 94N3]. On fcc(100) surfaces, the overlayers are frequently distorted uniaxially, i.e. they form a quasihexagonal structure in which domain walls form in one direction (e.g. for K/Ni(100) [92S2]). An interesting variation on these structures are the uniaxial structures formed by Na adsorption on Cu(100) [97G3]. These structures consist of rows of adatoms only a few atoms wide, separated by several lattice spacings. Since the corrugation experienced by Na on Cu(100) is only about 50 meV [97G2], the mechanism behind the formation of these structures seems to be different from those observed in other uniaxial structures, and apparently includes a condensation transition. These 1D structures are similar to the 1D structure observed for Tl on Cu(100) [91B3], which is proposed to exhibit a Peierls distortion [64P1]. The corrugation of the substrate also provides the field which leads to the non-symmetry rotation of incommensurate overlayers, as described in Section 3.2.1.2.7. Other substrate effects can arise from defects in the substrate structure. Substrate steps can cause pinning of the epitaxial rotation of the overlayer. Steppinning of incommensurate phases seems to be more prevalent at low coverages than at high coverage, and it has been demonstrated that alkali metal atoms at low coverage tend to adsorb at step sites [95L1]. This tendency to align along the steps is usually overridden at higher coverages, presumably by the increasingly important collective interactions as the density increases. Step pinning not only causes incommensurate overlayers to align along the step direction, it can cause or prevent the formation of particular commensurate phases. For instance, in the low-coverage potassium overlayer on Cu(111) or Ni(111), the (¥[¥ 5ƒ phase was not observed, possibly due to step pinning along the 0° direction. The saturation of the monolayer for most of these overlayers occurs when the adatom-adatom spacing is smaller than that dictated by their metallic diameters, as discussed in Section 3.2.1.2.8. In several cases it has been observed that the density of the monolayer does not saturate until part of the second layer is adsorbed. There have been few studies on the disordering of alkali metal overlayers. The low-density incommensurate structures on Cu(111) and Ni(111) were found to melt into fluids which are highly correlated [88F2, 89C2]. The highly correlated nearest-neighbor distance in these fluids should not come as a surprise since the appearance of diffraction rings at even lower coverages indicates strong adatom-adatom interactions. However, rotational correlations are observed in these overlayers over a wide temperature range and are interesting in light of the theories for 2D melting in systems having repulsive interactions [89C2].

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[Ref. p. 169

Non-equilibrium phase diagrams In cases where equilibrium phase diagrams are difficult to determine, it is useful at least to have a nonequilibrium structure vs. coverage diagram for a specific temperature. These diagrams are typically measured by observing the diffraction pattern as a function of coverage for a specified temperature. Non-equilibrium phase diagrams. All were determined using LEED with the exception of Na/Cu(100) at 50 K and 100 K, which was determined by He-atom diffraction. Alkali

Substrate

Temp [K]

Figure

Reference

Na K Rb Cs Na K Li Na Na K Cs Li Na K Rb Na

Al(111) Al(111) Al(111) Al(111) Al(111) Al(111) Cu(100) Cu(100) Cu(100) graphite(0001) graphite(0001) Ni(100) Ag(100) Ag(100) Ag(100) Pt(111)

100/300 100/300 100/300 100/300 100 100 180/300 50/100 180 90 90 230/370 180/300 180/300 180/300 85

22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37

[93A2] [93A2] [93A2] [93A2] [97L1] [97L1] [98T1] [97G3] [94M2] [91L3] [96H2] [98T1] [98T1] [98T1] [98T1] [88C2]

3.2.1.2.11 Adsorbate substrate intermixing Alkali metals on certain metal surfaces have a propensity to intermix with the substrate surface atoms, often producing complex surface alloy structures. A recent review of the complex structures formed by alkali adsorption on fcc surfaces describes many of these systems [98T1]. These structures will be discussed in chapter 4.1 in this volume; here we provide a summary. The intermixed structures that have been observed are all activated structures; i.e. their formation requires some thermal energy. The temperatures required to form these structures range from about 200 K to 400 K. Some general features of the intermixed structures studied thus far were summarized in Reference [98T1] as: 1) The intermixed structures reflect the symmetry of the substrate. 2) The formation of intermixed structures does not depend on miscibility of the alkalis and the substrate metals. 3) The alkali adatoms tend to occupy the highest coordination sites. 4) The alkali adatoms tend to be located closer to the vacuum side of the surface than substrate atoms. 5) The substrate atoms displaced in the intermixing process migrate to and from substrate step sites. The simplest cases of intermixing are those that involve the substitution of alkali atoms for top-layer substrate atoms, i.e. the alkali adatoms reside in vacancies in the substrate surface. Experimental measurements of these simple intermixed structures are included in Section 3.2.1.2.6, and are given below again for completeness. In general, these structures involve a higher adatom coordination than is possible without intermixing. The substitutional (¥[¥ 5ƒ VWUXFWXUH IRUPHG E\ alkalis on Al(111) has been studied in some detail theoretically. DFT calculations have found that the formation of these structures is related to the low energy required to form vacancies on the Al(111) surface [95S1], as well as the lowering of the total energy which results from the adatoms sitting closer to the surface and having a higher coordination [95S1]. Lando lt -Börnst ein New Ser ies III/42A1

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More complex intermixed structures involving a larger disturbance of the surface layers have also been observed and characterized. The structures that have been characterized are listed in the table below. Theoretical studies of these systems generally have found that the observed structures are in fact the lowest-energy structures [97Q1, 98O1]. The alkali-induced missing-row reconstructions of the fcc(110) can also be viewed as intermixed structures, although in these cases, the alkali adatoms do not necessarily form commensurate overlayers. These structures always involve missing single substrate rows, and the alkali adatoms reside in the troughs. The fcc(110) missing-row reconstructions were the first alkaliinduced reconstructions to be observed [83H1], and were ascribed to the instability of the fcc(110) surfaces since such structures were also observed on clean Au, Pt and Ir (110) surfaces. However, similar alkali-induced reconstructions have now been observed on stable fcc(100) surfaces. The stability of the missing-row structures has been attributed to the polar nature of the alkali bond to the surface which is maximized when the alkali atoms are embedded in the surface [87B1]. The evidence for this is that at higher alkali coverages where the bond formed is less polar, the number of alkali adatoms in substitutional sites decreases, sometimes to zero [87B1, 98T1]. In the following table, the intermixed structures have been classified according to the scheme employed in the recent review [98T1]. The first class, fcc(001)-(2x1)-xAM refers to structures in which the substrate undergoes a missing-row reconstruction, and alkali atoms occupy the resulting troughs. The "x" corresponds to a fractional number of alkali atoms per unit cell, typically between 0.6 and 0.8. A similar situation exists for the fcc(001)-(3x3)-xAM and fcc(110)-(1x2)-xAM structures. The notation 1x3L corresponds to "light" missing row structures in which there are double missing rows separated by single rows, while 1x3H corresponds to "heavy" missing row structures in which there are double rows separated by single missing rows. In some cases, the intermixing involves just one substrate layer, but in other cases several layers may be involved. These structures are discussed in more detail in Chapter 4.1 of this volume.

Intermixed structures All geometry determinations were made using LEED, with the exception of the SEXAFS study of Al(111)-(¥[¥ 5ƒ1D Structure

Adatom geometry

Ref.

Cu(100)-(2x1)-xLi Ag(001)-(2x1)-xNa Ag(001)-(2x1)-xK Ag(001)-(2x1)-xRb

incommensurate incommensurate incommensurate incommensurate

[93M3] [98T1] [98T1] [98T1]

Al(001)-c(2x2)-2Na Al(001)-c(2x2)-2Li

substitutional substitutional

[95B3] [99P1]

Cu(001)-(3x3)-5Li Cu(001)-(4x4)-10Li Ag(001)-(3x3)-5Na Ag(001)-(4x4)-10Na Fe(001)-(3x3)-K Ni(001)-(4x4)-10Li Ni(001)-(5x5)-17Li

complex complex complex complex substitutional complex complex

[95M2] [95M3] [98T1] [97J2] [96B2] [97J1] [97J1] cont.

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[Ref. p. 169

Intermixed structures (cont.) Structure

Adatom geometry

Ref.

Ag(001)-(3x1)-xK Ni(001)-c(6x2)-xNa Ag(110)-(1x2)-K Ag(110)-(1x2)-Cs Ag(110)-(1x2)-Cs Au(110)-(1x3) Cu(110)-(1x2)-K Cu(110)-(1x2)-Cs Cu(110)-(1x3L)-Cs Cu(110)-(1x3H)-Cs Ni(110)-(1x2)-K Pd(110)-(1x2)-Cs

incommensurate incommensurate incommensurate incommensurate incommensurate incommensurate incommensurate incommensurate incommensurate incommensurate incommensurate incommensurate

[91O1, 96I1] [98T1] [87F1] [89B1, 95S2] [95S2] [89H1] [90H1, 94H2] [90H1] [96M1] [96M1] [92J1, 93S1] [88B1]

Au(110)-c(2x2)-K

complex

[89H6]

Cu(110)-(4x2)-3Li

complex

[97M2]

Al(111)-(¥[¥ 5ƒ/L Al(111)-(¥[¥ 5ƒ1D Al(111)-(¥[¥ 5ƒ. Al(111)-(¥[¥ 5ƒ5E

substitutional substitutional substitutional substitutional

[96N1] [91S2, 94B3] [94S4] [94N2]

Al(111)-(2¥[¥ 5ƒ&V complex Al(111)-(2x2)-2Na complex Cu(111)-(2x2)-3Li complex

[96A1] [95B1] [95M1]

Al(111)-(2x2)-(Na+K) Al(111)-(2x2)-(Na+Rb) Al(111)-(2x2)-(Na+Cs)

[96C1] [96C1] [96C1]

complex complex complex

Lando lt -Börnst ein New Ser ies III/42A1

Ref. p. 169]

3.2.1 Alkali metals on metals

157

Figures for 3.2.1 3.0

Cs/Ru(0001)

2.5

Heat of adsorption Q [eV]

Work function φ

∆φML

∆φmin

2.0

1.5

1.0

0.5 0

0

0.2

0.4 0.6 Coverage θ

Alkali coverage

0.8

Fig. 2. The heat of Cs adsorption on Ru(0001) as a function of the coverage as derived from TPD measurements [96P1, 98O2]. The open points are from theory and the arrow on the right indicates the calculated cohesive energy of Cs [96P1].

Fig. 1. Typical behavior of the work function for alkali atoms adsorbed on a metal surface.

50

Li

45

frequency (meV)

40 35 30 25

K

Na perpendicular

20 15

Cs Rb

10

parallel

5 0

0

0.1

0.2

M-1/2

0.3

0.4

(amu-1/2 )

Fig. 3. On-surface alkali-metal perpendicular and parallel vibration energies plotted against the inverse square root of the mass number of the alkali. The lines are to guide the eye.

Lando lt -Bö rnst ein New Ser ies III/42A1

1.0

3.2.1 Alkali metals on metals

158

[Ref. p. 169

NM, dipole potential NM, Lennard-Jones potential Shiba HOC positions

25°

Rotation Angle

20°

15°

10°

5°

0° 0.0

0.1

0.2

0.3

Misfit

Fig. 4. The predictions of the various models for rotational epitaxy, for a hexagonal overlayer on a hexagonal substrate. Misfit is defined as (LO-2LS)/2LS, where LO is the overlayer lattice spacing and LS is the substrate lattice spacing. NM denotes the Novaco-McTague model, HOC denotes the higher-order commensurate positions.

700

K/Co(0001) desorption

(2×2) rotated

100

0

0.1

0.2

0.3 0.4 Coverage θ

450 350

p(1x1) lattice gas

distributed vacancy structure

250

ring

200

550

0.5

0.6

Fig. 5. Coverage-temperature phase diagram for K on Co(0001) [98V1].

multilayers

multilayers

c(2x2) high density domain wall

Temperature (K)

θsat = 0.31 ± 0.01

400 300

K/Co(1010)

650

disorder

low density domain wall

500

split

Temperature T [K]

600

150 0.0

0.1

0.2

0.3

0.4

0.5

0.6

Coverage Fig. 6. Phase diagram for K on Co( 10 10 ) [92M2]. The phase boundaries are approximate.

Lando lt -Börnst ein New Ser ies III/42A1

Ref. p. 169]

3.2.1 Alkali metals on metals

159

500

Cs/Cu(111) p(2×2)

Temperature T [K]

400 disordered

300 "hexatic" fluid

200

100

incommensurate solid 2nd layer onset

Fig. 7. The phase diagram determined by LEED for Cs on Cu(111) [88F1]. 0

0.1

0.2 Coverage θ

400

(W

Temperature T [K]

(LR)+(D)

320

(1×3R)+(D)

360

2 1×

R)+

0.3

0.4

K/Cu(110)

(S) (W1×3R)+(S)

(QHR)

(1×2R)+(S) (1×3R)+(S)

280 240 (RT)+(D)

200

(R

T )+

160

(SO

) (QHU)

(DU) 120 80

(QHU)+(IG) 0

0.1

0.2

0.3 0.4 Coverage θ

0.5

0.6

0.7

Fig. 8. Phase diagram for K adsorption on Cu(110). QHU indicates the quasihexagonal structure on the unreconstructed substrate. IG denotes the immobile gas. DU indicates the disordered Cs on the unreconstructed substrate. RT indicates the reconstructing phase transition region. SO indicates short-range-ordered quasihexagonal overlayer. D indicates disordered atoms on the reconstructed substrate. S denotes regions where there are streaks in the diffraction pattern. LR indicates a local substrate reconstruction. 1x2R and 1x3R indicate the reconstructed substrate. W1x2R and W1x3R indicated a well-ordered reconstructed substrate. QHR indicates the quasihexagonal layer on the 1x3 reconstructed substrate.

Lando lt -Bö rnst ein New Ser ies III/42A1

3.2.1 Alkali metals on metals

160

400

Cs/Cu(110)

(W1×2R)+(S)

(W1×3R)+(S)

Temperature T [K]

(LR)+(D)

(1×3R)+(D)

360 320

[Ref. p. 169

(1×2R)+(S) (1×3R)+(S)

280 240 (RT)+(D)

200

( RT

)+(

SO)

160

(QHU)

(DU) 120 80

(QHU)+(IG) 0

0.1

0.2

0.3 Coverage θ

0.4

0.5

0.6

Fig. 9. Phase diagram for Cs adsorption on Cu(110). QHU indicates the quasihexagonal structure on the unreconstructed substrate. IG denotes the immobile gas. DU indicates the disordered Cs on the unreconstructed substrate. RT indicates the reconstructing phase transition region. SO indicates short-range-ordered quasihexagonal overlayer. D indicates disordered atoms on the reconstructed substrate. S denotes regions where there are streaks in the diffraction pattern. LR indicates a local substrate reconstruction. 1x2R and 1x3R indicate the reconstructed substrate. W1x2R and W1x3R indicated a well-ordered reconstructed substrate. QHR indicates the quasihexagonal layer on the 1x3 reconstructed substrate.

Temperature (K)

500

p(2x2)

K/Ni(111)

incommensurate solid

400

2nd layer onset

modulated fluid

300 200

isotropic fluid 0

0.1

0.2

0.3

0.4

Coverage Fig. 10. Submonolayer coverage-temperature phase diagram for K/Ni(111) [93K1].

Lando lt -Börnst ein New Ser ies III/42A1

Ref. p. 169]

3.2.1 Alkali metals on metals

161

400

K/Ni(100)

th des erma orp l tion

isotropic fluid + c(4x2) c(4x2)

( 21 5/30 )

0.25

0.3

diffusion or desorption

2nd layer formation

uniaxially incommensurate phase

200

100 0.2

uniaxial incommensurate

300

isotropic fluid

Temperature (K)

disordered phase

epitaxial rotation

rectangular

hex

0.35

Fig. 11. Submonolayer coveragetemperature phase diagram for K/Ni(100) [92F2].

0.4

Coverage 500

Cs/Ni(111)

K/Pt(111)

400 400

200

150 100

IS 0

0.05

0.10

0.15 0.20 Coverage θ

HFD + second layer 0.25

0.30

0.35

Fig. 12. Submonolayer coverage-temperature phase diagram for Cs/Ni(111) [89C1].

Lando lt -Bö rnst ein New Ser ies III/42A1

100

0

0.1

0.2

0.3

MULTIPHASE

IR + second layer

(√3x√3)R30˚

AS or F1

F2

2x2

250

DISORDER

300

MIXED PHASE

300

coexistence

Temperature T [K]

IS IR + second layer

(√7x√7)R19.1˚

C

Temperature (K)

disordered

350

200

1st LAYER DESORPTION

RINGS

450

0.4

Coverage Fig. 13. Phase diagram for K adsorption on Pt(111) [88P1]. In the multiphase region a continuous compression of the overlayer results in rotational epitaxy or aligned structures.

3.2.1 Alkali metals on metals

162

400

Cs/Rh(100) (333±5) K

Temperature (K)

Lattice Gas 300

(Desorption)

(258±5) K 7 8

200

(155±5) K

4

5

3

(145±5) K

6

2

1

100

0 0

0.1

0.2

0.3

0.4

0.5

Coverage

500

[Ref. p. 169 Fig. 14. Experimental phase diagram for the system Cs/Rh(100) [87B2]. The encircled numbers denote the different phases observed: (1): c(2√2x4√2)R45º, (2): (√5x√5)Rarctan1/2, (3): c(4x2), (4): Incommen-surate phase with superstructure spots shifting from positions of phase (3) to positions of phase (5), (5): (3x2)-2Cs, (6): (√5x√5)Rarctan1/2-2Cs, (7): hexagonal incommensurate phase with rotational epitaxy, (8): hexagonal incommensurate phase c(2√2x2√2/3)R45º.

FIRST LAYER DESORPTION

Na/Ru(0001)

Temperature (K)

400 DISORDERED (3/2x3/2)

300

LARGE RING+ (3/2x3/2)

IRREVERISBLE TR

200 SMALL RING

100

(2x2)

TR

SPLIT (√3x√3)R30˚ (√3x√3) R30˚

TR

LARGE RING

(2x2) + (√3x√3)R30˚

0

0.2

0.3

0.4

Fig. 15. Phase diagram for Na adsorbed on Ru(0001) at 80 K [83D1]. Dashed lines indicate approximate phase boundaries. TR indicates transition region.

0.5

Coverage

Lando lt -Börnst ein New Ser ies III/42A1

Ref. p. 169]

3.2.1 Alkali metals on metals

500

K/Ru(0001)

Cs/Ru(0001)

400

Desorption

Ring

(2×2)

Ring

(2x2)

0.1

0.2

Ring

Multilayers

200

(√3x√3)R30˚

3

200

300

Rotated Structures

Temperature (K)

300

100

Desorption

Disorder

400 Temperature T [K]

163

100

0

0.1

0.2 Coverage θ

0.3

0.4

0

0.3

0.4

0.5

Coverage Fig. 16. Phase diagram for the adsorption of K on Ru(0001) [85D1].

Fig. 17. Phase diagram for the adsorption of Cs on Ru(0001). The hash-marked area represents a qualitative result [92O2].

400

75

K/Ag(111)

desorp

tion

F 60

0

IR 0

a

0.1

IA

0.2 Coverage

p(2×2)

IA

0.3

3

30

Co-

100

Co-(IA & IA30°)

200

45

p(3×3)

Temperature T [K]

F

Co-(IA & IA30°)

Temperature T [K]

300

IR

IR

HOC

0.14 0.16 Coverage θ

0.18

7

15

IA

0.4

b

0 0.10

0.12

0.20

Fig. 18a, b. (a) Coverage-temperature phase diagram for K/Ag(111) [96L2]. The open points indicate the inflection points of the disordering curves (LEED intensity vs. temperature plots). Regions which are shaded denote commensurate phases. IA denotes an incommensurate phase, aligned with the substrate, IA30° denotes an incommensurate phase, aligned at 30° with respect to the substrate, Co- denotes a coexistence of two phases, F denotes a fluid, ¥ GHQRWHV WKH ¥[¥ 5ƒ VWUXFWXUH ¥ GHQRWHV WKH ¥[¥ 5ƒ VWUXFWXUH +2& GHQRWHV D higher-order commensurate phase. (b) Provides an enlarged view of the coverage range 0.10 to 0.20.

Lando lt -Bö rnst ein New Ser ies III/42A1

3.2.1 Alkali metals on metals deso

Rb/Ag(111)

90 n

a

0

0.1

0.2 Coverage

3

0.3

60 IA

IA30°

45 30

2 3

15 Co-

IA

Co-(IA & IA30°)

IR

0

p(2×2)

IA

Co-(IA & IA30°)

200

Temperature T [K]

HOC

100

F

75

F

300 Temperature T [K]

rptio

0.4

b

0 0.06

0.10

7

IR

HOC

IR

Co-

400

[Ref. p. 169

p(3×3)

164

0.14 Coverage

0.18

0.22

Fig. 19a, b. (a) Coverage-temperature phase diagram for Rb/Ag(111) [96L2]. The open points indicate the inflection points of the disordering curves (LEED intensity vs. temperature plots). Regions which are shaded denote commensurate phases. IA denotes an incommensurate phase, aligned with the substrate, IA30° denotes an incommensurate phase, aligned at 30° with respect to the substrate, Co- denotes a coexistence of two phases, F denotes a fluid, 2¥ GHQRWHV WKH ¥[¥ 5ƒ VWUXFWXUH ¥ GHQRWHV WKH ¥[¥ 5ƒ VWUXFWXUH ¥ GHQRWHV WKH (¥[¥ 5ƒ VWUXFWXUH +2& GHQRWHV D KLJKHURUGHU FRPPHQVXUDWH SKDVH (b) provides an enlarged view of the coverage range 0.06 to 0.22. (Error: the arrow IA30o denotes the small region left of the Co- region !).

400

de

Cs/Ag(111)

sor

75 pti

F

on

60

IR 0

0.1

0.2 Coverage θ

0.3

IR

7

IR

30

IA Co-

IA

IA & IA30°

IA

3

45

2 3 IA30° CoIA p(3×3)

200

100

a

Temperature T [K]

F

p(2×2)

Temperature T [K]

300

15

0.4

b

0 0.06

0.08

0.10 0.12 Coverage θ

0.14

0.16

Fig. 20a, b. (a) Coverage-temperature phase diagram for Cs/Ag(111) [96L2]. The open points indicate the inflection points of the disordering curves (LEED intensity vs. temperature plots). Regions which are shaded denote commensurate phases. IA denotes an incommensurate phase, aligned with the substrate, IA30° denotes an incommensurate phase, aligned at 30° with respect to the substrate, Co- denotes a coexistence of two phases, F denotes a fluid, 2¥ GHQRWHV WKH ¥[¥ 5ƒ VWUXFWXUH ¥ GHQRWHV WKH ¥[¥ 5ƒ VWUXFWXUH ¥ GHQRWHV WKH (¥[¥ 5ƒ VWUXFWXUH (b) provides an enlarged view of the coverage range 0.06 to 0.16.

Lando lt -Börnst ein New Ser ies III/42A1

Ref. p. 169]

3.2.1 Alkali metals on metals

Na/Al(111)

500

Cs/W(100)

(1×1)W + 400 disordered Cs

"3×3"

Csdesorption

4×4

1×1

T = 100 K

300

c(2×2)W + 200 disordered Cs 130 K

c(2×2)W + incommens. Cs(II)

"ring"

0

0.1

0.2

2×2

1×1

RT

( 3× 3)R30°

c(2×2)W c(2×2)W + + incommens. p(2×2)Cs Cs(I)

100

second layer growth

Temperature T [K]

165

hex.

0.3 0.4 Coverage θ

0.5

0.6

0

0.1

0.2

0.3 0.4 Coverage θ

0.5

0.6

0.7

Fig. 21. Experimental phase diagram for the adsorption of Cs on W(100) [89M1].

Fig. 22. Na/Al(111)-structures observed following deposition at 100K and at 300K, respectively [93A2].

K/Al(111)

Rb/Al(111) ( 3× 3)R30° split 3

1×1

T = 100 K

( 3× 3)R30°

1×1 2×2

T = 100 K

( 3× 3)R30° RT

1×1

0

0.1

0.3 0.4 0.5 0.6 Coverage θ Fig. 23. K/Al(111)-structures observed following deposition at 100K and at 300K, respectively [93A2].

Lando lt -Bö rnst ein New Ser ies III/42A1

0.2

1×1

0

( 0.1

1 1 5 –6

)

( 3× 3)R30° RT

0.2 0.3 0.4 0.5 Coverage θ Fig. 24. Rb/Al(111)-structures observed following deposition at 100K and at 300K, respectively [93A2].

3.2.1 Alkali metals on metals

166

Cs/Al(111)

[Ref. p. 169

Na/Al(100) T = 100 K

( 3× 3)R30°

ring 1×1

T = 100 K

2×2

split c(2×2)

1×1

c(2×2)

ring

(

1×1

1 1 5 –6

)

( 3× 3)R30° RT

0.2 0.3 0.4 Coverage θ Fig. 25. Cs/Al(111)-structures observed following deposition at 100K and at 300K, respectively [93A2].

0.7 0.3 0.4 0.5 0.6 Coverage θ Fig. 26. Na/Al(100)-structures observed following deposition at 100 K.

K/Al(100)

Li/Cu(100)

T = 100 K

T = 180 K

0

0.1

0

0.1

0.2

complex * ** structures

c(2×2) compression

"ring"

T = 300 K

( 5/30 –12 )

1×1

2×1 c(2×2)

3×3

4×4

disorder

0.6

0.7

streak*** 0

0.1

0.2

0.3 0.4 0.5 0.6 Coverage θ Fig. 27. K/Al(100)-structures observed following deposition at 100 K.

0

0.1

0.2

0.3

0.4 0.5 Coverage θ

0.8

* c(7 2× 2)R45° ** c(5 2× 2)R45° *** 1/2Θ 0 –1/4Θ 2 Fig. 28. Surface structures observed for Li/Cu(100) at 180 K and 300 K as a function of Li coverage [98T1].

(

)

Lando lt -Börnst ein New Ser ies III/42A1

Ref. p. 169]

3.2.1 Alkali metals on metals

167

Na/Cu(100)

Na/Cu(100) T = 50 K

T = 180 K

c(2×2)

3×1

c(4 2×2 2)R45°

4×1

p(4×2)

( 10× 10)R18.4°

( –23 02 )

"ring"

"ring"

c(2×2) c(14×2)

"ring" T = 100 K 0

0.1

0.2 0.3 0.4 0.5 Coverage θ Fig. 29. Surface structures observed for Na/Cu(100) a 50 K and 100 K as a function of Na coverage [97G3].

0.2 0.3 0.4 0.5 Coverage θ Fig. 30. Surface structures observed for Na/Cu(100) a 180 K as a function of Na coverage [94M2]

K/C(graphite)

Li/Ni(001)

T = 90 K

"ring"+ p(2×2)

0

T = 230 K

p(2×2)

1×1

"ring" 0.22 0.25 Coverage θ Fig. 31. Schematic representation of the progression of equilibrium phases as a function of coverage for K on graphite at 90 K (the lable "ring" + p(2x2) applies to the whole section from 0.02 to 0.22) [91L2] . 0.02

0

rotated incomm. p(2×2)

"ring" 0.015

0.14 0.16 0.22 0.25 Coverage θ Fig. 32. Schematic representation of the progression of equilibrium phases as a function of coverage for Cs on graphite at 90 K [96H2].

Lando lt -Bö rnst ein New Ser ies III/42A1

0.2

0.3

* **

0.4 0.5 Coverage θ

0.6

q-hex. 0.7

0.8

** c(5 2× 2)R45°

T = 370 K c(2×2)

1×1

( 7× 7)R19.1° disorder

0.1

c(2×2)

* c(9 2× 2)R45°

Cs/C(graphite) T = 90 K

0.1

0

0.1

0.2

0.3

0.4 0.5 Coverage θ

4×4 0.6

* disorder 0.7

0.8

* 5×5 Fig. 33. Schematic diagram of the observed structures for Li adsorption on Ni(100) at 230K and 370K.

3.2.1 Alkali metals on metals

168

[Ref. p. 169

K/Ag(001)

Na/Ag(001) T = 300 K

T = 300 K

2×1

2×1

1×1

4×4 4×2 2×1

3×3

1×1

3×1

streak

streak

T = 180 K

T = 180 K

1×1

0

0.1

c(2×2)

0.2

0.3

0.4 0.5 Coverage θ

*

** *** q-hex.

0.6

0.7

0.8

* c(9 2× 2)R45° ** c(7 2× 2)R45° *** c(5 2× 2)R45°

q-hex.

1×1

0

0.1

0.2

0.3

c(2×2)

0.4 0.5 Coverage θ

hex.

0.6

0.7

0.8

Fig. 35. Structures observed for K/Ag(100) as a function of coverage at 180 K and 300 K, respectively [98T1].

Fig. 34. Structures observed for Na/Ag(100) as a function of coverage at 180 K and 300 K, respectively [98T1].

Rb/Ag(001)

Na/Pt(111) T = 85 K

T = 300 K 2×1 1×1

p(2×2) 0

T = 180 K

qc c (4×2) (3×2) hex.

1×1

0.1

incommensurap(2×2) te

3×3 streak

0

coexistence

"ring"

0.2

0.3

0.4 0.5 Coverage θ

0.7

0.2

0.3 Coverage θ

0.4

0.5

0.6

Fig. 37. Structures observed for Na/Pt(111) as a function of coverage at 85 K [88C2].

2nd layer

0.6

0.1

( 3× 3)R30°

0.8

Fig. 36. Structures observed for Rb/Ag(100) as a function of coverage at 180 K and 300 K, respectively [98T1].

Lando lt -Börnst ein New Ser ies III/42A1

3.2.1 Alkali metals on metals

169

References for 3.2.1 23L1 25L1 27T1 29L1 31L1 32L1 35G1 46M1 60P1 64P1 66S1 67G1 69G1 69M1 69S1 70F1 70G1 70M1 70P1 71C1 71F1 71L1 71P1 72A1 72K1 72T1 72V1 73A1 73D1 73M1 73P1 73P2 74A1 74M1 74P1 74T1 75A1 75A2 75B1 75D1 75P1 76B1 76H1 76M1 77B1

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91D2 91G1 91G2 91L1 91L2 91L3 91M1 91M2 91O1 91P1 91R1

3.2.1 Alkali metals on metals Barnes, C.J., Lindroos, M., Holmes, D.J., King, D.A.: Surf. Sci. 219 (1989) 143. Bonzel, H.P., Bradshaw, A.M., Ertl, G.: Physics and Chemistry of Alkali Metal Adsorption. Amsterdam: Elsevier, 1989. Chandavarkar, S., Diehl, R.D., Faké, A., Jupille, J.: Surf. Sci. 211/212 (1989) 423. Chandavarkar, S., Diehl, R.D.: Phys. Rev. B 40 (1989) 4651. Duszak, R., Prince, R.H.: Surf. Sci. 216 (1989) 14. Frank, K.H., Sagner, H.-J., Heskett, D.: Phys. Rev. B 40 (1989) 2767. Fan, W.C., Ignatiev, A.: J. Vac. Sci. Technol. A 7 (1989) 2115. Häberle, P., Fenter, P., Gustafsson, T.: Phys. Rev. B 39 (1989) 5810. Hohlfeld, A., Horn, K.: Surf. Sci. 211/212 (1989) 844. Horn, K., Hohlfeld, A., Somers, J., Lindner, T., Hollins, P., Bradshaw, A.M.: Phys. Rev. Lett. 63 (1989) 1536. Hu, Z.P., Li, J., Wu, N.J., Ignatiev, A.: Phys. Rev. B 39 (1989) 13201. Hrbek, J., Shek, M.-L., Sham, T.K., Xu, G.-Q.: J. Chem. Phys. 91 (1989) 5786. Häberle, P., Gustafsson, T.: Phys. Rev. B 40 (1989) 8218. Ishida, H.: Phys. Rev. Lett. 63 (1989) 1535. Müller, K., Besold, G., Heinz, K.: Structures and phases of adsorbed alkali metals, in: Physics and Chemistry of Alkali Metal Adsorption. Bonzel, H.P., Bradshaw, A.M., Ertl, G. (eds.), Amsterdam: Elsevier, 1989, p. 65. Maus-Friedrichs, W., Hoermann, H., Kempter, V.: Surf. Sci. 224 (1989) 112. Von Eggeling, C., Schmidt, G., Besold, G., Hammer, L., Heinz, K., Müller, K.: Surf. Sci. 221 (1989) 11. Wandelt, K.: Work-function changes due to alkali metal adsorption, in: Physics and Chemistry of Alkali Metal Adsorption. Bonzel, H.P., Bradshaw, A.M., Ertl, G. (eds.), Amsterdam: Surface Science,1989, p. 25. Winograd, N., Chang, C.-C.: Phys. Rev. Lett. 62 (1989) 2568. Astaldi, C., Rudolf, P., Modesti, S.: Solid State Commun. 75 (1990) 847. Campbell, C.T.: Ann. Rev. Phys. Chem 41 (1990) 775. Duszak, R., Prince, R.H.: Surf. Sci. 226 (1990) 33. Hu, Z., Pan, B., Fan, W., Ignatiev, A.: Phys. Rev. B 41 (1990) 9692. Lindgren, S.Å., Svensson, C., Walldén, L.: Phys. Rev. B 42 (1990) 1467. Modesti, S., Chen, C.T., Ma, Y., Meigs, G., Rudolf, P., Sette, F.: Phys. Rev. B 42 (1990) 538 1. Nielsen, H.B., Burghaus, U., Broström, G., Matthias, E.: Surf. Sci. 234 (1990) L271. Riffe, D.M., Wertheim, G.K., Citrin, P.H.: Phys. Rev. Lett. 64 (1990) 571. Rudolf, P., Astaldi, C., Modesti, S.: Phys. Rev. B 42 (1990) 1856. Barnes, C.J., Hu, P., Lindroos, M., King, D.A.: Surf. Sci. 251/252 (1991) 561. Bonzel, H., Pirug, G., Ritke, C.: Langmuir 7 (1991) 3006. Binns, C., Norris, C.: J. Phys.: Condens. Matter 3 (1991) 5425. Diehl, R.D.: Structures and phase transitions in alkali metal overlayers on transition metal surfaces, in: Phase Transitions in Surface Films 2, Taub, H., et al. (eds.), New York: Plenum Press, 1991, p. 97. Dudde, R., Johansson, L.S.O., Reihl, B.: Phys. Rev. B 44 (1991) 1198. Grey, F., Bohr, J.: Epitaxial rotation and rotational phase transitions, in: Phase Transitions in Surface Films 2, Taub, H., et al. (eds.), New York: Plenum Press, 1991, p. 83. Gaspar, J.A., Eguiluz, A.G., Tsuei, K.-D., Plummer, E.W.: Phys. Rev. Lett. 67 (1991) 54. Li, W., Lin, J.-S., Karimi, M., Moses, C., Vidali, G.: Appl. Surf. Sci. 48/49 (1991) 160. Li, Z.Y., Hock, K.M., Palmer, R.E.: Phys. Rev. Lett. 67 (1991) 1562. Li, Z.Y., Hock, K.M., Palmer, R.E., Annett, J.F.: J. Phys.: Condens. Matter 3 (1991) S103. Matthew, J.A.D., Netzer, F.P., Astl, G.: Surf. Sci. 259 (1991) L757. Memmel, N., Rangelov, G., Bertel, E., Dose, V.: Phys. Rev. B 43 (1991) 6938. Okada, M., Tochihara, H., Murata, Y.: Phys. Rev. B 43 (1991) 1411. Pirug, G., Ritke, C., Bonzel, H.P.: Surf. Sci. 257 (1991) 50. Rudolf, P., Astaldi, C., Cautero, G., Modesti, S.: Surf. Sci. 251/252 (1991) 127. Lando lt -Börnst ein New Ser ies III/42A1

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Scheffler, M., Droste, C., Fleszar, A., Máca, F., Wachutka, G., Barzel, G.: Physica B 172 (1991) 143. Schmalz, A., Aminpirooz, S., Becker, L., Haase, J., Neugebauer, J., Scheffler, M., Adams, D.L., Bøgh, E.: Phys. Rev. Lett. 67 (1991) 2163. Tang, D., McIlroy, D., Shi, X., Su, C., Heskett, D.: Surf. Sci. Lett. 255 (1991) L497. Wu, N.J., Hu, Z.P., Ignatiev, A.: Phys. Rev. B 43 (1991) 3805. Aminpirooz, S., Schmalz, A., Becker, L., Pangher, N., Haase, J., Nielsen, M.M., Batchelor, D.R., Bøgh, E., Adams, D.L.: Phys. Rev. B 46 (1992) 15594. Abernathy, D.L., Mochrie, S.G.J., Zehner, D.M., Grübel, G., Gibbs, D.: Phys. Rev. B 45 (1992) 9272. Argile, C., Rhead, G.E.: Surf. Sci. 279 (1992) 244. Castro, G.R., Busse, H., Janssens, T., Wandelt, K.: Phys. Scr. T41 (1992) 208. Fisher, D., Chandavarkar, S., Collins, I.R., Diehl, R.D., Kaukasoina, P., Lindroos, M.: Phys. Rev. Lett. 68 (1992) 2786. Fisher, D., Diehl, R.D.: Phys. Rev. B 46 (1992) 2512. Gierer, M., Bludau, H., Hertel, T., Over, H., Moritz, W., Ertl, G.: Surf. Sci. 279 (1992) L170. Jiang, Q.T., Statiris, P., Gustafsson, T., Häberle, P., Zehner, D.M.: J. Vac. Sci. Technol. A10 (1992) 2197. Janssens, T., Castro, G.R., Busse, H., Schneider, U., Wandelt, K.: Surf. Sci. 269/70 (1992) 664. Kerkar, M., Fisher, D., Woodruff, D.P., Jones, R.G., Diehl, R.D., Cowie, B.C.C.: Surf. Sci. 278 (1992) 246. Kerkar, M., Fisher, D., Woodruff, D.P., Jones, R.G., Diehl, R.D., Cowie, B.C.C.: Phys. Rev. Lett. 68 (1992) 3204. Kiskinova, M.P.: Poisoning and Promotion, in: Catalysis Based on Surface Science Methods; Studies in Surface Science and Catalysis Vol. 70. Amsterdam: Elsevier, 1992. Li, W., Lin, J., Karimi, M., Dowben, P.A., Vidali, G.: Phys. Rev. B 45 (1992) 3708. Muschiol, U., Bayer, P., Heinz, K., Oed, W., Pendry, J.B.: Surf. Sci. 275 (1992) 185. Masuda, T., Barnes, C.J., Hu, P., King, D.A.: Surf. Sci. 276 (1992) 122. Neugebauer, J., Scheffler, M.: Phys. Rev. B 46 (1992) 16067. Okada, M., Iwai, H., Klauser, R., Murata, Y.: J. Phys. Condens. Matter 4 (1992) L593. Over, H., Bludau, H., Skottke-Klein, M., Ertl, G., Moritz, W., Campbell, C.T.: Phys. Rev. B 45 (1992) 8638 . Stampfl, C., Scheffler, M., Over, H., Burchhardt, J., Nielsen, M.M., Adams, D.L., Moritz, W.: Phys. Rev. Lett. 69 (1992) 1532. Shrimpton, N.D., Fisher, D., Diehl, R.D.: Phys. Rev. B 45 (1992) 12118. Tochihara, H., Mizuno, S.: Surf. Sci. 279 (1992) 89. Adler, D.L., Collins, I.R., Liang, X., Murray, S.J., Leatherman, G.S., Tsuei, K.-D., Chaban, E.E., Chandavarkar, S., McGrath, R., Diehl, R.D., Citrin, P.H.: Phys. Rev. B 48 (1993) 17445. Andersen, J.N., Lundgren, E., Nyholm, R., Qvarford, M.: Surf. Sci. 289 (1993) 307. Bonzel, H.P., Pirug, G.: Interaction between Alkali metal adsorbates and adsorbed molecules (CO;H2O), in: The Chemical Physics of Solid Surfaces and Heterogeneous Catalysis Vol. 6. King, D.A., Woodruff, D.P. (eds.), Amsterdam: Elsevier, 1993, p. 51. Cui, J., White, J.D., Diehl, R.D.: Surf. Sci. Lett. 293 (1993) L841. Cassuto, A., Schmidt, S., Mane, M.: Surf. Sci. 284 (1993) 273. Dudde, R., Reihl, B.: Surf. Sci. 287/288 (1993) 614. Ellis, J., Toennies, J.P.: Phys. Rev. Lett. 70 (1993) 2118. Fischer, N., Schuppler, S., Fisher, R., Fauster, T., Steinmann, W.: Phys. Rev. B 47 (1993) 4705. Huang, Z., Wang, L.Q., Schach von Wittenau, A.E., Hussain, Z., Shirley, D.A.: Phys. Rev. B 47 (1993) 13626. Hock, K.M., Palmer, R.E.: Surf. Sci. 284 (1993) 349.

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3.2.2 Alkali metals on semiconductors E.G. MICHEL, R. MIRANDA

3.2.2.1 Introduction 3.2.2.1.1 Historical layout and general background The investigation of the electronic and crystallographic properties of metal-semiconductor junctions was prompted by their rectifying properties [74Bra, 87Flo, 88Rho, 90Mön, 91Lan, 91Lel, 92Bri, 93Bec, 94Flo]. This rectifying behaviour is due to the formation of a potential barrier (Schottky barrier) at the metal-semiconductor interface [38Mot, 38Sch, 87Sti, 88Ke1, 88Ke2, 88Pr2, 88Spi, 88Sti, 89Bat, 89Pri, 89Spi]. This interface has been intensively investigated in order to understand the mechanisms controlling the properties of the barrier [38Sch] (see also section 3.3). Several different models have been proposed in order to explain the main properties of the Schottky barrier, as barrier height, dependence with the nature of the metal and the semiconductor, and dependence with the thickness of the metallic layer. The first model was proposed by Schottky [39Sch, 40Sch] and Mott [38Mot], who suggested that the bands of the metal and the semiconductor in contact adjust so as to bring both vacuum levels in coincidence. In this case, the barrier height results as the energy difference between the metal work function and the semiconductor electron affinity (Schottky-Mott rule). This model does not reproduce the experimental results. Bardeen [47Bar] then was the first to consider electronic interface states in metal-semiconductor contacts. The barrier heights are still expected to vary linearly as a function of metal work-function but at a reduced slope [65Cow]. Such interface states are implying an interfacial dipole-layer [47Bar]. In a conceptually simple approach, Heine [65Hei] identified those interface states as the wave-function tails of the meta1 electrons in the energy region between the top of the semiconductor valence-band and the Fermi level, where the meta1 conduction-band overlaps the band gap of the semiconductor. That induced density of interface states (IDIS, [77Tej]) or continuum of meta1-induced gap states (MIGS, [76Lo1]) is then derived from the virtual gap states (ViGS) of the complex band structure of the semiconductor, which are solutions of Schrödinger's equation for complex wave vector. It is in this sense that the label "virtual" is used. Depending on the boundary conditions, intrinsic surface states at clean surfaces [35Mau, 39Goo], adsorbate-induced surface states on surfaces covered with adsorbates in submonolayer quantities, and meta1-induced gap states in meta1semiconductor interfaces [76Lo1, 76Lo2, 84Ter1, 84Ter2] are derived from those ViGS. Initially, this MIGS or IDIS model was not widespread accepted since it predicts, as the Schottky-Mott rule did, a linear relationship of the barrier height on the metal work function, but with a slope S less than unity. Meanwhile, there was, however, growing evidence that the chemical trends of barrier heights observed with different metals on a specific semiconductor, as well as of the slopes S reported for different semiconductors, are well described by the MIGS or IDIS model [86Mön, 87Mön, 88Mön]. In these circumstances and based on specific experimental results, which were obtained by using photoemission spectroscopy, Spicer et al. [79Spi] proposed that during the formation of metal-semiconductor contacts native defects are generated in the semiconductor at or close to the interface. The energy levels of those defects were supposed to determine the interface position of the Fermi level within the semiconductor band-gap. This defect model attracted much attention (for a review see, for example, [83Mön]). Nowadays, a consensus has been reached in the sense that both virtual gap states and defects are needed to explain the complete set of experimental data on real interfaces. Only when the experimental conditions can be controlled to reduce the defect density to below 1013 cm−2, the Schottky barrier height is determined by the virtual gap states. In highly defective interfaces, defect states play a role in the control of the barrier height [87Mön, 90Mön].

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3.2.2.1.2 Alkali metal/semiconductor interfaces The perspective on the metal-semiconductor interfaces that has allowed this consensus, changed in the late seventies, when synchrotron radiation was applied to these interfaces [85Bri, 89So1]. It was found that most interfaces were reactive, with a significant interdiffusion between the metal and the semiconductor [78Bri, 82Bri]. In order to understand the physics of the metal-semiconductor junctions, much work was devoted since then to a class of system that was considered close to ideal, the alkali-metal (AM)-semiconductor interface. These interfaces are non-reactive, at least at low temperature. AM's do not form three-dimensional islands but have a tendency to build well ordered one-