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Structure and Pronerties of Atomic Nanoclusters This page intentionally left blank Structure and ProDerties of Atomic Nanoclusters Julio A. Alonso Universidad de Valladolid, Spain Imperial College Press Published by Imperial College Press 57 Shelton Street Covent Garden London WC2H 9HE Distributed by World Scientific Publishing Co. Pte. Ltd. 5 Toh Tuck Link, Singapore 596224 USA office: 27 Warren Street, Suite 401-402, Hackensack, NJ 07601 UK office: 57 Shelton Street, Covent Garden, London WC2H 9HE British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library. STRUCTURE AND PROPERTIES OF ATOMIC NANOCLUSTERS Copyright © 2005 by Imperial College Press All rights reserved. This book, or parts thereof, may not be reproduced in any form or by any means, electronic or mechanical, including photocopying, recording or any information storage and retrieval system now known or to be invented, without written permission from the Publisher. For photocopying of material in this volume, please pay a copying fee through the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, USA. In this case permission to photocopy is not required from the publisher. ISBN 1-86094-551-1 Printed in Singapore. Dedicated to Yolanda, Cristina, Victor, Alejandra and Helena. This page intentionally left blank Foreword Towards the end of my stay as a postdoctoral fellow at the University of Pennsylvania, I asked my supervisor, Professor L. A. Girifalco, which are the topics, in his opinion, that would be good for research in the future. He suggested as one of the topics “small particles”, a term used in the early 1980s for an emerging field devoted to the study of small groups of atoms, or atomic clusters - nanoscience was not yet a fashionable term. This insightful advice was given a few years before the two key experimental discoveries in the field. One of those was the observation and explanation of electronic shell effects in metallic clusters in 1984. The second was the detection, only a few months later, of the fullerene cluster C~Oand the proposal for its peculiar cage structure. The First International Symposium on Small Particles and Inorganic Clusters (ISSPIC-1) had taken place in Lyon in 1976. With the passing of time this symposium established itself as the main joint activity in this field, and ISSPIC-12 took place in Nanjing in 2004. The advice I received from Professor Girifalco gave me the motivation to initially dedicate a modest fraction of my research effort to the study of atomic clusters, and this involvement later increased until it became my main research activity. Due to this interest I have been able to follow the development of the now mature cluster field. In this monograph I present some of the main developments in atomic clusters and the actual status of the field. The range of topics covered is broad, but evidently not comprehensive, and this is due to several reasons. One is my own interest, which is reflected in the selection of topics and illustrative examples. The second reason has to do with the limitations of my knowledge of the field. Third, I consider an in-depth presentation of a limited number of topics more adequate than a lighter presentation of an enlarged list of topics or systems. Finally, I have tried to achieve a proper balance between those considerations and the size of the monograph. vii viii Structure and Properties of Atomic Clusters The book is intended to be useful to graduate students in the fields of Nanoscience, Molecular Sciences and Condensed Matter, and also to scientists interested in entering the field of Atomic Clusters. Contents .. Foreword ............................................................................................ vii Acknowledgments .............................................................................. xv 1. Introduction to Clusters ............................................................ 1 1.1 The Field of Clusters .......................................................... 1 1.2 Types of Clusters ................................................................ 3 1.2.1 Van der Waals clusters ................................................ 3 1.2.2 Metal clusters .............................................................. 4 1.2.3 Clusters of ionic materials ........................................... 5 1.2.4 Network clusters .......................................................... 6 1.2.5 Cluster assembled solids .............................................. 6 References ................................................................................ 6 2 . Experimental Production of Clusters ........................................ 7 2.1 Formation of Clusters in Matrices ...................................... 7 2.1.1 Chemical reaction in a liquid medium ......................... 7 2.1.2 Irradiation of a solid .................................................... 8 2.1.3 Immersion of a porous glass in a liquid metal .............9 2.1.4 Condensation on a substrate ........................................ 9 2.2 Liquid Metal Ion Source ................................................... 10 2.3 Ion Bombardment ............................................................. 10 2.4 Supersonic Nozzle Sources .............................................. 10 2.4.1 Kinetics of coagulation .............................................. 12 2.4.2 Seeded nozzle sources ............................................... 13 2.4.3 Gas aggregation sources ............................................ 13 2.4.4 Laser vaporization ..................................................... 14 2.4.5 Clusters in helium droplets ........................................ 14 2.5 Mass Analysis ................................................................... 14 References .............................................................................. 18 ix X Structure and Properties of Atomic Clusters 3 . Van der Waals Clusters .......................................................... 21 3.1 Structure of Van der Waals Clusters ................................ 21 3.2 Transition to the Bulk ....................................................... 28 3.3 Thermal Properties ........................................................... 31 3.3.1 Solid to solid transitions ............................................ 31 3.3.2 Melting transition ...................................................... 33 3.3.3 Mixed inert gas clusters ............................................. 42 3.3.4 Liquid to gas phase transition in hydrogen clusters ..43 3.4 Electronic Effects ............................................................. 46 3.4.1 Delocalized electronic states of excess electrons ......46 3.4.2 Core level spectroscopy ............................................. 50 3.5 Clusters of SF6 and C02Molecules .................................. 52 3.6 Interaction with Ultrafast Laser Pulses ............................. 54 References .............................................................................. 56 4 . Electronic and Atomic Shells in Metal Clusters ..................... 59 4.1 Experimental Observation of Electronic Shells ................59 4.2 Spherical Well Model of Metallic Clusters ...................... 62 4.3 Electronic Shell Effects in Large Clusters........................ 69 4.4 Spheroidal Deformations of the Cluster Shape ................74 4.5 A Full Description of the Cluster Structure ...................... 77 4.6 Shells of Atoms ................................................................ 83 4.7 Approximate Treatment of the Geometrical Structure ..... 86 4.7.1 Spherically Averaged Pseudopotential Model ..........86 4.7.2 Cylindrically Averaged Pseudopotential (CAPS) Model .................................................................................. 88 4.8 Clusters of the Aluminum Group ..................................... 89 4.8.1 Aluminum clusters..................................................... 89 4.8.2 Boron clusters ............................................................ 91 References .............................................................................. 92 5 . Electronic and Optical Properties of Simple Metal Clusters ..97 5.1 Ionization Potential and Electron Affinity ........................ 97 5.2 Odd-Even Effects ........................................................... 104 5.3 Temperature Dependence of the Ionization Potential .... 108 5.4 Hardness and Reactivity ................................................. 110 5.5 Mass Spectrum Obtained at Near-Threshold Ionization Energies ................................................................................ 113 5.6 Response to a Static Electric Field ................................. 116 Contents xi 5.7 Dynamical Response ...................................................... 120 5.7.1 Relation between theory and experiment ................ 120 5.7.2 Sum rules ................................................................. 124 5.7.3 Calculation of the dynamical susceptibility............. 128 5.7.4 Spherical clusters ..................................................... 130 5.7.5 Effect of shape deformations................................... 135 5.7.6 Effect of the ion granularity .................................... 138 5.7.7 Vibrational structure of the optical response ........... 143 5.7.8 Thermal line broadening.......................................... 145 References ...........................................................................