Table Of Content

This book, together with its companion volume The science of crystallization: macroscopic phenomena and defect generation, make up a complete course to teach an advanced student how to understand and analyze scientifically any of the phenomena that are observed during natural or technological crystallization from any medium and via any technique of crystallization. It is an advanced text that goes into con- siderable detail concerning the many elements of knowledge needed to understand both qualitatively and quantitatively a crystallization event. This particular volume deals with the important atomistic-level pro- cesses occurring at the interface between a crystal and its nutrient. It also provides the necessary scientific background of both thermodynam- ics and kinetics needed for the understanding of crystallization for both bulk crystals and thin film formation. It focusses on the dual charac- teristics of terraces, ledges and kinks with respect to their role in both interface energetics and phase transition kinetics. In addition, it focusses on the role of these structural elements in many important morphological features of both bulk crystals and thin films. This book and its companion volume are much more broadly based and science oriented than other available books in this field, and are therefore more able to address any area of application, ranging from the production of dislocation-free single crystals in bulk or film form, at one extreme, to structurally sound large metal ingots, at the other. This book, together with its companion, provide the basis for advanced courses on crystallization in departments of materials science, metallurgy, electrical engineering, geology, chemistry, chemical engineering and physics. In addition the books will be invaluable to scientists and engineers in the solid state electronics, optoelectronics, metallurgi- cal and chemical industries involved in any form of crystallization and thin film formation. The science of crystallization: microscopic interfacial phenomena The science of crystallization: microscopic interfacial phenomena William A. Tiller Department of Materials Science and Engineering Stanford University CAMBRIDGE UNIVERSITY PRESS CAMBRIDGE UNIVERSITY PRESS Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, Sao Paulo Cambridge University Press The Edinburgh Building, Cambridge CB2 2RU, UK Published in the United States of America by Cambridge University Press, New York www.cambridge.org Information on this title: www.cambridge.org/9780521381383 © Cambridge University Press 1991 This publication is in copyright. Subject to statutory exception and to the provisions of relevant collective licensing agreements, no reproduction of any part may take place without the written permission of Cambridge University Press. First published 1991 Reprinted 1995 A catalogue record for this publication is available from the British Library Library of Congress Cataloguing in Publication data Tiller, William A. The science of crystallization: microscopic interfacial phenomena / William A. Tiller. p. cm. ISBN 0-521-38138-X (US) - ISBN 0-521-38827-9 (US: paperback) 1. Crystallization I. Title QD921.T52 1991 548'.5-dc20 89-48048 CIP ISBN-13 978-0-521-38138-3 hardback ISBN-10 0-521-38138-X hardback ISBN-13 978-0-521-38827-6 paperback ISBN-10 0-521-38827-9 paperback Transferred to digital printing 2006 To My Loving Wife Jean Contents Preface xiii Symbols xvii 1 Introduction and philosophy 1 1.1 Pathways to understanding 3 1.2 Identifying the fa in a systems problem 9 1.3 Extensions to the constrained growth mode 13 1.4 Generalization 13 1.5 Subprocess dominance 18 1.6 General path for resolving laboratory crystal growth 33 Problems 34 2 Interface energetics and molecular attachment kinetics 37 2.1 Interface energetics 40 2.1.1 Relaxation effects 44 2.1.2 Vicinal faces and the 7-plot 60 2.1.3 Equilibrium form 63 2.1.4 Gibbs-Thomson effects 67 2.1.5 Static interface shapes 70 2.2 Molecular attachment kinetics 74 2.2.1 Layer motion-limited kinetics 76 2.2.2 Layer source-limited kinetics 80 2.2.3 Growth regimes for increasing AGK 84 2.2.4 Micro-hillocks 90 Problems 90 3 Dynamic interface shape effects in bulk crystals 93