Structural Phase Transitions II PDF
Preview Structural Phase Transitions II
45 Topics in Current Physics Topics in Current Physics Founded by Helmut K. V. Lotsch Volume 39 Nonequilibrium Vibrational Kinetics Editor: M. Capitelli Volume 40 Microscopic Methods in Metals Editor: U. Gonser Volume 41 Structure and Dynamics of Surfaces I Editors: W. Schommers and P. von Blanckenhagen Volume 42 Metallic Magnetism Editor: H. Capellmann Volume 43 Structure and Dynamics of Surfaces II Phenomena, Models, and Methods Editors: W. Schommers and P. von Blanckenhagen Volume 44 Persistent Spectral Hole-Burning: Science and Applications Editor: W. E. Moerner Volume 45 Structural Phase Transitions II Editors: K. A. Muller and H. Thomas Volume 46 Photoacoustic, Photothermal and Photochemical Processes in Gases Editor: P. Hess Volume 47 Photoacoustic, Photothermal and Photochemical Processes at Surfaces and in Thin Films Editor: P. Hess Volumes 1-38 are listed on the inside back cover Structural Phase Transitions II Edited by K. A. Muller and H. Thomas With Two Contri butions by K. A. MOiler and J. C. Fayet F. Borsa and A. Rigamonti With 50 Figures and 47 Panels Springer-Verlag Berlin Heidelberg GmbH Professor Dr. h. c. mult. K. Alex Mu/ler IBM Research Division, Zurich Research Laboratory, CH-8803 Rlischlikon and University of Zurich, Physics Department, CH-8001 Zurich, Switzerland Professor Dr. Harry Thomas Institut lOr Physik, Universităt Basel, Klingelbergstrasse 82 CH-40S6 Basel, Switzerland ISBN 978-3-662-10115-5 Library 01 Congress Cataloging-in-Publication Data. (Revised lor voI. 2) Structural phase transitions. (Topics in current physics ; v. 23, ) Includes bibliographies and indexes. 1. Phase translormations (Statistical physics) 2. Solid state physics. 3. Order-disorder models. 1. Muller, K. A. (Karl A.), 1927- . II. Thomas, H. (Harry) III. Dorner, B. (Bruno) IV. Series. aC176.8.P45S77 1981 530.4'1 80-23544 ISBN 978-3-662-10115-5 ISBN 978-3-662-10113-1 (eBook) DOI 10.1007/978-3-662-10113-1 This work is subject to copyright. AII rights are reserved, whether the whole or part 01 the material is concerned, specilically the rights 01 translation, reprinting, reuse 01 iIIustrations, recitation, broadcasting, reproduction on microlilms or in other ways, and storage in data banks. Duplication 01 this publication or parts thereol is only permitted under the provisions 01 the German Copyright Law of September 9, 1965, in its current vers ion, and a copyright fee must always be paid. Violations fali under the prosecution act of the German Copyright Law. © Springer-Verlag Berlin Heidelberg 1991 Originally published by Springer-Verlag Berlin Heidelberg New York in 1991 Softcover reprint of the hardcover 1s t edition 1991 The use of registered names, trademarks, etc. in this publication does not imply, even in the absence 01 a specific statement, that such names are exempt Irom the relevant protective laws and regulations and therelore Iree lor general use. 2154/3140-543210 - Printed on acid-Iree paper Preface In the series Topics in Current Physics, this is Volume II on structural phase tran sitions. It is a continuation of Volume I with series number 23, and, like Volume I, is devoted to experiments. However, it is clearly distinct from it. Volume I con tains three chapters: on optical studies, inelastic neutron scattering and ultrasonic investigations, all of which probe collective excitations of the lattice. The present volume has two chapters, the first on electron paramagnetic resonance (EPR) and the second on nuclear magnetic and nuclear quadrupolar resonance (NMR-NQR). These techniques probe local properties and are relevant to the understanding of the phenomena in the field. The methods of investigation in structural phase transitions (SPT) range widely, so that, on initiating this group of books, it was decided that knowledgeable sci entists working with a particular technique should elucidate their method and its characteristic results as well as its advantages and limitations. As could be expected, each chapter of Volume I varied in style, but they were always kept such as to be comprehensible to the nonspecialist. This is also the case for the contributions in the present volume, but even more so as the presentation in the two chapters is really different. The first, by K.A. MUller and J.C. Fayet on EPR, is a review in the traditional style, whereas that by F. Borsa and A. Rigamonti uses a new didactic ap proach: In so-called panels containing figures and the relevant analytical equations, the essence of a phenomenon is condensed. The rationale for this approach is given hereafter. More importantly, the emphasis of the two chapters is rather different That on EPR is more heavily weighted towards static results, that on NMR more towards dynamics. This is also the main reason for their order: EPR has made substantial contributions to studies of static properties of SPT with high sensitivity. Thus, the first two-thirds of the EPR chapter reviews these results, ranging from mean-field behavior to critical and multicritical phenomena. The last part leads on to dynamical aspects, especially in order-disorder systems, and shows the remarkable success of EPR in incommensurate structures. Because of the importance of the method and requests from colleagues working in other fields for an introduction to EPR, considerable information on the methodology is given at the outset. NMR and NQR are powerful probes for studying solids and especially SPT in an intrinsic way, although less sensitive than EPR. However, what one really probes by the various NMR line splittings and relaxation times is even more remote than EPR to the non-resonance scientist, and this is a major reason why the authors adopt the presentation in the form of panels. In addition, NMR has yielded very interesting recent results on nonlinear dynamics, incommensurate transitions, disordered systems v and the central peak, so that a compact type of presentation was also needed to keep the chapter to a manageable size. Volume II appears a considerable time after Volume I. However, this is not a disadvantage as such, because new aspects in the SPT fields have been included, as mentioned above for the NMR chapter, as well as the recent analysis of extrinsic vs intrinsic properties of EPR parameters made possible by the superposition model. The latter were only elucidated in a conclusive way in 1986. Also, the important EPR results on incommensurate systems are very recent. The intended completion of this volume by 1987 would have been possible; however, in 1986 high-Tc super conductors were discovered As one of the editors and authors was directly involved in this discovery, he was no longer master of his time regarding other commitments. It was originally planned to include a third chapter on calorimetric and dielectric properties in the present book. A first draft was reviewed, but the final version was not available when printing was initiated. As the two chapters on resonance are already quite sizeable and together form a true unit addressed to local probing, it was felt more appropriate to include the review on calorimetry in the planned Vol ume III on theory, which will also contain a chapter on thermodynamics. Of course, calorimetry and dielectric behavior are closely related to the results in thermody namics. The introduction which appeared in Volume I was written with the intention of serving for all experimental chapters, including the present two. Its outline is still up to date and should be of help in opening the door to SPT for those interested Furthermore, each of the present chapters begins with an introduction, and thus it was felt that a separate introduction to this book would be superfluous. The editors hope that the present effort will serve to familiarize researchers and students with magnetic resonance techniques as applied to SPT. It may be pointed out that since the proceedings of the Enrico Fermi Varenna School on "Local Properties of Structural Phase Transitions", which was published in 1976, no comparable presentation on EPR and NMR studies of SPT has appeared in the literature. Rilschlikon and Basel, January 1990 K.A. MUller, H. Tlwmas VI Contents 1. Structural Phase Transitions Studied by Electron Paramagnetic Resonance By K. A. Maller and J. C. Fayet (With 50 Figures) ................. 1 1.1 Introduction .................................. . . . . . . . . . 1 1.2 Methodological Aspects .................................. 2 1.2.1 Choice of Paramagnetic Ions or Radicals ............. 3 1.2.2 The Spin-Hamiltonian Formalism ................... 4 1.2.3 Site Determination ............................... 7 1.2.4 Ligand-Field Parameters and the Superposition Model .. 8 1.3 Experimental Techniques ................................. 12 1.3.1 Standard Equipment .............................. 12 1.3.2 Special Requirements for Investigations of Structural Phase Transitions ..................... 14 1.4 Oxide Ferroelectrics ..................................... 18 1.4.1 EPR of Fe3+ and Gd3+ in Cubic and Tetragonal BaTi03. 19 1.4.2 Fe3+ and Gd3+ Spectra in Orthorhombic and Rhombohedral BaTi03 ........................ 21 1.4.3 erJ+ in BaTi03: A Centered Ion with a Flat Local Potential 23 1.4.4 Mn4+ on Ferroelectric n4+ Sites: Evidence for Intrinsic Low-Frequency Dynamics ....... 26 1.4.5 The EPR Parameter a of Fe3+ in Ban03 and KNb03 ... 28 1.5 Antiferrodistortive Transitions ............................. 31 1.5.1 The Cubic-to-Tetragonal Transformation in SrTi03 ..... 31 1.5.2 The Cubic-to-Trigonal Phase Transition in LaAI03 ..... 34 1.5.3 Critical Phenomena ............................... 37 1.5.4 Order-Parameter Behavior in PrAI03 ................ 41 1.6 Experiments on Multicritical Points ........................ 43 1.6.1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 1.6.2 Bicritical Points in Srn03 and LaAI03 .............. 44 1.6.3 Phases Induced by Competing Forces ................ 46 1.6.4 Uniaxial Stress Effects on the Antiferrodistortive Transition of RbCaF3 and Multicritical Behavior .......... . . . . . 48 1.7 Order-Disorder Transitions ............................... 55 1. 7.1 NHt Ordering in Pure Crystals ..................... 57 1.7.2 NHt Ordering in Mixed Crystals: RbxN~1_x)AIF4 .... 59 1.7.3 Room-Temperature Phases of Mixed Crystals ......... 61 VII 1.8 Incommensurate Phases ...............•.................. 62 1.8.1 EPR of Charge-Compensated Defects in the INC Phases of ThBr4 and ThC4:Gd3+ ........................ . 64 1.8.2 EPR of Mn2+ in Doped Betaine Calcium Chloride Dihydrate (BCCD) and Substitutional Probes ......... . 68 1.8.3 Incommensurate Phases in Diphenyl Studied via a Triplet-State Spin Probe ..................... . 75 References 77 2. Comparison of NMR and NQR Studies of Phase Transitions in Disordered and Ordered Crystals By F. Borsa and A. Rigamonti (With 47 Panels) ................. . 83 2.1 Ordering in "Ordered" and Disordered Crystals ............. . 83 2.1.1 Phase Transitions and Critical Effects in Conventional Ordered Systems ................................ . 84 2.1.2 Ordering Phenomena and Dynamics in Disordered Systems 89 2.1.3 Non-linear Dynamics: Anharmonicity, Damping, Solitons, and Tunneling .................................. . 92 2.1.4 Central Peak ................................... . 95 2.1.5 Incommensurate Phases .......................... . 98 2.2 Basic Concepts and Methodology of NMR-NQR in Crystals .. . 99 2.2.1 NMR-NQR Rigid-Lattice Spectra .................. . 103 2.2.2 Motional Effects on the Spectra ................... . 107 2.2.3 Relaxation Processes and Relaxation Rates .......... . 107 2.3 Phase Transitions and Critical Effects in Ordered Crystals: Insights from NMR-NQR ............................... . 114 2.3.1 Order Parameter Studies .......................... . 114 2.3.2 Symmetry and Anisotropy of Soft Modes ............ . 120 2.3.3 Order-Disorder Critical Dynamics .................. . 123 2.4 Collective Behavior and "Phase Transitions" in the Presence of Positional Disorder .................................. . 125 2.4.1 The Problem of the Order Parameter ............... . 125 2.4.2 The Problem of Critical Dynamics ................. . 137 2.5 Incommensurate Phases ................................. . 148 2.5.1 Modulation of Local Order Parameter and Phase Transitions ............................ . 149 2.5.2 Excitations in the Incommensurate Phase and Relaxation Rates ............................ . 155 2.5.3 Incommensurate Phases in Layers: Cs Ions Intercalated in Graphite .................................... . 157 2.6 Non-linear Phenomena, Central Peak and Pretransitional Clusters 162 2.6.1 Central Peak ................................... . 162 2.6.2 Pretransitional Phenomena ........................ . 166 References 173 Subject Index 177 VIII List of Contributors Ferdinando Borsa Universim di Pavia, Dipartimento di Fisica, "A. Volta", Unim INFM-GNSM and Sezione INFN, Via A. Bassi 6, 1-27100 Pavia, Italy Jean Claude Fayet Laboratoire de Spectroscopie du Solide, E.R.A., Faculte des Sciences, F-72017 Le Mans Cedex, France K. Alex Muller IBM Research Division, Zurich Research Laboratory, CH-8803 Riischlikon and University of Zurich, Physics Department, CH-8001 Zurich, Switzerland Attilio Rigamonti Universita di Pavia, Dipartimento di Fisica, "A. Volta", Unita INFM-GNSM and Sezione INFN, Via A. Bassi 6, 1-27100 Pavia, Italy IX 1. Structural Phase Transitions Studied by Electron Paramagnetic Resonance K.A. Muller and J.C. Fayet With 50 Figures 1.1 Introduction Electron Paramagnetic Resonance (EPR) has been one of the pioneering techniques used for detecting Structural Phase Transitions (SPT) and detennining the space groups involved and especially for investigating, with high precision, the order pa rameter and its dependence on temperature and stress. Earlier work on SPT was reviewed by one of us [1.1] and summarized for the model substances SrTi03 and LaAI03 over a decade ago by Muller and Von Waldkirch [1.2]. In the present re view, we attempt to cover a broader field, including the most recent progress in EPR research in incommensurate SPT's and random systems. Since the invention of the laser and the availability of intense neutron sources, a great deal of solid-state work has been carried out by scattering methods with the result that EPR, previously taught in most solid-state departments, is now accorded less emphasis. [However, it is still widely used along with Nuclear Magnetic Res onance (NMR)]. We have thus decided to review this method in Sect. 1.2 in some depth, for the benefit of those readers who are not familiar with it, or for those who wish to refresh their memories. For a thorough study we recommend, among many good books, the one by Pake and Estle [1.3], entitled Principles of Paramag netic Resonance, from which university courses have often been taught and where the material presented is of adequate sequence and length. Abragam and Bleaney's monumental treatise [1.4] is more detailed, and was useful as a general reference up to the midsixties when most of the fundamental aspects of EPR had been settled. To complete the picture, the new edition of the book by Altshuler and Kozyrev [1.5] gives more access to the Russian literature. For electron spin resonance of radicals, we would also like to mention the book by Atherton [1.6]. In Sects. 1.2 and 1.3 we further emphasize aspects of EPR that are specific to the study of SPT, namely the paramagnetic ions to be chosen, the use of the super position model, and the additional equipment necessary to employ this inexpensive method successfully. Particularly important is the recent progress due to the use of the superposition model. The subsequent sections fonn the heart of our arti cle and present characteristic examples. Because of the vast field covered by our review, we present highlights of the method rather than a complete study. Oxide ferroelectrics are presented in Sect. 1.4, antiferrodistortive transitions in Sect. 1.5, multicritical points in Sect. 1.6, EPR in order-disorder transitions in Sect. 1.7, and work on incommensurate systems in Sect. 1.8.
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