CONSULTANTS BUREAU. NEW YORK AND LONDONL1brary of Congress Catalog1ng-1n-PubI1cat1on Data Izlumov, fiJ. A. (fiJrll Aleksandrovlch), 1933-[Neltronografl1a Magnetlkov. Engllshl Neutrun dIffraction of magnetic ~aterlals I Yu. A. Izyu.ov, V.E. Naish, and R.P. Ozerov ; translatec from RuSSian by Joachim Buchner. p. cm. Translation of, Neltronografl1a magnetlkov. Includes bibliographical references and Index. All rights reserved 91-4773 CIP No part of this book may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, microfilming, recording, or otherwise, without written permission from the Publisher v vi PrefaceIt is therefore necessary to improve also the determination [decoding] of magnetic structures from neutron diffraction patterns after improving the interpretation of the results of neutron diffraction research.The improvement is based mainly on using the symmetry of the crystals examined. The present book is a step-by-step description of magnetic structures and of the method of their determination from neutron diffraction patterns with the aid of the theory of crystal symmetry, i.e., the theory of representations of space groups. Making use of the methods developed by the authors, the experimenter can independently perform a preliminary analysis of crystal symmetry and obtain the magnetic structures available through symmetry to select thereafter the true structures by best fit of the calculated scattering pattern to the observed pattern. This book expounds the entire mathematical apparatus required for such an analysis. At the same time, the book provides a systematic exposition of the theory of magnetic symmetry of crystals and of its relation to the theory of irreducible representations of space groups. This approach was not outlined in earlier monographs on this subject, not even in the latest edition of the book Neutron Diffraction by G. E. Bacon [64].Considering the symmetry analysis of magnetic structures and its use in the interpretation of neutron diffraction patterns of magnetic materials as the main subject of the book, the authors have intentionally excluded other problems of neutron diffraction involving magnets, since these problems are adequately treated in other monographs (this is true, in particular, of the monograph by Izyumov and Ozerov Magnetic Neutron Diffraction [24,134]). This book contains numerous examples of symmetry analysis of specific magnetic structures of substances. The authors hope that the book will be useful not only to experimenters and specialists in neutron diffraction, but also to theoretical physicists working on the theory of magnetic structures and magnetic phase transitions.In this book, the terms "atomic magnetic moment" and "atomic spin" are often used synonymously; the sections in which the contribution of the orbits to the total magnetic moment is specially treated are an exception.The authors are deeply indebted to Academician S. V. Vonsovskii for his support in writing this book, to their...

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O n the basis of numerous experiments using the mono-Laue method on the diffuse scattering of X-rays and electrons we have developed the Comes-Lambert-Guinier concept of the existence of co-operative thermal vibrations in perfect crystals in which one-dimensional or two-dimensional atomic objects, i.e. chains or planes of atoms, are moving in a double-well potential with conservation of coherence. For an approximate description of such a motion we have utilized the pseudospin king model approach which Is widely used in the theory of structural phase transitions. These ideas proved to be successful for the description of diffuse scattering patterns, and their temperature evolution in close connection with structural phase transitions.The developed theory gives the possibility through the observation of diffuse scattering at high temperatures and its analysis to predict the structural phase transition (and even the subsequent cascades of transitions) and to give the correct explanation for physical anomalies in the crystals, either with distortive (weak) or reconstructive (strong) transitions. A wide variety of crystallochemical situations and transitions in crystals of the perovskite family and in metals with a bcc lattice are analysed in detail. A number of new experimental diffuse scattering patterns from crystals of various types are obtained.KEY WORDS: mono-Laue method, crystal structure loose-packing, movable coherent extended objects, relrods and relplanes. I INTRODUCTIONIn this paper we shall consider only the spontaneous (occurring with temperature variation without outer interference) structural phase transitions of the displacement type. Two different types of such transitions are assumed to exist: distortive and reconstructive. Distortive transitions are weak structural phase transitions at which the structure is changed only slightly, and the atom displacements u are far less than the interatomic distances or lattice parameters, a so that u < a. Usually u/a % 10p2-10-3. At such a transition some symmetry elements of the initial phase vanish, but in such a way that the final and initial phases possess the subgroup relation: G, c Go. This is the fundamental relation for Landau theory and that is why the theory of such transitions is rather well developed. Among them one can find either second-order transitions or the so-called first-order transitions close to the secondorder ones. 89 Downloaded by [University of Cambridge] at 02:40 05 November 2014 90 F. A. KASSAN-OGLY, V. E. NAISH A N D I. V. SAGARADZEReconstructive transitions are strong first-order transitions at which a substantial crystal structure reconstruction with alteration of the actual structure type takes place, for example, bcc-fcc, bcc-hcp and so on. The displacements of atoms at these transitions are much greater (u i a) and the subgroup relation is absent completely; hence Landau theory in the usual way is not applicable to them. For this reason alone the theory of reconstructive transitions is far less developed.In the present paper, an...

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In part I of this series the problem of immanent chaotization of crystal structures was described in simple models and the mathematical approach to the calculation of diffuse scattering (DS) was described. It was formulated that the loose packing of most real crystals appears to be the universal microscopical cause of DS. In the present paper the microscopical nature of chaotization is analysed and a quantitative description of the structural loose packing is given for cubic perovskites; these are particularly convenient examples because the most vivid and thorough experimental data on DS were obtained for such crystals: KNbO3, BaTiO~, NaNbO3, KMnF3.