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X-Ray Diffraction by Disordered Lamellar Structures

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X-Ray Diffraction by Disordered Lamellar Structures Victor A. Drits Cyril Tchoubar x-Ray Diffraction by Disordered Lamellar Structures Theory and Applications to Microdivided Silicates and Carbons With the Collaboration of G. Besson, A. S. Bookin, F. Rousseaux B. A. Sakharov and D. Tchoubar Foreword by Andre Guinier Springer-Verlag Berlin Heidelberg New York London Paris Tokyo Hong Kong Barcelona Professor Victor A. Drits Professor Cyril Tchoubar Geological Institute Universite d'Orleans Academy of Sciences Laboratoire de Cristallographie 7 Pyzhevsky perspekt (associe au CNRS) 109017 Moscow, USSR Rue de Chartres F-45067 Orleans Cedex, France Translated from French by: R. Setton, National Center of Scientific Research (CNRS), C.R.S.o.C.I., Orleans, France Library of Congress Cataloging·in-Publication Data Cyril Tchoubar. X-ray diffraction by disordered lamellar structures: theory and applications to microdivided silicates and carbons 1 Victor A. Drits, Cyril Tchoubar [sic] with the collaboration of G. Besson ... [et al.]; [translated from the French by R. Setton]. Includes bibliographical references. lSBN-13: 978-3-642-74804-2 e-lSBN-13: 978-3-642-74802-8 DOl: 10.1007/978-3-642-74802-8 1. X-ray crystallography. 2. X-rays - Diffraction. I. Tchoubar, Cyril, 1932- . II. Title. III. Title: Disordered lamellar structures. QD945.D75 1990548'.83 - dc 20 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, re-use of illustrations, recitation, broadcasting, reproduction on microfilms or in other ways, and storage in data banks. Duplication of this publication or parts thereof is only permitted under the provisions of the German Copyright Law of September 9, 1965, in its current version, and a copyright fee must always be paid. Violations fall under the prosecution act of the German Copyright Law. © Springer-Verlag Berlin Heidelberg 1990 So/kover reprint of the hardcover 1st edition 1990 '!Ypesetting: K + V Fotosatz GmbH, Beerfelden 2132/3145 543210 - Printed on acid-free paper Foreword Saying that X-ray diffraction reveals the atomic structure of solids would be com­ monplace if one were not to add that two types of problems are involved, each re­ quiring its own method of approach. It is possible to obtain, from a "proper", isolated crystal of adequate size, a dif­ fraction pattern yielding the atomic structure unambiguously, even if the number of atoms in the lattice is large. The problem can be considered as solved, as witnessed by the importance of its results in chemistry, biology, etc. A different matter is that of imperfect crystals, in which the periodicity of the atomic positions is only partial, or even approximate. The difficulty is further compounded by the fact that, in general, only microcrystalline and poorly oriented powders are on hand. The experimental data are then insufficient for a complete determination of the structure at the atomic level since X-ray diffraction is not equivalent to a microscope with a resolution of the order of the atomic diameters, enabling us to "see" the structure. What could then be the maximum information to be drawn from the experimental determinations? The answer to this question is provided by the authors for lamellar solids, a very numerous class of imperfect crystals, of which clays are the best known example. The method consists in calculating the diffraction pattern of a model drawn up using all the available information on the sample, then in adjusting arbitrarily chosen parameters to obtain the best fit with the experimental data. The corre­ sponding structure is thus a possible structure, it may even be the likely one, but it has not been proved to be the actual true structure. From the many examples fully discussed in this work, a few capital ideas emerge: - one can no longer be content, as was done a few decades ago, with approx­ imate or even merely qualitative results; calculations on models are possible and the computerized comparison of these results with the experimental data can bring out exact values of unknown parameters; - it is imperative that the determination of the intensity of the diffracted wave be accurate and free from systematic errors, since results obtained otherwise could correspond to anything. Modern X-ray sources, new detectors, and the monochro­ matization of the incident beam permit excellent measurements, at least If one is willing to take the trouble to obtain them. The insistence of the authors on this most important point, a prerequisite to the increase in our knowledge of disordered structures, is all to their credit. The richness and progress in the knowledge of the structure of layered materials brings to our mind the merit and insight of one of the pioneers in this field, namely VI Foreword Jacques Mering. A gifted theoretician, he successfully computed the diffraction by model structures, while simultaneously impressing his co-workers with the need for excellence in the quality of the measurements. Many of the authors in this book were his students. Their extensive achievements are a fitting tribute to the memory of Jacques Mering. Paris, August 1990 Andre Guinier Preface It is well known that many physical and physico-chemical properties of solids are directly related to certain defects in their crystal structure: the structure of an ac­ tual crystal is always somewhat different from its idealized representation as deter­ mined by the symmetry group of the crystal and by the atomic motif, on the scale of the unit cell. Divergences from the idealized structure may vary greatly. They may be related, within the actual crystal, to isolated point defects due to voids or, in contrast, to interstitial atoms, or to the isomorphic replacement of certain atoms within the motif by atoms of a different nature. Structural defects may also gather in zones: for example, the hearts of screw or wedge dislocations are the origin of whole areas of linear defects, whereas stacking or twinning faults, or polysomatism, induce the formation of planar defects. Furthermore, many crystals are also subject to inter­ nal microtensions which perturb the perfect periodicity of the crystal structure along one or more directions in space. In the same way, among all natural or syn­ thetic compounds; some are found to have a so-called interstratified structure with a more or less regular stacking of layers differing in chemical composition as well as in crystal structure. In some cases, these interstratified compounds are made up of two-dimensional lattices non-commersurable with each other. Lastly, one may also find distortions or structural elements associated in such a way that the struc­ ture of the crystal is modulated and, possibly, non-commensurable as well. The crystallographer seeking to characterize such structures will have to deter­ mine parameters specific to different types of defects, as well as the proportions in which they occur, their exact location and their possible interactions. Two methods of analysis are used to determine these structural characteristics: - on one hand, spectroscopic methods - IR, Mossbauer, NMR, EXAFS, etc. - which allow the determination of local structures related to the order-disorder at short distances; these methods are suitable for the study of point defects, of deformed interatomic bindings, of the nature of sites where isomorphic replace­ ments occur and for the study of their distribution at short distances, etc.; - on the other hand, diffractometric methods - of X-rays, electrons or neutrons - which, with the help of statistical parameters, allow the characteriza­ tion of the distribution of point defects, of the nature of linear and planar defects, their localization, and the determination of their interactions within the solid. The diffractometric technique most commonly used in determining these char­ acteristics is X-ray diffraction (XRD). This is due, first of all, to the relative ease of application of the method and to the moderate cost of the equipment; in the VIII Preface second place, compounds thus analyzed generally do not need to be put under ex­ perimental conditions likely to modify them, such as vacuum. However, the crystallographer's task becomes particularly tricky when the object is microdivid­ ed - a case frequently encountered - for it will then only be possible to exploit data from a polycrystalline system. Thus, over a long period of time, most inter­ pretations of complicated diffraction effects produced by microdivided systems with a partially disordered crystal structure were based on an intuitive approach; it is only within the last few decades that methods of interpretation of diagrams have excluded the excessively large emphasis formerly placed on intuition. Our aim, in the present book, is to describe the methods best suited to the deter­ mination, by XRD, of deviations from real and idealized average structures, the basic idea being that the only methods permitting the determination, at one and the same time, of the nature, quantity, position and interaction of structural defects in a given solid are indirect or modelization methods. These are generally used in several steps: a first study examines all the structural models containing various types of defects compatible with the specific crystallo-chemical family to which a given solid belongs. The second step is the calculation of the 'synthetic' diagrams corresponding to each of the structural models examined and the deter­ mination of the effect produced by the variation of the parameters characteristic of each model on the intensity distribution of the diffracted waves. Finally, retain­ ing only the model or models producing synthetic diagrams closest to the ex­ perimental spectrum, the characteristic parameters of this model or models are modified step by step to obtain the best agreement between the experimental and calculated spectra. The concordance of the two spectra justifies the attribution of the parameters of the best possible model, considered to be representative of the real structure, to the solid under analysis.
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