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Elements of X-Ray Diffraction PDF

569 Pages·1978·25.016 MB·English
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Elements of X-RAY DIFFRACTION SECOND EDITION B. D. CULLITY Department of Metallurgical Engineering and Materials Science University of N(cid:244)tre Dame ADDISON-WESLEY PUBLISHING COMPANY INC. Reading, Massachusetts - Menlo Park, California London -Amsterdam - Don Mills, Ontario - Sydney This book is in the Addison-Wesley Series in Metallurgy and Materials Morris Cohen Consulting Editor 0 Copyright 1978, 1956 by Addison-Wesley Publishing Company, Inc. Philippines copyright 1978 by Addison-Wesley Publishing Company, Inc. All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior written permission of the publisher. Printed in the United States of America. Published simultaneously in Canada. Library of Congress Catalog Card No. 77-73950. ISBN 0-201-01174-3 Preface X-ray diffraction is a tool for the investigation of the fine structure of matter. This technique had its beginnings in von Laue's discovery in 1912 that crystals diffract x-rays, the manner of the diffraction revealing the structure of the crystal. At first, x-ray diffraction was used only for the determination of crystal structure. Later on, however, other uses were developed, and today the method is applied not only to structure determination, but to such diverse problems as chemical analysis and stress measurement, to the study of phase equilibria and the measurement of parti- cle size, to the determination of the orientation of one crystal or the ensemble of orientations in a polycrystalline aggregate. The purpose of this book is to acquaint the reader who has no previous knowl- edge of the subject with the theory of x-ray diffraction, the experimental methods involved, and the main applications. Because the author is a metallurgist, the majority of these applications are described in terms of metals and alloys. How- ever, little or no modification of experimental method is required for the examina- tion of nonmetallic materials, inasmuch as the physical principles involved do not depend on the material investigated. This book should therefore be useful to metallurgists, chemists, physicists, ceramists, mineralogists, etc., namely, to all who use x-ray diffraction purely as a laboratory tool for the sort of problems already mentioned. Members of this group, unlike x-ray crystallographers, are not normally con- cerned with the determination of complex crystal structures. For this reason the rotating-crystal method and space-group theory, the two chief tools in the solution of such structures, are described only briefly. This is a book of principles and methods intended for the student, and not a reference book for the advanced research worker. Thus no metailurgical data are given beyond those necessary to illustrate the diffraction methods involved. For example, the theory and practice of determining preferred orientation are treated in detail, but the reasons for preferred orientation, the conditions affecting its development, and actual orientations found in specific metals and alloys are not described, because these topics are adequately covered in existing books. In short, x-ray diffraction is stressed rather than metallurgy. The book is divided into three main parts: fundamentals, experimental meth- ods, and applications. The subject of crystal structure is approached through, and based on, the concept of the point lattice (Bravais lattice), because the point lattice of a substance is so closely related to its diffraction pattern. X-ray diffraction iii ... iv Preface phenomena are rather sharply divisible into those effects that are understandable in terms of the Bragg law and those that require a more advanced treatment, based on the reciprocal lattice. This book is written entirely in terms of the Bragg la6 and can be read without any knowledge of the reciprocal lattice. My experience with teaching x-ray diffraction to senior students in metallurgy, for many of whom this book represents a terminal course in the subject, is that there is insufficient time to attain both a real facility for "reciprocal thinking" and a good knowledge of the many applications of diffraction. I therefore prefer the Bragg-law approach for a first course. Those instructors who wish to introduce the reciprocal lattice at the beginning can interpose Appendix I, which contains the rudiments of the subject, between Chapters 2 and 3. Chapters on chemical analysis by x-ray diffraction and x-ray spectroscopy are included because of the industrial importance of these analytical methods. Electron and neutron diffraction are treated in appendices. This second edition includes an account of new developments made possible by the semiconductor detector and pulse-height analysis, namely, energy-dispersive spectrometry and diffractometry. Applications of position-sensitive detectors are also described. A new section is devoted to x-ray topography and other x-ray methods of assessing the quality of single crystals. Other additions include a quantitative treatment of the temperature factor and descriptions of the Auger effect, micro- cameras and Guinier cameras, and microanalysis in the electron microscope. References to original papers are now given, and the tables of wavelengths and absorption coefficients have been expanded. This edition contains more material on the measurement of preferred orien- tation and residual stress than the first edition, but the former chapter on chemical analysis by x-ray absorption has been dropped, as being of minor interest to most readers. The first edition carried the following acknowledgements: Like any author of a technical book, I am greatly indebted to previous writers on this and allied subjects. I must also acknowledge my gratitude to two of my former teachers at the Massachusetts Institute of Technology, Professor B. E. Warren and Professor John T. Norton: they will find many an echo of their own lectures in these pages. Professor Warren has kindly allowed me to use many problems of his devising, and the advice and encouragement of Professor Norton has been invaluable. My colleague at Notre Dame, Professor G.C . Kuczynski, has read the entire book as it was written, and his constructive criticisms have been most helpful. I would also like to thank the following, each of whom has read one or more chapters and offered valuable suggestions: Paul A. Beck, Herbert Friedman, S. S. Hsu, Lawrence Lee, Walter C. Miller, William Parrish, Howard Pickett, and Bernard Waldman. I am also indebted to C. G.D unn for the loan of illustrative material and to many graduate students, August Freda in particular, who have helped with the preparation of diffraction patterns. Finally, but not perfunctorily, I wish to thank Miss Rose Kunkle for her patience and diligence in preparing the typed manuscript. Preface v In the preparation of the second edition I have been helped in many ways by Charles W. Allen, A. W. Danko, Ron Jenkins, Paul D. Johnson, A. R. Lang, John W. Mihelich, J. B. Newkirk, Paul S. Prevey, B. E. Warren, Carl Cm. Wu, and Leo Zwell. To all these, my best thanks. Notre Dame, Indiana B. D. Cullity November 1977 Contents FUNDAMENTALS Chapter 1 Properties of X-rays Introduction . . . . . . . . . . . . . . . . 3 Electromagnetic radiation . . . . . . . . . . . . 3 The continuous spectrum . . 6 .The characteristic spectrum . . . . . . . . . . . . 8 Absorption . . . . . . . . . . . . . . . . . 13 Filters . . . . . . . . . . . . . . . . . . 19 Production of x-rays . . . . . . . . . . . . . . 21 Detection of x-rays . . . . . . . . . . . . . . 27 Safety precautions . . . . . . . . . . . . . . . 29 Chapter 2 Geometry of Crystals 2-1 Introduction . . . . . . . . . . . . . . . . 32 . . . . . . . . . . . . . . . . . . 2-2 Lattices 32 2-3 Crystal systems . . . . . . . . . . . . . . . . 34 2-4 Symmetry . . . . . . . . . . . . . . . . . 37 . . . . . . . . . . . 2-5 Primitive and nonprimitive cells 39 . . . . . . . . . . . 2-6 Lattice directions and planes 41 2-7 Crystal structure . . . . . . . . . . . . . . . 47 . . . . . . . . . . . . 2-8 Atom sizes and coordination 56 . . . . . . . . . . . . . . . . 2-9 Crystal shape 58 2-10 Twinned crystals . . . . . . . . . . . . . . . 59 2-1 1 The stereographic projection . . . . . . . . . . . . 63 Chapter 3 Diffraction I: Directions of Diffracted Beams . . . . . . . . . . . . . . . . 3-1 Introduction 81 . . . . . . . . . . . . . . . . . Diffraction 82 . . . . . . . . . . . . . . . . The Bragg law 86 . . . . . . . . . . . . . . X-ray spectroscopy 88 . . . . . . . . . . . . . . Diffraction directions 91 . . . . . . . . . . . . . . Diffraction methods 92 . . . . . . . . . . Diffraction under nonideal conditions 99 vii viii Contents . Chapter 4 Diffraction 11: Intensities of Diffracted Beams Introduction . . . . . . Scattering by an electron . . . Scattering by an atom . . . Scattering by a unit cell . . . Some useful relations . . . . Structure-factor calculations . . Application to powder method . Multiplicity factor . . . . . Lorentzfactor . . . . . . Absorptionfactor . . . . . Temperature factor . . . . Intensities of powder pattern lines Examples of intensity calculations Measurement of x-ray intensity . EXPERIMENTAL METHODS Chapter 5 Laue Photographs 5-1 Introduction . . . . . . . . . . . . . 1 49 5-2 Cameras . . . . . . . . . . . . . . . . 1 50 5-3 Specimens and holders . . . . . . . . . . . . 1 55 5-4 Collimators . . . . . . . . . . . . . 15 6 5-5 The shapes of Laue spots . . . . . . . . . . . . . 1 58 Chapter 6 Powder Photographs Introduction . . . . . . Debye-Scherrer method . . . Specimen preparation . . . . Filmloading . . . . . . Cameras for special conditions . Focusing cameras . . . . . Seemann-Bohlin camera . . . Back-reflection focusing cameras . . . . Pinhole photographs Microbeams and microcameras . Choice of radiation . . . . Background radiation . . . Crystal monochromators . . . Guinier cameras . . . . . Measurement of line position . Measurement of line intensity . Chapter 7 Diffractometer and Spectrometer Measurements 7-1 Introduction . . . . . . . . . . . . . . . . 1 88 7-2 General features . . . . . . . . . . . . . . . 189 Contents X-rayoptics . . . . . . Counters (general) . . . . Proportional counters . . . Geiger counters . . . . . Scintillation counters . . . . Semiconductor counters . . . Pulse-heightanalysis . . . . Special kinds of diffractometry . Scalers . . . . . . . . Ratemeters . . . . . . . Monochromatic operation . . APPLICATIONS Chapter 8 Orientation and Quality of Single Crystals Introduction . . . . . . . Crystal Orientation The back-reflection Laue method . . , Transmission Laue method . . . . . Diffractorneterrnethod . . . . . . Setting a crystal in a required orientation . Crystal Quality Laue methods . . . . . . . . . Topographic and other methods . . . . Chapter 9 Structure of Polycrystalline Aggregates Introduction . . . Crystal Size Grain size . . . . . . . . . . Particle size . . . . . . . . . Crystal Quality Crystal quality . . . . . Depth of x-ray penetration . Crystal Orientation General . . . . . . . . . . . The texture of wire (photographic method) The texture of sheet (diffractometer methods) . The texture of wire (diflractometer method) . Inverse pole figures . . . . . . . . ~morphokS olids Amorphous and semi-amorphous solids . . 9-12 Summary . . . . . . . . . . 10 Chapter Determination of Crystal Structure Introduction . . . . . . . . . . . : . . . . Preliminary treatment of data . . . . . . . . . . . Indexing patterns of cubic crystals . . . . . . . . . . Indexing patterns of noncubic crystals (graphical methods) . . . Indexing patterns of noncubic crystals (analytical methods) . . . The effect of cell distortion on the powder pattern . . . . . Determination of the number of atoms in a unit cell . . . . . Determination of atom positions . . . . . . . . . . Example of structure determination . . . . . . . . . . Chapter 11 Precise Parameter Measurements Introduction . . . . . . Debye-Scherrer cameras . . . Back-reflection focusing cameras Pinhole cameras . . . . . Diffractometers . . . . . Method of least squares . . . Cohen's method . . . . . General . . . . . . . . 1 Chapter 2 Phase-Diagram Determination . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . curves (disappearing-phase method) . . curves (parametric method) . . . . . Chapter 43 Order-Disorder Transformations Chapter 44 Chemical Analysis by X-ray Diffraction 141 Introduction . . . . . . . . . . . . . . . 1 Qualitative Analysis Basic principles . . . . . . . . . . . . . . . Powder diffraction file . . . . . . . . . . . . . . Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Examples of analysis Practical difficulties . . . . . . . . . . . . . .

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