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"Crystallography Dieter Schwarzenbach Institute of Crystallography University of Lausanne Switzerland Translated from the French by A Alan Pinkerton University of Toledo USA JOHN WILEY & SONS Chichester New York Brisbane Toronto Singapore © 1996 John Wiley & Sons Ltd Baffins Lane Chichester West Sussex P01 9 1UD England National 779777 International +44 1243 779777 © 1993 Presses Polytechniques et Universitaires Romandes 1015 Lausanne Switzerland All rights reserved No part of this book may be reproduced by any means or transmitted or translated into a machine language without the written permission of the publisher Other Wiley Editorial Offices John Wiley & Sons Inc 605 Third Avenue New York NY 10158-0012 USA Jacaranda Wiley Ltd 33 Park Road Milton Queensland 4064 Australia John Wiley & Sons Canada Ltd 22 Worcester Road Rexdale Ontario M9W 1Ll Canada John Wiley & Sons SEA Pte Ltd 2 Clementi Loop 02-01 Jin Xing Distripark Singapore 129809 Originally published in French under the title Cristallographie Library of Congress Cataloging-in-Publication Data Schwarzenbach Dieter Crystallography English Crystallography Dieter Schwarzenbach translated from the French by A Alan Pinkerton p Includes bibliographical references and index ISBN 0-471-95598-1 (alk paper) 1 Crystallography I Title QD9052 S3813 1996 11160 5488 dc20 P British Library Cataloguing in Publication Data A catalogue record for this book is available from the British Library ISBN 0 471 955981 Typeset in 10 12pt Times by Thomson Press (I) Ltd New Delhi Printed and bound in Great Britain by Biddies Guildford Surrey This book is printed on acid-free paper responsibly manufactured from sustainable forestation for which at least two trees are planted for each one used for paper production Contents Foreword Chapter 1 Geometrical Crystallography 11 Introduction Analytical Geometry with Oblique Bases Polyhedral Crystal Shapes Periodic Space Tiling and Crystal Structures What is a Crystal Chapter 2 Symmetry Introduction Symmetry Operations Symmetry Elements Symmetry and the Lattice Metric Crystal Classes and Systems Classification of Lattices Symmetry of Periodic Structures Crystal Structures MillerBravais Indices for Hexagonal Coordinate Systems Chapter 3 Diffraction of XRays by Crystals Introduction Scattering of XRays by an Electron Scattering of XRays by Matter Diffraction by a Periodic Structure Experimental Diffraction Methods Physics of Xrays Intensities of Diffracted Beams Space Group Determination Comments on the Solution of the Phase Problem Chapter 4 Tensor Properties of Crystals Anisotropy and Symmetry Tensors Stresses and Strains Examples of Tensor Properties Crystal Optics Chapter 5 Exercises Exercises Relating to Chapter 1 Exercises Relating to Chapter 2 Exercises Relating to Chapter 3 Exercises Relating to Chapter 4 Index Ключевые слова: symmetric, reflecting plane, manner, twofold, periodic pattern, threefold fourfold, laue group, lorentz factor, electric displacement, equation, laue, international, abstract group, vice versa, factor, law, oo, voigt notation, il, face, rays, ellipsoid, totally symmetric, represent, sin, isotropic medium, crystals, unit cell, exact science, microscopic structure, electric field, group, laue class, chemical stoichiometry, primary beam, group belonging, rank, ri, optical, international notation, mirror, metric, axis, ha, structure, electron, element, spatial average, operation, euclidean plane, parallel, three-dimensional structure, pure rotation, distance, angle, equal, general, order, crystal class, projection, mirror plane, principal, magnetic field, two-dimensional space, form, single cell, position, electrostatic potential, rotoreflection, h k, disordered, plane, rotation, symmetry element, ke le, sphere, path difference, wavelength, crystallography, jt jt, space group, light, longitudinal, maximum, origin, x-rays, constant, note, electrical conductivity, reflected beam, reciprocal space, symmetry, electric susceptibility, diffracted beam, laue method, reflection, space groups, center, glide, von laue, ax, translation, intensity, property, uniformly distributed, cyclic group, atomistic model, edge, dipole moment, diffraction, field, p xy, symbol, table, dimensional, dx dy, volume, solution, anomalous dispersion, u v, perpendicular, periodic, number, point, cell, class, screw, fourier transform, calculate, ray, integer, space, function, screw axis, direct space, solid, transforms, result, method, stress, international tables, chiral group, reciprocal, coordinate, powder pattern, atomic scale, three-dimensional lattice, zi ze, polarization, wave, focal plane, electromagnetic wave, series, translational lattice, cubic, phase, nth plane, periodic repeat, thermal vibration, metal forming, direction, segment o-a, hkl, structure factor, case, beam reflected, radiation, rotoinversion, bravais, squared structure, twofold point, recip space, electrostatic field, matrix, gradi, component, unit, vt, type, beam, x rt, -j, powder method, charge-e, lattice, condition, exercises relating, fourfold, represented, tangent plane, term, dot, density, energy, absence, equivalent, electric, crystal, atom, plane tangent, normal, angular velocity, eigenvalue, vector, penrose tiling, tensor, international union, respect, orientation