IIL X RAYS AND CRYSTAL STRUCTURE LONDON : G. BELL AND SONS, LTD., PORTUGAL ST., LINCOLN'S INN, W.C. NEW YORK: THE MACMILLAN CO. BOMBAY: A. H. WHEELER & CO. Presented to the LIBRARY o/M^ UNIVERSITY OF TORONTO ^- by J. R. McLeod t « X RAYS AND CRYSTAL STRUCTURE BY W. H. BRAGG, M.A., D.Sc, F.R.S. CAVENDISH I'KOFESSOR OF PHYSICS, UNIVERSITY OF LEEDS AND W. L. BRAGG, B.A. FELLOW OF TRINITY COLLEGE, CAMMRIUCiE LONDON G. BELL AND SONS, LTD. 1915 PREFACE. It is now two years since Dr. Laue conceived the ' idea of employing a crystal as a space diffraction ' grating- for X-rays. The successful realisation of the idea by Messrs. Friedrich and Knipping has opened up a wide field, of research in which results of great interest and importance have already been obtained. On the one hand the analysis of X-rays which has been rendered possible has led to remark- able conclusions concernincr the atoms which emit them under the proper stimulus, and has thrown an entirely fresh light on problems of atomic structure. On the other hand the architecture of crystals has been laid to examination is open ; crystallography no longer obliged to build only on the external forms of crystals, but on the much firmer basis of an exact knowledoe of the arranoement of the atoms within. It seems possible also that the thermal movements of the atoms in the crystal will be susceptible not only of observation but even of exact measurement. In order to grasp the meaning and progress of the new science, it is necessary to have some knowledge both of X-ray phenomena and of crystal- vi PREFACE have never lography. As these branches of science been linked together before, it is to be expected that many who are interested in the new develop- ment find themselves hampered by a tantalising ignorance of one or other of the essential contribu- little book son and I tory subjects. In this my have first made an attempt to set out the chief facts and to so and principles relating to X-rays crystals, far as they are of importance to the main subject. We have devoted the remaining and larger portion of the book to a brief history of the progress of the work, and an account of the most important of the results which have been obtained. The book is necessarily an introduction rather than a treatise. The subject is too new and too treat- unformed to justify a more comprehensive ment. We have tried to draw its main oudines for the use of those who wish to understand its general statement even bearings, and we hope that our may be of some service to those who wish to make its share in the fasci- acquaintance practically and to nating research work which it offers. No doubt the latter will consult also the original papers. had in Considering the purpose which we have view we have refrained from the discussion of a with other number of interesting points of contact sciences and with older work, such as for example Barlow. the remarkable investigations of Pope and W^e have not even given a complete account of all have been made the experimental investigations that been in connection with the subject itself, and have PREFACE vii content with the merest allusion to the serious mathematical discussions which it has received at several hands. The publication of the book has been delayed by the difficulties of these times, which have also hindered the continuance of some researches and the publication of others that are almost or quite complete A few results which could not be included in the book itself are given in supple- mentary notes at the end. The same circumstances have left me to write this preface alone. Probably, however, I should have demanded the privilege in any case. I am anxious to make one point clear, viz., that my son is ' ' responsible for the reflection idea which has made it possible to advance, as well as for much the greater portion of the work of unravelling crystal structure to which the advance has led. W. H. BRAGG. January, igij. CONTENTS. CHAl'TER I'ACE i I. Introductory ------- 8 II. Diffraction of Waves ----- III. The X-Rav Spectrometer - - - - 22 IV. Thk Properties of X-Rays - - - - 3^ V. Crystal Structure - - - - - - 5^ VI. X-Ray Spectra ------- 66 VII. The Analysis of Crystal Structure. I. - 88 VIII. The Analysis of Crystal Structure. II. - 112 ^ / IX. The Relation between Crystal Symmetry and the Arr.'^ngement of the Atoms - 14- X. The Analysis of Crystals. III. - - - 160 XL The Intensity of X-Ray Reflection - - 175 XII. The Analysis of the Laue Photographs - 207 - - Supplement A.^Y Notes - - - 227 Index --..- - - 229 CHAPTER I. INTRODUCTORY. Ever since the discovery by Rontgen of the rays which bear his name, their nature has been the subject of the keenest investigation. In many respects the rays resemble hght. They move in straight Hnes and cast sharp shadows, they traverse space without any obvious transference or interven- tion of matter, they act on a photographic plate, excite certain materials to phosphorescence, and can brinor about the ionisation of a ©as. In other respects the rays have seemed to differ from light. The mirrors, prisms and lenses which deflect light have no such action on our diffraction X-rays ; do not diffract them neither double refrac- gratings ; tion, nor polarisation is produced by the action of crystals. If the velocity of X-rays could have been shown without question to have been the same as that of light, it would have been a most important piece of evidence. E. Marx of Leipzig devoted the greatest skill and perseverance to the attempt to measure the velocity, and claimed that he had over- come all the many acute objections brought against his work. His results led him to assert the equality A B. R. 2 INTRODUCTORY of the velocities of the two kinds of but the rays ; difficulties of the experiment were so great that his work did not bring universal conviction. the evidence— to the Undoubtedly— strongest up present time of the similarity of nature of light and X-rays was supplied by the discovery of a form of polarisation of the latter rays. Barkla showed that the X-rays issuing from a bulb and impinging upon matter were less scattered by the matter in a direc- tion parallel to the stream of cathode rays in the bulb than in directions at riofht anoles to the stream. A pencil of rays selected from the scattered radiation, though more difficult to work with than primary rays, showed the same effect to a much higher degree. These facts were in accordance with the theory of the electromagnetic origin of X-rays due to Schuster, Wiechert, Stokes, J. J. Thomson, and others. Cathode particles, whose flight had been suddenly arrested by impact on the anticathode, should send out ether pulses, that is to say, a sort of liofht in which the vibrations would tend to be parallel to the direction of the cathode-ray stream. Such vibrations, impinging on matter and scattered thereby, would give rise to less radiation in the direction of the vibrations than in any other. The strongest evidence against the similarity of nature of light and X-rays has arisen from con- siderations of the transference of energy by means of the latter. Cathode rays impinge on the anti- cathode and give rise to X-rays : it is found that INTRODUCTORY 3 these in turn give rise to cathode rays, i.e. swiftly moving electrons, when they encounter matter of any kind. It is very remarkable that the speed of the secondary electron which the X-ray produces is nearly the same as that of the primary electron which produces the X-ray. This is so, no matter what the intensity of the X-rays may be, nor how far from the bulb the production of the secondary X-ray takes place, nor what the nature of the matter from which the secondary electron seems to spring. It seems almost imperative that we should con- sider the X-ray to have transferred so much energy from the one electron to the other, and this involves the conception of a 'quantum' of energy radiation travelling through space without alteration of form or content as it goes. The idea is quite foreign to orthodox conceptions of the transference of radiation energy. No one has been able to suggest how it is to be reconciled with the older hypotheses. It has, however, become increasingly clear that the phenomenon which appears so irreconcilable with light theory must in some way be made to fit ' ' in. The photo-electric action is found, on closer investigation, to be of exacdy the same kind as the X-ray action which has just been described. It is quite clear that we cannot explain our difficulties over the X-ray energy question by asserting that X-rays and light are not to be compared with each other because they are of different natures. Just when we are pondering on the difficulties of 4 INTRODUCTORY reconciling facts which appear to be in conflict, a new discovery is made of extraordinary interest. It tells us in the first place that the right path has been chosen in assuming light and X-rays to be identical in nature. Indeed, it shows that the identity is even closer than we had thought in that it precludes us from ascribing differences in character to anything else than mere differences in wave-length.