Contemporary Advances in Physics, XVIII 



The Diffraction of Waves by Crystals 



By KARL K. DARROW 



This is an elementary introduction to the phenomena of diffraction of 

 waves by crystals, one of the most striking and important discoveries of 

 the last twenty years of physics. These phenomena have proved that 

 X-rays and electrons are partly of the nature of waves, and have supplied 

 the best available methods of measuring their wave-lengths; while on 

 the other hand, the study of the diffraction-pattern of a crystalline substance 

 makes it possible to determine the arrangement and the interrelations of 

 the atoms with a precision and fullness heretofore unimagined, which 

 has already yielded knowledge of great value in all the fields of science 

 and promises immeasurably more. 



THE diffraction of waves by crystals was discovered in 1912, 

 the very year in which the first of the revolutionary new theories 

 of the atom was being thought out by Bohr. But while since then the 

 atomic theory has undergone mutation after mutation — until one can 

 hardly guess any more what is stable and what is unstable, what it is 

 expedient to retain and what should be forgotten — the consequences 

 of that other discovery have steadily and serenely broadened out. 

 Already they have penetrated into more fields of science than the 

 deductions from the new atomic theories. Eventually their effects, 

 not only on physics but on mineralogy and chemistry and engineering 

 practice and even on biology, may well become so great that diffraction 

 by crystals will prove the most valuable instrument for research which 

 the physicists of our time have presented to the world. 



The discovery was not an accident, but a rarely perfect example of 

 theoretical foresight. A mathematical physicist, von Laue, was 

 pondering the theory of diffraction by ruled gratings and the other 

 standard instruments of optical research. He was at a university 

 (Munich) where Roentgen was professor and interest in X-rays was 

 intense. There was a controversy then over the question whether 

 these rays are waves or corpuscles. In those days, the antithesis was 

 absolute; people thought that either answer must exclude the other; 

 they did not realize that in ten or fifteen years they would be accepting 

 both. Towards 1912 the weight of evidence seemed to be forcing the 

 wave-theory from the scene. There was however one piece of evidence 

 which could be interpreted in its favor, provided that the wave-length 

 of the rays was of the order 10~^ centimeter. It was also known, 



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