410 BELL SYSTEM TECHNICAL JOURNAL 



have drawn some profit; they have estimated the amount of the 

 thermal agitation and determined how it alters as the temperature 

 goes down. It decreases, of course; not however in such a way as 

 to imply entire standstill at absolute zero, but quite the contrary. 



(iii) The neglect of absorption. Since the energy of the scattered 

 waves is drawn from that of the primary beam, this cannot retain its 

 amplitude unaltered as it progresses through a crystal lattice; and 

 calculations based on the assumption that all the atom-groups of a 

 crystal scatter equally cannoi be correct, for they do not all have 



:f#,«5s» 



Fig. 12 — Laue pattern of an aluminium crystal, introduced to show that if the 

 primary beam does not happen to follow an axis of the crystal lattice there are still 

 diffraction-spots though not so regularly arranged as in the (previous leases. The 

 crystal appeared under the microscope as an irregular patch on the metal surface 

 (left-hand figure; the circle shows where the primary beam struck.) (Czochralski.) 



incident waves of the same amplitude to scatter. This might well be 

 serious, in a large crystal. It turns out however that large crystals 

 are seldom if ever perfect; instead, they are likely to consist of smaller 

 crystals tilted with respect to one another. The tilts are very small, 

 but they are sufficient to suspend the consequences which should 

 strictly follow from the assumption that absorption may be neglected. 

 (iv) The neglect of refraction. It has been tacitly assumed that 

 there is neither bending of path nor change of wave-length when 

 primary waves enter a crystal lattice or scattered waves emerge. 

 Refraction however entails both of these phenomena; and refraction 

 will in general occur. However with X-rays it is so slight (the refrac- 

 tive index is so nearly unity) that it need seldom be allowed for in 

 crystal analysis, and must indeed be looked for with care and skill if 

 it is to be detected. The like is true for short electron-waves. With 

 the long electron-waves first studied, however, the refraction is 

 considerable; and during the interpretation of the earliest data, there 

 was serious confusion. 



