Quantum theory of Lattice Vibrations

Author(s):  
R. Orbach

It is shown that the quantum theory of X -ray reflexion and scattering in crystals developed in Part I is in full accord with the experimental facts. The theory succeeds in giving a quantitative explanation of the experimental facts concerning these phenomena as observed with diamond, viz. (1) the specular character of the quantum reflexion from the (111) planes, (2) the geometric law of such reflexion and especially the fact that, in general, the reflexion falls outside the plane of incidence, (3) the subsidiary features accompanying the reflexion, viz. faint elliptic spots and elongated streamers noticed in certain special cases, (4) the absolute intensity of the reflexion which is an appreciable fraction of the intensity of the classical reflexion, (5) the failure of the (110) planes to exhibit similar reflexions, (6) the persistence of the reflexions by the (111) planes with undiminished intensity at liquid air temperature and the relatively small increase of intensity at high temperatures, and (7) the appearance of a diffuse scattering having an undiminished intensity at low temperatures. The differences between diamond and other crystals in respect of these X -ray phenomena are explained by taking into consideration the differences in the frequency and character of their lattice vibrations in the infra-red region as revealed by the spectroscope.


1998 ◽  
Vol 45 (2) ◽  
pp. 377-402 ◽  
Author(s):  
EDUARD SCHMIDT , JOHN JEFFERS , STEPHEN M.

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