The effect of thermal vibrations on the scattering of X -rays

Abstract

The structures discovered recently in the background of Laue photographs show a striking dependence on temperature. After discussing theories suggested by Raman and Nilakantan, and by Preston and Bragg, it is assumed that there can be no other explanation of this phenomenon than the effect of thermal vibrations, as first discussed by Debye. Although there is an extended literature on this subject, it seemed worth while to reconsider the problem. Formulae are derived representing the Laue spots and the background for any crystal as function of its structure and of temperature. These formulae are simplified by applying them to the case of the three cubic Bravais lattices; for the body centred lattices one obtains an expression for the position of the spots which is identical with that given by Bragg, but with an additional law expressing the dependence of intensity on temperature. Approximate formulae are developed for all three cubic Bravais lattices which describe the position, shape, and intensity of the ‘extra spots’ in the vicinity of Laue spots.