Reflexion and scattering of X-rays with change of frequency. I. Theoretical

Abstract

The paper sets out in an elementary way the theory of two new phenomena of fundamental importance, namely the quantum reflexion and the quantum scattering of X-rays. (1) The quantum or modified scattering is due to the excitation of the elastic solid or low frequency vibrations of the crystal lattice by the X-ray photon. It has a very low specific intensity proportional to N (the number of lattice cells) and is distributed over a wide range of solid angles. The view expressed by some authors that the elastic solid vibrations of the lattice are responsible for the additional spots visible in Laue diagrams is consequently erroneous. (2) The quantum or modified reflexion is due to the excitation of the infra-red or characteristic high frequency vibrations of the crystal lattice by the X-ray photons. Its intensity, like that of the classical or unmodified reflexions is of the order N², though usually smaller in absolute value than the intensity of the classical reflexions. The manner in which the direction and intensity of the quantum reflexions are connected with the specific modes of infra-red vibration is mathematically formulated and discussed. (3) The frequency changes which play a fundamental part in the theory of both phenomena appear as necessary consequences of both the classical and quantum theoretical points of view. The law of temperature dependence of intensity is, however, quite different in the classical and quantum formulations. The experimental study of intensity at low temperatures accordingly furnishes a conclusive criterion both for the reality of the frequency changes and for the quantum mechanical character of the effects. (4) The influence of the modified X-ray reflexions on the intensity of the classical reflexions and their variations with temperature is discussed and shown to be of even greater importance than the effect on the same of the X-ray scattering by the elastic solid vibrations.