Quantum theory of X-ray reflexion

Abstract

In a memoir which appeared in 1926, Laue showed by purely classical reasoning that the X-rays scattered by elastic solid waves of thermal origin in a crystal have the frequency v±v*, v being the primary X-ray frequency and v* the frequency of the elastic waves. He evaluated I_v and I_v±v*, these being respectively the intensities of the reflexion and the scattering by any assigned set of lattice planes in the crystal. The value of I_v±v* for any specified direction of scattering may be found by assigning the appropriate wavelength and orientation to the elastic waves in Laue's formula. The ratio I_v/I_v±v* comes out, as might naturally be expected, to be of the order N, this being the total number of atoms in the irradiated solid. Even for a tiny crystal only 1μ in size, the ratio is thus of the order 10¹¹. In other words, the scattering in any specified direction by the lattice planes has an intensity wholly negligible in comparison with that of the coherent reflexion by the same planes.