Determination of elastic constants from diffuse reflexion of X-rays

Abstract

Elastic constants of crystals may be determined from measurements of diffuse X-ray reflexions given by them. According to the theory of Waller, diffuse reflexions are produced as a result of the superposition of thermal waves (into which the random thermal vibrations of atoms in the crystal can be resolved) on the ideal Bravais làttice. This dynamic stratification makes possible reflexion at angles other than the Bragg setting. The diffuse reflexion at a particular angle of incidence and of reflexion is produced by thermal waves having a definite wavelength and orientation, and from its intensity the frequency of the wave can be calculated. Combining the two data, the velocity of the wave can be obtained and, assuming that there is no dispersion of acoustical velocity, the elastic constants can be calculated from the velocities of waves propagated in different directions.