Thermal Scattering of X-Rays by Crystals

Abstract

THE influence of the thermal vibrations on the diffraction of X-rays by a crystal can be represented by a distribution of scattering power in the reciprocal lattice. The theoretical formula for this is the product of two parts: one, consisting of slowly varying factors which correspond to the atomic scattering factor, the polarization factor, Debye's temperature factor, the Lorentz factor, of Laue-Bragg scattering ; the other part consisting of a function characteristic of the dynamics of the crystal vibrations, the diffusion factor d(Q). For a simple lattice the latter has the form where Q_l Q₂, Q₃ are the co-ordinates in the reciprocal lattice, and S_αβ(Q) are the elements of the scattering matrix S, periodic functions of the Q. S can be expressed as a function of the dynamical matrix D, which is denned in terms of the coefficient matrix of the second order terms of the potential energy of the lattice. At normal temperatures one has, with a high degree of accuracy.