Thermal scattering of X-rays by crystals - I. Dynamical foundation

Abstract

The dynamical properties of a crystal for small vibrations can be described by the set of coefficients of the potential energy forming the dynamical matrix. The elastic constants and many other observable quantities can be calculated in terms of the elements of the dynamical matrix (but in general not vice versa). The formulae given in previous publications are based on too narrow assumptions (central forces). In the present paper (Part I) this theory is developed in the most general form, without any assumption about the nature of the atomic forces. It contains, further, the method for reducing the dynamical matrix with the help of the space group of the lattice.