On the Diffuse Scattering of X-Rays by a Partially Ordered Crystal

Abstract

A general theory of the diffraction phenomena of X-rays by a crystal having irregularities of its atomic arrangements has been developed. First, the intensity formula was written as a sum of three terms, havingg distinct meanings : the first term represents a normal Laue pattern, the second a diffuse pattern similar to that due to a gas, and the third an anomalous Laue pattern. The third term is that which we are most interested in, and is due to the correlations between the irregularities possessed by any two lattice points. It is a function J (b) of the reciprocal lattice vector b, being given by equation (2.8) . It can be concluded that the weight of the scattering power for it is in general concentrated near the reciprocal lattice points, so that it gives a diffuse pattern lying near the normal Laue spots. Explicit calculation of J (b) was carried out for two cases: (1) the irregularities are due to lattice vibrations (obtaining Waller's formula in a more exact form) and (2) they are due to the order-disorder arrangements of the atoms in an alloy of, the type AB with the simple cubic structure. In the second case, a general formula was first set up, and then Zernike's theory of the propagation of orders was. applied to represent it in a more closed form. Some aspects of the intensity of the anomalous scattering were discussed in connection with the change of the degree of orders.