Correlations in disordered crystals and diffuse scattering of x rays or neutrons

Abstract

The scattering cross section for diffuse scattering of x rays or neutrons from disordered crystals is expressed systematically in terms of density-correlation functions by using a cumulant expansion. This approach allows one to distinguish between contributions owing to pair-, three-, and higher-order correlations of the defects; the latter ones enter even within the first Born approximation due to the nonlinear dependence of the scattering amplitude on the lattice displacements. The terms involving even and odd correlation functions, respectively, can be classified according to their inversion symmetry properties. This analysis is applied to x-ray scattering data obtained from niobium-molybdenum alloys loaded with hydrogen. Furthermore, we propose how to test, on the basis of the scattering data alone, approximation schemes for the three-point correlation function, such as, e.g., the Kirkwood superposition principle.