Patterson Functions and Diffuse Scattering

Abstract

Starting in Chapter 3, the kinematical theory of diffraction has been developed by calculating the diffracted wave from crystals with increasing amounts of disorder. The amplitude of the diffracted wave, ψ, is the sum of phase factors of wavelets emitted from individual atoms. We have evaluated these sums analytically (as a geometric series, for example), graphically (with a phase-amplitude diagram), and numerically. These calculations of ψ(Δk) were performed for crystals having only small departures from ideality, such as crystals of small size, crystals with strain distributions, or isolated defects imaged with a TEM. In many respects these calculations were extensions of the calculation of wave interference from atoms in a perfect crystal. Recall that when accurate phase information is present in ψ(Δk), the inverse Fourier transformation, F ⁻¹ ψ(Δk), gives f(r), the scattering factor distribution. Knowing f(r) is equivalent to knowing the positions of all atoms in the material.