A Theoretical Study of the Diffuse Scattering of X-Rays by Crystals

A new derivation is made of the intensity expression for the coherent scattering of x-rays by a small crystal. The accepted intensity formula for the diffuse scattering---the well-known Debye formula---is shown to be incorrect and is replaced by a more complicated expression. According to the revised theory the intensity of the diffuse scattering varies much more rapidly with the scattering direction and exhibits a series of diffraction maxima. These maxima are found in the directions kₘ satisfying equations of the type (1+λτₘᵢₙ)kₘ=k₀+BH, where kₒ is the direction of incidence (with kₘ=k₀=1λ, the reciprocal wave-length) and BH a reciprocal lattice vector. The consequences of the theory are discussed in detail.