Anisotropic corrections of measured integrated Bragg intensities for thermal diffuse scattering – general formula

The correction of measured integrated intensities for the first-order thermal diffuse scattering (TDS) is considered on the basis of the existing theory of X-ray thermal diffuse scattering for an elastic wave of long wave length. Generalized formula for the TDS correction α is found to be represented by a quadratic form in the Miller indices h, k, l and a tensor Δβ, as α = Δβ₁₁h² + Δβ₂₂k² + Δβ₃₃l² + 2Δβ₁₂hk + 2Δβ₂₃kl + 2Δβ₃₁lh. Δβ is a tensor introduced in this paper which characterizes the anisotropy of the TDS correction. The form of the tensor Δβ is shown to depend only on the crystallographic system. The relation between Δβ and the temperature-parameter tensor is presented.