Absorption correction A* for cylindrical and spherical samples with extended range and high accuracy calculated by the Thorkildsen and Larsen analytical method.

Tables of the absorption correction A* for cylindrical and spherical crystals were calculated by the Thorkildsen & Larsen [Acta Cryst. (1998), A54, 186-190] analytical method in the range of 0 ≤ μR ≤ 30 and 0 ≤ θ ≤ 90° with accuracies of 10(-6) for cylindrical crystals and 2.0 × 10(-6) for spherical crystals.

The influence of different Student's T mosaic distributions on the extinction factor in mosaic crystals.

During the preparation of versatile tables for the secondary extinction factor Y(μ) of cylindrical and spherical mosaic crystals expressed as functions of the Bragg angle θ, absorption coefficient times radius μρ and reduced radius τ(0) = σ(0)ρ [σ(0) = (2π)(1/2)Q/η], or of θ, τ(0) and ξ(0) = μ/σ(0), five kinds of Student's Tn probability functions T1, T2, T3, T4, T∞ for describing the mosaic distribution of crystals have been tested. T1 is Lorentzian (L) and T∞ is close to Gaussian (G). The influence of these different mosaic distributions upon the reflection power ratio, the integrated reflection power ratio (the area under the rocking curve) and the extinction factor Y(μ) in cylindrical crystals has been thoroughly investigated.

Precise analysis of the components of diffraction by cylindrical crystals.

A detailed quantitative analysis of the various Bragg and Laue components of the integrated reflection power ratio for cylindrical crystals, and the dependence of these components on the Bragg angle, thetaB, the reduced radius, tau0 = sigma0rho, and the ratio of absorption coefficient to diffraction cross section, mu/sigma0 = xi0, is presented. The result indicates that the percentage of Laue and Bragg components of the integrated reflection power ratio is larger than 50% when thetaB < or = 20 degrees and murho < or = 1, and when thetaB > or = 10 degrees and murho > or = 5. The reflection power ratio profile for cylindrical crystals with large murho is also discussed.

Secondary extinction and diffraction behaviors in cylindrical crystals.

The X-ray and neutron diffraction properties in absorbing cylindrical crystals are systematically explored within the framework of transfer equations and the kinematic diffraction approximation. The calculated power ratio distribution, the integrated reflection power ratio and the secondary-extinction factor y( micro ) are expressed as functions of the Bragg angle theta(B), the reduced radius sigma(0)rho = tau(0) and the ratio of absorption coefficient to diffraction cross section micro /sigma(0) = xi(0). Numerical solutions were obtained for all theta(B) (0-90 degrees ) and samples with tau(0) from 0 to 30, and xi(0) from 0 to 25.