Secondary extinction and diffraction behaviors in cylindrical crystals.

Abstract

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. The relationship between the power ratio distribution curves, the integrated reflection power ratio and the diffraction geometry of cylindrical crystals is obtained for the first time and analyzed in detail. A dip was found in the curve of the extinction factor y( micro ) against tau(0) for given theta(B) and xi(0), and the position of this minimum shifts toward smaller tau(0) with increasing xi(0) or theta(B). A large decrease of y( micro ) with decreasing theta(B) at low angle appears when micro rho > 3.5 and 25 > xi(0) > 0.2. The rate of change of y( micro ) in this region increases with tau(0). All of this will be important for the refinement of diffraction data. The influence of different kinds of mosaic distributions on the integrated reflection power ratio and the extinction factor was also studied. The transmission coefficients A(*) were calculated using two different methods, and an inaccuracy of these numbers in Vol. II of International Tables for X-ray Crystallography (1972) in the range theta(B) < or = 15 degrees and micro rho > or = 15 was found by comparison.