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. For a weakly absorbing cylindrical crystal with τ(0) = 30, the value of Y(μ) for the T2 distribution turns out to be nearly two times the value for G, but the difference between these distributions becomes small when ξ(0) > 1. The L distribution has been found to be unsuitable for describing the mosaic distribution. The determination of different types of mosaic distribution from the rocking curves is discussed based on these results. Finally T2, T4 and the G distribution have been found to be acceptable for the calculation of secondary extinction factor tables for cylindrical and spherical crystals.