Extinction in finite perfect crystals: case of a sphere

The extinction factor in finite perfect crystals is calculated from pure dynamical theory. In particular, a detailed solution is proposed for a sphere, in which case the extinction factor depends on the Bragg angle θ and the parameter (R/Λ), where R is the radius of the crystal and Λ the extinction length. An approximate solution based on the Laue geometry is proposed and corrections to take care of the complex boundary conditions are presented. An expression easily usable in refinement programs is proposed that fits the exact value to better than 1%.