Single and multiple diffraction in non-absorbing perfect crystal spheres bathed in the monochromatic parallel incident beam: The intensity pattern of $\psi$-scans calculated in the framework of the kinematical approach

Expressions for the calculation of multiple diffraction patterns for perfect crystals spheres are given in the kinematical approach. Two experimental ψ-scans of the ‘almost forbidden’ 222 reflection of silicon, measured with AgKα-radiation and with synchrotron radiation at λ = 0.5612 Å, are compared with simulations performed with the program UMWEG-97. It is shown that multiple diffraction patterns of perfect spherical crystal samples can be satisfactorily predicted on absolute scale