The thermal neutron scattering by single crystals. Reflectivity and secondary extinction

General equations for integral and peak reflectivity and also the secondary extinction coefficient of crystals have been derived in unified form for a plate, cylinder and sphere in reflexion and transmission. The numerical calculations of these formulae have been carried out. The dependence on both the scattering and absorption coefficients, the mosaic spread parameter, the crystal size, and beam collimation are discussed separately with respect to the secondary extinction and the scattering geometry. Experimental verification conditions for the theoretical calculations are considered too.