Evidence for the Fankuchen effect in neutron diffraction by curved crystals

Experimental evidence of the Fankuchen effect for neutron diffraction by curved crystals is presented and discussed. The Fankuchen effect consists of a space condensation of neutrons (or X-rays) diffracted by an asymmetrically cut crystal. Theoretical considerations are presented on the Fankuchen effect in the case of ideal mosaic crystals, perfect crystals and ideal curved crystals. This analysis shows that mosaic crystals behave quite differently from perfect crystals. Whereas for perfect crystals the asymmetric cut is expected to induce a real gain in neutron current density, for mosaic crystals no gain is expected. Curved crystals are expected to behave in a similar way to perfect crystals. The experiments were carried out on chemically curved Si crystals. The neutron-diffraction characteristics of a symmetrically cut Si crystal and an asymmetrically cut Si crystal were compared. A gain in the neutron current density of a factor of 4 was observed in the case of the asymmetric crystal. This value is in good agreement with the estimated theoretical value of 4.2. This fact could lead to interesting applications in the selection of monochromatic beams to be used in neutron diffractometry of small biological crystals.