Random-walk algorithm for the simulation of neutron diffraction in deformed mosaic crystals

A sampling formula is derived for random-walk steps, which simulate neutron transport through mosaic crystals with deformation gradient. The formula describes both purely gradient (elastically deformed) and undeformed mosaic crystals as limit cases. Simulations of reflection in a mosaic Ge crystal at asymmetric (Fankuchen defocusing) reflection geometry are shown as an example. The results demonstrate the effects of crystal deformation on reflectivity, neutron propagation inside the crystal and spatial profile of the diffracted beam.