CAN A GRADIENT CRYSTAL COMPETE WITH A MOSAIC CRYSTAL AS A MONOCHROMATOR IN NEUTRON-DIFFRACTION OR X-RAY-DIFFRACTION

First a description of the Bragg reflection in polar coordinates is developed. Subsequently this formalism is applied to describe diffraction for mosaic crystals, gradient crystals and to include the Doppler effect on moving crystals. Within this framework the performance of a powder diffractometer as a two crystal configuration is evaluated. A traditional mosaic monochromator seems to be well suited when large values of reciprocal lattice vectors G are of main interest. However, a gradient crystal monochromator becomes competitive for G(2)/G(1)<0.5 with G(2) and G(1) representing the reciprocal lattice vectors of the sample and the monochromator, respectively. This holds in particular for a reflectometer, where the scientific interest focuses at small G(2) values. It is argued that particularly performant designs can be expected on a reflectometer for a monochromator which combines a reflection on a gradient crystal with a suitably chosen Doppler effect.