Bragg reflection in mosaic crystals .2. Neutron monochromator properties

In the preceding article, the general solution of the Darwin equations has been obtained for a mosaic crystal slab for both the Laue case (transmission geometry) and the Bragg case (reflection geometry). This now allows the calculation, for the first time, of the reflectivity of an absorbing crystal of finite thickness in situations where the Bragg planes make an arbitrary angle with the surface of the crystal. In this paper, these results are applied to a numerical calculation of the reflecting properties of a number of commonly used neutron monochromator crystals. The incident-neutron flux is taken to be Maxwellian with an epithermal tail and it is investigated how the various properties depend on the neutron wavelength, the crystal thickness, the mosaic spread and the angle that the Bragg planes make with the surface of the crystal. It is found, for example, that for asymmetrical reflections gains in flux of 25 to 50% or more can easily be achieved for a wide range of wavelengths in crystals with the kinds of thickness and mosaic spread that are available in practice.