Bragg Reflection in Mosaic Crystals. II. Neutron Monochromator Properties

Abstract

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 (refection 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.

Single-crystal diamond: a potential gem in neutron instrumentation

“…This is even more evident from Table 4, showing results for a neutron wavelength of 1 Å and the same mosaic spread of 0.3 . The results obtained for the optimum (x = 0.8) thickness are in good agreement with those calculated by Sears (1997b).…”

A double-supermirror monochromator for neutron instrumentation at Laboratoire Léon Brillouin

“…Only a few materials with suitable lattice spacing (d) and mosaicity can possibly be used. Graphite intercalation compounds are the most interesting materials for this purpose but the maximum selected wavelength is quite small, lower than 0.89 nm [12]. Moreover, the crystal mosaicity obtained (1 or 2 • ) leads to a very good wavelength resolution but with a low bandwidth, i.e.…”

X-ray reflectivity of chemically vapor-deposited diamond single crystals in the Laue geometry

“…The analytical solution for the general case of asymmetric diffraction in the transmission (Laue) geometry was reported by Dietrich and Als-Nielsen [4]. Generalized solutions in both Laue and Bragg geometries were reported and studied in more details by Sears [5,6]. To date, diffraction theories of imperfect crystals have evolved substantially (see [7] for a review).…”