On the neutron reflectivity of bent perfect crystals

Abstract

The neutron reflectivity of deformed perfect crystals is examined for different types of uniform and nonuniform bending. The peculiarities of the pneumatic bending are discussed. Check measurements with bent perfect silicon crystals are presented.

SPHERES, Jülich's high-flux neutron backscattering spectrometer at FRM II

“…The relative change of the lattice constant at a distance d from the neutral surface is κd/R with a material constant κ = 0.776 for Si(111). 35 Assuming a rectangular distribution of lattice constants, and neglecting Darwin tails and other dynamical scattering effects, one would expect a rectangular distribution of backscattered energies with a full width of E = 0.81 μeV. Convoluting this distribution with itself, to account for monochromator and analyzer, one obtains a triangular distribution with the same full width E. This is in reasonable agreement with the observed overall resolution of SPHERES, which is in first approximation a Gaussian with a full width at half maximum of about 0.62 μeV (Sec.…”

Resolution calculations for novel neutron beam elements

“…Among these elements are rectangular-pro®le collimators (Cussen, 1998;Krist & Mezei, 2000), monochromating crystals with rectangular mosaic pro®les (Hamelin, 1996) and gradient monochromator crystals, of which the crystal lattice parameter varies rather than the orientation of the crystal axes (Magerl, 1994). Bent perfect crystals also provide an approximation to a rectangular mosaic pro®le, but the bending leads to a lattice-spacing gradient as well (Kulda & Saroun, 1996;Stoica & Popovici, 1989).…”

Neutron imaging with bent perfect crystals. I. Imaging conditions

“…The variation of the reciprocal-lattice vector in an elastically deformed crystal has been examined before (Stoica & Popovici, 1989). The general formulae expressing the relative deviations of the reciprocal-lattice vector (Á( || /(, Á( c /(), see Fig.…”

“…The local value of the reciprocal-lattice vector is de®ned for every point of the crystal (Stoica & Popovici, 1989). Neutrons along a given path in the crystal are re¯ected with a certain probability at the points where the Bragg condition is ful®lled (Kulda, 1984).…”

“…However, systematic studies of bent perfect crystal monochromators were not made until the eighties. Cylindrical mechanical bending of bulk crystals (Mikula et al, 1984(Mikula et al, , 1986(Mikula et al, , 1987(Mikula et al, , 1990 and of multi-wafer packets (Rekveldt, 1983;Arrott & Templeton, 1985), and two-dimensional pneumatic bending of crystals (Popovici et al, 1987;Stoica & Popovici, 1989) have been employed. Matrix computer codes for bent crystal instrument optics have been developed (Popovici et al, 1987(Popovici et al, , 1994(Popovici et al, , 1997.…”