Interpretation of bent-crystal rocking curves

Abstract

The optics of successive Bragg reflection by two bent crystals is considered in the lamellar approximation. The optimal curvatures ensuring minimal rockingcurve widths and good reflection efficiencies are determined. The conditions under which a rocking curve reproduces the reflectivity curve of a bent crystal are indicated. Analytical formulae for the rocking-curve width and peak intensity are derived for three simple limiting cases. The computations are supported by experimental results obtained with bent perfect silicon crystals.

X-ray reflectivity of bent perfect crystals in Bragg and Laue geometry

“…Different approaches have been introduced by Brown & Fatemi (1974, 1980, who apply Zachariasen's theory of extinction to the curved crystals, and by Kalman & Weissmann (1983), who deduce the general form of the integrated reflection and calculate the parameters from the limiting values at small and large bending radii. The integrated reflection is measured quite easily, and many results are available, but after the pioneering work by White only a few reflectivity curves measured by neutrons have been published (see Mikula et al, 1984, andPopovici, Stoica, Chalupa &Mikula, 1988). The integrated reflection is measured quite easily, and many results are available, but after the pioneering work by White only a few reflectivity curves measured by neutrons have been published (see Mikula et al, 1984, andPopovici, Stoica, Chalupa &Mikula, 1988).…”

X-ray diffraction of bent crystals in Bragg geometry. I. Perfect-crystal modelling

“…This paper forms the basis of the present discussion. Suortti, Pattison & Weyrich (1986), Popovici, Stoica, Chalupa & Mikula (1988) and Erola, Etel/iniemi, Suortti, Pattison & Thomlinson (1990) have used similar models. Fig.…”

Line shifts in crystal powder diffractometers

“…The general formula for the covariance-matrix modification by a linear constraint is easily derived by a method described in the mathematical appendix of a previous paper (Popovici, Stoica, Chalupa & Mikula, 1988). For a set of initial variables xl,..., x, on which a constraint of the form Z aixi : 0 (10) i is imposed, the second-order moments (XiXj>' of the reduced set of variables Xl .... , x,_ 1 that remain after having excluded x, by using the constraint are given by…”