Darwin Width Research Articles

Resolution function of an X-ray triple-crystal diffractometer

The resolution function of an X-ray triple-crystal diffractometer is calculated on the assumption that the resolution is controlled by the properties of the monochromating and analysing crystals. The expressions are then evaluated when these crystals have either a mosaic structure or when they are perfect flat crystals with a reflectivity controlled by the Darwin width. Within the Gaussian approximation for the Darwin curve, simple expressions for the resolution are then obtained both for a conventional X-ray source and for an X-ray synchrotron source, although the expressions differ in detail. The expressions are used to discuss the intensity obtained when a triple-crystal diffractometer is used to measure the integrated Bragg reflection intensity, the intensity associated with rods in reciprocal space and the intensity of diffuse scattering.

Dynamical diffraction of x rays by perfect magnetic crystals.

The classical dynamical diffraction theory of x rays is extended to include the interaction with electron spin. A simple example is presented which shows that a purely magnetic Darwin width from a perfect magnetic crystal is approximately 3 orders of magnitude smaller than the usual charge-scattering Darwin width. Magnetic reflections are thus comparable in intensity to ``forbidden'' charge reflections in perfect crystals, which suggests that magnetic dynamical diffraction phenomena would be observable from crystals of sufficiently high quality.

The N-crystal spectrometer

It is shown that a recurrence relation exists such that the resolution function and luminosity of an optical system consisting of any number of alternate collimators and reflecting crystals can be calculated analytically. Certain cases of practical interest in neutron and X-ray diffraction are evaluated explicitly using a Gaussian approximation for the transmission functions of the collimators, and for the mosaic spread distributions or reflection profiles of the crystals. It is shown that true absorption has a negligible effect on luminosity when the Darwin width of a reflection is of the order of the opening angle of the X-ray beam from a synchrotron source.

Estimating thermal distortion of monochromator crystals

Excessive distortion of monochromator crystals exposed to high thermal fluxes can cause undesirable losses in photon beam intensity. Distortion of this kind can often be reduced to an acceptable level by indirect cooling with water. Recently, the method of finite elements was used to estimate the distortion of the first crystal in a monochromator being designed for use at the National Synchrotron Light Source Facility. Several crystal and cooling jacket configurations were evaluated for the predicted worst case thermal flux in this application. Results of the analysis indicated that, for these configurations using single crystal silicon and practical heat transfer coefficients, the thermal distortion is only a fraction of the Darwin width, or acceptance angle, of the crystal.

A channel-cut crystal monochromator for x-ray standing wave measurements

Abstract In many X-ray diffraction experiments (e.g., small angle scattering and perfect crystal experiments) it is necessary to use a monochromator with high angular resolution, often much better than the intrinsic Darwin width of a perfect crystal Bragg reflection. A monolithic silicon crystal monochromator with a variable angular resolution function has been designed and fabricated. It is tunable over a wide range of X-ray energies, and is particularly well suited for X-ray standing wave experiments using synchrotron sources. Although independently conceived, this monochromator is similar is design to one developed by Bonse et al. [1] for a different purpose. It is functionally equivalent to an asymmetric crystal monochromator in providing a narrow angular transmission, yet has several advantages over the latter for standing wave experiments, especially at a synchrotron source. Rocking curves and standing wave measurements are presented.