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Asymmetrically cut perfect crystals, in both the Laue and Bragg geometries, are examined as single crystal monochromators for x‐ray beams that are collimated to a small fraction of the Darwin width, as is typical in experiments with coherent x rays. Both the Laue and asymmetric Bragg geometries are plagued by an inherent chromatic aberration that increases the beam divergence much beyond that of the symmetric Bragg geometry. Measurements from a recent experiment at the ESRF are presented to compare Si(220) (symmetric Bragg), diamond(111) (asymmetric Laue), and diamond(111) (symmetric Bragg inclined) geometries.

Sagittal focusing of synchrotron x rays with asymmetric Laue crystals has been proposed and demonstrated [Z. Zhong, C. C. Kao, D. P. Siddons, and J. B. Hastings, J. Appl. Crystallogr., Pts I&II (submitted)]. At high x-ray energies, sagittal focusing by a Laue crystal is preferred because of the small extent of the beam’s footprint on such a crystal, and the ability to use the inverse-Cauchois geometry in the meridional plane to improve energy resolution. Reflectivity curves of sagittally bent Laue crystals were measured at x rays energies from 15 to 70 keV. A model for the diffraction properties of sagittally bent Laue crystals, which takes into account the anisotropy in the elastic property of the crystals, was developed. Analytical formulas were derived for the rocking-curve width of such crystals, including both the contribution from the lattice angle change and the d-spacing change due to sagittal bending, across the thickness of the crystal. The contribution of the orientation-dependent elastic compliance S23 is as important as S13 in the specific case of sagittally bent Laue crystals. The widths of the rocking curves, calculated using the analytical model, were compared with measurements on crystals of two different orientations (111) and (100). Good agreements were found. An interesting sign reversal in the slope of the lattice angle versus depth curve between the (111)- and (100)-oriented crystals is predicted by the model, as a result of the highly anisotropic properties of silicon crystal. Results of depth-resolved rocking-curve measurements and high-resolution diffraction, designed to confirm these theoretical findings, are discussed.

An algorithm and the accompanying analysis is described for quickly and accurately orienting cubic crystals by Laue x‐ray back reflection. This technique utilizes three parameters as inputs: the film‐to‐specimen distance, the radial distance from the center of the photograph, and the angular displacement from horizontal. The outputs consist of interplanar angles between and indices of the planes producing the diffraction spots as well as the appropriate coordinate positions of the poles of those planes on a Wulff net. Also included is a statistical analysis of the errors involved. By the self‐consistent approach employed, interplanar accuracies of ±0.25° are obtained.

An extension of the method for calculating the shapes of diffracting planes from the shape of the observed Laue spots is described in this paper. The method can be used for determining the shapes of the Laue spots diffracted from ideally perfect and deformed sets of planes. The method has been applied for calculating the shapes of several Laue spots by considering the planes to be ideally perfect. The calculated shapes are then compared with the shapes observed on Laue photographs.

The position and width of the x‐ray beam transmitted through calcite in Laue diffraction has been measured. For the extinction case, the transmitted beam has the same position and width as the incident beam. For the anomalous transmission case, the transmitted beam widens showing that the radiation propagates through the crystal along the diffracting planes. These results are in general accord with the theoretical calculations of von Laue.