Correct interpretation of diffraction properties of quartz crystals for X-ray optics applications

Quartz has hundreds of strong Bragg reflections that may offer a great number of choices for making fixed-angle X-ray analyzers and polarizers at virtually any hard X-ray energies with selectable resolution. However, quartz crystals, unlike silicon and germanium, are chiral and may thus appear in two different forms of handedness that are mirror images. Furthermore, because of the threefold rotational symmetry along the c axis, the {h1h2h3L} and {h2h1h3L} Bragg reflections may have quite different Darwin bandwidth, reflectivity and angular acceptance, although they have the same Bragg angle. The design of X-ray optics from quartz crystals therefore requires unambiguous determination of the orientation, handedness and polarity of the crystals. The Laue method and single-axis diffraction technique can provide such information, but the variety of conventions used in the literature to describe quartz structures has caused widespread confusion. The current studies give detailed guidelines for design and fabrication of quartz X-ray optics, with special emphasis on the correct interpretation of Laue patterns in terms of the crystallography and diffraction properties of quartz. Meanwhile, the quartz crystals examined were confirmed by X-ray topography to have acceptably low densities of dislocations and other defects, which is the foundation for developing high-resolution quartz-based X-ray optics.