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

Abstract

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.

Quartz conditioning crystal for X-ray rocking curve topography

“…planes parallel to an r plane (Parish & Gordon, 1945). The crystal was cut from a right-handed stock piece that was described previously (Huang et al, 2018). The cut was made parallel to the c direction in order to create a (1010) surface that faced the incident beam at grazing incidence.…”

“…It may be useful, for example, to characterize crystals serving as analyzers for resonant inelastic X-ray scattering (RIXS) (Gog et al, 2013). The key parameter for backscattering analyzers for RIXS is a close coincidence between an interesting atomic transition and the energy at perfect backscattering for an analyzing crystal (Huang et al, 2018). The uniformity of the reflected intensity over the surface of such crystals is crucial, and a good way to evaluate such crystals is with RCTOPO.…”

Confusion over the description of the quartz structure yet again

“…Thus statements such as 'Interestingly, the polarization planes rotate in the same direction, either left or right, as the SiO 4 chains' (Akhavan, 2015) are incorrect or at best misleading. As Huang et al (2018a) referred to Akhavan in their paper, this may be why they were misled. The same facts are true for the two settings of righthanded low quartz shown in Figs.…”

“…When one talks about left and right quartz one refers to its morphology and sense of optical rotation as viewed down the [001] direction. More importantly, Huang et al (2018a) also considered a unit cell in which the Si coordinates are at (u, 0, 0), (Àu, Àu, 1/3) and (0, u, 2/3), which they correctly described as forming a left-handed helix (LS), 1 but then they stated that the handedness of this helix is the same as the 'optical handedness' (i.e. the direction the quartz crystal rotates the plane of polarized light).…”

“…Recently, a paper appeared entitled the Correct interpretation of diffraction properties of quartz crystals for X-ray optics applications (Huang et al, 2018a). Interestingly, despite the authors' reference to the Donnay and Le Page paper, they still managed to make a subtle error in their description (Huang et al, 2018b).…”