Double Bragg scattering observed in small-angle X-ray scattering from highly oriented pyrolytic graphite

Abstract

In small-angle X-ray scattering from highly oriented pyrolytic graphite, radial streak patterns are observed. The streaks change their direction with sample rotation and appear and disappear in pairs. This streak pattern can be explained by double Bragg scattering. The directions of the streaks calculated as functions of the rotation angle are in good agreement with experiment. In addition, asymmetry in the intensity of the streaks and a small deviation from the radial pattern are observed, and they can be explained by the finite sample-size effect. The necessity of taking double Bragg scattering into account in small-angle X-ray scattering studies of crystalline materials is emphasized. research papers J. Appl. Cryst. (2016). 49, 835-844 Yoshinori Ohmasa et al. Double Bragg scattering in HOPG 837

Intensity distribution profile of double Bragg scattering in the small-angle region from highly oriented pyrolytic graphite

“…The two streaks labelled '1' and '2' correspond to the two solutions ' f streak1 and ' f streak2 of equation (40), respectively. (Ohmasa et al, 2016), which is consistent with the theoretical prediction È ' È 0 = À B1 À 1c = 85.2 . In the present work, the streaks can be treated as straight lines because the curvature of the streaks given in equation (40) can be neglected.…”

“…G 2 ' ÀG 1 . As shown in the previous article (Ohmasa et al, 2016), it is found that double Bragg scattering in the small-angle region mainly consists of ðh 1 k 1 l 1 ; h 1 k 1 l 1 Þ type scatterings (h 2 = h 1 , k 2 = k 1 , l 2 = Àl 1 ). In this case, the two reciprocal-lattice vectors are nearly the same length.…”

“…Guinier and Guyon discussed the broadening of double Bragg scattering due to the finite sample size effect in the special case of a slab-shaped perfect single-crystalline sample (Guinier & Guyon, 1959). In the previous article (Ohmasa et al, 2016), we explained briefly the broadening of the streak of double Bragg scattering for the same sample geometry as in the present work, and calculated analytically in the special case where È = 90 and the width of the incident X-ray beam is negligibly small. In the present work, we have treated the instrumental broadening effect numerically for a more general angle of È and a finite beam size.…”

“…We use the same coordinate system as in the previous article (Ohmasa et al, 2016), shown schematically in Fig. 1(a).…”

“…In a previous article (Ohmasa et al, 2016), we performed small-angle X-ray scattering experiments for highly oriented pyrolytic graphite (HOPG) and found that a streak-like pattern appears in the small-angle region, and that it is caused by double Bragg scattering by the HOPG sample. In the past, the existence of double Bragg scattering in the small-angle region was reported for polycrystalline or plastically deformed single-crystalline materials and studied experimentally and theoretically (Atkinson, 1959;Robinson & Smoluchowski, 1959;Webb & Beeman, 1959;Guinier & Guyon, 1959;Ogier et al, 1959;Warren, 1959aWarren, ,b, 1960Thomas & Franks, 1959;Fricke & Gerold, 1959;Terminasov & Tuzov, 1964;Taglauer, 1968;Skrytnyy & Yaltsev, 2016).…”