Exploratory Study of Plural X-Ray Reflection Methods Applied to the Problem of the Diffraction Pattern of Calcite

Abstract

An exploration of the possibilities and difficulties in the study of the x-ray diffraction patterns of crystals with the method of the plural reflection spectrometer is described. This method, first suggested to the present authors by P. Kirkpatrick, has been analyzed in a recent ${\mathrm{article}}^{1}$ by one of us and the present article describes our first attempts to apply these ideas and to refine and extend the suggested methods of the first article. Diffraction patterns of calcite samples for Mo $K\ensuremath{\alpha}$-radiation were studied with three nearly parallel crystal faces reflecting x-rays in (1,-1,1) order, Allison's notation, or {1,1,1} order, DuMond's notation, and it was found that the fillets to be expected as approaches on the sides of the Prins diffraction pattern offer a serious obstacle to the direct use of this simple method. Two methods of circumventing the fillet difficulty are proposed, but not tried. A third method more readily adaptable to the equipment at hand, involving the use of three crystals and five successive reflections, was tried with a fair measure of success. Four successive reflections occur between two nearly parallel adjacent faces of a pair of large calcites. By adjusting these two calcites 1.5 seconds of arc off parallel there is good reason to believe that a narrower "tool" beam with reduced fillets was prepared with which the "object" crystal diffraction pattern was then explored. The observed diffraction patterns for the two calcite object crystals studied are shown. No asymmetry of the top of the pattern could be observed with reproducible certainty but this is to be expected since the theoretical asymmetry for Mo $K\ensuremath{\alpha}$-radiation in the first order on calcite is very small. An extension of present methods to longer wave-lengths in the vacuum region could quite possibly reveal such asymmetrical pattern shapes for at longer wave-lengths the asymmetry is more marked and the pattern is several times broader.Our results make it appear very doubtful whether the ideal flat topped diffraction pattern of Prins really obtains at the wave-lengths we have studied, the indications being that the real diffraction pattern has a sharper peak.