Crystal Orientation and Lattice Parameters from Kossel Lines

Abstract

A Kossel x-ray diffraction pattern of a single crystal contains information concerning crystal orientation, structure, and lattice parameters. Procedures have been developed for determining orientations to within ±0.5°, identifying conics and calculating d spacings to within ±0.5%, and determining lattice parameters in any crystal system with errors as small as 10 ppm. Orientation and structure calculations can be made starting with position measurements taken directly from a Kossel pattern. Precision parameter determinations require that suitable intersections of conics appear in the Kossel pattern. This can be assured by selection of appropriate conics and wavelengths and the aid of a stereographic projection of the pattern. Computer programs handle the bulk of the calculations.

Kossel patterns

“…Pitsch and his coworkers (Ryder, H~ilbig & Pitsch, 1967, 1968 have shown that the minimum radius of curvature ofa Kossel line (hkl) which is the radius of curvature of the osculating circle at the apex of the conic, is given by the equation:…”

“…8"3. Heise's (1962a, b) method [For a systematic treatment of this method, see also Gielen, Yakowitz, Ganow & Ogilvie (1965) and Morris (1968)].…”

“…The main limitation to this method is that the centre of the lens configuration must be near the centre of the pattern, although corrections can be applied if this is not the case (Yakowitz, 1965;Morris, 1968). Heise .gave _+ 1.10 -4 fit on nickel.…”

Theory and application of Kossel x‐ray diffraction in the scanning electron microscope

“…of Kassel Diffraction in SEM 81 Tixier and Wache (1970) near or exact Kosselline intersections 1 in 10 4 3 Lonsdale (1947) bracketing of Kossellines 3 2 Kossel (1936a, b) near tangency of Kossel lines 1 in 10 4 3 4 Mackay (1966) near tangency of Kossellines 1 in 10 4 3 1 Schwarzenberger (1959) near Kosselline intersections 4 in 10 4 3 1 Heise (1962) lens method 1 in 10 4 -2 x 10 4 3 4 Hanneman et al (1962) lens method 1 in 105 -2 x 10 4 3 2 Gielen et al (1965) lens method 3 4 Morris (1968) lens method 1 in 10 4 -2 x 10 4 3 4 Yakowit: (1973) lens method 1 in 10 4 -2 x 10 4 3 2…”

Untitled

“…of Kassel Diffraction in SEM 81 Schneider and Weik (1968) variable camera geometry 2 1 Fisher and Harris (1970) variable camera geometry 1 in 10 3 2 1 Morris (1968) conic fitting 1 in 200 2 conic fitting 1 Harris and Kirkham (1971) conic fitting 1 in 10 3 1 Kossel (1936a, b) comparison with prepared projection 4 Lonsdale (1947) comparison with prepared projection 4 Peters and Ogilvie (1965) stereographic proj ection 4 1 Mackay (1966) superposition of prepared charts 4 1 Ryder, Halbig and Pitsch (1967) radius of curvature 4 1 Rowlands and Bevis (1968) superposition of prepared charts 4 1 Harris and Kirkham (1971) conic fitting 1 Heise (1962) cylindrical film 2°4 1 Peters and Ogilvie (1965) stereographic projection 1-2°4 1 Bevis and Swindells (1967) Kossel line intersections 1.5°4 2 Ryder et al (1967) Kosselline intersections 0.15°4 Rowlands and Bevis (1968) superposition of prepared charts 0.5°4 1 Bevis et al (1970) conic fitting 1 Harris and Kirkham (1971) conic fitting 1 * From Biggin and In describing the essential elements of the patterns, Kossel (1936a) found it useful to construct an imaginary sphere of radius 2//L and centred at the origin of reciprocal space. For each permitted reflection, he drew a cone of semi-apex angle (90 -e B ) , whose axis joined the corresponding reciprocal lattice point with the origin.…”