A single-exposure method for the determination of lattice spacings and crystal orientation from Kossel diffraction patterns

Abstract

A single exposure method is described for the calculation of lattice spacings and crystal orientation, from Kossel diffraction patterns. This method is extremely simple from an experimental viewpoint since the only data required are the coordinates of five or more points on each Kossel diffraction curve in an arbitrary orthogonal system and the wavelength of the characteristic X‐ray radiation forming the pattern. The method requires the analysis of at least two diffraction curves which can be either elliptical or hyperbolic. The equation of each curve is first derived in the arbitrary system. It is then transformed to a coordinate system in which the coefficients may be equated with those of an equation of the same curve derived in terms of the lattice spacing, the orientation of the crystal planes responsible for the diffraction cone and the X‐ray wavelength. The lattice spacings and the directions of the crystal plane normals are calculated. A computer program has been written to handle the lengthy arithmetical operations required for the analysis, and application of the method to a Kossel pattern from a single grain of Swedish iron is described.

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

“…Lattice spacing Imura et al (1962) variable camera geometry 2 1 Ellis et al (1964) variable camera geometry 2 in 10 4 2 1 Shrier et al (1966) variable camera geometry 1 in 10 3 2 1 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…”

“…Indexing 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…”

“…Orientation 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.…”

Untitled

“…"".JlJL, the form of the is similar to that of Kikuchi lines and also to that obtained the methods of electron channeling (Coates Booker et al 1975) and electron (Venables and Harland 1973), 1t"Dor'h-rl,llrllllllDoCl r1IDo'(TDoI.n.-yo"Dor1l earlier for use in the SEM. Umeno and Shinoda (1968) Peters and Ogilvie (1965) Hanneman and Ogilvie (1962) Cort and Steeds (1972) Harris and Kirkham (1971) Schwarzenberger (1959 D. J.…”

“…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.…”