Three-dimensional grain mapping by x-ray diffraction contrast tomography and the use of Friedel pairs in diffraction data analysis

Abstract

X-ray diffraction contrast tomography ͑DCT͒ is a technique for mapping grain shape and orientation in plastically undeformed polycrystals. In this paper, we describe a modified DCT data acquisition strategy which permits the incorporation of an innovative Friedel pair method for analyzing diffraction data. Diffraction spots are acquired during a 360°rotation of the sample and are analyzed in terms of the Friedel pairs ͑͑hkl͒ and ͑hkl͒ reflections, observed 180°apart in rotation͒. The resulting increase in the accuracy with which the diffraction vectors are determined allows the use of improved algorithms for grain indexing ͑assigning diffraction spots to the grains from which they arise͒ and reconstruction. The accuracy of the resulting grain maps is quantified with reference to synchrotron microtomography data for a specimen made from a beta titanium system in which a second phase can be precipitated at grain boundaries, thereby revealing the grain shapes. The simple changes introduced to the DCT methodology are equally applicable to other variants of grain mapping.

Cooperative material transport during the early stage of sintering

“…In future work, one could identify the crystallographic orientations of the individual spheres in various sintering stages by including further methods such as electron backscatter diffraction, 3D X-ray contrast tomography 28,29 or 3D X-ray diffraction [30][31][32][33][34] . Combined with in-situ SCT analysis, one would be able to measure all rotations during the sintering process and to match the respective crystallographic orientations of all particles.…”

Multigrain crystallography

“…Indexing in this case means finding the orientation matrices of the grains in the sample and sorting the G-vectors according to the grain of origin. Following the presentation of the program GRAINDEX in 2001, several alternative approaches have been proposed Wright, 2005;Ludwig, 2009, Moscicki, 2009. Some of these rely on the use of direct space information on grain position, derived either from a near field detector (Ludwig, 2009, Moscicki, 2009 or from scanning of the sample .…”

“…Following the presentation of the program GRAINDEX in 2001, several alternative approaches have been proposed Wright, 2005;Ludwig, 2009, Moscicki, 2009. Some of these rely on the use of direct space information on grain position, derived either from a near field detector (Ludwig, 2009, Moscicki, 2009 or from scanning of the sample . While such methods are relevant for 3D materials science studies, they are of less interest for crystallographic studies, where the size of the entire polycrystalline sample may be a few mm or less.…”

Measuring the stress field around an evolving crack in tensile deformed Mg AZ31 using three-dimensional X-ray diffraction

“…With 3DXRD up to 1000 grains are illuminated simultaneously and the diffracted signals from these grains are monitored on one or more detectors, while rotating the sample around an axis perpendicular to the beam. In the variant called Diffraction Contrast Tomography (DCT) only one near field-detector is used [15][16][17]. DCT has been shown to be a powerful tool for studies of short cracks, as space-filling 3D maps of grains and grain orientations can be provided and directly compared to 3D movies of the crack front as it penetrates through the sample [18,19].…”