The mechanical properties of polycrystalline materials are largely determined by the kinetics of the phase transformations during the production process. Progress in x-ray diffraction instrumentation at synchrotron sources has created an opportunity to study the transformation kinetics at the level of individual grains. Our measurements show that the activation energy for grain nucleation is at least two orders of magnitude smaller than that predicted by thermodynamic models. The observed growth curves of the newly formed grains confirm the parabolic growth model but also show three fundamentally different types of growth. Insight into the grain nucleation and growth mechanisms during phase transformations contributes to the development of materials with optimal mechanical properties.

A fast and non-destructive method for generating three-dimensional maps of the grain boundaries in undeformed polycrystals is presented. The method relies on tracking of micro-focused high-energy X-rays. It is veri®ed by comparing an electron microscopy map of the orientations on the 2.5 Â 2.5 mm surface of an aluminium polycrystal with tracking data produced at the 3DXRD microscope at the European Synchrotron Radiation Facility. The average difference in grain boundary position between the two techniques is 26 mm, comparable with the spatial resolution of the 3DXRD microscope. As another extension of the tracking concept, algorithms for determining the stress state of the individual grains are derived. As a case study, 3DXRD results are presented for the tensile deformation of a copper specimen. The strain tensor for one embedded grain is determined as a function of load. The accuracy on the strain is Á4 9 10 À4 .

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.

The principles of a novel technique for nondestructive and simultaneous mapping of the three-dimensional grain and the absorption microstructure of a material are explained. The technique is termed X-ray diffraction contrast tomography, underlining its similarity to conventional X-ray absorption contrast tomography with which it shares a common experimental setup. The grains are imaged using the occasionally occurring diffraction contribution to the X-ray attenuation coefficient each time a grain fulfils the diffraction condition. The three-dimensional grain shapes are reconstructed from a limited number of projections using an algebraic reconstruction technique. An algorithm based on scanning orientation space and aiming at determining the corresponding crystallographic grain orientations is proposed. The potential and limitations of a first approach, based on the acquisition of the direct beam projection images only, are discussed in this first part of the paper. An extension is presented in the second part of the paper [Johnson, King, Honnicke, Marrow & Ludwig (2008). J. Appl. Cryst. 41, 310-318], addressing the case of combined direct and diffracted beam acquisition. research papers J. Appl. Cryst. (2008). 41, 302-309 Wolfgang Ludwig et al. X-ray diffraction contrast tomography I 303

A method is presented for fast and non-destructive characterization of the individual grains inside bulk materials (powders or polycrystals). The positions, volumes and orientations of hundreds of grains are determined simultaneously. An extension of the rotation method is employed: a monochromatic beam of high-energy X-rays, focused in one dimension, impinges on the sample and the directions of the diffracted beams are traced by translation of two-dimensional detectors. Algorithms suitable for on-line analysis are described, including a novel indexing approach, where the crystal symmetry is used directly by scanning in Euler space. The method is veri®ed with a simulation of 100 grains.

X-ray diffraction contrast tomography is a recently developed, non-destructive synchrotron imaging technique which characterizes microstructure and grain orientation in polycrystalline materials in three dimensions. By combining it with propagation-based phasecontrast tomography it is possible to get a full picture description for the analysis of local crack growth rate of short fatigue cracks in three dimensions: the three-dimensional crack morphology at different propagation stages, and the shape and orientation of the grains around the crack. An approach has been developed on the metastable beta titanium alloy Ti 21S that allows for visualization and analysis of the growth rate and crystallographic orientation of the fracture surface.

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Generation of realistic artificial 3D grain structures for use in modeling has gained increasing attention during the last two decades due to significant enhancements in the capabilities of large-scale 3D computer simulations. One commonly chosen model is the Laguerre tessellation (also known as weighted Voronoi tessellations or power diagrams). [1] As in the case of the classical Voronoi tessellation, Laguerre tessellations also partition space into convex polyhedra with planar faces. The advantage of the Laguerre tessellations, compared to the classical Voronoi tessellation, is that it allows for a wider range of grain structures by means of weighting factors.