E.M. Lauridsen

Three-dimensional maps of grain boundaries and the stress state of individual grains in polycrystals and powders

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 verified by comparing an electron microscopy map of the orientations on the 2.5 × 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 µm, 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 Δ∊ ≃ 10−4.

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

X-ray diffraction contrast tomography (DCT) 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 degrees rotation of the sample and are analyzed in terms of the Friedel pairs ((hkl) and (hkl) reflections, observed 180 degrees apart in rotation). 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 arise) 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.

X-ray microscopy in four dimensions

Three-dimensional X-ray diffraction (3DXRD) microscopy offers the possibility of time-resolved mapping of structures down to the micrometer scale 1 , 2 , 3 , 4 , 5 , 6 , i.e. four-dimensional studies. In this review, the principles of the 3DXRD microscope are described and various examples of its applications are presented.

A three-dimensional X-ray diffraction microscope for deformation studies of polycrystals

The microstructure in polycrystalline materials has mostly been studied in planar sections by microscopy techniques. Now the high penetration power of hard X-ray synchrotron radiation makes three-dimensional (3-D) observations possible in bulk material by back tracing the diffracted beam. The three-dimensional X-ray diffraction (3DXRD) microscope installed at the European Synchrotron Radiation Facility in Grenoble provides a fast and non-destructive technique for mapping the embedded grains within thick samples in three dimensions. All essential features like the position, volume, orientation, stress-state of the grains can be determined, including the morphology of the grain boundaries. The accuracy of this novel tracking technique is compared with electron microscopy (EBSP), and its 3-D capacity is demonstrated.

High-resolution three-dimensional mapping of individual grains in polycrystals by topotomography

By orienting a crystal grain with its diffraction vector along the sample rotation axis, it is possible to use powerful tomographic and topographic imaging techniques to reconstruct the three-dimensional grain shape inside a polycrystalline sample. The acquisition and reconstruction can be performed from projection images with the detector positioned either in the diffracted-beam or in the direct-beam position. In the first case, the projection data consist of a series of integrated, monochromatic beam X-ray diffraction topographs of the grain under investigation. In the second case, the corresponding diffraction contrast in the transmitted beam may be interpreted as an additional contribution to the X-ray attenuation coefficient of the material. This latter variant is restricted to grains with small orientation spread but offers the possibility to characterize simultaneously the three-dimensional grain shape and the absorption microstructure of the surrounding sample material. The contrast mechanism is sensitive to local strain fields and can, in certain cases, reveal details of the grain microstructure, such as the presence of second-phase inclusions. The methodology is successfully demonstrated on an aluminium polycrystal, with a resulting three-dimensional mapping accuracy better than 7 µm. The possibilities and limitations of the technique are listed and its performance relative to other three-dimensional mapping techniques is discussed.

Application of high-energy synchrotron radiation for texture studies

A novel experimental technique that employs high-energy synchrotron radiation is used for the investigation of through-thickness texture gradients in two aluminium plates, cold-rolled 40% with either intermediate or small draughts. In these two plates, crystallographic textures are inspected in a large number of layers. Texture maps of pole densities throughout the sample thickness are presented. A texture of the rolling type is developed through the plate thickness after intermediate draught rolling. Pronounced inhomogeneities associated with the shear texture are observed in the sample rolled with small draughts. For selected layers, direct pole figures are compared with those obtained by traditional low-energy X-ray diffraction and by the electron backscattering pattern technique using a scanning electron microscope. A good qualitative agreement between textures measured using the three different techniques is obtained. Experimental aspects and potentials of the new technique are discussed.

Non-destructive mapping of grain orientations in 3D by laboratory X-ray microscopy.

The ability to characterise crystallographic microstructure, non-destructively and in three-dimensions, is a powerful tool for understanding many aspects related to damage and deformation mechanisms in polycrystalline materials. To this end, the technique of X-ray diffraction contrast tomography (DCT) using monochromatic synchrotron and polychromatic laboratory X-ray sources has been shown to be capable of mapping crystal grains and their orientations non-destructively in 3D. Here we describe a novel laboratory-based X-ray DCT modality (LabDCT), enabling the wider accessibility of the DCT technique for routine use and in-depth studies of, for example, temporal changes in crystallographic grain structure non-destructively over time through ‘4D’ in situ time-lapse studies. The capability of the technique is demonstrated by studying a titanium alloy (Ti-β21S) sample. In the current implementation the smallest grains that can be reliably detected are around 40 μm. The individual grain locations and orientations are reconstructed using the LabDCT method and the results are validated against independent measurements from phase contrast tomography and electron backscatter diffraction respectively. Application of the technique promises to provide important insights related to the roles of recrystallization and grain growth on materials properties as well as supporting 3D polycrystalline modelling of materials performance.

3D-characterisation of microstructure evolution during annealing of a deformed aluminum single crystal

Abstract The microstructure within a 3D volume of a deformed Al single crystal is studied by a novel diffraction method before and after annealing for 5 min at 300 °C. The 99.996% pure single crystal of the S-orientation was channel die deformed to a strain of ϵ =1.5, producing a cell-block structure with distances of about 1 μm between dislocation boundaries. By means of micro-focused hard X-rays from a synchrotron the orientations within a volume of 0.2×0.2×2 mm 3 were mapped non-destructively. Cells or cell-blocks with orientations far from those of the principal poles can be identified individually with a resolving limit of 0.6 μm. The diffraction pattern related to these parts of the orientation distribution show little correlation between the as-deformed and annealed states. They indicate the emergence of recovered cells and/or nuclei with orientations not present in the deformed state.

3DXRD - Mapping grains and their dynamics in 3 dimensions

3-Dimensional X-Ray Diffraction (3DXRD) microscopy is a tool for fast and non-destructive characterization of the individual grains, sub-grains and domains inside bulk materials. The method is based on diffraction with highly penetrating hard x-rays, enabling 3D studies of millimeter - centimeter thick specimens. The position, volume, orientation, elastic and plastic strain can be derived for hundreds of grains simultaneously. Furthermore, by applying novel reconstruction methods 3D maps of the grain boundaries can be generated. With the present 3DXRD microscope set-up at the European Synchrotron Radiation Facility, the spatial resolution is ~ 5 µm, while grains of size 100 nm can be detected. 3DXRD microscopy enables, for the first time, dynamic studies of the individual grains and sub-grains within polycrystalline materials. The methodology is reviewed with emphasis on recent advances in grain mapping. Based on this a series of general 3DXRD approaches are identified for studies of nucleation and growth phenomena such as recovery, recrystallisation and grain growth in metals.

Nondestructive approaches for 3-D materials characterization

Three-dimensional (3-D) microstructural characterization has proven to be indispensable for the thorough understanding of the often highly complex microstructures studied in materials science. However, most 3-D characterization techniques of opaque materials such as metals and ceramics are destructive and therefore prohibit 3-D studies of the dynamic microstructural evolution processes. In this paper we describe two complimentary techniques capable of nondestructive 3-D characterization and provide examples of the application of these techniques to investigate microstructural evolution processes in metallic systems.