Henning Friis Poulsen

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.

Determining grain resolved stresses in polycrystalline materials using three‐dimensional X‐ray diffraction

An algorithm is presented for characterization of the grain resolved (type II) stress states in a polycrystalline sample based on monochromatic X-ray diffraction data. The algorithm is a robust 12-parameter-per-grain fit of the centre-of-mass grain positions, orientations and stress tensors including error estimation and outlier rejection. The algorithm is validated by simulations and by two experiments on interstitial free steel. In the first experiment, using only a far-field detector and a rotation range of 2 × 110°, 96 grains in one layer were monitored during elastic loading and unloading. Very consistent results were obtained, with mean resolutions for each grain of approximately 10 µm in position, 0.05° in orientation, and 8, 20 and 13 × 10−5 in the axial, normal and shear components of the strain, respectively. The corresponding mean deviations in stress are 30, 50 and 15 MPa in the axial, normal and shear components, respectively, though some grains may have larger errors. In the second experiment, where a near-field detector was added, ∼2000 grains were characterized with a positional accuracy of 3 µm.

Lattice rotations of individual bulk grains. Part I: 3D X-ray characterization

Three-dimensional X-ray diffraction has been applied to characterise the plastic deformation of individual grains deeply embedded in a 99.6% pure aluminium specimen. The specimen is 4 mm thick with an average grain size of 75 μm. The average lattice rotation for each grain as well as the degree of internal orientation spread within the grain is measured in-situ during 6% elongation. The rotation paths for 95 grains with nearly random initial orientations are reported. The quality of this data set is sufficient to make distinctions between plasticity models. The rotation paths exhibit a clear dependence on the initial orientation, while the influence of grain interaction is relatively small. All grains deform plastically. Averaged over grains and reflections the rotation of the tensile axis and the FWHM of the internal spread is 2.0 and 0.8°, respectively, at 6% strain.

Applications of high-energy synchrotron radiation for structural studies of polycrystalline materials.

The large penetration power of high-energy X-rays (>60 keV) raises interesting prospects for new types of structural characterizations of polycrystalline materials. It becomes possible in a non-destructive manner to perform local studies, within the bulk of the material, of the fundamental materials physics properties: grain orientations, strain, dislocation densities etc. In favourable cases these properties may be mapped in three dimensions with a spatial resolution that matches the dimensions of the individual grains. Imbedded volumes and interfaces become accessible. Moreover, the high energies allow better in-situ studies of samples in complicated environments (industrial process optimization). General techniques for research in this energy range have been developed using broad-band angle-dispersive methods, on-line two-dimensional detectors and conical slits. Characterizations have been made at the level of the individual grains and grain boundaries as well as on ensembles of grains. The spatial resolution is presently of the order of 10-100 micom. Four examples of applications are presented along with an outlook.

Measurements of plastic displacement gradient components in three dimensions using marker particles and synchrotron X-ray absorption microtomography

Abstract A universal method is presented for characterising the three-dimensional (3D) plastic displacement gradient field in bulk materials that contain particles or voids observable by X-ray tomography. Millimetre sized samples are investigated by absorption contrast microtomography using high intensity X-rays from a synchrotron source. The positions of dispersed marker particles are determined as a function of imposed strain. The particle diameter can be in the micrometre range, and the volume fraction can be less than 1%. The method is demonstrated by evaluation of compression deformation of a cylindrical Al specimen containing W marker particles. By interpolating the displacement gradient components determined at each particle on a 30×30×30 μm 3 grid, 3D maps of the displacement gradient components are obtained with a resolution of 10 −2 in each component. Limitations of the method are discussed, and the potential for application in materials science is outlined.

Strain tensor development in a single grain in the bulk of a polycrystal under loading

First results are presented on the development of the elastic strain tensor in a single embedded grain during tensile loading of a copper sample. The technique is based on the use of focused high-energy X-rays from a synchrotron source. Measurements are performed by the rotation method, and automated indexing routines are used to group reflections belonging to a single grain. In total, 17 reflections were monitored as a function of tensile load. At each load level three elements of the strain tensor were fitted using a singular value decomposition routine for over-determined linear systems. Sources of systematic error are discussed, and a method for extending the technique towards simultaneous measurements of ensembles of grains is outlined.

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.

Three-Dimensional Orientation Mapping in the Transmission Electron Microscope

Electron microscopy is used to nondestructively map the three-dimensional grain orientations in nanocrystalline aluminum. Over the past decade, efforts have been made to develop nondestructive techniques for three-dimensional (3D) grain-orientation mapping in crystalline materials. 3D x-ray diffraction microscopy and differential-aperture x-ray microscopy can now be used to generate 3D orientation maps with a spatial resolution of 200 nanometers (nm). We describe here a nondestructive technique that enables 3D orientation mapping in the transmission electron microscope of mono- and multiphase nanocrystalline materials with a spatial resolution reaching 1 nm. We demonstrate the technique by an experimental study of a nanocrystalline aluminum sample and use simulations to validate the principles involved.

Dark-field X-ray microscopy for multiscale structural characterization

Many physical and mechanical properties of crystalline materials depend strongly on their internal structure, which is typically organized into grains and domains on several length scales. Here we present dark-field X-ray microscopy; a non-destructive microscopy technique for the three-dimensional mapping of orientations and stresses on lengths scales from 100 nm to 1 mm within embedded sampling volumes. The technique, which allows ‘zooming’ in and out in both direct and angular space, is demonstrated by an annealing study of plastically deformed aluminium. Facilitating the direct study of the interactions between crystalline elements is a key step towards the formulation and validation of multiscale models that account for the entire heterogeneity of a material. Furthermore, dark-field X-ray microscopy is well suited to applied topics, where the structural evolution of internal nanoscale elements (for example, positioned at interfaces) is crucial to the performance and lifetime of macro-scale devices and components thereof.

A conical slit for three-dimensional XRD mapping

Traditionally, depth resolution in diffraction experiments is obtained by inserting pinholes in both the incoming and diffracted beam. For materials science investigations of local strain and texture properties this leads to very slow data-acquisition rates, especially when characterization is performed on the level of the individual grains. To circumvent this problem a conical slit has been manufactured by wire-electrodischarge machining. The conical slit has six 25 microm-thick conically shaped openings matching six of the Debye-Scherrer cones from a face-centred-cubic powder. By combining the slit with a microfocused incoming beam of hard X-rays, an embedded gauge volume is defined. Using a two-dimensional detector, fast and complete information can be obtained regarding the texture and strain properties of the material within this particular gauge volume. The average machining and assemblage errors of the conical slit are found both to be of the order of 5 microm. An algorithm for alignment of the slit is established, and the potential of the technique is illustrated with an example of grain mapping in a 4.5 mm-thick Cu sample.