L. Margulies

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.

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.

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.

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.

Ferrite formation during slow continuous cooling in steel

Ferrite formation during austenite decomposition in carbon-manganese steel is studied during slow continuous cooling by three-dimensional x-ray diffraction microscopy at a synchrotron source. The ferrite fraction and nucleation rate are measured simultaneously and independently in real time in the bulk of the specimen. Thermodynamic calculations involving both ortho- and paraequilibrium have been performed to determine the driving force for nucleation. From the experiments and thermodynamic calculations the activation energies are estimated for nucleation and the transfer of iron atoms across the interface of the cluster during ferrite nucleation in steel.

Quantification of Minor Texture Components by Hard X-Rays

Non-destructive methods to determine the volume fraction of minor texture components with very low reflection intensities are presented. The methods are based on polycrystalline diffraction of hard X-rays from synchrotron sources. By focusing the X-rays and scanning the specimen, it is shown that volume fractions as low as 10-9 can be registered, provided that the crystallographic orientations of such volume elements are far away from any major texture component. Simultaneously, the spatial resolving power is of the order 0.03 μm3. The relevance of such methods for nucleation studies and trace analysis is outlined.

Growth of Individual Austenite Grains Measured with 3DXRD Microscopy

Studying austenitisation in steel, so far, was either limited to observations at the surface of the material or to the determination of the average grain growth behavior in the bulk. The development of the three-dimensional X-ray diffraction (3DXRD) microscope at beam line ID11 of the European Synchrotron Radiation Facility in Grenoble, France, made it possible to study the transformation kinetics in-situ and at the level of individual grains in the bulk of the material. Unique in-situ observations of austenite growth kinetics during continuous heating experiments were made for two commercial low-alloy steels (C22 and C35). The observed growth behavior of individual austenite grains gives a valuable contribution to understanding the phase transformations on heating, i.e. austenite formation from ferrite and pearlite.

Dynamic in-situ investigation of the texture and strain state within a plastically deformed solid AlMg3 torsion sample using high energy synchrotron radiation

A solid torsion sample made from non-age hardenable single-phase Al alloy AlMg3 is continuously deformed until failure. The low speed deformation with free ends is carried out at room temperature. For the first time, the dynamic in-situ development of the local texture and strain state within the sample are observed by means of a novel strain and texture scanning technique. The technique is based on the combination of a microfocussed high energy synchrotron beam, a conical slit system and a large area X-ray detector. The experimental results clearly show the deformation dependent evolution of axial forces (the so-called Swift effect). The texture development exhibits a change from the initial 111 / 100 fibre texture to the dominance of ideal torsion texture orientations.