Nicola Viganò

Three-dimensional full-field X-ray orientation microscopy.

A previously introduced mathematical framework for full-field X-ray orientation microscopy is for the first time applied to experimental near-field diffraction data acquired from a polycrystalline sample. Grain by grain tomographic reconstructions using convex optimization and prior knowledge are carried out in a six-dimensional representation of position-orientation space, used for modelling the inverse problem of X-ray orientation imaging. From the 6D reconstruction output we derive 3D orientation maps, which are then assembled into a common sample volume. The obtained 3D orientation map is compared to an EBSD surface map and local misorientations, as well as remaining discrepancies in grain boundary positions are quantified. The new approach replaces the single orientation reconstruction scheme behind X-ray diffraction contrast tomography and extends the applicability of this diffraction imaging technique to material micro-structures exhibiting sub-grains and/or intra-granular orientation spreads of up to a few degrees. As demonstrated on textured sub-regions of the sample, the new framework can be extended to operate on experimental raw data, thereby bypassing the concept of orientation indexation based on diffraction spot peak positions. This new method enables fast, three-dimensional characterization with isotropic spatial resolution, suitable for time-lapse observations of grain microstructures evolving as a function of applied strain or temperature.

A feasibility study of full-field X-ray orientation microscopy at the onset of deformation twinning

textabstractThree-dimensional X-ray orientation microscopy based on X-ray full-field imaging techniques such as diffraction contrast tomography is a challenging task when it comes to materials displaying non-negligible intragranular orientation spread and/or intricate grain microstructures as a result of plastic deformation and deformation twinning. As shown in this article, the optimization of the experimental conditions and a number of modifications of the data analysis routines enable detection and three-dimensional reconstruction of twin lamellae down to micrometre thickness, as well as more accurate three-dimensional reconstruction of grains displaying intragranular orientation spreads of up to a few degrees. The reconstruction of spatially resolved orientation maps becomes possible through the use of a recently introduced six-dimensional reconstruction framework, which has been further extended in order to enable simultaneous reconstruction of parent and twin orientations and to account for the finite impulse response of the X-ray imaging detector. The simultaneous reconstruction of disjoint orientation domains requires appropriate scaling of the scattering intensities based on structure and Lorentz factors and yields three-dimensional reconstructions with comparable density values for all the grains. This in turn enables the use of a global intensity-guided assembly procedure and avoids problems related to the single-grain thresholding procedure used previously. Last but not least, carrying out a systematic search over the list of known twin variants (forward modelling) for each of the indexed parent grains, it is possible to identify additional twins which have been left undetected at the previous stage of grain indexing based on diffraction spot peak positions. The enhanced procedure has been tested on a 1% deformed specimen made from a Ti-4%Al alloy and the result has been cross-validated against a two-dimensional electron backscatter diffraction orientation map acquired on one of the lateral sample surfaces.

An Orientation-space Super Sampling Technique for Six-dimensional Diffraction Contrast Tomography

textabstractDiffraction contrast tomography (DCT) is an X-ray full-field imaging technique that allows for the non-destructive three-dimensional investigation of polycrystalline materials and the determination of the physical and morphological properties of their crystallographic domains, called grains. This task is considered more and more challenging with the increasing intra-granular deformation, also known as orientation-spread. The recent introduction of a sixdimensional reconstruction framework in DCT (6D-DCT) has proven to be able to address the intra-granular crystal orientation for moderately deformed materials. The approach used in 6D-DCT, which is an extended sampling of the six-dimensional combined position-orientation space, has a linear scaling between the number of sampled orientations, which determine the orientation-space resolution of the problem, and computer memory usage. As a result, the reconstruction of more deformed materials is limited by their high resource requirements from a memory and computational point of view, which can easily become too demanding for the currently available computer technologies. In this article we propose a super-sampling method for the orientation-space representation of the six-dimensional DCT framework that enables the reconstruction of more deformed cases by reducing the impact on system memory, at the expense of longer reconstruction times. The use of super-sampling can further improve the quality and accuracy of the reconstructions, especially in cases where memory restrictions force us to adapt to inadequate (undersampled) orientation-space sampling.

Discrete representation of local orientation in grains using diffraction contrast tomography

In this work we introduce a new model for dealing with the problem of local orientation reconstruction in grains, when using data from X-ray Diffraction Contrast Tomography experiments. The model explores the use of well established minimization algorithms from the field of mathematical optimization, like FISTA, and the possible use of recent mathematical devices for the solution of highly undetermined systems of equations, like the l1-minimization over the Haar transform of the tomographic volumes. Along with a detailed explanation of how such algorithms can be applied to our six-dimensional problem, we report encouraging results obtained on simulated data.