A. King

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.

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 100u2009nm to 1u2009mm 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.

Total variation minimization approach in in-line x-ray phase-contrast tomography

The reconstruction problem in in-line X-ray Phase-Contrast Tomography is usually approached by solving two independent linearized sub-problems: phase retrieval and tomographic reconstruction. Both problems are often ill-posed and require the use of regularization techniques that lead to artifacts in the reconstructed image. We present a novel reconstruction approach that solves two coupled linear problems algebraically. Our approach is based on the assumption that the frequency space of the tomogram can be divided into bands that are accurately recovered and bands that are undefined by the observations. This results in an underdetermined linear system of equations. We investigate how this system can be solved using three different algebraic reconstruction algorithms based on Total Variation minimization. These algorithms are compared using both simulated and experimental data. Our results demonstrate that in many cases the proposed algebraic algorithms yield a significantly improved accuracy over the conventional L2-regularized closed-form solution. This work demonstrates that algebraic algorithms may become an important tool in applications where the acquisition time and the delivered radiation dose must be minimized.

In-Situ Synchrotron Diffraction Studies on Transformation Strain Development in a High-Strength Quenched and Tempered Structural Steel—Part II. Martensitic Transformation

In-situ phase transformation behavior of a high strength (830xa0MPa yield stress) quenched and tempered S690QL1 (Fe-0.16C-0.2Si-0.87Mn-0.33Cr-0.21Mo (wt pct)) structural steel during continuous cooling under different mechanical loading conditions has been studied. Time-temperature-load resolved 2D synchrotron diffraction patterns were recorded and used to calculate the phase fractions and lattice parameters of the phases during heating and cooling cycles under different loading conditions. In addition to the thermal expansion behavior, the effects of the applied stress on the elastic strains during the formation of bainite from austenite and the effect of carbon on the lattice parameter of bainitic ferrite were calculated. The results show that small tensile stresses applied at the transformation temperature do not change the kinetics of the phase transformation. The start temperature for the bainitic transformation decreases upon increasing the applied tensile stress. The elastic strains increase with increase in the applied tensile stress.

Revisiting the blocking force test on ferroelectric ceramics using high energy x-ray diffraction

The blocking force test is a standard test to characterise the properties of piezoelectric actuators. The aim of this study is to understand the various contributions to the macroscopic behaviour observed during this experiment that involves the intrinsic piezoelectric effect, ferroelectric domain switching, and internal stress development. For this purpose, a high energy diffraction experiment is performed in-situ during a blocking force test on a tetragonal lead zirconate titanate (PZT) ceramic (Pb0.98Ba0.01(Zr0.51Ti0.49)0.98Nb0.02O3). It is shown that the usual macroscopic linear interpretation of the test can also be performed at the single crystal scale, allowing the identification of local apparent piezoelectric and elastic properties. It is also shown that despite this apparent linearity, the blocking force test involves significant non-linear behaviour mostly due to domain switching under electric field and stress. Although affecting a limited volume fraction of the material, domain switching is responsible for a large part of the macroscopic strain and explains the high level of inter- and intra-granular stresses observed during the course of the experiment. The study shows that if apparent piezoelectric and elastic properties can be identified for PZT single crystals from blocking stress curves, they may be very different from the actual properties of polycrystalline materials due to the multiplicity of the physical mechanisms involved. These apparent properties can be used for macroscopic modelling purposes but should be considered with caution if a local analysis is aimed at.

Identification of crystalline elastic anisotropy in PZT ceramics from in-situ blocking stress measurements

High energy x-ray diffraction measurements of lattice strains were performed on a rhombohedral Lead Zirconate Titanate ceramic (PZT 55-45) under combinations of applied electric field and compressive stress. These measurements allow the construction of blocking stress curves for different sets of crystallographic orientations which reflect the single crystal elastic anisotropy. A micro-mechanical interpretation of the results is then proposed. Assuming cubic symmetry for the crystalline elastic stiffness tensor and isotropy for the macroscopic elastic properties, the elastic properties of the single crystal are extracted from the measured data. An anisotropy ratio close to 0.3 is found (compared to 1 for isotropic materials). The high level of anisotropy found in this work suggests that crystalline elastic anisotropy should not be neglected in the modelling of ferroelectric materials.

Transformation-Induced Diffraction Peak Broadening During Bainitic and Martensitic Transformations Under Small External Loads in a Quenched and Tempered High Strength Steel

Insitu phase transformation behavior of a high strength S690QL1 steel during continuous cooling under different mechanical loading conditions has been used to investigate the effect of small external loads on the transformation-induced plasticity during bainitic and martensitic transformations. The results show that during phase transformations, the untransformed austenite undergoes plastic deformation, thereby retarding further transformation to bainite/martensite. This occurs independent of external load.

Corrigendum: Dark-field X-ray microscopy for multiscale structural characterization

Nature Communications 6: Article number: 6098 (2015); Published: 14 January 2015; Updated: 5 March 2015 The authors inadvertently omitted Frederik Stohr, who developed the silicon condenser lens used for the acquisition of data presented in this Article, from the author list. This has now been corrected in both the PDF and HTML versions of the Article.

Anisotropy in Thermal Expansion of Bainitic Ferrite

The evolution of local d-spacings between lattice planes of bainitic ferrite in a high strength quenched and tempered structural steel, S690QL1 (Fe-0.16C-0.2Si-0.87Mn-0.33Cr-0.21Mo (wt pct)), has been determined to calculate the thermal expansion behavior. For this purpose, in-situ continuous cooling tests have been carried out in a high-energy synchrotron X-ray diffractometer. The results indicate thermal anisotropy in the bainitic ferrite planes.

In-line x-ray phase-contrast tomography and diffraction-contrast tomography study of the ferrite-cementite microstructure in steel

This work presents the development of a non-destructive imaging technique for the investigation of the microstructure of cementite grains embedded in a ferrite matrix of medium-carbon steel. The measurements were carried out at the material science beamline of the European Synchrotron Radiation Facility (ESRF) ID11. It was shown that in-line X-ray phase-contrast tomography (PCT) can be used for the detection of cementite grains of several microns in size. X-ray PCT of the cementite structure can be achieved by either a ‘single distance’ or a ‘multiple distance’ acquisition protocol. The latter permits quantitative phase retrieval. A second imaging technique, X-ray diffraction-contrast tomography (DCT), was employed to obtain information about the shapes and crystallographic orientations of the distinct ferrite grains surrounding the cementite structures. The initial results demonstrate the feasibility of determining the geometry of the cementite grains after the austenite-ferrite phase-transformation in a non-destructive manner. The results obtained with PCT and DCT are verified with ex-situ optical microscopy studies of the same specimen.