András Borbély

X-ray and neutron imaging – Complementary techniques for materials science and engineering

Abstract Using X-ray and neutron radiography and tomography, images of material and component inhomogeneities and their development with time can be obtained. Due to their non-destructiveness and non-invasive nature both methods give insight into the function of devices and their decay processes. Fundamentals of X-ray and neutron radiography and tomography are briefly outlined, examples for both techniques are given, their complementarities are highlighted and emerging techniques and frontiers are discussed.

On the calibration of high‐energy X‐ray diffraction setups. I. Assessing tilt and spatial distortion of the area detector

The geometry of high-energy X-ray diffraction setups using an area detector and a rotation axis is analysed. The present paper (part 1) describes the methodology for determining continuously varying spatial distortions and tilt of the area detector based on the reference diffraction rings of a certified powder. Analytical expressions describing the degeneration of Debye rings into ellipses are presented and a robust calibration procedure is introduced. It is emphasized that accurate detector calibration requires the introduction of spatial distortion into the equation describing the tilt. The method is applied to data sets measured at the Advanced Photon Source and at the European Synchrotron Radiation Facility using detectors with different physical characteristics, the GE 41RT flat-panel and the FReLoN4M detector, respectively. The spatial distortion of the detectors is compared with regard to their use in structural and strain tensor analysis, a subject treated in part 2 of the calibration work [Borbely, Renversade & Kenesei (2014). J. Appl. Cryst. Submitted].

Three-dimensional analysis of creep voids in copper by serial sectioning combined with large field EBSD

Abstract The three-dimensional granular and damage structure of two creep deformed copper specimens has been reconstructed using an improved serial sectioning method combining optical profilometry, scanning electron imaging and backscatter electron diffraction. The reconstructions permitted associating creep voids to grain boundaries and evaluating the damage probability of each grain boundary type. The results indicate that creep damage of oxygen free high conductivity copper is governed by topological factors. Quadruple/grain boundaries have the highest probability of damage followed by two- and three-grain boundaries with decreasing percentages. The damage probability of quadruple and three-grain boundaries increases with decreasing stress due to a larger contribution of grain boundary sliding to void nucleation. The relative frequency of damaged two-grain boundaries increases with stress, suggesting a significant role of creep plasticity and the associated grain boundary ledges. No correlation between void location and the crystallographic orientation of neighbour grains was found.

Microtomographic assessment of damage in P91 and E911 steels after long-term creep

Abstract Two flat hollow cylinders made of martensitic 9 wt.% Cr steels were creep deformed under in-service conditions typical of steam pipes at fossil-fuel fired power plants. Damage in the tubes was assessed through synchrotron X-ray microtomography by evaluating the shape, size and spatial-distribution of voids. The analysis of the size distribution of non-coalesced voids suggested that void growth is controlled by the plasticity constrained diffusional mechanism, a hypothesis verified by micromechanical simulations. A much higher void density was found in steel grade P91 compared to E911.

On the calibration of high‐energy X‐ray diffraction setups. II. Assessing the rotation axis and residual strains

The calibration of high-energy X-ray diffraction setups using an area detector and a rotation axis is discussed. The characterization of the tilt and spatial distortions of an area detector was discussed in part one of this series [Borbely, Renversade, Kenesei & Wright (2014). J. Appl. Cryst. 47, 1042–1053]. Part II links the detector frame to the laboratory frame comprising an additional rotation axis and introduces a general diffractometer equation accounting for all sources of misalignment. Additionally, an independent high-accuracy method for the evaluation of the crystallographic orientation and cell parameters of the undeformed reference crystal is presented. Setup misalignments are mainly described in terms of a residual strain tensor, considered as a quality label of the diffractometer. The method is exemplified using data sets acquired at beamlines ID11 (European Synchrotron Radiation Facility) and 1-ID (Advanced Photon Source) on Al and W single crystals, respectively. The results show that the residual strain tensor is mainly determined by the detector spatial distortion, and values as small as 1–2 × 10−4 can be practically achieved.

Accurate strain determination from digital image correlation of Laue diffraction spots

Accurate strain/stress characterization has important implications in practice, where it is typically connected with safe operation of engineering components. Improving the accuracy and spatial resolution of the measurement techniques can be therefore very beneficial for materials science by helping the understanding of complex material behaviour and the development of novel materials with improved properties. Strain measurement by diffraction methods is based on Bragg’s law, which in the case of a strained crystal predicts a shift of the diffraction peaks compared to their position measured on a reference state. Classically, this shift is determined as the difference between the corresponding absolute peak positions, which requires in many cases accurate knowledge of (i) the geometrical setup and its stability, (ii) the calibration sample, and (iii) a well matching mathematical model of the intensity distribution. In view of this large number of parameters it is intriguing to ask what the accuracy of today’s X-ray diffraction (XRD) methods is and which are the possible ways of improvement. Limiting our survey to methods able to determine the strain tensor at micrometre scale, one can rapidly find that the error of most strain tensor components is about a few times 10 . Transformed to stress (using Young’s modulus of 100 GPa) this represents an uncertainty of tens of MPa, which might be too large for the study of certain phenomena, such as for example the plastic yield of metals. Therefore, efforts are continuously undertaken to ameliorate the precision of the evaluation methods. The majority of the solutions, however, concern point (i), suggesting the use of large area detectors with many pixels and without distortion, or fixing instabilities of the wavelength or micro-spot position by applying more stable optical elements. Progress in this case depends on technical advancement, which sometimes might be slow compared to the needs of the scientific community. Increasing strain/stress accuracy when working with conventional setups needs, therefore, a paradigm change, i.e. a method different from the classical approach based on absolute peak positions. Two recently published articles by Petit et al. (2015) and Zhang et al. (2015) break the tradition and introduce evaluation schemes based on the shift of diffraction peaks determined by digital image correlation (DIC). This new idea, which plays a central role in experimental mechanics, is applied in both papers to white-beam Laue microdiffraction, a popular method often analysed in terms of error sources impeding accurate determination of the deviatoric strain tensor (Hofmann et al., 2011; Poshadel et al., 2012). As argued by Petit et al. (2015), the gain in accuracy of the Laue-DIC method is related to two factors: (a) the smaller uncertainty of the peak shift determined by DIC and (b) the higher sensitivity of the merit function expressing peak positions as a function of reference cell parameters, compared to the sensitivity of the gradient of the merit function, the latter appearing in the formulation of Laue-DIC. From the point of view of the error sources highlighted above it becomes clear that the new approach eliminates the uncertainties related to the choice of an adequate mathematical model describing the experimental intensity distribution. The authors emphasize that relatively good fits can be obtained for the spots of the non-deformed reference specimen using Gaussian or Pearson VII profiles, but already as the specimen is strained, peak quality deteriorates and the uncertainty in peak position increases above 0.1 pixel, characteristic for the reference peaks. Compared to this the uncertainty of DIC is one order of magnitude ISSN 1600-5767

Damage fluctuations in creep deformed copper studied with synchrotron X-ray microtomography

Abstract Damage localization during power law creep of copper has been investigated in situ with synchrotron X-ray microtomography. The analysis of the area fraction of cavities corresponding to a given material slice has revealed that damage localization begins relatively early at half of the creep lifetime. The amplitude of the maximum fluctuation shows parabolic behavior as a function of mean void volume fraction. Existing models of damage evolution underpredict the amount of real damage and overpredict power-law creep life-time.

Texture and Hardness in Wire Drawn [001] Copper Single Crystals

The crystallographic texture and Vickers hardness which develop nduring wire-drawing of [001] oriented copper single ncrystals have been studied experimentally as well by simulations. nThe experiments revealed orientation changes producing ncross-shaped patterns in the {200} pole figures and nimportant variations in the Vickers hardness across the diameter. nMetallographic investigations showed the presence of deformation nbands perpendicular to the initial 〈100〉 directions. By adopting a model for the velocity field ninside the die, simulations have been carried out by using a nTaylor type rate sensitive crystal plasticity model, including nmicroscopic hardening. The simulated pole figures show the nfeatures of the experimental ones and the predicted stress levels ncorrelate well with the measured hardness data.

Evaluation of intragranular strain and average dislocation density in single grains of a polycrystal using K-map scanning

Quick scanning X-ray microscopy combined with three-dimensional reciprocal space mapping was applied to characterize intragranular orientation and strain in a single grain of uniaxially deformed Al polycrystal. The strain component perpendicular to the direction of the applied tensile load was found to be very heterogeneous with high compressive and tensile values in the grain interior and near two grain boundaries, respectively. The distribution of the magnitude of diffraction vectors indicates that dislocations are the origin of the strain. The work opens new possibilities for analysing dislocation structures and intragranular residual stress/strain in single grains of polycrystalline materials.

XTOP: high-resolution X-ray diffraction and imaging

The latest virtual special issue of Journal of Applied Crystallography includes some highlights of the 12th Conference on High-Resolution X-ray Diffraction and Imaging (XTOP), which took place in Villard-de-Lans and Grenoble in September 2014.