S. Erik Offerman

A fast methodology to determine the characteristics of thousands of grains using three-dimensional X-ray diffraction. I. Overlapping diffraction peaks and parameters of the experimental setup

A data-analysis methodology is presented for the characterization of three-dimensional microstructures of polycrystalline materials from data acquired using three-dimensional X-ray diffraction (3DXRD). The method is developed for 3DXRD microscopy using a far-field detector and yields information about the centre-of-mass position, crystallographic orientation, volume and strain state for thousands of grains. This first part deals with pre-processing of the diffraction data for input into the algorithms presented in the second part [Sharma, Huizenga & Offerman (2012). J. Appl. Cryst. 45, 705–718] for determination of the grain characteristics. An algorithm is presented for accurate identification of overlapping diffraction peaks from X-ray diffraction images, which has been an issue limiting the accuracy of experiments of this type. The algorithm works in two stages, namely the identification of overlapping peaks using a seeded watershed algorithm, and then the fitting of the peaks with a pseudo-Voigt shape function to yield an accurate centre-of-mass position and integrated intensity for the peaks. Regions consisting of up to six overlapping peaks can be successfully fitted. Two simulations and an experiment are used to verify the results of the algorithms. An example of the processing of diffraction images acquired in a 3DXRD experiment with a sample consisting of more than 1600 grains is shown. Furthermore, a procedure for the determination of the parameters of the experimental setup (global parameters) without the need for a calibration sample is presented and validated using simulations. This is immensely beneficial for simplifying experiments and the subsequent data analysis.

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.

Phase retrieval in in-line x-ray phase contrast imaging based on total variation minimization

State-of-the-art techniques for phase retrieval in propagation based X-ray phase-contrast imaging are aiming to solve an underdetermined linear system of equations. They commonly employ Tikhonov regularization - an L2-norm regularized deconvolution scheme - despite some of its limitations. We present a novel approach to phase retrieval based on Total Variation (TV) minimization. We incorporated TV minimization for deconvolution in phase retrieval using a variety of the most common linear phase-contrast models. The results of our TV minimization was compared with Tikhonov regularized deconvolution on simulated as well as experimental data. The presented method was shown to deliver improved accuracy in reconstructions based on a single distance as well as multiple distance phase-contrast images corrupted by noise and hampered by errors due to nonlinear imaging effects.

Multipurpose furnace for in situ studies of polycrystalline materials using synchrotron radiation

We report a multipurpose furnace designed for studies using synchrotron radiation on polycrystalline materials, namely, metals, ceramics, and (semi)crystalline polymers. The furnace has been designed to carry out three-dimensional (3D) x-ray diffraction measurements but can also be used for other types of synchrotron radiation research. The furnace has a very low thermal gradient across the specimen (<0.2 degrees C/mm). Accurate determination of the temperature can be carried out by welding a thermocouple to the specimen. The furnace can be rotated over an angle of 90 degrees in order to determine the crystallographic orientation of each individual grain. It is possible to follow growth kinetics of all grains in the illuminated volume of the specimen. The specimen environment can be controlled varying from vacuum (up to 10(-5) mbar) to gas or air filled. The maximum temperature of operation is 1500 degrees C, with the possibility of achieving high heating (up to 20 degrees C/s) and cooling rates (up to 30 degrees C/s without quenching gas). 3D maps of the microstructure of the specimen can be generated at elevated temperatures by bringing the high-resolution detector close to the specimen. We show an example of a simulation of the heat affected zone during the thermal cycle of a weld in a transformation-induced plasticity steel carried out using the furnace. The unique characteristics of the furnace open possibility of new fields in materials research using synchrotron radiation.

Formation of (Fe,Cr) carbides and dislocation structures in low-chromium steel studied in situ using synchrotron radiation

The evolution of the size distribution of (Fe,Cr) carbides and the dislocation structure in low-chromium steel is studied during quenching and rapid heating by in situ small-angle X-ray scattering (SAXS). The two-dimensional SAXS patterns consist of streaks on top of an isotropic SAXS signal. The evolution of the size distribution of the (Fe,Cr) carbides during heat treatment is determined from the isotropic component of the SAXS patterns. The isotropic part of the SAXS patterns shows that, after austenitization and quenching to room temperature, the average precipitate radius is 4.74 nm and the dispersion parameter for the lognormal size distribution is 0.33. Subsequent rapid heating to 823 K results in an average precipitate size of 5.25 nm and a dispersion parameter of 0.26. Bright-field transmission electron microscopy and high-resolution transmission electron microscopy reveal the nearly spherical morphology of the precipitates. The microstructural evolution underlying the increase in the average precipitate size and the decrease in the dispersion parameter after heating to and annealing at 823 K is probably that at room temperature two types of precipitates are present, i.e. (Fe,Cr)23C6 and (Fe,Cr)7C3 precipitates according to thermodynamic calculations, and at 823 K only (Fe,Cr)7C3 precipitates are present. Additional measurements have been carried out on a single crystal of ferrite containing (Fe,Cr) carbides by combining three-dimensional X-ray diffraction (3DXRD) and SAXS during rotation of the specimen at room temperature, in order to investigate the origin of the streaks at low angles in the SAXS pattern. From simulations based on the theory of SAXS from dislocations, it is shown that the measured streaks, including the spottiness, in the two-dimensional SAXS patterns correspond to a dislocation structure of symmetric low-angle tilt boundaries, which in turn corresponds to the crystallographic orientation gradient in the single crystal of ferrite as measured by 3DXRD microscopy.

Characterization of an x-ray phase contrast imaging system based on the miniature synchrotron MIRRORCLE-6X

PURPOSE The implementation of in-line x-ray phase contrast imaging (PCI) for soft-tissue patient imaging is hampered by the lack of a bright and spatially coherent x-ray source that fits into the hospital environment. This article provides a quantitative characterization of the phase-contrast enhancement of a PCI system based on the miniature synchrotron technology MIRRORCLE-6X. METHODS The phase-contrast effect was measured using an edge response of a plexiglass plate as a function of the incident angle of radiation. We have developed a comprehensive x-ray propagation model based on the systems components, properties, and geometry in order to interpret the measurement data. Monte-Carlo simulations are used to estimate the systems spectral properties and resolution. RESULTS The measured ratio of the detected phase-contrast to the absorption contrast is currently in the range 100% to 200%. Experiments show that with the current implementation of the MIRRORCLE-6X, a target smaller than 30-40 μm does not lead to a larger phase-contrast. The reason for this is that the fraction of x-rays produced by the material (carbon filament and glue) that is used for mounting the target in the electron beam is more than 25% of the total amount of x-rays produced. This increases the apparent source size. The measured phase-contrast is at maximum two times larger than the absorption contrast with the current set-up. CONCLUSIONS Calculations based on our model of the present imaging system predict that the phase-contrast can be up to an order of magnitude larger than the absorption contrast in case the materials used for mounting the target in the electron beam do not (or hardly) produce x-rays. The methods described in this paper provide vital feedback for guiding future modifications to the design of the x-ray target of MIRRORCLE-type system and configuration of the in-line PCI systems in general.

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.

In Situ Observation of Changing Crystal Orientations During Austenite Grain Coarsening

Understanding the underlying mechanisms of grain coarsening is important to control the properties of metals, which strongly depend on the microstructure that forms during the production process or use at high temperature. Grain coarsening of austenite at 1,273 K in a binary Fe-2 wt% Mn alloy was studied using synchrotron radiation. The evolution of volume, average crystallographic orientation and mosaicity of more than 2,000 individual austenite grains was tracked during annealing. It was found that there exists an approximately linear relationship between grain size and mosaicity, which means that orientation gradients are present in the grains. The orientation gradients remain constant during coarsening and consequently the character of grain boundaries changes during coarsening, affecting the coarsening rate. Furthermore, changes in the average orientation of grains during coarsening were observed. The changes could be understood by taking the observed orientation gradients and anisotropic movement of grain boundaries into account. Five basic modes of grain coarsening were deduced from the measurements which include: anisotropic (I) and isotropic (II) growth (or shrinkage); movement of grain boundaries resulting in no change in volume but change in shape (III), movement of grain boundaries resulting in no change in volume and mosaicity, but change in crystallographic orientation (IV); and no movement of grain boundaries (V).