Laue-DIC: a new method for improved stress field measurements at the micrometer scale

Laue microdiffraction on polycrystalline samples above 1500 K achieved with the QMAX-µLaue furnace

X-ray Laue microdiffraction aims to characterize microstructural and mechanical fields in polycrystalline specimens at the sub-micrometre scale with a strain resolution of ∼10-4. Here, a new and unique Laue microdiffraction setup and alignment procedure is presented, allowing measurements at temperatures as high as 1500 K, with the objective to extend the technique for the study of crystalline phase transitions and associated strain-field evolution that occur at high temperatures. A method is provided to measure the real temperature encountered by the specimen, which can be critical for precise phase-transition studies, as well as a strategy to calibrate the setup geometry to account for the sample and furnace dilation using a standard α-alumina single crystal. A first application to phase transitions in a polycrystalline specimen of pure zirconia is provided as an illustrative example.

LaueNN: neural-network-based hkl recognition of Laue spots and its application to polycrystalline materials

A feed-forward neural-network-based model is presented to index, in real time, the diffraction spots recorded during synchrotron X-ray Laue microdiffraction experiments. Data dimensionality reduction is applied to extract physical 1D features from the 2D X-ray diffraction Laue images, thereby making it possible to train a neural network on the fly for any crystal system. The capabilities of the LaueNN model are illustrated through three examples: a two-phase nano-structure, a textured high-symmetry specimen deformed in situ and a polycrystalline low-symmetry material. This work provides a novel way to efficiently index Laue spots in simple and complex recorded images in <1 s, thereby opening up avenues for the realization of real-time analysis of synchrotron Laue diffraction data.

Processing Laue Microdiffraction Raster Scanning Patterns with Machine Learning Algorithms: A Case Study with a Fatigued Polycrystalline Sample

The massive amount of diffraction images collected in a raster scan of Laue microdiffraction calls for a fast treatment with little if any human intervention. The conventional method that has to index diffraction patterns one-by-one is laborious and can hardly give real-time feedback. In this work, a data mining protocol based on unsupervised machine learning algorithm was proposed to have a fast segmentation of the scanning grid from the diffraction patterns without indexation. The sole parameter that had to be set was the so-called “distance threshold” that determined the number of segments. A statistics-oriented criterion was proposed to set the “distance threshold”. The protocol was applied to the scanning images of a fatigued polycrystalline sample and identified several regions that deserved further study with, for instance, differential aperture X-ray microscopy. The proposed data mining protocol is promising to help economize the limited beamtime.

Using Powder Diffraction Patterns to Calibrate the Module Geometry of a Pixel Detector

The precision and accuracy of diffraction measurements with 2D area detectors depends on how well the experimental geometry is known. A method is described to measure the module geometry in order to obtain accurate strain data using a new Eiger2 4M CdTe detector. Smooth Debye–Scherrer powder diffraction rings with excellent signal to noise were collected by using a fine-grained sample of CeO2. From these powder patterns, the different components of the module alignment errors could be observed when the overall detector position was moved. A least squares fitting method was used to refine the detector module and scattering geometry for a series of powder patterns with different beam centers. A precision that is around 1/350 pixel for the module positions was obtained from the fit. This calibration was checked by free refinement of the unit cell of a silicon crystal that gave a maximum residual strain value of 2.1 × 10−5 as the deviation from cubic symmetry.

Full strain tensor measurements with X-ray diffraction and strain field mapping: a simulation study

Strain tensor measurements are important for understanding elastic and plastic deformation, but full bulk strain tensor measurement techniques are still lacking, in particular for dynamic loading. Here, such a methodology is reported, combining imaging-based strain field mapping and simultaneous X-ray diffraction for four typical loading modes: one-dimensional strain/stress compression/tension. Strain field mapping resolves two in-plane principal strains, and X-ray diffraction analysis yields volumetric strain, and thus the out-of-plane principal strain. This methodology is validated against direct molecular dynamics simulations on nanocrystalline tantalum. This methodology can be implemented with simultaneous X-ray diffraction and digital image correlation in synchrotron radiation or free-electron laser experiments.

Alignment of sample position and rotation during in situ synchrotron X-ray micro-diffraction experiments using a Laue cross-correlation approach

Laue micro-diffraction has proven to be able to reveal material properties at the sub-grain scale for many polycrystalline materials and is now routinely available at several synchrotron facilities, providing an approach for nondestructive three-dimensional probing of the microstructures and mechanical states of materials. However, for in situ experiments, maintaining the positioning of the sample throughout the experiment, to achieve a good alignment of the characterized volumes, is a challenging issue. The aim of the present work is to address this problem by developing an approach based on digital image correlation of focused-beam Laue diffraction patterns. The method uses small changes in the diffraction signal as a focused X-ray beam is scanned over a surface region to allow corrections to be made for both sample lateral movement and rotation. The method is demonstrated using a tensile deformation experiment on an Al sample with 2.5 µm average grain size. The results demonstrate an accuracy of 0.5 µm for sample position registration and a precision in sample rotation of ∼0.01°. The proposed method is fast to implement and does not require the use of additional surface markers.

Microsecond time-resolved X-ray diffraction for the investigation of fatigue behavior during ultrasonic fatigue loading

A new method based on time-resolved X-ray diffraction is proposed in order to measure the elastic strain and stress during ultrasonic fatigue loading experiments. Pure Cu was chosen as an example material for the experiments using a 20 kHz ultrasonic fatigue machine mounted on the six-circle diffractometer available at the DiffAbs beamline on the SOLEIL synchrotron facility in France. A two-dimensional hybrid pixel X-ray detector (XPAD3.2) was triggered by the strain gage signal in a synchronous data acquisition scheme (pump-probe-like). The method enables studying loading cycles with a period of 50 µs, achieving a temporal resolution of 1 µs. This allows a precise reconstruction of the diffraction patterns during the loading cycles. From the diffraction patterns, the position of the peaks, their shifts and their respective broadening can be deduced. The diffraction peak shift allows the elastic lattice strain to be estimated with a resolution of ∼10^-5. Stress is calculated by the self-consistent scale-transition model through which the elastic response of the material is estimated. The amplitudes of the cyclic stresses range from 40 to 120 MPa and vary linearly with respect to the displacement applied by the ultrasonic machine. Moreover, the experimental results highlight an increase of the diffraction peak broadening with the number of applied cycles.

Estimation of elastic strain by integrated image correlation on electron diffraction patterns

High-angular-resolution electron backscattered diffraction (HR-EBSD) has been developed to study local elastic strains in crystals. An integrated digital image correlation (DIC) procedure for high resolution diffraction patterns, as recently proposed to bypass several problems of the conventional cross-correlation-based algorithm, was implemented. Through two examples of experimental data where the algorithm was used and compared to conventional means, the current paper illustrates the benefits of the integrated DIC method. It is found that both measurement uncertainty and computation time were simultaneously reduced. Moreover, an enhanced robustness was obtained for relatively high misorientations relative to methods based on cross-correlation. Different computing conditions are explored on experimental data. A number of practical usage conditions are proposed to achieve better precision and speed.

EBSD-assisted Laue microdiffraction for microstrain analysis

The X-ray Laue microdiffraction (µLaue) technique has been establishing itself as a reliable means for microstrain analysis for the past few decades. One problem with this technique is that when the crystal size is significantly smaller than the probed volume and when the diffracting crystals are closely oriented, a large number of individual µLaue patterns are superimposed in a complex way on the recorded diffraction images. In that case, because of the difficulty of isolating unambiguously a single-grain µLaue pattern, a reliable analysis of strains is tedious manually and hardly achievable with current automated methods. This issue is even more severe for low-symmetry crystals or when high-energy X-rays are used, since each single-crystal µLaue pattern already contains a large number of spots. This paper proposes overcoming this challenge through the development of a combined approach coupling µLaue and electron backscatter diffraction (EBSD). The capabilities of this `EBSD-assisted µLaue' automated method are illustrated on a monoclinic zirconia-based specimen and µLaue diffraction patterns are analysed with the crystal orientation input from EBSD. The obtained results are statistically reliable, reproducible and provide a physical insight into the micromechanical characteristics of the material.

Accuracy of stress measurement by Laue microdiffraction (Laue-DIC method): the influence of image noise, calibration errors and spot number

Laue microdiffraction, available at several synchrotron radiation facilities, is well suited for measuring the intragranular stress field in deformed materials thanks to the achievable submicrometer beam size. The traditional method for extracting elastic strain (and hence stress) and lattice orientation from a microdiffraction image relies on fitting each Laue spot with an analytical function to estimate the peak position on the detector screen. The method is thus limited to spots exhibiting ellipsoidal shapes, thereby impeding the study of specimens plastically deformed. To overcome this difficulty, the so-called Laue-DIC method introduces digital image correlation (DIC) for the evaluation of the relative positions of spots, which can thus be of any shape. This paper is dedicated to evaluating the accuracy of this Laue-DIC method. First, a simple image noise model is established and verified on the data acquired at beamline BM32 of the European Synchrotron Radiation Facility. Then, the effect of image noise on errors on spot displacement measured by DIC is evaluated by Monte Carlo simulation. Finally, the combined effect of the image noise, calibration errors and the number of Laue spots used for data treatment is investigated. Results in terms of the uncertainty of stress measurement are provided, and various error regimes are identified.

Single-shot full strain tensor determination with microbeam X-ray Laue diffraction and a two-dimensional energy-dispersive detector

By simultaneously measuring changes in energy and reflection angle of Laue spots with respect to a reference position, it is possible to measure all lattice parameters of a unit cell and calculate the full strain/stress tensors in a single-shot experiment with high spatial resolution.

The full strain and stress tensor determination in a triaxially stressed single crystal using X-ray diffraction requires a series of lattice spacing measurements at different crystal orientations. This can be achieved using a tunable X-ray source. This article reports on a novel experimental procedure for single-shot full strain tensor determination using polychromatic synchrotron radiation with an energy range from 5 to 23 keV. Microbeam X-ray Laue diffraction patterns were collected from a copper micro-bending beam along the central axis (centroid of the cross section). Taking advantage of a two-dimensional energy-dispersive X-ray detector (pnCCD), the position and energy of the collected Laue spots were measured for multiple positions on the sample, allowing the measurement of variations in the local microstructure. At the same time, both the deviatoric and hydrostatic components of the elastic strain and stress tensors were calculated.

Direct measurement of local constitutive relations, at the micrometre scale, in bulk metallic alloys

Multiscale models involving crystal plasticity are essential to predict the elastoplastic behavior of structural materials with respect to their microstructure. However, those models are often limited by a poor knowledge of the local constitutive behavior. This article reports a method to measure the mechanical behavior directly, at the micrometre scale, in bulk crystalline materials. Local strain and stress states were evaluated at the surface of a bent stainless steel crystal by combining total strain measurements – performed with the digital image correlation technique on optical images – with elastic strain measurements obtained by Laue microdiffraction. A local constitutive relation was measured, in an efficient nondestructive way, without the need for full-field simulations. The method was validated by a comparison between the measured local behavior and the macroscopic behavior of the single crystal.

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.

Detection of Alzheimer's disease by displacement field and machine learning

Aim. Alzheimer's disease (AD) is a chronic neurodegenerative disease. Recently, computer scientists have developed various methods for early detection based on computer vision and machine learning techniques. Method. In this study, we proposed a novel AD detection method by displacement field (DF) estimation between a normal brain and an AD brain. The DF was treated as the AD-related features, reduced by principal component analysis (PCA), and finally fed into three classifiers: support vector machine (SVM), generalized eigenvalue proximal SVM (GEPSVM), and twin SVM (TSVM). The 10-fold cross validation repeated 50 times. Results. The results showed the "DF + PCA + TSVM" achieved the accuracy of 92.75 ± 1.77, sensitivity of 90.56 ± 1.15, specificity of 93.37 ± 2.05, and precision of 79.61 ± 2.21. This result is better than or comparable with not only the other proposed two methods, but also ten state-of-the-art methods. Besides, our method discovers the AD is related to following brain regions disclosed in recent publications: Angular Gyrus, Anterior Cingulate, Cingulate Gyrus, Culmen, Cuneus, Fusiform Gyrus, Inferior Frontal Gyrus, Inferior Occipital Gyrus, Inferior Parietal Lobule, Inferior Semi-Lunar Lobule, Inferior Temporal Gyrus, Insula, Lateral Ventricle, Lingual Gyrus, Medial Frontal Gyrus, Middle Frontal Gyrus, Middle Occipital Gyrus, Middle Temporal Gyrus, Paracentral Lobule, Parahippocampal Gyrus, Postcentral Gyrus, Posterior Cingulate, Precentral Gyrus, Precuneus, Sub-Gyral, Superior Parietal Lobule, Superior Temporal Gyrus, Supramarginal Gyrus, and Uncus. Conclusion. The displacement filed is effective in detection of AD and related brain-regions.