Ulrich Lienert

Forward modeling method for microstructure reconstruction using x-ray diffraction microscopy: Single-crystal verification

We describe and illustrate a forward modeling method for quantitatively reconstructing the geometry and orientation of microstructural features inside of bulk samples from high-energy x-ray diffraction microscopy data. Data sets comprise charge-coupled device images of Bragg diffracted beams originating from individual grains in a thin planar section of sample. Our analysis approach first reduces the raw images to a binary data set in which peaks have been thresholded at a fraction of their height after noise reduction processing. We then use a computer simulation of the measurement and the sample microstructure to generate calculated diffraction patterns over the same range of sample orientations used in the experiment. The crystallographic orientation at each of an array of area elements in the sample space is adjusted to optimize overlap between experimental and simulated scattering. In the present verification exercise, data are collected at the Advanced Photon Source beamline 1-ID using microfocused ...

Far-field high-energy diffraction microscopy: a tool for intergranular orientation and strain analysis

The far-field high-energy diffraction microscopy technique is presented in the context of high-energy synchrotron x-ray diffraction. For each grain in an illuminated polycrystalline volume, the volume-averaged lattice orientations, lattice strain tensors, and centre-of-mass (COM) coordinates may be determined to a high degree of precision: better than 0.05°, 1 × 10−4, and 0.1 pixel, respectively. Because the full lattice strain tensors are available, corresponding mean stress tensors may be calculated unambiguously using single-crystal elastic moduli. A novel formulation for orientation indexing and cell refinement is introduced and demonstrated using two examples: first, sequential indexing and lattice refinement of a single-crystal ruby standard with known COM coordinates; and second, indexing and refinement of simulated diffraction data from an aggregate of 819 individual grains using several sample rotation ranges and including the influence of experimental uncertainties. The speed of acquisition and penetration depth achievable with high-energy (that is, >50 keV) x-rays make this technique ideal for studies of strain/stress evolution in situ, as well as for residual stress analysis.

Strain and texture analysis of coatings using high-energy x-rays

We investigate the internal strain and crystallographic orientation (texture) in physical-vapor deposited metal nitride coatings of TiN and CrN. A high-energy diffraction technique is presented tha ...

Three-dimensional plastic response in polycrystalline copper via near-field high-energy X-ray diffraction microscopy

The evolution of the crystallographic orientation field in a polycrystalline sample of copper is mapped in three dimensions as tensile strain is applied. Using forward-modeling analysis of high-energy X-ray diffraction microscopy data collected at the Advanced Photon Source, the ability to track intragranular orientation variations is demonstrated on an ∼2 µm length scale with ∼0.1° orientation precision. Lattice rotations within grains are tracked between states with ∼1° precision. Detailed analysis is presented for a sample cross section before and after ∼6% strain. The voxel-based (0.625 µm triangular mesh) reconstructed structure is used to calculate kernel-averaged misorientation maps, which exhibit complex patterns. Simulated scattering from the reconstructed orientation field is shown to reproduce complex scattering patterns generated by the defected microstructure. Spatial variation of a goodness-of-fit or confidence metric associated with the optimized orientation field indicates regions of relatively high or low orientational disorder. An alignment procedure is used to match sample cross sections in the different strain states. The data and analysis methods point toward the ability to perform detailed comparisons between polycrystal plasticity computational model predictions and experimental observations of macroscopic volumes of material.

Synchrotron applications of an amorphous silicon flat-panel detector

A GE Revolution 41RT flat-panel detector (GE 41RT) from GE Healthcare (GE) has been in operation at the Advanced Photon Source for over two years. The detector has an active area of 41 cm x 41 cm with 200 microm x 200 microm pixel size. The nominal working photon energy is around 80 keV. The physical set-up and utility software of the detector system are discussed in this article. The linearity of the detector response was measured at 80.7 keV. The memory effect of the detector element, called lag, was also measured at different exposure times and gain settings. The modulation transfer function was measured in terms of the line-spread function using a 25 microm x 1 cm tungsten slit. The background (dark) signal, the signal that the detector will carry without exposure to X-rays, was measured at three different gain settings and with exposure times of 1 ms to 15 s. The radial geometric flatness of the sensor panel was measured using the diffraction pattern from a CeO(2) powder standard. The large active area and fast data-capturing rate, i.e. 8 frames s(-1) in radiography mode, 30 frames s(-1) in fluoroscopy mode, make the GE 41RT one of a kind and very versatile in synchrotron diffraction. The loading behavior of a Cu/Nb multilayer material is used to demonstrate the use of the detector in a strain-stress experiment. Data from the measurement of various samples, amorphous SiO(2) in particular, are presented to show the detector effectiveness in pair distribution function measurements.

A rotational and axial motion system load frame insert for in situ high energy x-ray studies

High energy x-ray characterization methods hold great potential for gaining insight into the behavior of materials and providing comparison datasets for the validation and development of mesoscale modeling tools. A suite of techniques have been developed by the x-ray community for characterizing the 3D structure and micromechanical state of polycrystalline materials; however, combining these techniques with in situ mechanical testing under well characterized and controlled boundary conditions has been challenging due to experimental design requirements, which demand new high-precision hardware as well as access to high-energy x-ray beamlines. We describe the design and performance of a load frame insert with a rotational and axial motion system that has been developed to meet these requirements. An example dataset from a deforming titanium alloy demonstrates the new capability.

Probing Microstructure Dynamics With X-Ray Diffraction Microscopy

We describe our recent work on developing X-ray diffraction microscopy as a tool for studying three dimensional microstructure dynamics. This is a measurement technique that is demanding of experimental hardware and presents a challenging computational problem to reconstruct the sample microstructure. A dedicated apparatus exists at beamline 1-ID of the Advanced Photon Source for performing these measurements. Submicron mechanical precision is combined with focusing optics that yield ≈2 μm high × 1.3 mm wide line focused beam at 50 keV. Our forward modeling analysis approach generates diffraction from a simulated two dimensional triangular mesh. Each mesh element is assigned an independent orientation by optimizing the fit to experimental data. The method is computationally demanding but is adaptable to parallel computation. We illustrate the state of development by measuring and reconstructing a planar section of an aluminum polycrystal microstructure. An orientation map of ∼90 grains is obtained along with a map showing the spatial variation in the quality of the fit to the data. Sensitivity to orientation variations within grains is on the order of 0.1 deg. Volumetric studies of the response of microstructures to thermal or mechanical treatment will soon become practical. It should be possible to incorporate explicit treatment of defect distributions and to observe their evolution.

Validation of a crystal plasticity model using high energy diffraction microscopy

High energy diffraction microscopy is used to measure the crystallographic orientation and evolution of lattice strain in an Al–Li alloy. The relative spatial arrangement of the several pancake-shaped grains in a tensile sample is determined through in situ and ex situ techniques. A model for crystal plasticity with continuity of lattice spin is posed, where grains are represented by layers in a finite element mesh following the arrangement indicated by experiment. Comparison is drawn between experiment and simulation.

Microscale damage evolution and stress redistribution in Ti–SiC fiber composites

Abstract Local damage evolution in a composite is the primary micromechanical process determining its fracture toughness, strength, and lifetime. In this study, high energy X-ray microdiffraction was used to measure the lattice strains of both phases in a Ti–SiC fiber composite laminate. The data provided in situ load transfer information under applied tensile stress at the scale of the microstructure. To better understand damage evolution, predictions of a modified shear lag model were compared to the strain data. This comparison (1) demonstrated the importance of accounting for the matrix axial and shear stiffness, (2) optimized the stiffness ratio for load transfer, and (3) improved the interpretation of the ideal planar geometry commonly used in micromechanical composite models. In addition, the results proved the matrix within and around the damage zone sustained substantial axial load and locally yielded. It was also shown that an area detector is essential in such a diffraction study as it provides multi-axial strain data and helps eliminate the “graininess” problem.

High spatial resolution, high energy synchrotron x-ray diffraction characterization of residual strains and stresses in laser shock peened Inconel 718SPF alloy

Laser shock peening (LSP) is an advanced surface enhancement technique used to enhance the fatigue strength of metal parts by imparting deep compressive residual stresses. In the present study, LSP was performed on IN718 SPF alloy, a fine grained nickel-based superalloy, with three different power densities and depth resolved residual strain and stress characterization was conducted using high energy synchrotron x-ray diffraction in beam line 1-ID-C at the Advanced Photon Source at the Argonne National laboratory. A fine probe size and conical slits were used to non-destructively obtain data from specific gauge volumes in the samples, allowing for high-resolution strain measurements. The results show that LSP introduces deep compressive residual stresses and the magnitude and depth of these stresses depend on the energy density of the laser. The LSP induced residual stresses were also simulated using three-dimensional nonlinear finite element analysis, with employment of the Johnson-Cook model for describing the nonlinear materials constitutive behavior. Good agreement between the experimental and simulated data was obtained. These various results are presented and discussed.