Jette Oddershede

Determining grain resolved stresses in polycrystalline materials using three‐dimensional X‐ray diffraction

An algorithm is presented for characterization of the grain resolved (type II) stress states in a polycrystalline sample based on monochromatic X-ray diffraction data. The algorithm is a robust 12-parameter-per-grain fit of the centre-of-mass grain positions, orientations and stress tensors including error estimation and outlier rejection. The algorithm is validated by simulations and by two experiments on interstitial free steel. In the first experiment, using only a far-field detector and a rotation range of 2 × 110°, 96 grains in one layer were monitored during elastic loading and unloading. Very consistent results were obtained, with mean resolutions for each grain of approximately 10 µm in position, 0.05° in orientation, and 8, 20 and 13 × 10−5 in the axial, normal and shear components of the strain, respectively. The corresponding mean deviations in stress are 30, 50 and 15 MPa in the axial, normal and shear components, respectively, though some grains may have larger errors. In the second experiment, where a near-field detector was added, ∼2000 grains were characterized with a positional accuracy of 3 µm.

Modelling the X-ray powder diffraction of nitrogen-expanded austenite using the Debye formula

Stress-free and homogeneous samples of nitrogen-expanded austenite, a defect-rich f.c.c. structure with a high interstitial nitrogen occupancy (between 0.36 and 0.61), have been studied using X-ray powder diffraction and Debye simulations. The simulations confirm the presence of deformation stacking faults in the structure, while twin or growth faulting can be ruled out. Screw dislocations are abundant and the dislocation density increases with the interstitial nitrogen occupancy. Whether the N atoms are clustered or distributed randomly among the octahedral interstices was found to be indistinguishable to X-ray powder diffraction.

Heterogeneous grain-scale response in ferroic polycrystals under electric field

Understanding coupling of ferroic properties over grain boundaries and within clusters of grains in polycrystalline materials is hindered due to a lack of direct experimental methods to probe the behaviour of individual grains in the bulk of a material. Here, a variant of three-dimensional X-ray diffraction (3D-XRD) is used to resolve the non-180° ferroelectric domain switching strain components of 191 grains from the bulk of a polycrystalline electro-ceramic that has undergone an electric-field-induced phase transformation. It is found that while the orientation of a given grain relative to the field direction has a significant influence on the phase and resultant domain texture, there are large deviations from the average behaviour at the grain scale. It is suggested that these deviations arise from local strain and electric field neighbourhoods being highly heterogeneous within the bulk polycrystal. Additionally, the minimisation of electrostatic potentials at the grain boundaries due to interacting ferroelectric domains must also be considered. It is found that the local grain-scale deviations average out over approximately 10–20 grains. These results provide unique insight into the grain-scale interactions of ferroic materials and will be of value for future efforts to comprehensively model these and related materials at that length-scale.

Quantitative grain-scale ferroic domain volume fractions and domain switching strains from three-dimensional X-ray diffraction data

A method for the extension of the three-dimensional X-ray diffraction technique to allow the extraction of domain volume fractions in polycrystalline ferroic materials is presented. This method gives access to quantitative domain volume fractions of hundreds of independent embedded grains within a bulk sample. Such information is critical to furthering our understanding of the grain-scale interactions of ferroic domains and their influence on bulk properties. The method also provides a validation tool for mesoscopic ferroic domain modelling efforts. The mathematical formulations presented here are applied to tetragonal coarse-grained Ba0.88Ca0.12Zr0.06Ti0.94O3 and rhombohedral fine-grained (0.82)Bi0.5Na0.5TiO3–(0.18)Bi0.5K0.5TiO3 electroceramic materials. The fitted volume fraction information is used to calculate grain-scale non-180° ferroelectric domain switching strains. The absolute errors are found to be approximately 0.01 and 0.03% for the tetragonal and rhombohedral cases, which had maximum theoretical domain switching strains of 0.47 and 0.54%, respectively. Limitations and possible extensions of the technique are discussed.

Ammonium 1-hydroxy-2-(2-pyridinio)ethane-1,1-diyldiphosphonate dihydrate and potassium 1-hydroxy-2-(2-pyridinio)ethane-1,1-diyldiphosphonate dihydrate.

The crystal structures of the title compounds, ammonium risedronate dihydrate, NH4+.C7H10NO7P2-.2H2O, (I), and potassium risedronate dihydrate, K+.C7H10NO7P2-.2H2O, (II), have been determined from single-crystal X-ray data collected at 120 K. Compound (I) forms a three-dimensional hydrogen-bonded network which connects the ammonium and risedronate ions and the water molecules. In compound (II), the K+ ions are seven-coordinated in a capped distorted trigonal prism. The coordination polyhedra form chains by corner-sharing, and these chains are connected by phosphonate groups into layers in the ac plane. The layers are stacked and connected by hydrogen bonds in the b direction. The risedronate conformation is determined by intramolecular interactions fine-tuned by crystal packing effects. All H-atom donors in both structures are involved in hydrogen bonding, with D...A distances between 2.510 (2) and 3.009 (2) A.

Using X-ray powder diffraction and principal component analysis to determine structural properties for bulk samples of multiwall carbon nanotubes

It has been attempted to derive the structural properties of bulk multiwall carbon nanotubes (MWCNTs) from a combination of powder diffraction and principal component analysis (PCA). By a transformation of the direct PCA basis functions to a structural parameter set it was possible to obtain average values of inner radius, number of turns and d-spacing. The true tube lengths cannot be correctly estimated due to correlations to other properties, tube bending and defects in the tubes. Improvements can be expected by including distributions of the structural properties, further developing the functional relationships between the PCA and parameter functions and including the chiral angle (rolling direction) as a separate parameter.

Measuring Type II Stresses Using 3DXRD

An algorithm is presented for characterization of the grain resolved (type II) stress states in a polycrystalline sample based on monochromatic X-ray diffraction data. The algorithm is a robust 12-parameter-per-grain fit of the centre-of-mass grain positions, orientations and stress tensors including error estimation and outlier rejection. As examples of use results from two experiments – one on interstitial free (IF) steel and one on copper – will be presented. In the first experiment 96 grains in one layer of IF steel were monitored during elastic loading and unloading. Very consistent results were obtained, with resolutions for each grain of approximately 10 μm in position, 0.05˚ in orientation and 80 μstrain. When averaging over all grains a resolution of 10 μstrain was obtained. In the second experiment it was demonstrated that the strain states of more than 1000 grains in a plastically deformed Cu specimen could be determined to an accuracy of 100 μstrain.

Direct observation of grain rotations during coarsening of a semisolid Al–Cu alloy

Significance Computational modeling of materials phenomena promises to reduce the time and cost of developing new materials and processing techniques—a goal made feasible by rapid advances in computer speed and capacity. Validation of such simulations, however, has been hindered by a lack of 3D experimental data of simultaneously high temporal and spatial resolution. In this study, we exploit 3D X-ray diffraction microscopy to capture the evolution of crystallographic orientations during particle coarsening in a semisolid Al–Cu alloy. The data confirm a long-standing hypothesis that particle rotation is driven (in part) by the dependence of grain boundary energy on misorientation. In addition, the results constitute an experimental foundation for testing the predictive power of next-generation computational models for sintering. Sintering is a key technology for processing ceramic and metallic powders into solid objects of complex geometry, particularly in the burgeoning field of energy storage materials. The modeling of sintering processes, however, has not kept pace with applications. Conventional models, which assume ideal arrangements of constituent powders while ignoring their underlying crystallinity, achieve at best a qualitative description of the rearrangement, densification, and coarsening of powder compacts during thermal processing. Treating a semisolid Al–Cu alloy as a model system for late-stage sintering—during which densification plays a subordinate role to coarsening—we have used 3D X-ray diffraction microscopy to track the changes in sample microstructure induced by annealing. The results establish the occurrence of significant particle rotations, driven in part by the dependence of boundary energy on crystallographic misorientation. Evidently, a comprehensive model for sintering must incorporate crystallographic parameters into the thermodynamic driving forces governing microstructural evolution.

The effect of inter-granular constraints on the response of polycrystalline piezoelectric ceramics at the surface and in the bulk

The electro-mechanical coupling mechanisms in polycrystalline ferroelectric materials, including a soft PbZrxTi1−xO3 (PZT) and lead-free 0.9375(Bi1/2Na1/2)TiO3-0.0625BaTiO3 (BNT-6.25BT), have been studied using a surface sensitive low-energy (12.4 keV) and bulk sensitive high-energy (73 keV) synchrotron X-ray diffraction with in situ electric fields. The results show that for tetragonal PZT at a maximum electric field of 2.8 kV/mm, the electric-field-induced lattice strain (e111) is 20% higher at the surface than in the bulk, and non-180° ferroelectric domain texture (as indicated by the intensity ratio I002/I200) is 16% higher at the surface. In the case of BNT-6.25BT, which is pseudo-cubic up to fields of 2 kV/mm, lattice strains, e111 and e200, are 15% and 20% higher at the surface, while in the mixed tetragonal and rhombohedral phases at 5 kV/mm, the domain texture indicated by the intensity ratio, I111/I111¯ and I002/I200, are 12% and 10% higher at the surface than in the bulk, respectively. The obse...

A multiple length scale description of the mechanism of elastomer stretching

Conventionally, the stretching of rubber is modeled exclusively by rotations of segments of the embedded polymer chains; i.e. changes in entropy. However models have not been tested on all relevant length scales due to a lack of appropriate probes. Here we present a universal X-ray based method for providing data on the structure of rubbers in the 2–50 A range. First results relate to the elongation of a silicone rubber. We identify several non-entropic contributions to the free energy and describe the associated structural changes. By far the largest contribution comes from structural changes within the individual monomers, but among the contributions is also an elastic strain, acting between chains, which is 3–4 orders of magnitude smaller than the macroscopic strain, and of the opposite sign, i.e. extension of polymer chains in the direction perpendicular to the stretch. This may be due to trapped entanglements relaxing to positions close to the covalent crosslinks.