Ben C Larson

Experimental characterization of the mesoscale dislocation density tensor

The dislocation density tensor has been an important variable in the theoretical characterization of dislocations in deformed crystals since its introduction over 5 decades ago. However, the non-destructive, three-dimensional (3D) measurements of lattice rotations and elastic strain needed to determine dislocation density tensors with micron spatial resolution over mesoscopic length scales have until now not been available. We have used 3D X-ray microscopy with sub-micron point-to-point spatial resolution to demonstrate 3D, spatially resolved measurements of the dislocation density tensor in elastically and plastically deformed silicon single crystal plates. Measurements were made of the dislocation density tensor along a line in a ∼35 µm thick silicon plate that was bent (elastically) to a 5.42 mm radius of curvature at room temperature, and in a similar sample deformed plastically by annealing to 700°C under bending stress. We discuss the theoretical background for the dislocation density tensor with respect to lattice rotation and elastic strain, we describe the X-ray microscopy technique used to make non-destructive measurement of local rotations and elastic strains with sub-micron resolution in 3D, and we discuss the analysis procedures for extracting dislocation tensors on mesoscopic length scales.

Backstress, the Bauschinger Effect and Cyclic Deformation

Backstresses or long range internal stresses (LRIS) in the past have been suggested by many to exist in plastically deformed crystalline materials. Elevated stresses can be present in regions of elevated dislocation density or dislocation heterogeneities in the deformed microstructures. The heterogeneities include edge dislocation dipole bundles (veins) and the edge dipole walls of persistent slip bands (PSBs) in cyclically deformed materials and cell and subgrain walls in monotonically deformed materials. The existence of long range internal stress is especially important for the understanding of cyclic deformation and also monotonic deformation. X-ray microbeam diffraction experiments performed by the authors using synchrotron x-ray microbeams determined the elastic strains within the cell interiors. The studies were performed using, oriented, monotonically deformed Cu single crystals. The results demonstrate that small long-range internal stresses are present in cell interiors. These LRIS vary substantially from cell to cell as 0 % to 50 % of the applied stress. The results are related to the Bauschinger effect, often explained in terms of LRIS.

On the elastic boundary value problem of dislocations in bounded crystals

A new formulation of the elastic boundary value problem of dislocations in bounded crystals is developed. This formulation is based on the ansatz that the stress field of dislocations in bounded domains can be constructed as the sum of a contribution corresponding to the classical infinite-domain solution plus a correction that is determined here from a mathematically well posed problem. The formulation of the elastic boundary value problem given here ensures that the equilibrium of the overall stress field is rigorously satisfied, specifically when dislocations intersect the boundary. The implications of this new formalism for dislocation dynamics simulation are discussed for the cases of bounded crystals and crystal volumes representative of uniformly loaded infinite crystals. An approximate computational solution of the elastic boundary value problem is presented based on the concept of virtual dislocations and the use of a non-singular form of the infinite-domain solution of the dislocation stress field. This computational solution addresses the issues of singularity and global equilibrium of the boundary traction associated with the corrective field. Sample results are presented for the internal stress in bounded crystals containing 3D dislocation configurations produced using the dislocation dynamics simulation method. The results illustrate the statistical character of the internal elastic field.

Three-Dimensional Micron-Resolution X-Ray Laue Diffraction Measurement of Thermal Grain-Evolution in Aluminum

A new technique for investigating 3D grain growth in polycrystalline materials using white x-ray microdiffraction with micron point-to-point spatial resolution is presented. This technique utilizes focused polychromatic x-rays at the Advanced Photon Source, differential aperture depth-profiling, CCD measurements, and automated analysis of spatially-resolved Laue patterns to measure local lattice structure and orientation. 3D thermal grain growth studies of hotrolled aluminum have been initiated to demonstrate the capabilities of this method. Complete 3D grain orientation maps were obtained from a hot-rolled aluminum polycrystal. The sample was then annealed to induce grain growth, cooled to room temperature, and re-mapped to measure the thermal migration of all grain boundaries within the same volume region. Initial observations reveal significant grain growth above 360°C, involving movement of both low- and high-angle boundaries. Systematic measurements have been obtained of the as-rolled grain structure and of the microstructural evolution after annealing at successively higher temperatures. Small second-phase precipitates have been identified. Such measurements will provide the detailed 3D experimental link needed for testing theories and computer models of 3D grain growth in bulk materials.

Submicrometre-resolution polychromatic three-dimensional X-ray microscopy

The ability to study the structure, microstructure and evolution of materials with increasing spatial resolution is fundamental to achieving a full understanding of the underlying science of materials. Polychromatic three-dimensional X-ray microscopy (3DXM) is a recently developed nondestructive diffraction technique that enables crystallographic phase identification, determination of local crystal orientations, grain morphologies, grain interface types and orientations, and in favorable cases direct determination of the deviatoric elastic strain tensor with submicrometre spatial resolution in all three dimensions. With the added capability of an energy-scanning incident beam monochromator, the determination of absolute lattice parameters is enabled, allowing specification of the complete elastic strain tensor with three-dimensional spatial resolution. The methods associated with 3DXM are described and key applications of 3DXM are discussed, including studies of deformation in single-crystal and polycrystalline metals and semiconductors, indentation deformation, thermal grain growth in polycrystalline aluminium, the metal–insulator transition in nanoplatelet VO2, interface strengths in metal–matrix composites, high-pressure science, Sn whisker growth, and electromigration processes. Finally, the outlook for future developments associated with this technique is described.

Electron-hole and plasmon excitations in 3d transition metals: Ab initio calculations and inelastic x-ray scattering measurements

CHESS, Cornell University, Ithaca, NY 14853(Dated: February 2, 2008)We report extensive all-electron time-dependent density-functional calculations and nonresonantinelastic x-ray scattering measurements of the dynamical structure factor of 3d transition metals.For small wave vectors, a plasmon peak is observed which is well described by our calculations.At large wave vectors, both theory and experiment exhibit characteristic low-energy electron-holeexcitations of d character which correlate with the presence of d bands below and above the Fermilevel. Our calculations, which have been carried out in the random-phase and adiabatic local-densityapproximations, are found to be in remarkable agreement with the measured dynamical structurefactor of Sc and Cr at energies below the semicore onset energy (M-edge) of these materials.

Long-range internal stresses in monotonically and cyclically deformed metallic single crystals

Abstract Selected experimental measurements and theoretical predictions for the magnitude of long-range internal stress in monotonically and cyclically deformed metals are assessed and recently developed, spatially-resolved X-ray micro-beam techniques for direct measurements of long-range internal stress are discussed. The results of previously reported differential-aperture X-ray microscopy spatially-resolved measurements of long-range internal stress in dislocation-cell interiors in monotonically deformed copper are compared with predictions and analyses associated with the composite model of deformation. In addition, the results of volume-integrating X-ray line-profile measurements and spatially-resolved differential-aperture X-ray microscopy measurements of strains in <100> oriented copper single crystals that were cyclically deformed to pre-saturation (without persistent slip bands) are presented.

Large crystal local-field effects in the dynamical structure factor of rutile TiO2

We present ab initio time-dependent density-functional calculations and nonresonant inelastic x-ray scattering measurements of the dynamical structure factor of rutile TiO{sub 2}. Our calculations are in good agreement with experiment and prove the presence of large crystal local-field effects below the Ti M edge, which yield a sharp loss peak at 14 eV whose intensity features a remarkable nonmonotonic dependence on the wave vector. These effects, which impact the excitation spectra in the oxide more dramatically than in transition metals, provide a signature of the underlying electronic structure.

Thermal and Electromigration‐Induced Strains in Polycrystalline Films and Conductor Lines: X‐ray Microbeam Measurements and Analysis

X‐ray microbeam measurements of thermal and electromigration‐induced strains have been made at NSLS using white‐beam energy dispersive x‐ray diffraction, averaging over many grains, and at APS using white‐beam Laue x‐ray diffraction, from single grains. Grain‐by‐grain deviatoric strain measurements in Al films show wide variation in behavior for different grains in the films. Room temperature relaxation of residual strains was observed to occur at different rates for Al films with different bonding layers and substrates. X‐ray microbeam measurements of strain development during electromigration for Cu and Al conductor lines show that strain gradients do not develop in the copper lines under conditions similar to those for which large strain gradients have been seen for Al lines.

Polychromatic X‐ray Micro‐ and Nano‐Beam Science and Instrumentation

Polychromatic x‐ray micro‐ and nano‐beam diffraction is an emerging nondestructive tool for the study of local crystalline structure and defect distributions. Both long‐standing fundamental materials science issues, and technologically important questions about specific materials systems can be uniquely addressed. Spatial resolution is determined by the beam size at the sample and by a knife‐edge technique called differential aperture microscopy that decodes the origin of scattering from along the penetrating x‐ray beam. First‐generation instrumentation on station 34‐ID‐E at the Advanced Photon Source (APS) allows for nondestructive automated recovery of the three‐dimensional (3D) local crystal phase and orientation. Also recovered are the local elastic‐strain and the dislocation tensor distributions. New instrumentation now under development will further extend the applications of polychromatic microdiffraction and will revolutionize materials characterization.