Judy Pang

The Race to X-ray Microbeam and Nanobeam Science

X-ray microbeams are an emerging characterization tool with broad implications for science, ranging from materials structure and dynamics, to geophysics and environmental science, to biophysics and protein crystallography. We describe how submicrometer hard x-ray beams with the ability to penetrate tens to hundreds of micrometers into most materials and with the ability to determine local composition, chemistry, and (crystal) structure can characterize buried sample volumes and small samples in their natural or extreme environments. Beams less than 10 nanometers have already been demonstrated, and the practical limit for hard x-ray beam size, the limit to trace-element sensitivity, and the ultimate limitations associated with near-atomic structure determinations are the subject of ongoing research.

Methods for obtaining the strain-free lattice parameter when using diffraction to determine residual stress

The determination of residual stress by diffraction depends on the correct measurement of the strain-free lattice spacing d(hkl)(0), or alternatively the enforcement of some assumption about the state of strain or stress within the body. It often represents the largest uncertainty in residual stress measurements since there are many ways in which the strain-free lattice spacing can vary in ways that are unrelated to stress. Since reducing this uncertainty is critical to improving the reliability of stress measurements, this aspect needs to be addressed, but it is often inadequately considered by experimenters. Many different practical strategies for the determining of d(hkl)(0) or d(ref) have been developed, some well known, others less so. These are brought together here and are critically reviewed. In practice, the best method will vary depending on the particular application under consideration. Consequently, situations for which each method are appropriate are identified with reference to practical examples.

Polychromatic X-ray Microdiffraction Studies of Mesoscale Structure and Dynamics

Polychromatic X-ray microdiffraction is an emerging tool for studying mesoscale structure and dynamics. Crystalline phase, orientation (texture), elastic and plastic strain can be nondestructively mapped in three dimensions with good spatial and angular resolution. Local crystallographic orientation can be determined to approximately 0.01 degree and elastic strain tensor elements can be measured with a resolution of approximately 10(-4) or better. Complete strain tensor information can be obtained by augmenting polychromatic microdiffraction with a monochromatic measurement of one Laue-reflection energy. With differential-aperture depth profiling, volumes tens to hundreds of micrometers below the surface are accessible so that three-dimensional distributions of crystalline morphology including grain boundaries, triple points, second phases and inclusions can all be mapped. Volume elements below 0.25 microm3 are routinely resolved so that the grain boundary structure of most materials can be characterized. Here the theory, instrumentation and application of polychromatic microdiffraction are described.

Phonon Density of States and Anharmonicity of UO 2

Phonon density of states (PDOS) measurements have been performed on polycrystalline UO2 at 295 and 1200 K using time-of-flight inelastic neutron scattering to investigate the impact of anharmonicity on the vibrational spectra and to benchmark ab initio PDOS simulations performed on this strongly correlated Mott-insulator. Time-of-flight PDOS measurements include anharmonic linewidth broadening inherently and the factor of ~ 7 enhancement of the oxygen spectrum relative to the uranium component by the neutron weighting increases sensitivity to the oxygen-dominated optical phonon modes. The first-principles simulations of quasi-harmonic PDOS spectra were neutron-weighted and anharmonicity was introduced in an approximate way by convolution with wavevector-weighted averages over our previously measured phonon linewidths for UO2 that are provided in numerical form. Comparisons between the PDOS measurements and the simulations show reasonable agreement overall, but they also reveal important areas of disagreement for both high and low temperatures. The discrepancies stem largely from an ~ 10 meV compression in the overall bandwidth (energy range) of the oxygen-dominated optical phonons in the simulations. A similar linewidth-convoluted comparison performed with the PDOS spectrum of Dolling et al. obtained by shell-model fitting to their historical phonon dispersion measurements shows excellent agreement with the time-of-flight PDOS measurements reported here. In contrast, we show by comparisons of spectra in linewidth-convoluted form that recent first-principles simulations for UO2 fail to account for the PDOS spectrum determined from the measurements of Dolling et al. These results demonstrate PDOS measurements to be stringent tests for ab initio simulations of phonon physics in UO2 and they indicate further the need for advances in theory to address lattice dynamics of UO2.

X-Ray Study of Pd40Cu30Ni10P20 Bulk Metallic Glass Brazing Filler for Ti-6Al-7Nb Alloy

Crystalline precipitates in a bulk-metallic-glass (BMG) braze were investigated with an intense x-ray microbeam. The precipitates were found in the Pd40Cu30P20Ni10 BMG braze matrix after joining crystalline Ti-6Al-7Nb. However, the role (if any) played by the precipitates in improving the mechanical bond of the BMG/crystalline joint is unknown. X-ray microdiffraction and microfluorescence measurements from small sample volumes were made with an ~ 0.5 x 0.5 μm2 beam. Spatially-resolved Laue diffraction and x-ray fluorescence measurements were made on several second-phase crystals within the BMG matrix. Although precipitate crystals with the observed compositions were anticipated to be predominantly hexagonal, one of the crystals was found to be cubic or tetragonal. The instrumentation includes capabilities for 3D depth-resolved measurements of crystal structure and for fluorescence analysis of elemental composition. Depth profiling gave information about the grain distribution and morphology in the BMG matrix.

Strain-Resolved Polychromatic X-ray Microdiffraction

Polychromatic microdiffraction is a powerful method for characterizing the threedimensional (3D) phase, local orientation and deviatoric-elastic-strain distributions in crystalline materials.[1,2] Measurements can be made on sub cubic micron volumes and on single-crystal, polycrystalline and deformed materials. The method is well suited to near-surface characterization, but can also probe 3D distributions mm’s below the surface in low Z materials. Spatial resolution transverse to the incident beam is determined by the beam size. Spatial resolution along the beam is obtained by a method called differential aperture x-ray microscopy. [2] Samples with small or highly deformed grains are the most challenging, because the local crystallographic orientation changes rapidly with position. For these samples, various strategies can improve strain resolution. For example, spatial resolution can be significantly improved by the use of more advanced focusing optics [3] and as spatial resolution improves, the local volume probed by the beam, can be accurately modeled by a crystal with a uniform defect density. We have recently demonstrated [4] the capability of forming polychromatic hard x-ray beams below 100 nm (Fig. 1) and with better vibration control and higher precision alignment control there is evidence that beams below 30 nm may be possible with optics already in hand. [5] Another way to improve the strain resolution in deformed materials is to use energy scans to accurately determine the 2d spacing independent of deformation. With energy scans, a Laue reflection that is badly streaked due to the presence of lattice rotations within the crystal is resolved into a series of much sharper spots that move in angle as a function of energy. This approach allows the 2d spacing and local orientation of the Bragg planes to be unambiguously determined. In principle, the full strain-tensor distribution can be built up by studying the energy/angle/ sample volume dependence of many Laue reflections. Although this process is currently very time consuming, the development of much faster area detectors and the development of area detectors with good energy resolution will make such methods routine in the near future. Applications of microdiffraction to such diverse and long-standing materials issues as 2D and 3D grain growth, deformation and the mesoscale structure of cracks are currently underway.

The 3D X‐Ray Crystal Microscope: An Unprecedented Tool for ICME

There is a long-standing debate over the length scales needed to understand the behavior of materials and the role of surfaces, defects, and inhomogeneities. Indeed the properties of most materials are ultimately determined by defects —including grain boundaries and surfaces-that are either introduced during processing or in-service, and defect density and distribution must be considered for high-fidelity integrated computational modeling and engineering. Scientists at ORNL together with partners at Argonne have developed a powerful 3D X-ray Crystal Microscope that can nondestructively characterize the local 3D crystal structure of polycrystalline materials with submicron resolution and with sensitivity to the local crystal structure, orientation, elastic strain tensor and the local Nye tensor. This emerging tool provides unprecedented tests of materials models under different processing/environmental conditions and provides new insights into the impact of unpaired dislocations, elastic strain and surfaces and interfaces. The promise of the 3D Microscope and the emergence of similar instruments at synchrotrons around the world will be discussed with respect to ICME.

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.

Polychromatic X-ray Microdiffraction Characterization of Local Crystallographic Structure and Defect Distributions

Three-dimensional (3D), nondestructive, spatially resolved characterization of local crystal structure is conveniently made with polychromatic x-ray microdiffraction. In general, polychromatic microdiffraction provides information about the local (subgrain) orientation, unpaired-dislocation density, and elastic strain. This information can be used for direct comparison to theoretical models. Practical microbeams use intense synchrotron x-ray sources and advanced x-ray focusing optics. By employing polychromatic x-ray beams and a virtual pinhole camera method, called differential aperture microscopy, 3D distributions of the local crystalline phase, orientation (texture), and elastic and plastic strain tensors can be measured with submicron 3D resolution. The local elastic strain tensor elements can typically be determined with uncertainties less than 100 ppm. Orientations can be quantified to {approx} 0.01{sup o} and the local unpaired dislocation-density tensor can be simultaneously characterized. The spatial resolution limit for hard x-ray polychromatic microdiffraction is < 40nm and existing instruments operate with {approx} 500 to 1000nm resolution. Because the 3D x-ray crystal microscope is a penetrating nondestructive tool, it is ideal for studies of mesoscale evolution in materials.