Supporting Online Material for

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1 Supporting Online Material for The Race to X-ray Microbeam and Nanobeam Science Gene E. Ice,* John D. Budai, Judy W. L. Pang *To whom correspondence should be addressed. Published 2 December 2011, Science 334, 1234 (2011) DOI: /science This PDF file includes: SOM Text Figs. S1 to S5 References Other Supporting Online Material for this manuscript includes the following: (available at Movies S1 to S3

2 Re: Manuscript Number Supplemental Information: The Race To X-ray Micro/Nano Science Gene E. Ice, John D. Budai, Judy W.L. Pang Spatial Resolution in three dimensions (3D) As described briefly in the main article, special methods have evolved to characterize materials in 3D with micron or submicron resolution: tomography, confocal microscopy, differential aperture microscopy, and three-dimensional diffraction microscopy. Doubly-focused x-ray microbeams are essential for fluorescence tomography, confocal microscopy and for differentialaperture microscopy. One-dimensionally focused beams are used for three-dimensional x-ray diffraction microscopy. Direct imaging of fluorescence is also under development but is still limited by chromatic aberration and/or limited aperture and spectral range of most x-ray focusing optics. Some simple movies and pictures are presented below to clarify how the most common methods work. Fluorescence tomography: Tomography is a widely used method for determining the density distribution in materials. In most tomographic studies, the sample is bathed in an x-ray beam and area detectors are used to provide high-resolution images of the internal structure as the sample is rotated and/or translated. Tomography can be made sensitive to elemental distributions by tuning the x-ray energy above and below an absorption edge. When trace element distributions are important, however, doubly-focused microbeams allow for 3D fluorescence tomography measurements with much greater trace-element sensitivity (13,18). Consider for example, the geometry of Fig. S1A used for fluorescence tomography. As illustrated, the distributions of elements within a plane of the sample is resolved by rotating and translating the sample while it is illuminated by a focused microbeam. The spatial distribution of various elements can be determined by a number of algorithms and one simple example is outlined in the figure caption. The ultimate spatial resolution is determined by the beam size and by the number of rotation and translation steps. Once the elemental distribution in one plane is determined, the sample is translated to study adjacent planes. Fluorescence tomography has been used for example to study trace element distributions in SiC shells of advanced nuclear fuel (19). The small shells are only microns thick and the measurements provide information about the amount and distribution of trace elements in the shells (Fig. S1B).

3 Fig. S1. A. Consider a sample where we wish to resolve the elemental distributions in 4 regions. The fluorescence signal is determined primarily by the elemental composition illuminated by a small x ray beam, the geometry of the detector and by self absorption of the x ray fluorescence in the sample. As shown in the figure, when the x ray beam passes through the lower two quadrants, the elemental distributions from both regions contribute to the x ray fluorescence signal monitored by a detector. This makes it possible to guess at the distribution of elements in the lower two boxes. By rotating and translating the sample, every box can be measured multiple times to refine the guess as to the elemental distribution. The starting guess from the individual measurements can be iterated to converge to a model, which is consistent with the individual measurements. This simple example illustrates the technique but does not capture the elegance and sophistication of actual code currently in use. B. An experimental tomographic reconstruction of the Zn distribution in a SiC shell from an advanced coated nuclear fuel particle. The ~700 μm diameter and 17 μm thick SiC shell forms the primary containment barrier for the fuel. Trace element measurements were used to monitor diffusion and transport through the shell.(19) Confocal Microscopy: Confocal x-ray fluorescence microscopy is an emerging method for studying 3d composition distributions in materials. As shown in Fig. S2, a penetrating x-ray micro/nanobeam excites fluorescence from an extended region within the sample. Resolution along the incident beam is defined by an x-ray lens with its optical axis perpendicular to the beam direction or by a slit placed near to the sample. Typically the volume element (voxel) defined by the beam and the slit/lens is elongated along the beam direction. The sample is translated to study other volume elements and to ultimately map the elemental distribution. This method is particularly well suited for studying layered structures where the sample can be aligned so the layers are at glancing angle with respect to the x-ray beam. In this geometry the spatial resolution normal to the layers is determined primarily by the beam size.

4 Fig. S2. In this typical confocal fluorescent microscopy arrangement, an incident x ray microbeam penetrates into a sample. Fluorescence is collected from a defined region along the beam path using a polycapillary x ray lens aligned with its axis perpendicular to the beam direction. Differential aperture microscopy: Differential aperture microscopy is a recently-developed method for determining the 3D spatial distribution of scattered intensity (14). Differential aperture microscopy directly resolves the problem of distinguishing the scattering source point from along the incident probe beam. The method is similar to a knife-edge scan that has long been used for determining incident x-ray microbeam size and shape. With the method, an absorbing wire is placed between the sample and an x-ray sensitive area detector. At each pixel of the detector, scattering from sequential volume elements along the incident beam are blocked as the edge of the wire occludes the line of sight between the pixel and the sample volume element. This results in a blank strip (i.e. shadow) on the detector image. Laue diffraction patterns corresponding to individual spatial locations along the beam path (z) are reconstructed through triangulation of the series of the partially blocked images. Depth resolution of the differential aperture technique can be submicron and about 400 images are needed for a typical wire-scan. MovieS1.mov shows a 3D aperture in action. Differential aperture microscopy is particularly valuable for nondestructive studies of materials processes such as deformation or grain growth. Although differential-aperture microscopy does not yet directly resolve individual dislocations, it can readily determine the orientation relations between subgrains or between deformation cell blocks caused by the collective dislocation motion in different individual volume elements. Deterioration of surface quality with deformation poses little effect on the measurements at greater depths. 3D resolved near-surface regions: Consider for example, a measurement of how the surface region of a deformation sample responds to load compared to interior volumes (33). The Laue patterns arising from both near-surface and interior volumes were reconstructed from a series of measurements made as the wire passed the sample surface. The results are illustrated in MovieS2.mov As can be seen, the streaking of the image is much larger near the surface than in the interior of the sample. Streaking is a consequence of unpaired geometrically necessary dislocations (GNDs) and geometrically necessary boundaries (GNBs). These inhomogeneous dislocation distributions are introduced during the plastic deformation process. Measurements before and after deformation clearly show that the observed streaking is not due to the original

5 preparation of the sample surface, but a real microstructural effect that cannot now be accurately considered by deformation theory. The streaked Laue patterns observed in the 1 μm depth-resolved images indicate that the deformation microstructure is finer than the 1 μm depth resolution. The experimental results may be analyzed within strain gradient plasticity theory. The shape of the observed Laue streaks can be interpreted by simulations of the diffracted Laue patterns and reveals the scalar dislocation density distribution. By analyzing the intensity distributions of the streaked Laue peaks for different spatially-resolved volume elements, the densities and gradients of GNDs and GNBs can be determined. These results, in turn, can be associated with particular slip systems and can be used to help develop quantitative models of deformation in ductile materials. 3D resolved subsurface interface/inter-crystalline regions: Differential aperture microscopy can also be used to identify buried intercrystalline regions such as grain boundaries and triple junctions. This capability enables nondestructive mapping of 3D grain morphologies such as is shown in Fig 3B in the main text (29). A simplified example illustrating how the depth-resolved Laue pattern changes at the boundary between two grains (Fig. S3) at a depth of z=11μm beneath surface of a tensile strained Ni sample is shown in MovieS3.mov Since Laue patterns are obtained from each micron-sized volume element, grain boundaries are readily identified. In addition, the local crystallographic structure and the evolution of the local deformation-tensor distribution of a polycrystalline sample can be resolved near and within a single grain and its neighbors. The measurements include information about the initial and evolving boundary conditions imposed by the grain-boundary network and neighboring grains. The detailed measurements of local grain boundary evolution, together with internal defect and strain fluctuations, provide new insights into a wide range of materials processes such as 3D grain growth and deformation behavior as a function of depth beneath the surface of the sample.

6 Fig. S3. Schematic of two grains inside a tensile strained Ni sample. As shown in MovieS3.mov, a series of Laue diffraction patterns were obtained for each micron of depth as the incident beam penetrates the sample. The Laue pattern changes abruptly at z=11μm, indicating the boundary between grains G1 and G2. Three-dimensional x-ray diffraction microscopy: Three-dimensional x-ray diffraction (3DXRD) microscopy is a third emerging method that uses x-ray microbeams to study crystal structure in 3D. This method uses elements of ray-tracing and tomography to understand the distribution of crystal structures in complex polycrystalline samples. The method is rapidly advancing based on improving detector spatial resolution, efficiency and pixel numbers. Because the experiments use penetrating high-energy x rays, the microstructures of bulk engineering samples can be resolved.

7 Fig. S4. Basic geometry for 3D diffraction microscopy. As illustrated, grains within the sample are illuminated by a singly focused (line focused) high energy x ray beam. Diffraction from the grains occurs when the crystals are oriented to satisfy the Bragg condition. At the rotation angle of the illustration, the green grain diffracts into the detector. The Bragg reflections observed at the two detector positions can be ray traced back to the incident beam plane to define the crystal shape. Additional reflections improve the estimated grain intercept with the beam. Consider for example the geometry illustrated in Fig. S4. A singly focused x-ray beam is used to illuminate a polycrystalline sample. The beam defines the plane from which x rays will be scattered, but not the position from within the plane. The sample is rotated to satisfy the Bragg condition for diffraction from the different crystals illuminated by the plane beam. Scattering is observed by a detector at two locations, and then ray traced back onto the origin plane. Multiple Bragg reflections are excited for each grain intercepted by the beam by rotating the sample. The multiple reflections define the projection of the grain along the reflection direction. The measurements are then repeated for different planes to build up a complete 3D volume. The spatial resolution depends both on the resolution of the detector and the geometry between the two detector positions and the sample. A number of variants of this method are rapidly evolving that exploit various strategies to improve speed and accuracy of the measurements. For example, information from neighbor grains can be made self-consistent to fill volume if the sample is assumed to be void free. Sophisticated tomographic methods can also be used to exploit the limited number of projections from the observed Bragg reflections. In addition, there are changes in the direct-beam intensity that arise from scattering of x rays out of the direct beam by the crystal grains. These can be used to further improve spatial resolution. A typical reconstructed 3D image from measurements by Suter and co-workers is shown in Fig. S5.

8 Fig. S5. Image of the grain microstructure in a 1 mm diameter nickel sample. The sample was annealed to study grain growth/coarsening by the group of Robert Suter (Carnegie Mellon). The gray outline is used to indicate the overall sample dimensions while the colors for individual grains are used to follow the evolution of the microstructure with annealing steps.

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