During the past 18 months, we have developed a novel micro-beam Laue diffraction setup on beamline B16 with a dedicated in situ loading capability. This setup has been used to study the evolution of lattice orientation and Laue diffraction spot shape during in situ loading of a large grained Ni polycrystalline sample. Lattice orientation could be successfully mapped up to 14% plastic strain. Individual grains were predicted to appear “hard” or “soft” depending on their lattice orientation with respect to the sample loading direction. It was found that the reflections from “hard” grains remain largely unchanged during deformation, whilst “soft” grain reflections show streaking or breaking up of the diffraction spots, corresponding to an increase in the spread of lattice orientation within the scattering volume.
Figure 1: Initial micro-beam Laue diffraction setup on B16 with insitu loading device.
This increasing spread of local lattice misorientation can be studied more closely using reciprocal space mapping or monochromatic pencil beam topography. In particular the link between the diffraction spot shape observed in micro-beam Laue diffraction and by reciprocal space mapping is interesting. Using the novel setup on B16, we have studied a single 311 reflection arising from a grain within a Ni polycrystal deformed to 9% plastic strain. Maps of the reflection from reciprocal space mapping and high resolution Laue diffraction were found to exhibit very similar features in terms of local lattice misorientation within the scattering volume. This suggests that a combined setup, using micro-beam Laue diffraction and high resolution white pencil beam topography of a single Laue spot would provide very useful complementary information. Overall local lattice orientation can be found from the Laue images, whilst the topograph would provide a very high angular resolution image of the scattering volume in the tangential reciprocal space directions. The development of such a setup is currently under way and has shown some first promising results.
For future developments of micro diffraction on B16, it is becoming increasingly clear that micro focussing will be required in order to further improve spatial resolution and reduce acquisition times. Incorporating this into the present setup will be one of the major challenges to face, but also open up some very promising and exciting possibilities.
Figure 2: Evolution of local Schmid factor in a polycrystalline Ni sample during in situ tensile loading.
Understanding the deformation of polycrystalline structural materials is the key to improving performance and reliability of modern engineering materials and the components made from them. Capturing the full details of polycrystalline deformation either experimentally or through modelling at the sub-grain level is a significant challenge due to the sheer volume of information involved, the complexity of inter- and intra-granular mechanical interactions and the interplay between global and local effects – it is very much a multi-scale problem. Self-consistent models have been put forward on the premise that groups of grains sharing similar orientation may be represented by a single ellipsoidal inclusion with the corresponding elastic and plastic properties, embedded within a homogeneous infinitely extended matrix with the effective properties of all the remaining grain orientations. These models can capture successfully the average mechanical deformation response of many structural alloys . A limitation of self-consistent models is that they do not capture the effects of complex grain shape, intragranular strain variation and mesoscopic neighbourhood on the deformation of a particular grain. For example if a “soft” grain happens to be located immediately next to a “hard” grain, its behaviour will be different from that of a grain embedded in a uniform matrix, especially close to the grain boundary. These effects may not exert a significant influence on the average properties, such as stiffness. However, properties such as flow stress and fatigue limit which are governed by the “weakest link” mechanism are particularly sensitive to these local effects. In fact, it may be expected that the deviation of the local stress from the grain group average stress may be of the same order of magnitude as the average stress itself, i.e. the mesoscopic neighbourhood effect can be very strong . This suggests that methods for the investigation of grain-level deformation must involve suitably refined simulation techniques to account fully for the local grain environment, complemented by experimental techniques with sufficient spatial resolution to map the variations of elastic strains and stresses within individual crystallites.
Micro-beam Laue diffraction is an experimental technique ideally suited to this purpose. A polychromatic X-Ray beam with an energy spectrum from 5 to 30keV was used to illuminate regions within individual crystallites in a polycrystal. The resulting diffraction pattern consists of a number of Laue spots that are recorded by an area detector. From the spot locations, lattice orientation and deviatoric elastic strain can be computed. This technique has been successfully applied to the study of lattice orientation in thin films , Sn whisker growth , electro migration  and in situ deformation of FIB-machined single crystal micro pillars . Over the past 18 months we have developed a novel micro-beam Laue diffraction setup on beamline B16 (Fig. 1). As an initial trial sample, a large grained Ni dogbone was considered. This sample had been specially heat treated to promote grain growth, resulting in crystallites with up to 500 micron diameter with most of the grains extending through the thickness of the sample to give an approximately two-dimensional microstructure. Using the micro-beam Laue technique, the central gauge region of the sample was mapped at a number of load increments. From the resulting Laue diffraction patterns, lattice orientation in the sample could be deduced and followed during the deformation process (Fig. 2).
Figure 3: Evolution of Laue spot shape in three different grains. Grain 1 is a “hard” grain which is unfavourably oriented for slip. Grain 2 is a “soft” grain which is oriented favourably for slip. Grain 3 is a grain in which a uniform variation of lattice rotation in the gauge volume is present, resulting in a streaked Laue pattern.
We also observed how the shape of individual reflections changed with increasing deformation, depending on the local lattice orientation. In a grain oriented unfavourably for slip, diffraction spot shape remained largely unchanged. In grains favourably oriented for slip diffraction spots were observed to fragment with increasing deformation  (Fig. 3). This fragmentation arises due to increasing spread of lattice orientations in the scattering volume and can be linked to the local dislocation microstructure. More typically this fragmentation is studied by reciprocal space mapping .
In order to establish a firmer link between the spot fragmentation evolution found in Laue diffraction and reciprocal space mapping, we carried out a combined reciprocal space mapping and Laue diffraction experiment on B16. The shape of a single 311 reflection from a grain within a Ni foil deformed to 9% plastic strain was studied. We found good agreement between the reflection shapes found by Laue diffraction and reciprocal space mapping. Certain features of the reflection were clearly present in all maps, albeit at much lower resolution in the Laue images due to the smaller sample to detector distance and hence lower angular resolution  (Fig. 4).
Figure 4: Detailed maps of a 311 reflection from a single grain within an Ni polycrystal after 9% plastic deformation. A) Micro-beam Laue orientation map. B) High angular resolution micro-beam Laue orientation map. C) Composite energy scanning micro beam orientation map. D) Reciprocal Space Mapping orientation map.
This suggests that an experimental setup combining both micro-beam Laue diffraction and white, pencil beam topography, would allow the measurement of both local lattice orientation and strain from the Laue image, as well as providing high angular resolution information of local lattice misorientation within the scattering volume, hinting at local dislocation arrangement. We have recently started the development of such a setup and collected some promising looking results, though the analysis is still under way (Fig. 5).
Figure 5: Overview of the novel combined white beam Laue/topography setup. 1. Imagestar - diffraction detector; 2. PCO - tomography camera; 3. Mini FDI - topography camera; 4. Photodiode - transmission point.
During the developments thus far, the incident beam was collimated using apertures of various sizes, in the most recent case down to a spot size of about 5 microns. The advantage of using a collimated rather than focussed beam is that the beam incident on the sample has very low divergence. This makes the topographs significantly easier to interpret, as any spreading out of the reflection can be directly linked to lattice rotation in the gauge volume. However, placing such a small aperture in the beam also means that efficiency of data collection is reduced, especially in the case of the Laue images and long counting times up to several minutes are required to achieve satisfactory statistics. A much more efficient procedure would be to use achromatic focussing optics, such as Kirkpatrick-Baez mirrors, to focus the incident beam to the desired small spot size on the sample, allowing much more rapid data collection at higher spatial resolution for the Laue images. Incorporating this into the present setup seems a logical next step for the further development of polychromatic micro diffraction on B16.
 A.M. Korsunsky et al., Intergranular stresses in polycrystalline fatigue: diffraction measurement and self-consistent modelling, Engineering Fracture Mechanics, 71:805 (2004).
 N. Tamura et al., Scanning X-ray microdiffraction with submicrometer white beam for strain/stress and orientation mapping in thin films, Journal of Synchrotron Radiation,10:137 (2003).
 R. Spolenak et al., Local Plasticity of Al Thin Films as Revealed by X-Ray Microdiffraction, Physical Review Letters, 90:096102, (2003).
 W.J. Choi et al., Structure and Kinetics of Sn Whisker Growth on Pb-free Solder Finish, Electronic Components and Technology Conference (2002).
 W.J. Choi et al. ,Tin whiskers studied by synchrotron radiation scanning X-ray micro-diffraction, Acta Materialia, 51:6253 (2003).
 R.I. Barabash et al., Quantitative characterization of electromigration-induced plastic deformation in Al(0.5wt%Cu) interconnect, Microelectronic Engineering, 75:24 (2004).
 R. Maass et al. ,Crystal rotation in Cu single crystal micropillars: In situ Laue and electron backscatter diffraction, Applied Physics Letters, 92:071905 (2008).
 R. Maass et al., Time-Resolved Laue Diffraction of Deforming Micropillars, Physical Review Letters, 99:145505 (2007).
 F. Hofmann et al., Probing intra-granular deformation by micro-beam Laue diffraction, Procedia Engineering,1:193 (2009).
 F. Hofmann et al. ,Synchrotron based reciprocal space mapping and dislocation substructure analysis, Materials Letters, 63:1077 (2009).
 F. Hofmann et al. Intragranular Lattice Misorientation Mapping by Synchrotron X-Ray Micro-Beams: Laue vs Energy-Resolved Laue vs Monochromatic Reciprocal Space Analysis, International Journal of Modern Physics B, 24:279–287 (2009).
Principal Publications and Authors
F. Hofmann, X. Song, I. Dolbnya, B. Abbey, AM. Korsunsky. Probing intra-granular deformation by micro-beam Laue diffraction. Procedia Engineering,1:193 (2009).
F. Hofmann, B. Abbey, X. Song, I. Dolbnya, AM. Korsunsky. Intragranular Lattice Misorientation Mapping by Synchrotron X-Ray Micro-Beams: Laue vs Energy-Resolved Laue vs Monochromatic Reciprocal Space Analysis. International Journal of Modern Physics B, 24:279–287 (2009).
This work was supported by Engineering and Physical Sciences Research Council, UK grants under the DTA scheme.
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