Strain tensor evaluation in polycrystalline materials by scanning high‐energy X‐ray diffraction

During the past 20 years, third-generation high-energy synchrotron sources have made possible the development of several diffraction-imaging methods, which have led to meaningful physical insights into the real structure and dynamics of bulk polycrystalline materials. A not exhaustive list could include work on stress corrosion cracking (King et al., 2008), predictions of crystal plasticity (Pokharel et al., 2014), stress variation in copper through-Si vias (Levine et al., 2015), martensitic transformation (Sedmák et al., 2016) and long-range symmetry breaking in embedded ferroelectrics (Simons et al., 2018). The pioneering work of Poulsen (2004) paved the way for the majority of the techniques using monochromatic radiation, commonly called three-dimensional X-ray diffraction (3DXRD) or high-energy diffraction microscopy (HEDM) (Suter et al., 2006). Since then, a wide variety of techniques have been developed, which are mostly classified on the basis of the distance between the detector and the specimen as (a) far-field or (b) near-field techniques. However, from the point of view of the final reconstruction describing the spatial distribution of the crystallographic orientation (implicitly the grain shape) and strain/stress, a classification based on their spatial and angular resolutions seems to be more appropriate. According to this ‘two-resolution criterion’, all existing techniques can be included in one of the following three categories: (a) High-spatialand low-angular-resolution methods use a near-field setup with a highresolution detector (effective pixel size of about 1 mm), closely placed downstream of the specimen at a distance of a few millimetres. Their angular resolution is relatively low ( 0.1 ), but they can resolve the structure at micrometre/sub-micrometre length scales over millimetre sample sizes. Grain and intragrain orientations are obtained via scans done with either a broad (Ludwig et al., 2008) or a planar beam (Li & Suter, 2013), the beam size being usually adapted to the grain size to avoid peak overlap. (b) Low-spatialand high-angular-resolution methods involve a low-resolution detector with a pixel size of about 50–200 mm placed in the far field ( 0.2–1 m as a function of the pixel size and beam energy). Since diffraction peak positions can be determined with sub-pixel accuracy (Borbely et al., 2014), this setup has high angular resolution (<0.01 ) that allows the elastic strain to be determined. However, the grain shape remains unknown. Measurements are usually performed with a broad beam. (c) Finally, high-spatialand high-angular-resolution methods enable characterization of both the crystallographic orientation and the strain inside single grains at submicrometre length scales, even for deformed materials. It is expected that these ‘holy grail’ methods will provide the missing local experimental evidence for understanding unsolved problems in materials science such as polycrystal plasticity, recrystallization and damage initiation. There are already two methods achieving high spatial and high angular resolution: differential-aperture X-ray microscopy (DAXM; Larson et al., 2002) and dark-field X-ray microscopy (DFXM; Simons et al., 2015). The first uses a polychromatic pencil beam with sub-micrometre cross section for identifying the local orientation from the resulting Laue pattern and an additional energy scan (Chung & Ice, 1999) for strain determination. DFXM uses monochromatic radiation and compound refractive lenses in the diffracted beam, which magnify a small diffractive volume of the analyzed grain/ subgrain. To improve the spatial resolution of the low-spatialand high-angular-resolution methods, Hayashi et al. (2015) proposed a ‘scanning 3DXRD’ approach, using a monochromatic pencil beam, where the spatial resolution could be controlled by the beam size. Combining a lateral scanning of the sample and a tomographic approach (rotation ISSN 1600-5767