Scanning 3DXRD Measurement of Grain Growth, Stress, and Formation of Cu6Sn5 around a Tin Whisker during Heat Treatment

Abstract

The 3D microstructure around a tin whisker, and its evolution during heat treatment were studied using scanning 3DXRD. The shape of each grain in the sample was reconstructed using a filtered-back-projection algorithm. The local lattice parameters and grain orientations could then be refined, using forward modelling of the diffraction data, with a spatial resolution of 250 nm. It was found that the tin coating had a texture where grains were oriented such that their c-axes were predominantly parallel to the sample surface. Grains with other orientations were consumed by grain growth during the heat treatment. Most of the grain boundaries were found to have misorientations larger than 15∘, and many coincidence site lattice (CSL) or other types of low-energy grain boundaries were identified. None of the grains with CSL grain boundaries were consumed by grain growth. During the heat treatment, growth of preexisting Cu6Sn5 occurred; these grains were indexed as a hexagonal η phase, which is usually documented to be stable only at temperatures exceeding 186 ∘normalC. This indicates that the η phase can exist in a metastable state for long periods. The tin coating was found to be under compressive hydrostatic stress, with a negative gradient in hydrostatic stress extending outwards from the root of the whisker. Negative stress gradients are generally believed to play an essential role in providing the driving force for diffusion of material to the whisker root.

Three-dimensional reconstruction of intragranular strain and orientation in polycrystals by near-field X-ray diffraction

“…A robust, although time-consuming, technique for the local measurement of intra-granular strains in the bulk at micrometre spatial and 10 −4 strain accuracy is Differential Aperture X-ray Microscopy (DAXM) (Larson et al, 2002;Levine et al, 2006;Robach et al, 2013;Tardif et al, 2016) [32,33,34,35], a variant of polychromatic X-ray Laue micro-diffraction. More recently, using monochromatic micro-beam scanning, a far-field detector and an established 3DXRD indexing procedure (ImageD11) (Wright, 2017) [36], Hektor et al has shown local sensitivity of the method to hydrostatic strain (Hektor et al, 2019) [37], and Hayashi et al has demonstrated mapping the full strain tensor over a region containing 37 3 voxels at 1.2 µm spacing deep inside a steel specimen (Hayashi et al, 2019) [38]. Simons et al, 2018) [39,40,41].…”

“…In the monochromatic scanning method in (Hektor et al, 2019) [37] and (Hayashi et al, 2019) [38], the 2D deformation reconstruction problem is circumvented and reduced to an indexing problem. The local strain values represent a weighted mean of the total volume contributing to the indexed reflections for one voxel.…”

Intragranular strain estimation in far-field scanning X-ray diffraction using a Gaussian process

“…This tool has been used with success in the past (cf. Hektor et al, 2019;Henningsson et al, 2020) and can provide an understanding of the limitations and benefits of scanning 3DXRD reconstruction methods. Briefly, the simulation input is specified as a set of cubic single-crystal voxels featuring individual strains and orientations together with an experimental setup.…”

“…Initially, Hayashi et al (2015Hayashi et al ( , 2017 proposed a method for a per-voxel strain refinement to approximate intragranular strains using scanning 3DXRD data. Unfortunately, this procedure was shown to introduce bias in the reconstruction related to strain state (Hayashi et al, 2019;Hektor et al, 2019). These obstacles were later overcome by Henningsson et al (2020), who proposed an inversion method that takes the tomographic nature of the problem into account.…”

In situ 4D mechanical testing of structural materials: The data challenge

“…Point scanning techniques using a focused X-ray beam such as DAXM [27] have been the most capable technique to perform elastic strains mapping [28] but remain limited to small volume close to the specimen surface. More recently, the scanning 3DXRD modality, first introduced by Hayashi [29], allowed to characterize local strains at sub-micrometre length scales [30,31]. The method was further refined by Hektor et al [32] using forward simulation to improve its sensitivity.…”