Fig. 3. 3D microstructure models from 2D EBSD maps.

a EBSD β-Sn orientation map with IPF-X colouring of a typical beachball microstructure with three twinned β-Sn grains whose 3D boundaries intersect the EBSD cross section forming near-linear 2D trace vectors A and B. b A stereogram plotting the 2D trace vectors A and B from (a) with respect to the β-Sn orientations on either side of Sn-Sn boundaries. The four datapoints (A1, A2, B2 and B3) are repeated 8 times according to the 4/mmm point group symmetry of β-Sn. c Summary of 82 IPF-trace vectors measured from 29 solder joints showing that macroscopic beachball grain boundaries are approximately {101}Sn planes. d A 3D digital model of the microstructure assuming that (a) was polished to the centre of the joint and that {101}Sn beachball boundaries emanate from a point where the common 〈010〉 twin axis touches the intermetallic reaction layer (the top side here). The 3D viewing direction in (d) is close to the 〈010〉 twin axis.