Fig 1.
(a) TKD IPF map of the Al bi-crystal atom probe specimen. (b) Unique grain color quick map. (c) IPF-X with crystallographic direction along x-axis plotted. (d) Orientation unit cell and Bunge-Euler notation of grains with TKD detector frame.
Fig 2.
(a) FDM of experimental APT data of Al bi-crystal with crystallographic patterns indexed. (b) Al-density map of reconstruction, ≈ 1.2 nm thick, through the centre of the reconstruction on the YZ-plane. (c) Stereographic projection representation of the two grains, showing low index poles and zone-lines, colored corresponding to the IPF-Z. (d) The orientation cells and Bunge-Euler notation within the APT detector frame.
Fig 3.
The experimentally informed simulation setup for direct comparison with experiment.
Fig 4.
Grain boundary is observed in a series of detector hit map images.
The goal is to follow the movement of grain boundary and reconstruct it in 3-D Cartesian space.
Fig 5.
A flowchart of the BooT-PCA on an aluminum bi-crystal dataset: Firstly, image processing is performed on a series of detector hit maps, secondly tracking and line detection are performed.
Next the collected data is reconstructed into 3D Cartesian coordinates, thirdly, a slope filter, PCA and triangulation (consists of mesh vertices) are applied sequentially to filter out zone lines atoms and fully reconstruct the GB surface.
Fig 6.
Principle of the boosting tracker: At each frame, positive and negative samples are collected and fed into the boosting algorithm to create a strong classifier, then the classifier predicts the position of the target in the next frame.
(Xn, 1/0) indicates group n that contains either positive (1) or negative (0) samples.
Fig 7.
(a) A tracking window is user-defined (dotted black rectangle); Hough transformation detects all the features within the frame; Dotted white lines indicate the detected grain boundary and black dotted lines indicate the zone lines. (b) Direct 3D reconstruction is performed based on the coordinates in (a); Blue points represent the atoms whereas red represent the extracted ‘GB’ points. (c) Refined 3D reconstruction with the slope filter. (d) After the slope filter is implemented, the lines with slope smaller than 2 are removed.
Fig 8.
Visualization of GB atoms and principal components.
(a) Front view of GB atoms, first and second principal vector are plotted, on this two components the variance are the highest. Additionally some GB atoms are missing mainly due to the limited size of tracking window. (b) Side view of GB atoms, a few zone line atoms can be seen as well.
Fig 9.
(a) TAPSim specimen geometry. The grain boundary normal is set to nh (Eq 1). (b) Reconstruction from TAPsim detector hit map using BooT-PCA.
Fig 10.
TAPSim-based detector hit map: The lines detected (shown in white) are quasi-linear local ion density fluctuations which the Hough transform picks up.
These are affected by the geometry, e.g. the thickness of the boundary, the atomic structure of the adjoining crystals, and known TAPSim field evaporation artifacts [11].
Fig 11.
Visualization of GB atoms and surface after the PCA; Red and blue dots indicate the GB atoms and non-GB atoms respectively.
(a) Front view of GB surface. (b) Side view of GB surface. It can be observed that the surface is not perfectly flat. (c) Mass spectrum of the GB, the majority of ions are Al2+ or Al+; In contrast to the spectrum of the bulk, the peak of O+ is absent.