Extended Data Figure 7: 3D precision estimation for atomic coordinate measurements and 3D identification of anti-phase boundaries.

a, By comparing the measured atomic coordinates with an ideal fcc FePt lattice and using a cross-validation (CV) method⁵⁰, we estimated an average 3D precision of 21.6 pm for all the atoms, which agrees well with the multislice result (22 pm). The CV score was computed by using half of the randomly selected atomic sites to fit the lattice and then measuring the fitting error of the remaining half of the atomic sites. The results of this error metric are shown in the upper panel as a function of the number of variables used to fit the lattice. This value reaches a minimum where the lattice fitting function is neither over- nor under-fit. The resulting position error was estimated by using all sites to fit a lattice using the minimum-CV number of fitting variables, shown in the lower panel as the displacement (root-mean-square fitting) error. b, 3D atomic positions (Fe, red; Pt, blue) overlaid on the 3D reconstructed intensity for an anti-phase boundary (white dashed lines) between two L1₂ FePt₃ grains. The arrows indicate two anti-site point defects. The background colours of red, yellow and blue correspond to high, medium and low intensity, respectively.