Extended Data Fig. 7: Statistics for La atoms and the estimation for uncertainty.

a, Projected MEP image presented in the gray scale. b, Linecut along the blue curve in a. The peaks correspond to La atoms, which is assumed to be free from defects. The spatial fluctuation along the line represents the uncertainty in phase. c-e, Histogram for the phases of La and outer apical O from the region with δ = 0.04 ± 0.11 (c), δ = 0.17 ± 0.12 (d) and δ = 0.34 ± 0.22 (e), respectively. The phase values are normalized to the average phase of La atoms, as described in Methods, with the mean value and standard deviation labeled in each panel. The phases of outer apical O are identical within experimental uncertainty, so we can safely neglect the vacancies on this site. Besides, the estimated uncertainty in phase is around 7% for O and around 4% for La.