Fig. 3. Phase structures (before and after fatigue).

a Low-magnification cross-sectional STEM-HAADF image of virgin HZO thin film (left panel). The framed yellow dashed rectangle is the oxygen vacancy penetration zone (~150 nm). The right-hand panel shows the simulated atomic structure for the [010]-Pca2₁ phase. b, c STEM-iDPC images of the O phases beyond and within the penetration zone framed in a, respectively. d, e Line scans over the rows of the oxygen columns framed in b, c, respectively. The dashed lines represent the intensities of the reference fully O-occupied columns, and the peak intensities that are lower than the reference line in e indicate the appearance of random oxygen vacancies at the O₅ and O₈ sites. f STEM-iDPC image of the [010]-oriented Pca2₁’ phase after fatigue. The inset in the top-left corner shows the simulation of this phase. g, h Two line scans of the atomic columns within the dashed rectangles framed in (f). Periodic changes in the oxygen intensities that deviate from the reference full-O dashed lines at the O₂, O₄ and O₅ sites consistently implies the appearance of ordered oxygen vacancies when measured along two different $\left(\left[10\overline{1}\right]\mathrm{and}\left[\overline{1}0\overline{1}\right]\right)$ directions.