Fig. 2: Observation of V_O channels and the compositional phase transition point in BCFO films.

a Schematics of three types of oxygen ion migration in 2D potentials. Oxygen ions avoid residing on the 1D atomic-scale channels because the potential therein is not relatively deep. Ionized V_Os are mainly present in the channel regions, which offer more positive potential in a self-consistent way. Free energy landscapes over the ionic configuration indicate competition between two types of channels along [100] or [110]. Configuration fluctuations can be significantly large at the phase transition point, leading to enhancement of generalized susceptibilities such as elastic compliance and ionic conductivity. b, c Representative ABF-STEM images along [010] ([\(\bar{1}\)10]) in the V_O layers present in BCFO (x_Ca = 0.3, 0.45 and 0.6), and corresponding intensity line profiles. The intensity line profiles averaged over 15 pixels were extracted from the ABF-STEM images along the [100] ([110]) direction, i.e., across the Fe/O–O atomic columns. The black arrows in b indicate that the intensity of the oxygen atomic columns is not uniform, instead V_O ordering is observed. The black arrows in c show that the Fe–Fe distances are not uniform; instead two clearly different Fe–Fe distances alternate along the [110] direction. The Fe–Fe distances are 0.24 ± 0.02 and 0.33 ± 0.02 nm for the x_Ca = 0.6 phase, and 0.27 ± 0.01 and 0.30 ± 0.01 nm for the x_Ca = 0.3 and 0.45 phases. d Schematics of the atomic configuration of the BCFO films with V_O channels.