Fig. 3: Atomic scale electron microscopy characterization to explain the recovered mobility of entropy-engineered thin films.

a Schematic of the possible mechanism of electron scattering and localization in Ti-displaced TiO₆ octahedrons. C point marked is the center of the TiO₆ octahedron, and the length of Ti displacement is the length of C-Ti. b, c SAED patterns along [110] to prove the absence of octahedron tilting in SBLTO and SBCPLTO. d–f ABF images in the atomic resolution after filtering to show the Ti displacement in SBLTO (d), SBCLTO (e), and SBCPLTO (f). The orange scale bar denotes 5 Å. The orange, red, and blue spheres represent A-site atoms, O, and Ti, and the overlapped spheres were omitted. g The relation between room temperature weighted mobility (μ_W) and average normalized Ti displacement (\({\bar{d}}_{{{\rm{Ti}}}}\)) of SBLTO, SBCLTO, and SBCPLTO with increased entropy. The displacement was normalized by the ratio d_Ti = length(C-Ti)/length(C-O_b) in (a). The error bar is the standard deviation δ_d. The blue and red arrows are the guides to show the trends of weighted mobility and displacement. The details of the analysis and results can be found in supplementary materials.