Fig. 4: TTCG model for multi-element oxides.

a Structure models of CoFe2O4 and MnxFeyCo3-x-yO4. Metal ions occupy the centers of tetrahedrons or octahedrons sites surrounded by oxygen atoms. Dashed rectangles represent unit cells. b Total ∆E with and without circumstance correction terms for CoFe2O4 with different orientations based on the TTCG model. Red triangles indicate the lowest energy. c, d Top-view STEM-ADF images of CoFe2O4 (c) and MnxFeyCo3-x-yO4 (d) nanoflakes, inserted with corresponding projected atomic models along the [111] orientation. The orange, purple, and blue spheres represent O atoms, octahedral sites, and tetrahedral sites, respectively. Inset shows the corresponding FFT pattern, indicating the [111] orientation. e Energy-dispersive X-ray spectroscopy (EDS) elemental mapping images of ultrathin MnxFeyCo3-x-yO4 alloy. Scale bars: c, d 0.5 nm; e 1 nm.