Fig. 1: The structure and atomic arrangement of the TCP phases and the intrinsic defect, the faulted twin boundary (FTB).

a A HAADF image (left, [1-11] zone axis), in direct comparison with the schematic (right) of μ phase with seven nonequivalent (110) layers. Note that the hexagonal description is also often used for the rhombohedral μ phase. Some typical plane/orientation relationships are: (110) corresponds to (1-12)^H, [1-11] corresponds to [42-1]^H, and [1-10] corresponds to [110]^H. Please refer to Supplementary Fig. 1 for details. b The left panel displays the experimental HAADF image of the [1-11] projection of (110) FTB; the inset displays the simulated HAADF image together with the schematic of the interface structure TS_[001]-5. c The HAADF image (left) of (110) FTB observed along [1-10]_μ and simulated HAADF images (right) of TS_[001]-5 along this axis. d The HAADF image ([1-10] zone axis) of the μ phase, showing pentagonal configurations. e The projected atomic arrangement of μ phase and the TS_[001]-5 along [1-10]_μ in which the pentagonal anti-prism structures are highlighted. f The HAADF image and the schematic of the P phase and μ phase, projected along [011]_P and [1-11]_μ, respectively; the boundary plane marked by orange dotted line between the two phases is (110)_μ, parallel to (100)_P. The white framed box marks the unit cell of the P phase. The lower left corner inset displays the bright-field TEM micrograph and the corresponding SAED patterns of the two phases.