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· The nucleation and transition sequences of TCP phases in a Re -containing Ni-based single crystal superalloy were investigated. · The σ and P phases coherently nucleated at the γ/γ′ interface near the γ matrix side at the initial stage of heat-exposure at 1100 °C. · The TCP phase ultimately existed as the most stable μ phase during heat-exposure at 1100 °C. · The transition sequences of the TCP phase were classified as: γ matrix→σ→μ, γ matrix→P→μ, and γ matrix→σ→P→μ. The nucleation and transition sequences of topologically close-packed (TCP) phases in a Re -containing Ni-based single crystal superalloy were systematically investigated using in-situ transmission electron microscopy (TEM) and three-dimensional atom probe technology (3D-APT). During the initial stage of heat-exposure at 1100 °C, the TCP phase forming elements (Re , Co, Cr, etc.) segregated at the γ/γ′ interface near the γ matrix side to provide the concentration undulations for the nucleation sites of TCP phases, following which the σ and P phase coherently nucleated along the (1 11 ‾) γ and (022) γ planes from the γ/γ′ interface near the γ matrix side, respectively. With prolonged heat-exposure time, transitions from σ phase to P phase, σ phase to μ phase, and P phase to μ phase occurred. Besides, the orientation relationships of TCP phase intergrowth structures indicated that the P phase grew along the (1 ¯ 01) σ plane of the σ phase by co-lattice precipitation, meanwhile, the µ phase grew with smaller lattice misfits along the (0 4 ¯ 0) σ plane of the σ phase and the (400) P plane of the P phase. Additionally, the result by first-principles calculation evidenced that the μ phase had the lowest system energy to make the transition of σ phase and P phase to μ phases inevitable, therefore, the TCP phase ultimately existed as the most stable μ phase. Finally, the transition sequences of TCP phase during heat-exposure could be summarized into three types: γ matrix→σ→μ, γ matrix→P→μ, and γ matrix→σ→P→μ. [Display omitted] [ABSTRACT FROM AUTHOR]