Fig. 1 a SEM image of the crept Ni-based SX superalloy, b magnified image corresponding to the area of the white frame in a

Fig. 2 a Bright-field TEM micrograph of σ phase and γ' phase. The interface is marked by the dotted white line, b SAED patterns of σ phase and γ' particle in a, c, e the HAADF micrographs for σ phase with the different orientations of [110]σ and [$4{\bar{\text{1}}}0$]σ, respectively, d, f FFT patterns of c and e, g model of σ phase with specified planes and directions highlighted in different colors, h schematic representation of the overlaid top view projection of the (001)σ plane onto the ($1{\bar{\text{1}}}1$)γ’ plane, revealing the orientation relationship (001)σ//($1{\bar{\text{1}}}1$)γ'

Fig. 3 Crystal structure and interface models of σ phase. a Ternary σ phase with 30 atoms distributing at 5 non-equivalent positions (2a, 4f, 8i1, 8i2, 8j). Different colors are employed for the purpose of distinguishing the three constituent elements comprising the ternary σ phase, b σ phase atomic structure with the alternating stacking of four atomic layers. Corresponding atomic structure is shown on the right, c four distinct (001)σ surface models are named by 001-1, 001-2, 001-3, 001-4, based on their respective contact atomic layers with the matrix phase

Fig. 4 Occupation tendency of elements in the σ phase. a Element distributions in the two σ phases. Scale bar: 1 nm, b the energy trend of W element at different sites in σ phase, c distribution of W in atomic models viewed along [110]σ and [$4{\bar{\text{1}}}0$]σ. Scale bar: 0.5 nm

Fig. 5 Different termination types of σ/γ' interface. a, c T1 type of σ/γ' interface, b, d T2 type of σ/γ' interface. The orientation relationships between σ and γ' in (a, b) and (c, d) are [110]σ//[110]γ' and [$4{\bar{\text{1}}}0$]σ//[011]γ', respectively, e HAADF images and corresponding simulated HAADF images for different termination interfaces (T1 and T2) viewed along [110]σ axis, f σ phase interfacing with γ' by two termination types, accompanied by two thickening steps, viewed along [110]σ//[110]γ', g σ phase interfacing with γ' phase by two termination types, accompanied by one thickening step, viewed along [$4{\bar{\text{1}}}0$]σ//[011]γ'

Fig. 6 Four distinct interface types accompanied by their corresponding work of separation and interface energy. a Lower half of each interface corresponds to the σ phase, which exhibits two distinct (001)σ surface types, namely T1 (001–1/4) and T2 (001–2/3) and two atomic coordination types, namely fcc and top, b work of separation of four possible interfaces formed by the orientation relationships (001)σ//($1{\bar{\text{1}}}1$)γ, c interface energy of four possible interfaces

Fig. 7 EDS mappings of σ/γ' interfaces, with orientation relationships between σ and γ' as a [110]σ//[110]γ' and b [$4{\bar{\text{1}}}0$]σ//[011]γ', respectively

Fig. 8 Effect of different Co contents on interfacial stability

Fig. 9 Differential charge density images of the σ/γ interfaces with/without Co segregation on the interface. The cross-section (110)σ//(11${\bar{\text{2}}}$)γ is selected here for the analysis. a Charge density images for 001–1-top interface viewed along [011]γ. σ/γ interfaces with no Co coverage and with full Co coverage are given at the right for comparison, b charge density images for 001–3-fcc interface viewed along [011]γ. σ/γ interfaces with no Co coverage and with full Co coverage are given at the right for comparison