Fig. 1. Temporal evolution of (a) and (b) number density, Nt, (c) and (d) average radius, Ravg, and (e) and (f) volume fraction, $f_{t}^{\ {{\gamma }^{\prime }}}$, of γ′ precipitates in alloys (A) Ni-7.5Al-8.5Cr at.% and (B) Ni-5.2Al-14.2Cr at.% at 873 K isothermal ageing. The black dots correspond to the experimental data of Booth-Morrison et al. [16].

Fig. 2. Temporal evolution of the relationship between average radius, Ravg, and effective radius, ${{r}_{\text{eff}}}$(which can be seen equally as critical radius,${{r}^{*}}$), in the alloy (A) Ni-7.5Al-8.5Cr at.% at 873 K isothermal ageing.

Fig. 3. Time dependencies of (a) number density, Nt, and (b) average radius, Ravg, in alloy (A) Ni-7.5Al-8.5Cr at.% at 873 K isothermal ageing, after 104 s.

Fig. 4. Compositional trajectories of γ matrix and γ′ phase for alloys (A) Ni-7.5Al-8.5Cr at.% (red line) and (B) Ni-5.2Al-14.2Cr at.% (blue line) during isothermal ageing, in a partial Ni-Al-Cr ternary phase diagram at 873K, calculated by Thermo-Calc, employing the TCNi8 database. Two types of drawn equilibrium solvus curves are determined by Thermo-Calc utilizing databases from Saunders [28] (black dash line) and Dupin and Sundman [29] (gray line), respectively. The experimental APT data of compositional evolution in the γ matrix and γ′ phase for alloys (A) Ni-7.5Al-8.5Cr at.% (open red circles) and (B) Ni-5.2Al-14.2Cr at.% (open blue circles) are extracted from the work of Booth-Morrison et al. [16].

Fig. 5. Temporal evolution of compositions in γ matrix and γ′ phase for alloys (A) Ni-7.5Al-8.5Cr at.% (red line) and (B) Ni-5.2Al-14.2Cr at.% (blue line) at 873 K isothermal ageing. The equilibrium compositions at 873K for alloys (A) Ni-7.5Al-8.5Cr at.% (red short dash line) and (B) Ni-5.2Al-14.2Cr at.% (blue short dash line) are calculated by Thermo-Calc and TCNi8 database.

Fig. 6. Influence of compositional variation of Al on (a) number density, Nt, (b) average radius, Ravg, and (c) volume fraction, $f_{t}^{{{\gamma }'}}$, of γ′ precipitates as a function of time in the alloy (A) Ni-7.5Al-8.5Cr at. % at 873 K isothermal ageing.

Fig. 7. Influence of compositional variation of Al on (a) chemical driving force for precipitation, $\text{ }\!\!\Delta\!\!\text{ }G_{\text{V}}^{\ \gamma \prime }$, (b) nucleation barrier, $\text{ }\!\!\Delta\!\!\text{ }{{G}^{*}}$, and (c) nucleation rate, I, of γ′ precipitates as a function of time in the alloy (A) Ni-7.5Al-8.5Cr at.% at 873 K isothermal ageing. The inserted zoom shows the time points when nucleation finish and their positions on chemical driving force curves, for different Al content.

Fig. 8. Influence of modifying diffusion distance on (a) number density, Nt, (b) average radius, Ravg, and (c) volume fraction, $f_{t}^{{{\gamma }'}}$, of γ′ precipitates as a function of time in the alloy (A) Ni-7.5Al-8.5Cr at.% at 873 K isothermal ageing (traditional diffusion distance setting, $\partial $r?=?R: red lines, modified diffusion distance, $\partial $r?=?RV – R: blue short dot lines).

Fig. 9. Spatial distribution of precipitates and Voronoi cells within a 100 nm×100 nm×100 nm characteristic cell at different time points in the alloy (A) Ni-7.5Al-8.5Cr at.% at 873 K isothermal ageing (the compartmentalization of particle distribution can meet the criteria that each particle is within one Voronoi cell).