Fig. 1. Evolution of microhardness as a function of aging time for the Ni50Ti30Hf20 alloy aged at 450, 550, and 650 °C.

Fig. 2. A series of TEM images of Ni50Ti30Hf20 alloy aged at different regimes and the corresponding precipitate size distribution histograms. Bright-field TEM of samples aged at 650 °C for 6 min (a, b), 30 min (c) and 1 h (e). Bright-field TEM of samples aged at 450 °C for 3 h (f, g) and 10 h (j). SAED pattern taken from 10 h aged sample at 450 °C with reflects of H-phase (k). (d, h, i, l) The corresponding precipitate size distribution histograms.

Fig. 3. Typical STEM-HAADF images of Ni50Ti30Hf20 alloy aged at 650 °C for 15 min (a), 550 °C for 3 h (b) and 450 °C for 50 h (c). The insets in (a-c) show the volume fraction distribution histograms. Evolution of surface area fraction of the H-phase in the polycrystalline matrix of Ni50Ti30Hf20 alloy for the aging temperatures ranging from 450 °C to 650 °C (d) and the temperature dependence of the volume fraction of the H-phase at thermodynamic equilibrium state (e). Note: in figure volume fraction presented in% while all calculations were carried out in relative parts.

Fig. 4. (a) Determination of n and k parameters of the Johnson-Mehl-Avrami-Kolmogorov equation where n corresponds to the slope of the ln(ln(1/(1-f)) versus ln(t) plot while k can be calculated from the intercept. (b) Evolution of n parameter as a function of temperature.

Fig. 5. Arrhenius plots of ln(k) vs. 1000/T for the precipitation kinetics of H-phase in Ni50Ti30Hf20 alloy.

Fig. 6. TTT diagrams of NiTiHf alloy where the red line represents the solvus temperature of the H-phase. (a) TTT diagram where the gray lines mark the beginning, middle and end of H-phase precipitation. (b) TTT diagram showing the volume fractions of H-phase at different time and temperatures. Solid lines represent JMAK model within the considered temperature range and dash lines represent the extrapolated data.

Fig. 7. (a) Temporal evolution of average length and width of H-precipitate of NiTiHf alloy during isothermal aging at 450, 550 and 650 °C. (b) Plots of ln(r) vs. ln(t) for isothermal aging temperatures giving temporal growth exponent of H-precipitates, which corresponds to classical LSW growth exponent. (c) Plots showing linear fit of radius equivalent size of H-phase precipitate (r3 in nm3) vs. aging time (t) during isothermal aging at 450, 550 and 650 °C along with respective LSW rate constant..

Fig. 8. Plot between the coarsening rate constant (ln(Kr,T) vs. inverse of heat-treatment temperature (1000/T) with linear fit using linear regression analysis to calculate activation energy (QCoarsening).

Fig. 9. Evolution of critical size of H-phase precipitates as a function of temperature.

Fig. 10. HRTEM images and corresponding FFT patterns of NiTiHf alloy after 30 min (a, b) and 1 h (c, d) at 650 °C.

Fig. 11. The gain in hardness (∆HV) as a function of $f_{\text{t}}^{0.5}{{L}^{0.5}}$ (a) and $f_{t}^{0.5}/L$ (b). The insets in (a) and (b) show the temperature dependence of Ccut and Cb constants, respectively.

Fig. 12. (a) Data from the present study for Ni50Ti30Hf20 alloy compared with the model of Eq. (11). (b) TTH diagrams of aged Ni50Ti30Hf20 alloy.

Fig. 13. Evolution of Mp temperatures as a function of aging time for Ni50Ti30Hf20 alloy (a) and the influence of volume fraction (b) and size (c) of H-phase on ∆Mp temperature.