## 3 Results and Discussions
### Creep Behaviors  
Figure 3 shows the creep curves of the alloys obtained under the conditions indicated. The 0.09 Hf alloy shows the longest creep life under the condition of 650 \({}^{\circ}\)C/60 MPa while the 0.33 Hf alloy showed the longest life under the condition of 700 \({}^{\circ}\)C/30 MPa. A clear stress dependence was found, as seen in a Larson-Miller-type plot for the present results in Figure 4; the 0.09 Hf alloy shows the longest creep life at higher stress conditions whereas the 0.33 Hf alloy shows the longest creep life at lower stress conditions. The creep data are summarized in Table 2.  
Figure 3: Creep curves of the alloys tested under creep conditions of (**a**) 650 \({}^{\circ}\)C/60 MPa [11] and (**b**) 700 \({}^{\circ}\)C/30 MPa.  
Figure 2: Electron backscatter diffraction (EBSD) inverse pole figure maps of the alloys for creep tests: (**a**) 0.03 Hf alloy, (**b**) 0.09 Hf alloy, (**c**) 0.33 Hf alloy. The orientations are indexed by \(\alpha\)-ferrite (body-centered cubic structure). Black lines denote boundary level above 15\({}^{\circ}\) and yellow lines, boundary level between 2\({}^{\circ}\) and 15\({}^{\circ}\).  
The creep behaviors were analyzed in detail using the creep rate vs. time curve diagrams, which are displayed in logarithmic time scale and linear time scale in Figures 5 and 6, respectively. The transient creep rates of the 0.03 Hf and 0.33 Hf alloys are similar, but the rate of the 0.09 Hf alloy is about a half of the former alloys under the creep conditions (see Figure 5). The minimum creep rate is the lowest in the 0.09 Hf alloy under the two conditions. The alloys show weak acceleration regimes after reaching their minimum creep rates (see Figure 6). The duration of the weak acceleration regime is longer in the 0.33 Hf alloy than in the 0.03 Hf alloy at the higher stress condition, which leads to a longer creep life in the former alloy, in spite of their similar minimum creep rates (see Figures 5a and 6a). The duration of the weak creep acceleration in the 0.33 Hf alloy is even longer than that in the 0.09 Hf alloy under the lower stress condition, which leads to the longest creep life among the alloys (Figure 6b).  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Sample**} & **Creep** & **Time to** & **Strain to** & **LMP** \\  & **Condition** & **Rupture or** & **Rupture/\%** & **(C = 25)** \\  & **Temp/Stress** & **Interrupt/h** & **Rupture/\%** & \(\times\) **10\({}^{-3}\)** \\ \hline \multirow{3}{*}{0.03 Hf} & 650 \({}^{\circ}\)C/60 MPa & 280.7 & 23.0 & 25.3 \\  & 700 \({}^{\circ}\)C/40 MPa & 140.9 & 17.9 & 26.4 \\  & 700 \({}^{\circ}\)C/30 MPa & 534.6 & 26.3 & 27.0 \\ \hline \multirow{3}{*}{0.09 Hf} & 650 \({}^{\circ}\)C/60 MPa & 240.0 1  & - & 25.3 \\  & 650 \({}^{\circ}\)C/60 MPa & 3104.1 & 29.7 & 26.3 \\  & 700 \({}^{\circ}\)C/30 MPa & 813.7 & 24.6 & 27.2 \\ \hline \multirow{3}{*}{0.33 Hf} & 650 \({}^{\circ}\)C/60 MPa & 240.0 1  & - & 25.3 \\  & 650 \({}^{\circ}\)C/60 MPa & 1495.8 & 57.4 & 26.00 \\ \cline{1-1}  & 700 \({}^{\circ}\)C/40 MPa & 313.8 & 67.0 & 26.8 \\ \cline{1-1}  & 700 \({}^{\circ}\)C/30 MPa & 934.7 1  & - & 27.2 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Summary of creep data obtained in the present study.  
Figure 4: Stress vs. Larson-Miller parameter plot (LMP) for creep rupture time in the alloys tested under the creep conditions indicated. LMP is a parameter to describe the equivalence of time, expressed by T (log\(t\) + C) where T is the creep test temperature, \(t\) is the time to rupture. C is a constant (25 is taken here).