Alinger’s results indicate that the mechanically alloyed powder annealed at 700 °C shows the smallest radius and highest density in Y-Ti complex oxide particles,8 as shown in Figure 1. Considering that

Y2O3 particles are decomposed during MA, subsequent annealing results in the formation and precipitation of Y—Ti complex oxide particles at elevated temperatures of 700 °C or higher. Since the reverse transformation of a-g-phase takes place at a temperature over 850 °C, which is higher than the precipitation temperature of Y-Ti complex oxide particles, it is possible that the retention of the residual a-ferrite can be attributed to the presence of Y-Ti complex oxide particles in 9Cr-ODS steels. These particles could block the motion of the a-g interface, thereby partly suppres­sing the reverse transformation from a — to g-phase. This section presents a quantitative evaluation of this process.

The chemical driving force (AG) for the reverse transformation from a — to g-phase in the Fe-0.13C — 2W-0.2Ti system without Y2O3, can be evaluated in terms of Gibbs energy versus carbon content curves at each temperature. These curves were derived using the Thermo-Calc code and the TCFE6 database. The result of the calculation is presented in Figure 8.22,23 The peak value of the driving force for the reverse transformation from a — to g-phase reaches 4 MJ m— at 1000 °C in the case of 0.13 wt% C.

The pinning force (F) against the motion of the a-g interface can be expressed as the following equation, which was derived from the modified Zener equation of Mishizawa et a/.24

8r

where, s(Jm—2) is the interfacial energy between a — and g-phases, and its value was selected to be 0.56J m—225 The character r represents the radius of the oxide particles (m) in the a-phase; its value was determined as 1.5 nm by using TEM observation. The character fp represents the volume fraction of dispersed oxide particles (—), and was derived on the basis of the experimental evidence that oxide particles consist of Y2Ti2O7. By substituting these values into the afore­mentioned equation, the value of pinning force F was determined for 0.1, 0.35, and 0.7 wt% Y2O3, which are also shown in Figure 8.2 , The value of F increases with the amount of Y2O3 added according to the relation off2=3.

The velocity of the a-g interface motion (v) is proportional to the difference between Fand AG, as shown in the following equation:

v = M(AG — F). [4]

M is the mobility of the interface. AG and F are competitive, and AG > Findicates a positive velocity for the interface motion, that is, the reverse trans­formation from a — to g-phase. On the other hand, AG < F indicates that the a-g interface can be

Figure 9 Formation process of residual ferrite in 9Cr-ODS steel (Fe-0.13C-2W-0.2Ti-0.35Y2O3). Reproduced from Yamamoto, M.; Ukai, S.; Hayashi, S.; Kaito, T.; Ohtsuka, S. Mater. Sci. Eng. A 2010, 527, 4418-4423.

pinned by oxide particles so that the a-phase is, thus, retained. The results of the calculation shown in Figure 822 reveal that in the case of Y2O3 con­tents of 0.35 and 0.7 wt%, the pinning force is larger than the driving force for 0.13 wt% C. These results are reasonably consistent with our observation of the retainment of residual ferrite during a—g reverse transformation.

On the basis of the aforementioned discussion, the formation process of the residual ferrite in Fe-0.13C — 2W-0.2Ti-0.35Y2O3 is schematically illustrated in Figure 9. At the AC1 point, the carbide begins to decompose, and a—g inverse transformation takes place in the area of higher carbon content around the decomposed carbide, where the driving force of the reverse transformation exceeds the pinning force because the carbon content may be >0.2 wt% (see Figure 8). The g-phase could be enlarged by these processes. Approaching the AC3 point, the matrix carbon content achieves equilibrium at 0.13 wt%, where the pinning force (0.35Y2O3) exceeds the driving force (0.13C), and the velocity of the a—g interface motion is markedly reduced due to dragging by the oxide particles. Thus, the a-ferrite could be retained even beyond the AC3 point.