## 3 Results and Discussion
However, no Laves phase was found in the 9 Cr steels during creep-fatigue at 550 \({}^{\circ}\)C. The selected area diffraction patterns indicated Cr\({}_{23}\)C\({}_{6}\) carbide and NbC carbide. The number of precipitates was measured by image software for the 10 micrographs. The study of particle effects on the magnetic properties of steels is complicated by the inhomogeneous distribution of some precipitates, which preferentially nucleate on grain boundaries, and also due to the ferromagnetic nature of Fe\({}_{3}\)C and some other carbides below their Curie temperatures. Figure 4 shows the relation between dynamic coercivity and the number of precipitates of each sample. Figure 3: Transmission electron microscopy (TEM) micrographs showing the variation in precipitates morphology of 600 s hold time; (**a**) 0.1N\({}_{f}\), (**b**) 0.2N\({}_{f}\), and (**c**) 1N\({}_{f}\). Figure 2: Transmission electron micrographs at each fatigue damage fraction of 600 s hold time showing dislocation substructures and precipitates; (**a**) as-tempered, (**b**) 0.2N\({}_{f}\), (**c**) 1N\({}_{f}\), (**d1**) selective area diffraction (SAD patterns of Cr\({}_{23}\)C\({}_{6}\) and (**d2**) SAD patterns of NbC. The nonlinear curve fits with the allometric model. The dynamic coercivity is closely related to the number of Cr\({}_{23}\)C\({}_{6}\) precipitates (\(N^{0.8}\)) having a correlation coefficient of 0.85. In this study, the primary precipitates are the M\({}_{23}\)C\({}_{6}\) and (Nb,V)C carbides in the ferritin 9 Cr steel, which are analyzed by the SEM and TEM. Even though the (Nb,V)C carbide does not noticeably change due to being very stable at high temperature, the M\({}_{23}\)C\({}_{6}\) carbide is slightly changed during the creep-fatigue test. Therefore, this M\({}_{23}\)C\({}_{6}\) carbide possibly acts as an obstacle to the Bloch wall pinning site. [PERSON] et al. calculated the area variation of the boundaries due to the pinning effect of the inclusion. They proposed an analytical expression for the interaction potential between 180 Bloch walls and nonmagnetic obstacles such as precipitates and pores. The energy per area of the wall boundary is associated with each pinning center. The coercive field is as the following equation [15]. \[H\mathrm{c}=K\bigg{(}\frac{\pi\omega_{0}R}{2\mu_{0}M_{\mathrm{s}}}\bigg{)}N^{ 2/3}\]  
where K = 1.09, \(\sigma_{0}\) is energy surface density, \(R\) is the radius of the nonmagnetic particle, \(\mu_{0}\) is the permeability of free space, \(M_{\mathrm{s}}\) is the magnetization of the saturated state, and \(N\) is the particle concentration of pinning center. In this study, the Cr\({}_{23}\)C\({}_{6}\) and MX precipitates are nonmagnetic particles and can be considered as pinning obstacles to the 180 Bloch wall movement in 9 Cr ferritic steel. The MX type precipitates are very stable at this test temperature due to their high-temperature stability. Therefore, there are no changes in size and volume fraction during creep-fatigue, although Cr\({}_{23}\)C\({}_{6}\) precipitates change their shape and coarsened during creep-fatigue. The number of precipitates reduced with the fatigue cycles as already shown in TEM micrographs. The relationship between dynamic coercivity and precipitate concentration can be obtained as shown in Figure 4. In this study, the dynamic coercivity depends on the Cr\({}_{23}\)C\({}_{6}\) precipitate concentration with \(N^{0.8}\) more than \(N^{2/3}\). This discrepancy may be caused by several microstructural characteristics of materials but, in this study, there are difficulties in measuring the nano-size precipitates with an image analyzer. Therefore, it is not considered the dependence of nano-size precipitates and less than several tens of nanometer particles on the dynamic coercivity. In addition, plastic deformation evolves lattice defects in materials such as vacancy and dislocation. It creates a significant increase in dislocation density and dislocation tangles are believed to be the pinning sites of domain wall movement [8; 9].