356 Qin Shen et al.


Figure 7. Cu (green), Ni (red), and Al (blue) atom maps of the Fe–NiAl–Cu alloy 500°C aged for (a) 0.5 h, (b)4h, (c) 128 h in the 15×15×1 nm3 selected regions. The 1-nm-thick selected regions were cut through the centers of the precipitates in the Fe–NiAl–Cu alloy. The circle around the Cu segregation zone is a 20% Cu isoconcentration surface, the circle around the Ni and Al segregation zone is a 15% (Ni+Al) isoconcentration surface.


where kB is Boltzmann’s constant, T the temperature, and ΔG* the critical energy for nucleation, which is described by (Aaronson & Legoues, 1992)


ΔG*= 16πγ3 3 ΔGV -ΔGϵ ðÞ 2 ; (3)


where γ is the interfacial energy between the nanoparticles and the matrix, ΔGV the chemical driving force for nuclea- tion, and ΔGɛ the elastic strain energy. The beneficial effects of Cu in promoting the nucleation


of the NiAl particles can be discussed in terms of the che- mical driving force ΔGV and the interfacial energy γ of nucleation. First, the NiAl particles contain significant amounts of Cu, so the segregation of Cu in the Fe–NiAl–Cu alloy is equivalent to increasing the total concentration of the nanoparticle-forming elements. The matrix supersaturation of Ni, Al, and Cu in the Fe–NiAl–Cu alloy is higher as compared with that of Ni and Al in the Fe–NiAl alloy, resulting in an increase in chemical driving forceΔGV for the nucleation of the nanoparticles. Second, the Cu precipitates nucleate in the Fe–NiAl–Cu alloy, obviously by a hetero- geneous process leading to the reduction of interfacial energy γ. As a result, the chemical driving force ΔGV is increased and the interfacial energy γ is decreased, so the critical energy for nucleation of NiAl nanoparticles is reduced, leading to an increased nucleation rate of NiAl precipitates in the Fe–NiAl–Cu alloy. Consequently, the number density of NiAl particles in the Fe–NiAl–Cu alloy is increased as compared with that in the Fe–NiAl alloy.


Effect of Cu on the Evolution of Precipitation


By comparing the atom maps of the 0.5-h-aged Fe–NiAl and Fe–NiAl–Cu alloys, as shown in Figure 4, it can be inferred that the addition of Cu promotes the formation of NiAl nanoparticles. It was reported that in an Fe matrix, Cu pre- cipitates nucleate after extremely short aging times due to the


low solubility of Cu in ferrite and martensite below 500°C (Hattestrand et al., 2004). So Cu can easily segregate from the matrix, as shown in Figure 4b. For the short aging times, Cu- rich particles exhibit a bcc structure (Maruyama et al., 1999), which is coherent with the ferrite matrix. Hence, the inter- face between Cu nanoparticles and matrix will generate a lot of coherent strain energy, which can provide the nucleation energy for the NiAl nanoparticles. In addition, Cu nano- particles act as nucleation sites for NiAl nanoparticles, leading to that NiAl clusters are located adjacent to Cu clusters, as shown in Figure 7a. Upon aging, the NiAl precipitates of the Fe–NiAl and


Fe–NiAl–Cu alloys increase in size and decrease in number density. This is attributed to the fact that the larger pre- cipitates grow at the expense of the smaller ones during the ripening of the precipitates. In addition, the standard deviations of the values of the average sizes also gradually increase with prolonged aging. The phenomenon is mainly due to the presence of small NiAl precipitates that are either a result of the ripening of precipitates or is related to the limited volume analyzed by APT. In comparison, the NiAl precipitates of the Fe–NiAl–Cu alloy grow at a slower rate than that of the Fe–NiAl alloy. There are two reasons which explain the slower growth. First, the diffusion rate of Cu in α-Fe at 500°C is 1.9×10−21m2/s, which is lower than the dif- fusion rate of Ni (3.4×10−21m2/s) and Al (6.6×10−21m2/s) (Kolli & Seidman, 2008). The coarsening of NiAl particles is driven by diffusion of elements. The slower diffusion rate ofCu reduces the coarsening of NiAl nanoparticles in the Fe–NiAl–Cu alloy. Second, the content of Ni and Al in the matrix of the Fe–NiAl–Cu alloy is lower than in the Fe–NiAl alloy, as shown in Table 4, leading to a smaller chemical driving force for growth of NiAl nanoparticles in the Fe–NiAl–Cu alloy. As a result, the Fe–NiAl–Cu alloy contains many small precipitates. At the prolonged aging of 128 h, the NiAl nanoparticles do not encapsulate the Cu nanoparticles completely as in


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