Figure 3.1 shows the XRD profiles of the seven alloys in the as-quenched condition. The profile of alloy A (5 C) reveals only the fundamental (200)γ reflection. However, sideband peaks around the (200)γ reflection could be observed in alloys B (5.5 C) through G (8 C).
The peak appearing on the low-angle side was the (200)k′ reflection of C-rich k′ carbides, whereas that appearing on the high-angle side was the (200)γ0 reflection of the C-depleted γ0 phase[9]. The presence of sidebands demonstrates that the ordered C-rich k′ carbides and C-depleted γ0 phase were formed through spinodal decomposition during quenching in alloys with 5.5≤C≤8.0 at.% [5-7,9]. Moreover, the intensity of the (200)k′ peak increased with increasing carbon content, and the (200)γ, (200)k′, and (200)γ0 peaks all shifted to smaller Bragg angles. This indicates that the amount of k′ particles, as well as all the lattice parameters of γ, k′ carbides, and γ0 phases, increased with increasing carbon content. It is also shown in Figure 3.1 that with increasing carbon content, the sidebands moved closer to the main (200)γ peak, indicating that differences in the parameters between k′ carbides and γ0 phase decreased. The experimental data above measured from the XRD profiles are listed in Table 3.1. The misfit (δk′-γ0) was calculated using the equation:
Figure 3.1 X-ray diffraction profiles around the (200)γ Bragg reflection for
the present seven alloys.
δk′-γ0 = 2
For comparison, the misfit δk′-γ was also calculated. Both are listed in Table 3.1. The modulation wavelength was determined using the Daniel-Lipson equation [6-9]:
Δθ(h +k +l ) θ tan
= ha
λ 2γ 2 2 (2)
where λ = the average modulation wavelength; θ = the Bragg angle for the γ peak; Δθ = the angular spacing between the sideband and the main (200)γ Bragg peak; and h, k, l = the Miller indices of the Bragg peak (h = 2, and k, l = 0). From Table 3.1, it is clear that increasing the carbon content causes the misfit to decrease and the wavelength to increase.
Figures 3.2a through c show selected-area diffraction patterns (SADPs) of alloys A (5 C), D (6.5 C), and G (8 C), respectively. In addition to the fundamental (200)γ diffraction spot, neither the diffraction spot of ordered k′ carbides nor the satellites could be detected in alloy A (5 C).
However, both the ordered k′ carbides diffraction spot and satellites could clearly be observed in alloys D (6.5 C) and G (8 C). Evidently, spinodal decomposition and formation of ordered k′ carbides occurred during quenching. In Figures 3.2b and c, it is also seen that in alloy G (8 C), which has a higher carbon content, the (100) spot is relatively brighter
Figure 3.2 Transmission electron micrographs of the present alloys in the
as-quenched condition. (a)-(c) SADPs of alloys A (5 C), D(6.5
C), and G (8 C), respectively. （hkl: k′ carbides）, (d)-(e) (100)k′
DF images of alloys D (6.5 C) and G (8 C), respectively.
and the spacing between satellites and the main spot is comparatively smaller. The misfit (δk′-γ0) and wavelength (λ), obtained from measurements of the spacing between the satellites and the main spot along the [100] direction in the SADPs, were 2.24% and 15.7 nm for alloy D (6.5 C), as well as 1.59% and 22.3 nm for alloy G (8 C), respectively.
Figures 3.2d and e are two dark-field (DF) electron micrographs taken with the (100)k′ superlattice reflection in the [001] zone. They reveal that the amount of ordered k′ carbides in alloy G (8 C) was significantly greater than that in alloy D (6.5 C). In these figures, it is also seen that fine k′ carbides were formed along the <100> direction, consistent with the appearance of the satellites along the <100> reciprocal lattice directions in Figures 3.2b and c. These results obtained by TEM were in good agreement with those investigated by XRD. Image analyses of Figures 3.2d and e indicated that the mean sizes of fine k′ carbides formed in alloys D (6.5 C) and G (8 C) were about 6 and 11 nm, respectively. A detailed TEM examination revealed that although the values of misfit (δk′-γ0) in alloys D (6.5 C) and G (8 C) reached 2.24 and 1.59%, respectively, no misfit dislocations could be observed on the interface between the k′ carbides and the γ0 phase. The reason is probably that the fine k′ carbides are very small. According to the values
of misfit (δk′-γ0), the expected distances between two misfit dislocations in alloys D (6.5 C) and G (8 C) were calculated to be about 16.6 and 23.6 nm, respectively, which is much larger than the size of the k′ carbides.
Based on the preceding results, some discussion is appropriate. The microstructure of the present alloy A (5 C) in the as-quenched condition was single-phase γ, which is similar to that observed in as-quenched austenitic FeAlMnC alloys with 3.1≤C≤5.2 at.% [1-11]. However, spinodal decomposition and formation of ordered k′ carbides occurred during quenching in the present alloys with 5.5≤C≤8.0 at.%. Regarding spinodal decomposition, two important factors should be considered: (1) interfacial energy effects, and (2) coherency strain energy effects [13]. The k′
carbides is a fcc-based phase of L′12 ordered crystal structure with a C atom at the body center site, an Al atom at the corner positions, and three (Fe, Mn) atoms positioned randomly at the face center sites in its fcc-based unit cell [8]. On the other hand, γ0 is a disordered fcc phase with C atoms positioned randomly at the octahedral interstitial sites. As the γ0
phase and ordered k′ carbides have the same fcc-based crystal structure and similar lattice parameters, their interface would be fully coherent.
Therefore, only chemical contributions should be considered to the interfacial energy [13]. The carbon concentration in the equilibrium
(Fe,Mn)3AlCX carbides of austenitic FeAlMnC alloys aged at 500–550 °C for longer times has been studied by several workers. Consequently, three different values of X have been obtained (0.4, 0.6, and 0.66) [6,9,11].
Furthermore, to the authors’ knowledge, no information concerning the interfacial energy between the γ0 phase and ordered k′ carbides has been provided in previous studies. Additionally, in the early stage of spinodal decomposition, the composition fluctuation profile exhibited a sinusoidal wave [6,14]. Therefore, a conclusive description of the interfacial energy between the γ0 phase and ordered k′ carbides cannot be given in the present study.
Since the composition ratio of (Fe, Mn) and Al in all of the present alloys approximates that of (Fe,Mn)3AlCX carbides, it is plausible to suggest that the composition fluctuation was primarily due to the carbon atom. As is evident from the experimental results above, all the lattice parameters of the phases increased with increasing carbon content of the alloy. This suggests that the carbon concentration in these phases increased simultaneously. However, the carbon contribution to the increase in the lattice parameter of the ordered k′ carbides is distinctively less than in the disordered γ0 phase [15]. Therefore, although all the lattice parameters of the phases increased with increasing carbon content,
the increment in the disordered γ0 phase was larger than that in the ordered k′ carbides. Consequently, the misfit between the ordered k′
carbides and disordered γ0 phase would be reduced with increasing carbon content, which is consistent with the results obtained by XRD and TEM. To emphasize the characteristics, the variations in the lattice parameters and misfits as a function of carbon content are plotted in Figure 3.3. For a fully coherent interface, the coherency strain energy would be roughly proportional to δ2 [13]. In Table 3.1, it is clearly seen that the δ2k′-γ0 in alloy G (8 C) is only 2.424, whereas that in alloy B (5.5 C) is 8.638. This indicates that the strain energy in alloy B (5.5 C) is about 3.56 times that of alloy G (8 C). The average change in δ2k′-γ0 between two adjacent alloys (Δδ2k′-γ0/0.5 at.%) was calculated from Table 3.1. In terms of our calculations, it was found that the values between alloys B (5.5 C)-C (6 C), alloys C (6 C)-D (6.5 C), alloys D (6.5 C)-E (7 C), alloys E (7 C)-F (7.5 C), and alloys F (7.5 C)-G (8 C) were about 4.261, 3.406, 2.260, 1.406, and 1.096, respectively, which corresponds to a ratio of 3.89: 3.11:
2.06: 1.28: 1. This means that the average increment of strain energy per decrement of at.% C between 6 and 5.5 at.% C is 3.89 times greater than that between 8 and 7.5 at.% C. The variation in δ2k′-γ0 with carbon content is also plotted in Figure 3.3. The dotted line shows the expected values
Figure 3.3 Variations in the lattice parameters of k′(■), γ ( ), and◆ γ0 (●)
phases, as well as δk′-γ0 (□) and δ2k′-γ0 (○), as a function of the
carbon content.
Table 3.1. Experimental data obtained from the X-ray diffraction profiles of k′ — 48.816 48.777 48.722 48.676 48.615 48.468
γ 49.7 49.600 49.461 49.311 49.192 49.073 48.882 2θ
γ0 — 50.364 50.125 49.88 49.688 49.511 49.276
ak′ (nm) — 0.3728 0.3731 0.3735 0.3738 0.3743 0.3753 aγ (nm) 0.3666 0.3673 0.3683 0.3693 0.3701 0.3710 0.3723 Lattice
extrapolated from the δ2k′-γ0－C plot. It is evident that the slope of the δ2k′-γ0
－C curve increased gradually with decreasing carbon content from
8.0 at.% C, and became very steep as the carbon content approached concentrations slightly below 5.5 at.%. Accordingly, it is reasonable to expect that a small amount of decrease in carbon content below 5.5 at.%
would cause the coherency strain energy to increase dramatically. As a result, undercooling may be insufficient to overcome the strain energy effects. Consequently, spinodal decomposition was completely suppressed and not detected in the present alloy A (5 C). In addition, the experimental results revealed that both the wavelength and the amount of ordered k′ carbides increased with increasing carbon content. This suggests that the temperatures of both spinodal decomposition and ordering reaction increased with increasing carbon content.
In previous studies, it was seen that when austenitic FeAlMnC alloys with 3.1≤C≤5.2 at.% were solution heat-treated at 980–1050 °C and then rapidly quenched in room-temperature water or ice water, the microstructure was single-phase γ [1-11]. When the as-quenched alloy was aged at 500–550 °C, both spinodal decomposition and formation of ordered k′ carbides could be detected during the early stage of isothermal
aging [3-11]. Han et al. proposed that ordered k′ carbides nucleate in C-rich zones of the γ matrix after undergoing spinodal decomposition [4].
In contrast to this proposition, Choo et al. claimed that spinodal decomposition and formation of ordered k′ carbides occurred concurrently within the γ matrix during aging [8]. Additionally, depending on the chemical composition, aging temperature, and aging time, the wavelength was determined in the range of 23 to 35 nm [6~9]. In spite of the different propositions for the process of spinodal decomposition and ordering, it can generally be concluded that austenitic FeAlMnC alloys with 3.1≤C≤5.2 at.% also lay within the spinodal, and that spinodal decomposition and formation of ordered k′ carbides can only be detected in the alloys during isothermal aging. However, in the present alloys with 5.5≤C≤8.0 at.%, spinodal decomposition and formation of ordered k′
carbides could occur during quenching. The apparent difference may be attributed to the following two reasons: (I) the effect of strain energy between the k′ carbides and γ0 phase, as discussed above, and (II) the degree of carbon supersaturation in the initial γ phase. As mentioned above, the lattice modulation that occurred in the present alloys is mainly caused by concentration fluctuations in the carbon atom, and the lattice parameter of k′ carbides increased with increasing carbon content of the
alloy. The carbon concentration in k′ carbides can be estimated using the equation [15]: ak′ = 0.36626 + 0.00059Cx,where the lattice parameter ak′
and carbon concentration Cx are presented in nanometers and atomic percent, respectively. The calculated results are also listed in Table 1. It is clear from the table that by increasing the carbon content of the alloy from 5.5 to 8.0 at.%, the carbon concentration in k′ carbides gradually increased from 11.08 at.% (X = 0.50) to 15.32 at.% (X = 0.73). It is evident that a higher degree of carbon supersaturation in the initial γ phase would increase not only the amount of fine k′ carbides but also the carbon concentration in the k′ carbides. Interestingly, it is noted here that the carbon concentrations of 11.08–15.32 at.% (X = 0.50–0.73) are comparable to the values of 9–13 at.% (X = 0.4–0.66) reported by other workers in austenitic Fe-(14–20) at.%Al-(27–30) at.%Mn-(3.7–5) at.%C alloys aged at 500–550 °C for longer periods of time [6,9,11].
Finally, it is worth pointing out that no information concerning the spinodal decomposition curve of the FeAlMnC alloy system has been provided in the literature. Clearly, additional work is needed to further understand the effects of carbon content on spinodal decomposition and ordering in austenitic FeAlMnC alloys.
3-4
Conclusions
In summary, spinodal decomposition and formation of ordered k′
carbides were observed in the present Fe-20 at.%Al-26 at.%Mn-C alloys with 5.5≤C≤8.0 at.% under the as-quenched condition. The gradual increase in both the wavelength and the amount of ordered k′
carbides indicates that the reaction temperatures of both spinodal decomposition and ordering increased with increasing carbon content.
With increasing carbon content, the lattice parameters of both the ordered k′ carbides and the disordered γ0 phase increased, whereas the misfit between the two phases decreased. The coherency strain energy was expected to increase dramatically as the carbon content approached slightly below 5.5 at.%. Given the remarkable increase in strain energy, undercooling may be insufficient to overcome the strain energy effects, which are responsible for the absence of spinodal decomposition and formation of ordered k′ carbides in the present alloy A (5 C) and in previous austenitic FeAlMnC alloys with 3.1≤C≤5.2 at.%
under the as-quenched condition. Additionally, the carbon concentration in the k′ carbides formed in the present alloys increased with increasing carbon content. This indicates that a higher degree of carbon supersaturation in the initial γ phase might promote a tendency toward
C-rich k′ carbide formation during quenching.
References
1. Kalashnikov, O. Acselrad, A. Shalkevich, L.C. Pereira: J. Mater. Eng.
Perform. 9 (2000) 597-602.
2. K.H. Han: Mater. Sci. Eng. A 279 (2000) 1-9.
3. Acselrad, A.R. de Souza, I.S. Kalashnikov, S.S. Camargo Jr.: Wear 257 (2004) 999-1005.
4. K.H. Han, J.C. Yoon, K.W. Choo: Scripta Metall. 20 (1986) 33-36.
5. I.S. Kalashnikov, O. Acsrlrad, A. Shalkevich, L.D. Chumakova, L.C.
Pereira: J. Mater. Process. Tech. 136 (2003) 72-79.
6. K. Sato, K. Tagawa, Y. Inoue: Metall. Trans. A 21A (1990) 5-11.
7. K.H. Han, W.K. Choo, D.E. Laughin: Scripta Metall. 22 (1988) 1873-1878.
8. W.K. Choo, J.H. Kim, J.C. Yoon: Acta Mater. 45 (1997) 4877-4885.
9. K. Sato, K. Tagawa, Y. Inoue: Mater. Sci. Eng. A 111 (1989) 45-50.
10. G.S. Krivonogov, M.F. Alekseyenko, G.G. Solov’yeva: Fitz. Metal.
Metalloved 39 No.4 (1975) 775-781.
11. N.A. Storchak, A.G. Drachinskaya: Fitz. Metal. Metalloved 44 No.2
(1977) 373-380.
12. C.S. Wang, C.N. Hwang, C.G. Chao, T.F. Liu: Scripta Mater. 57 (2007) 809-812.
13. D.A. Porter, K.E. Easterling, M. Sherif: Phase Transformations in Metals and Alloys 3rd Ed., (Nelson Thornes Ltd, Cheltenham, 2009),
pp308-314.
14. B. Ditchek, L.H. Schwartz: Acta Metall. 28 (1980) 807-822.
15. W.K. Choo, K.H. Han: Metal. Trans. A 16A (1985) 5-10.