A transition of ω-Fe3C → ω′-Fe3C → θ′-Fe3C in Fe-C martensite

Carbon steel is strong primarily because of carbides with the most well-known one being θ-Fe3C type cementite. However, the formation mechanism of cementite remains unclear. In this study, a new metastable carbide formation mechanism was proposed as ω-Fe3C → ω′-Fe3C → θ′-Fe3C based on the transmission electron microscopy (TEM) observation. Results shown that in quenched high-carbon binary alloys, hexagonal ω-Fe3C fine particles are distributed in the martensite twinning boundary alone, while two metastable carbides (ω′ and θ′) coexist in the quenched pearlite. These two carbides both possess orthorhombic crystal structure with different lattice parameters (aθ′ = aω′ = aω = \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\sqrt{2}$$\end{document}2aα-Fe = 4.033 Å, bθ′ = 2 × bω′ = 2 × cω = \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\sqrt{3}$$\end{document}3aα-Fe = 4.94 Å, and cθ′ = cω′ = \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\sqrt{3}$$\end{document}3aω = 6.986 Å for aα-Fe = 2.852 Å). The θ′ unit cell can be constructed simply by merging two ω′ unit cells together along its bω′ axis. Thus, the θ′ unit cell contains 12 Fe atoms and 4 C atoms, which in turn matches the composition and atomic number of the θ-Fe3C cementite unit cell. The proposed theory in combination with experimental results gives a new insight into the carbide formation mechanism in Fe-C martensite.

The main phase constituents in carbon steels are ferrites (α-Fe) and carbides according to the equilibrium binary Fe-C phase diagram. Therefore carbides have long been considered as a critical phase in strengthening carbon steels. Among all the carbides, the most well-known one is θ-type Fe 3 C cementite, which possesses orthorhombic crystal structure (space group Pnma) with its lattice parameter being a θ = 4.524 Å, b θ = 5.088 Å and c θ = 6.741 Å 1,2 . Although the θ-Fe 3 C cementite has been studied extensively due to its importance and popularity in carbon steels [3][4][5][6][7][8][9][10][11][12][13][14][15][16] , its formation mechanism remains unclear. This is particularly true for the θ-Fe 3 C formation during martensitic transformation. One possible reason for this is its ultra-fine particle size, which makes it difficult for the normal characterization techniques to detect the earlier stage of the carbide formation.
Thus far, several types of carbides, which are thought to be the precursors of cementite, have been investigated [17][18][19][20][21][22][23][24][25] . However, detailed crystal structural relationship between these carbides has not been explained yet. To explain the formation mechanism of the cementite in martensitic structure, a martensite decomposition mechanism (martensite → ε-Fe carbide → cementite) has been proposed previously during tempering at low temperature around 200 °C 23,[26][27][28][29] . However, most of the alloys used for studying carbide formation were ternary (such as Fe-Ni-C) alloys or other complex alloy systems, which may complicate the analysis and interpretation of carbide formation mechanism. In order to study the fundamental formation mechanism of cementite, the simple binary Fe-C is more appropriate.
Each unit cell of the θ-Fe 3 C cementite with the formula Fe 3 C contains 12 Fe atoms and 4 C atoms, leading to a ratio of Fe to C being 3 1,2,30 . Interestingly, a recently discovered ω-Fe phase located in the martensite twin boundary has three iron atoms in its unit cell as well 31,32 . If one interstitial carbon atom were to join this ω-Fe unit cell, the product would have the formula ω-Fe 3 C. The possibility that there exists certain relationship between the ω-Fe 3 C and θ-Fe 3 C stimulates the investigation into the possible unknown carbides formed earlier than θ-Fe 3 C cementite in the binary Fe-C system.
Metastable hexagonal ω-Fe 3 C phase particles, which are 1 to 2 nm big in size, distribute only at the body-centered cubic (BCC) {112}<111>-type twinning boundary region in twinned high-carbon Fe-C martensite [33][34][35][36][37][38][39][40] . It was observed by in-situ heating transmission electron microscopy (TEM) that these twinning boundary ω-Fe 3 C particles eventually transformed into θ-Fe 3 C carbides [41][42][43][44] . However, the ω → θ transition speed is too fast for any details to be recorded. Thus, indirect approach is needed to figure out the formation mechanism of these metastable carbides that might exist in the quenched high carbon Fe-C alloys in which several types of ultra-fine carbides with pearlite-like structures have been observed 45,46 . Furthermore, as mentioned above, it is difficult     www.nature.com/scientificreports www.nature.com/scientificreports/ device (Fischione Model 1050 TEM Mill) was used to prepare the specimens at 4 kV. Sample microstructure was observed using a JEM 2000FX TEM operated at 200 kV. Electron diffraction patterns were calculated using the commercial CrystalMaker software. All electron diffraction patterns shown in the present work were calculated such that the spot intensity saturation was 100 in the software.

ω′-variants.
As an interstitial atom, the position of carbon atoms in crystals determines carbide structure.
Two different coarsening behaviors of the ultra-fine ω-Fe 3 C particles are illustrated in Fig. 1. Figure 1(a) shows the atomic structure of one ω-Fe 3 C unit cell. The coarsening route ( Fig. 1(b)) will generate a new kind of carbide, with its unit cell outlined by red dashed lines in Fig. 1(c). Its corresponding three-dimensional (3D) atomic structure is shown in Fig. 1(d). There are six iron atoms and one carbon interstitial atom in this unit cell, which has been designated as ω′-Fe 6 C in our previous study 46 . On the other hand, if the positions of two ω-Fe 3 C (ω1, ω4) and two ω-Fe (ω2, ω3) in Fig. 1b exchange, the ω′-Fe 6 C will has the carbon atom at (0 0 0.5) as shown in Fig. 2a. Obviously, ω′-Fe 6 C has two forms because of the different carbon atom position as shown in Figs. 1d and 2a.
When the coarsening of the ultra-fine ω-Fe 3 C particles follows the route shown in Fig. 1(e-g), new carbide consisting of six iron atoms and two carbon atoms in its unit cell will form as shown in Fig. 1(g), with its formula being ω′-Fe 6 C 2 or ω′-Fe 3 C. There is no any difference in the calculated electron diffraction patterns between the ω′-Fe 6 C 2 and ω-Fe 3 C carbides since both carbide crystals have the exact same atomic positions. As can be seen in Fig. 1, the transformation of the ω-Fe 3 C hexagonal structure to an orthorhombic structure depends on the carbon content and/or positons alone. Once the ordering of carbon atoms occurs, the orthorhombic structure can form in a spontaneous way. The electron diffraction spots associated with such an ordering has been observed in the ω′-Fe 6 C carbide 46 .
Since there is no obvious difference in the calculated electron diffraction patterns between ω-Fe 3 C carbide and ω-Fe phase 45 , the three phases (ω-Fe, ω-Fe 3 C, ω′-Fe 6 C 2 (ω′-Fe 3 C)) would have similar electron diffraction patterns, which may cause difficulty in charactering the carbides experimentally. Simply speaking, there are three phases (hexagonal ω-Fe, orthorhombic ω-Fe 3 C and ω′-Fe 6 C 2 (ω′-Fe 3 C)) present theoretically. However, it is difficult to distinguish among them since they show similar electron diffraction pattern experimentally. Formation of this new ω′-Fe 3 C carbide can actually explain why the ultra-fine ω-Fe 3 C particles never grow big in real materials. The ω-Fe 3 C particle size is just only 1-2 nm.
The carbide coarsening can be achieved via the several fine ω-Fe 3 C particles merged together. The driving force for the movement of fine ω-Fe 3 C particles comes from the recrystallization of ultra-fine α-Fe matrix grains. There are two crystalline phases, namely fine α-Fe as a matrix grain and fine ω-Fe 3 C particles at the α-Fe twinning boundaries that co-exist in the twinned martensitic structure. Thus, the coarsening behavior is actually controlled by the recrystallization process of the α-Fe matrix grains upon tempering. The α-Fe recrystallization results in a movement of the α-Fe grain boundaries and/or twinning boundaries, which promotes the ω-Fe 3 C particles at the boundaries to move and meet other ω-Fe 3 C particles. The coarsening behavior of the fine ω-Fe 3 C particles and the recrystallization process of the ultra-fine α-Fe grains have been experimentally confirmed and explained in our previous work 35  www.nature.com/scientificreports www.nature.com/scientificreports/ θ′-variants. Following the same coarsening mechanism explained in Fig. 1, new carbide, here designated as θ′, can be formed by combining two variants of ω′. The atomic structures of possible θ′ variants are shown in Fig. 2. Figure 2(a) shows one of the ω′ variants, while the other two ω′ variants are shown in Fig. 1(d,g). After two variants of ω′ merge together along its b axis, three θ′ variants (θ′-Fe 12 C 2 or θ′-Fe 6 C ( Fig. 2(b)), θ′-Fe 12 C 3 or θ′-Fe 4 C www.nature.com/scientificreports www.nature.com/scientificreports/ ( Fig. 2(c)), θ′-Fe 12 C 4 or θ′-Fe 3 C (Fig. 2(d))) can be formed. Thus, the θ′ carbides possess lattice parameter of a θ′ = 4.033 Å, b θ′ = 2 × 2.47 Å = 4.94 Å, and c θ′ = 6.986 Å and retain an orthorhombic crystal structure. During the coarsening of fine ω′ particles, one ω′ particle with the crystal structure in Fig. 1(g) may combine with another ω′ particle with the same crystal structure along its b ω′ axis. When this occurs, it is possible for a θ′-Fe 3 C carbide particle to form.
The formation of θ′-Fe 12 C 4 or θ′-Fe 3 C variant involves merging two ω′-Fe 6 C 2 or ω′-Fe 3 C carbide particles together alone without any atomic movement or variation in carbon content. It can be seen from Figs. 1 and 2 that the position of both Fe and C atoms during the ω → ω′ → θ′ transition are kept unchanged, meaning that this transition depends completely on the size of the ω-Fe 3 C carbide particle. The atomic positions of Fe and C atoms in the ω-Fe 3 C, ω′-Fe 3 C and θ′-Fe 3 C unit cells have been listed in the Tables 1-3, respectively.

Metastable carbide Variant composition Notes
ω′, orthorhombic a ω′ = 4.033 Å, b ω′ = 2.47 Å, c ω′ = 6.986 Å ω′-Fe 6 C C atoms at different (001) atomic planes ω′-Fe 6 C ω′-Fe 6 C 2 (ω′-Fe 3 C) θ′, orthorhombic a θ′ = 4.033 Å, b θ′ = 4.94 Å, c θ′ = 6.986 Å θ′-Fe 12 C 2 (θ′-Fe 6 C) C concentration varies at different (001) atomic planes θ′-Fe 12 C 3 (θ′-Fe 4 C) θ′-Fe 12 C 4 (θ′-Fe 3 C) Table 4. The structural parameters and chemical composition of possible variants of the ω′ and θ′ carbides. The electron diffraction patterns of the ω′-Fe 6 C 2 (ω′-Fe 3 C) and θ′-Fe 12 C 4 (θ′-Fe 3 C) are the same with that of the ω-Fe 3 C. www.nature.com/scientificreports www.nature.com/scientificreports/ As explained in Figs. 1 and 2, ω′ and θ′ can have other variants with lower carbon content than that in the ω′-Fe 6 C 2 (ω′-Fe 3 C) and θ′-Fe 12 C 4 (θ′-Fe 3 C) unit cells. The ω′ variant (ω′-Fe 6 C) has been experimentally observed previously. 46 Fig. 3 shows the evidence that there exist other type θ′ variants in the quenched high carbon Fe-C alloys. Simulated electron diffraction pattern of the θ′-Fe 12 C 3 carbide with its [100] zone axis parallel to the electron beam is shown in Fig. 3(a), while the corresponding experimental electron diffraction pattern is shown in Fig. 3(b). The experimental diffraction pattern is composed of two sets of diffraction spots. One set is from [011] α-Fe zone axis and the other is from the [100] zone axis of the θ′-Fe 12 C 3 carbide as shown in Fig. 3(a). The mixed electron diffraction patterns of α-Fe and fine carbides are frequently observed in the quenched Fe-C alloy with pearlite structure since both phases have ultra-fine particles (the region selected for experimental observations depends on the selected aperture size in TEM equipment, the smallest diameter size of the aperture is about 250 nm). Figure 3(c) shows a particular experimental pattern, which is composed of three sets of diffraction spots: (1) the strong spots from [011] α-Fe zone axis as outlined by the yellow dashed lines, (2) the spots shown in Fig. 3(a), which is from [100] zone axis of the θ′-Fe 12 C 3 carbide, and (3) the spots [100] zone axis of the θ′-Fe 12 C 2 carbide as shown in Fig. 3(d). Experimental diffraction patterns are usually obtained from an area of several hundreds of nanometers in diameter. Thus, the diffraction pattern is composed of several sets of diffraction spots, which come from various carbides present in the pearlite-like region. Figure 3(e) shows the simulated electron diffraction patterns of the θ′-Fe 12 C 3 carbide along its [110] zone axis. This pattern can also be observed experimentally along the α-Fe [012] zone axis as shown in Fig. 3(f).
The results in Fig. 3 reveal that various θ′ variants can co-exist in the quenched sample, and the formation of different type of variants is dependent on carbon concentration and positions. The possible variants of both θ′ carbides and ω′ carbides are summarized and listed in Table 4. Both ω′ and θ′ carbides possess orthorhombic crystal structure. The unit cell of θ′ carbides is composed of two ω′ unit cells merged along its b axis. The formation mechanism of θ′ carbides is the variation in carbon atoms or concentration on different atomic planes, which causes an ordering structure of ω-Fe. Since the carbon atoms or concentration are the same in (001) planes of ω′-Fe 6 C 2 (ω′-Fe 3 C) and θ′-Fe 12 C 4 (θ′-Fe 3 C) and the electron diffraction patterns of ω-Fe 3 C, ω′-Fe 6 C 2 (ω′-Fe 3 C) and θ′-Fe 12 C 4 (θ′-Fe 3 C) are similar, no carbon-ordering diffraction spots could be observed. However, that is not to say the ω′-Fe 6 C 2 (ω′-Fe 3 C) or θ′-Fe 12 C 4 (θ′-Fe 3 C) does not exist in the sample. www.nature.com/scientificreports www.nature.com/scientificreports/ θ-fe 3 c cementite. The diffraction patterns of θ-Fe 3 C cementite from two different zone axes ([101] θ in Fig. 4(a) and [111] θ in Fig. 4(b)) are shown here in comparison with that of previous carbides (ω-Fe 3 C, ω′-Fe 6 C 2 (ω′-Fe 3 C) or ω′-Fe 6 C and various θ′-variants). It can be seen from Fig. 4(c), the experimental 303 θ spot is completely separated from the α-Fe 21 1 spot, unlike the corresponding ω and ω′ or θ′ spots, which overlap perfectly with the corresponding α-Fe spots. This kind of separation can also be clearly observed in other direction as shown in Fig. 4(d). The results shown in Fig. 4 explain that the carbide with the well-known cementite structure has lost the perfect overlapping in diffraction spots compared with other carbides mentioned earlier.
The electron diffraction patterns of ω-related carbide structures (ω, ω′, θ′ and θ) in quenched high-carbon binary Fe-C alloys are illustrated in Fig. 5. Figure 5(a-d) show the schematics of diffraction patterns based on the experimental results. 45,46 All these patterns are obtained from the same α-Fe [011] zone axis. The pattern shown in Fig. 5(a) can only be observed within twinned martensite (Fig. 5(e)). The pattern (Fig. 5(a)) reveals a complete overlapping between the 211 α and the 330 ω spots. In Fig. 5(b), the ω-Fe 3 C diffraction pattern is converted into ω′-Fe 6 C with an ordering pattern and the original three spots (1 10 ω , 2 20 ω and 3 30 ω ) turn out to be six spots between the transmitted (central) and the 211 α diffraction spots. When two ω′-Fe 6 C unit cells merge together to form a θ′-Fe 12 C 3 variant with its b θ′ = 2 bω ′ , an extra row of diffraction spots would occur in reciprocal space as shown in Fig. 5(c). The corresponding diffraction pattern from θ-Fe 3 C is shown in Fig. 5(d) for a comparison with that of the ω-Fe 3 C-related carbides to show a crystal structural similarity among these carbides. The patterns shown in Fig. 5(b-d) are normally observed in quenched pearlite-like microstructure like that shown in Fig. 5(f). Not only can ω′ carbides be observed in the pearlite-like microstructure, but θ′ and θ fine carbides can also be observed in the same pearlite-like region. Nevertheless, it is difficult to differentiate these carbides based on particle size or morphology alone since all of them are several nanometers in size.
In experimental TEM observations, these three carbides (ω, ω′ and θ′) can be identified easily based on the superimposition of certain diffraction spots on 211 α-Fe. Once these carbides start to transform into the well-known θ-Fe 3 C cementite, the separation of the 303 θ diffraction spots from 211 α-Fe spots can be clearly seen as shown in Fig. 5(d). Such a separation will produce complex diffraction patterns and cause difficulty in carbide characterization.
conclusion Ultra-fine carbides formed in quenched Fe-C alloys were investigated by comparing experimental results with simulated electron diffraction patterns.
1. Based on the unit cells of the ω′-Fe 3 C and its variants, an orthorhombic θ′ carbide structure with lattice parameter of a = 4.033 Å, b = 4.94 Å, and c = 6.986 Å was constructed and experimentally confirmed. The θ′ carbide can be: θ′-Fe 12 C 2 (or θ′-Fe 6 C), θ′-Fe 12 C 3 (or θ′-Fe 4 C) and θ′-Fe 12 C 4 (or θ′-Fe 3 C) compounds. 2. A transition route (ω → ω′→ θ′) has been proposed during the coarsening of ultra-fine ω-Fe 3 C particles to explain the formation mechanism of the θ′ carbide with various variants. The transition occurs accompanying the variation in the position and concentration of carbon atoms, while the position of Fe atoms is kept unchanged. 3. It was observed that the ω′, θ′ and θ metastable carbides with ultra-fine particle size co-existed in the pearlite-like microstructure of quenched high carbon Fe-C alloys.