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[求助]
ε-Fe2C的模型构建问题 已有2人参与
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| RT，本人新手，找了几篇文献，这方面的资料实在不多，ε-Fe2C模型的构建有些也相互矛盾，急需这方面有经验的大侠的帮助，请有相关资料的朋友们友情分享下资源啊，最好能具体到空间构型和晶格常数，不胜感激啊！有帮助者呈上金币5枚，第一次悬赏，不知道高低，各位将就吧，万谢 |
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yingzan163
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2楼2014-12-02 09:36:50
yingzan163
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3楼2014-12-02 09:38:38
感谢壕的友情赞助啊
4楼2014-12-02 22:16:40
valenhou001
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cuiky(ljw4010代发): 金币+5, 谢谢指导解答！ 2014-12-03 21:04:44
感谢参与，应助指数 +1
cuiky(ljw4010代发): 金币+5, 谢谢指导解答！ 2014-12-03 21:04:44
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ε-Fe2C较复杂，文献里存在很多分歧之处，下面的这篇文献研究的很仔细。相信你能从它里面可以找到答案。 参考这篇文献： Structure and stability of Fe2C phases from density-functional theory calculations C.M. Fang, M.A. van Huis, and H.W. Zandbergen Scripta Materialia 63 (2010) 418–421 Fe2C plays a crucial role in the precipitation of iron carbides. Jack’s structural models for ε-Fe2C, and non-stoichiometric ε-Fe2.4C, are analyzed using first-principles calculations. Several new configurations of ε-Fe2C with even higher stability are found. Jack and co-workers first reported ε-Fe2C with a small hexagonal unit cell as shown in Figure 1a [1], [2] and [8]. This model (Ia in Table 1) is here named Jack-1. It has space group View the MathML sourceP3ˉm1 (No. 164) with lattice parameters a0 ≈ 2.75 Å and c0 ≈ 3.88 Å [1] and [8]. There are two Fe atoms at the Wyckoff 2d sites ±(1/3, 2/3, z) with z = ¼, and 1 C atom at site 1b (0, 0, ½  . Our calculations show that the lattice parameters are a0 = 2.8339 Å, c0 = 4.1673 Å for Jack-1. The Fe atoms are displaced about 0.014 Å towards the C atom (z = 0.2534). Recently, Lv and co-workers proposed another model for ε-Fe2C. The structure is hexagonal with space group P63/mmc [13]. The Fe atoms are at 4f (1/3, 2/3, 0) and the C atoms at 2a (0, 0, 0). Their calculated lattice parameters are a = 2.993 Å; c = 4.624 Å using density-functional theory within local density approximation (DFT-LDA), and a = 2.888 Å; c = 4.627 Å using density-functional theory with generalized gradient approximation (DFT-GGA). In this model, the Fe atoms form a hexagonal plane with the C atoms coordinated by six Fe atoms in the plane. We also performed calculations for this model using DFT-GGA, and obtained lattice parameters a = 3.6881 Å, c = 5.2513 Å. The calculated (DFT-GGA) formation enthalpy here is as high as about 1083 meV atom−1. Employing the same Fe sublattice, we also performed calculations for the configuration with carbon atoms at the (octahedral) 2b (0, 0, 1/4) sites. The calculations show that the latter arrangement has even higher formation energy (1526 meV atom−1), indicating that the model by Lv and co-workers [13] is energetically not feasible. The third model for ε-Fe2C employs a supercell with ah = √3a0, ch = c0 (here a0 and c0 are the lattice parameters of Jack-1), which contains six Fe atoms. There are several possibilities to arrange the carbon atoms into the octahedral (Wyckoff, 2a, 2b, 2c 2d) sites of the ε-Fe6 configurations. Our calculations showed that the ones with C atoms at 2c or 2d and at one of the 2b sites have the lowest formation energy (35.3 meV atom−1), as shown in Figure 1b and in Table 1. Please note that the 2c and 2d sites structurally are equivalent. This model is isostructural to ε-Fe2N as proposed by Jack [18] and named Jack-2. Another arrangement with 2 C atoms in one plane at the c and d sites and the third one in another layer at one of the b sites also exhibits a moderate formation enthalpy (about 44 meV atom−1). The Jack-2 model of ε-Fe2C is strongly related to η-Fe2C [8], [11] and [18]. As shown in Figure 1b, the 2 C atoms at the c and b sites can be considered as corner atoms of an orthorhombic cell with aorth = ahex/√3 = 2.7380 Å, borth = ahex = 4.7742 Å, corth = chex = 4.2784 Å. Here ahex and chex are the lattice parameters of model-IIb (Jack-2). The corresponding lattice parameters for η-Fe2C are: (aη =) 4.7066 Å, (bη =) 4.2796 Å, and (cη =) 2.8242 Å. The calculations show that η-Fe2C is more stable than ε-Fe2C (ΔHf = 17.3 meV vs 35.3 meV atom−1, respectively, see Table 1). This indicates that the energy gain of the structural relaxation from ε-Fe2C to the η-phase is about 54 meV per formula unit. In the above structural models of ε-Fe2C, the distribution of carbon atoms in the different layers of the interstitial octahedral sites is not the same. Therefore, we investigate the distribution of carbon atoms at the 2b sites using a supercell with lattice parameters ah = 2√3a0, ch = c0 (again a0 and c0 are the lattice parameters of Jack-1). This supercell contains 24 Fe atoms with 8 C atoms at the 8c sites and 4 C atoms at the 8b sites. This model is named Fe24. There are several possible configurations with the 4 carbon atoms at the b sites in different layers, while avoiding 2 C atoms at the b sites on-top of each other (along the c axis). Note that the arrangements of carbon atoms in this way has broken the symmetry of the Jack-2 model; however, we still employ the Wyckoff sites to describe the Fe hcp sheets and octahedral sites for carbon atoms because the Fe sublattice is almost unchanged. The calculations show that shifting 1 carbon atom at one of the b sites to another layer decreases the formation enthalpy about 6.6 meV atom−1 or about 238 meV (unit cell)−1. The most stable configuration contains 2 carbon atoms in each layer of the b sites ( Fig. 1c). This configuration has a formation enthalpy as low as 28 meV atom−1. The Fe lattice of model-III provides a possibility to investigate the well-known non-stoichiometric ε-Fe2.4C [1], [8] and [11]. There are many configurational possibilities to add 2 C atoms into ε-Fe24C8 in which all C atoms occupy the 8c sites. Our calculations showed that the most stable configuration for ε-Fe2.4C is to have 8 C atoms at the 8c sites with 2 C atoms occupying 2b sites of different layers (ε-Fe2.4C-a, Table 1). The calculations showed high stability of ε-Fe2.4C-a with a low formation enthalpy of 24.0 meV atom−1. In summary, the stability of well-known ε-Fe2C phase with ah = √3a0, ch = c0 (Jack-2) is confirmed. This structure can transform into η-Fe2C through local relaxations. Furthermore, our calculations also show that ε-Fe2C exhibits more stable configurations, e.g. the IIIb ( Fig. 1c) and IIIc models in Table 1. Furthermore, the well-known non-stoichiometric ε-Fe2.4C is calculated to exhibit high stability, as well. These highly stable configurations should therefore be incorporated into the understanding of the precipitation of iron carbides during steel-manufacturing processes. |
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