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Investigation of iron adsorption on composite transition metal carbides in steel by first-principles calculation
Journal of Physics and Chemistry of Solids 116 (2018) 30–36
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Investigation of iron adsorption on composite transition metal carbides in steel by first-principles calculation Hui-Hui Xiong a, b, *, Lei Gan a, Zhi-Fang Tong a, Heng-Hua Zhang b, Yang Zhou a a b
School of Metallurgy and Chemical Engineering, Jiangxi University of Science and Technology, Ganzhou, 341000, China School of Materials Science and Engineering, Shanghai University, Shanghai 200072, China
A R T I C L E I N F O
A B S T R A C T
Keywords: Adsorption energy Composite transition metal carbides First-principles calculation Iron
The nucleation potential of transition metal (TM) carbides formed in steel can be predicted by the behavior of iron adsorption on their surface. Therefore, Fe adsorption on the (001) surface of (A1-xmx)C (A ¼ Nb, Ti, m ¼ Mo, V) was investigated by the first-principles method to reveal the initialization of Fe nucleation. The Mulliken population and partial density of state (PDOS) were also calculated and analyzed in this work. The results show that Fe adsorption depends on the composition and configuration of the composite carbides. The adsorption energy (Wads) of Fe on most of (A1-xmx)C is larger than that of Fe on pure TiC or NbC. The maximum Wads is found for Fe on (Nb0.5Mo0.5)C complex carbide, indicating that this carbide has the high nucleation capacity at early stage. The Fe adsorption could be improved by the segregation of Cr and Mn atoms on the surfaces of (Nb0.5Mo0.5) C and (Ti0.5Mo0.5)C. The PDOS analysis of (Cr, Mn)-doped systems further explains the strong interactions between Fe and Cr or Mn atoms.
1. Introduction Because of their excellent yield strength and toughness, high-strength low-alloy (HSLA) steels have been widely used in many fields, such as high-pressure vessels, ships, railways, and energy transportation [1–5]. The mechanical properties of HSLA steels can be controlled through dispersion strengthening and grain refinement [6]. Grain refinement can be achieved by the heterogeneous nucleation of ferrite and austenite on the transition metal (TM) carbides [7,8]. Actually, the interfacial energy between carbides and matrix can be used to evaluate the nucleation potential for various carbides [9,10]. For example, Yang et al. [11] investigated the electronic, structural, and interfacial properties of the Fe–TiC interface by first-principles calculations, and found that ferrite heterogeneous nucleation preferably occurred on the C-termination interface. Similarly, the first-principles method was also used to study the Fe–NbC [12,13], Fe–WC [14,15], Fe–VN [16], Fe–ZrC [17], Fe–TiN [18,19] interfaces, and their interfacial properties and bonding characteristics were revealed. In addition, the interfacial energies of coherent and semicoherent fcc Fe/MX and bcc Fe/MX (M ¼ Ti, Zr, Hf, V, Nb, Ta, X ¼ C, N) were explored using the first-principles approach [20–22], which confirmed that NbC has the largest nucleation potential. It is reported that heterogeneous nucleation during the early stage of solidification is an adsorption process [23,24], and the larger adsorption
ability of Fe atoms on the precipitate surface is associated with a higher nucleation potential of particles. At present, first-principles calculations have been considerably applied to research the metal atom adsorption on particle surfaces, which can provide the atomic and electronic structures of the adsorption system. Wang et al. [19] used density functional theory (DFT) simulations to study the adsorption of Fe on the TiN(001) surface, and the heterogeneous nucleation mechanism of Fe on TiN precipitate was revealed. Furthermore, the iron adsorption on the (001) surface of TM carbides and nitrides was calculated using the first-principles method, and the nucleation tendency and potential of these precipitates in steel were confirmed [25]. Besides the pure carbides, the addition of alloying elements also could result in the formation of composite carbides in steel, such as (Ti, Mo)C [26], (Ti, V)C [27], and (Nb, Mo)C [28]. Those particles can lead to grain refinement and thus improve mechanical properties of steel. However, the theoretical research of Fe adsorption on composite carbide surfaces has not been previously reported in the literature. In this article, first-principles calculations about Fe adsorption on the possible (001) surfaces of composite carbides (A1-xmx)C (A ¼ Nb or Ti, m ¼ Mo, V) were performed to explore their nucleation behaviors. The electronic structure and bonding characteristics of those adsorption structures were also analyzed. Moreover, the segregation of alloying elements on (A1-xmx)C surfaces may affect the Fe adsorption, as is the case
* Corresponding author. School of Metallurgy and Chemical Engineering, Jiangxi University of Science and Technology, Ganzhou, 341000, China. E-mail address: [email protected] (H.-H. Xiong). https://doi.org/10.1016/j.jpcs.2018.01.013 Received 11 September 2017; Received in revised form 9 January 2018; Accepted 10 January 2018 Available online 10 January 2018 0022-3697/© 2018 Elsevier Ltd. All rights reserved.
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Journal of Physics and Chemistry of Solids 116 (2018) 30–36 Table 1 Calculated lattice constants “a,” volume “V0,” bulk modulus “B,” and surface energy “γs” [(001) surface] of NbC and TiC compared with experimental results and other references. Phases
Method
a ¼ b ¼ c (Å)
V0 (Å3)
B (GPa)
γs (J/m2)
TiC
GGAthis work GGA [36] Expt. [37] GGAthis work GGA-PBE [38] Exp. [39]
4.332 4.331 4.329 4.480 4.493 4.470
81.3 81.2 81.1 89.9
250 248 242 301 307 311 [40]
1.69 1.60 [25]
NbC
89.3
1.49 1.42 [25] 1.55 [41]
the calculations in this work. The ultra-soft pseudopotential method [33] was used to describe the interactions between ionic core and valence electrons. The valence electrons of the atoms chosen were Nb 4s24p64d45s1, Ti 3s23p63d24s2, and C 2s22p2, respectively. Generalized gradient approximation (GGA) of Perdew–Burke–Ernzerh of(PBE) functional [34] was used to treat the exchange–correlation interactions. The Brillouin zone was sampled with the Monkhorst–Pack k-point grid. The cutoff energy was selected as 400 eV and the k-point sampling was set as 8 8 8 for the bulk and 8 8 1 for the surfaces, respectively. The geometry optimization was performed using the Broyden–Fletcher–Goldfarb–Shanno (BFGS) algorithm [35] to achieve relaxation of atoms fully. The convergence parameters used in the calculations were as follows: total energy tolerance, 1.0 105 eV/atom; maximum force tolerance, 0.03 eV/Å; and maximal displacement, 1.0 104 nm. Lekakh et al. [25] have demonstrated that the optimal adsorption position for Fe on TMC(001) is the C-top site instead of the TM-top site or bridge site. Therefore, the Fe adsorption on only the C-top site of TMC(001) was considered in this work. First, we established the model of Fe adsorption on complex carbides with different configurations of (A1-xmx)C. Taking the Fe adsorption on the 2 1 (Nb1-xmx)C(001) surface (Fig. 1) for example, each adsorption model consists of eight atomic layers with four atoms in each layer that corresponds to the Fe monolayer (ML) covering of 0.25ML. The atomic structures of (Nb1-xmx)C (x ¼ 0, 0.25, 0.50, and 1) with different stacking sequences are shown in Fig. 1 (b)-(d). In Fig. 1 (a), Fe adsorption on the NbC(001) surface is defined as “Fe@NbC” (where A@B means A adsorption on B) and N and m represent Nb and alloying elements (e.g., Mo, V, and Ti), respectively. It is reported that Fe adsorption can be affected by the segregation of alloying elements on TM carbide surfaces [25]. Therefore, we also studied iron adsorption on the (A1-xmx)C(001) surface covered with 3d TM(TM ¼ Ti, V, Cr, Mn, Co, and Ni) to understand how these substitutional atoms influence the Fe nucleation. The (Nb0.5Mo0.5)C and (Ti0.5Mo0.5)C complexes, having the relatively large Fe adsorption ability (see the “Adsorption Energy” section), were chosen to investigate the influences of 3d TM on Fe adsorption. Fig. 2 shows the supercell structure of Fe adsorption on the 3d-TM-doped 2 2 (Nb0.5Mo0.5)C(001) surface; each adsorption model is composed of eight atomic layers with one 3d atom substituting an Mo atom in the first layer. Here the nonmagnetic iron was considered due to the simulation of the initial process. The adsorption energy (Wads) of Fe on complex carbide surfaces is derived according to the following equation:
Fig. 1. (a) Supercell model of Fe adsorption on NbC(001) surface. Atomic structures of (b) ðNb0:75 m0:25 ÞC, (c) ðNb0:5 m0:5 ÞC, (d) ðNb0:25 m0:75 ÞC, where N and m represent Nb and alloying elements (e.g., Mo, V, and Ti). The brown, blue, and red spheres are C, Nb, and Fe atoms, respectively. The stacking sequence of (Nb1-xmx)C is shown from the top to the bottom. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)
with Ni alloys with Ni3Al precipitate [29,30]. Therefore, we also discuss the Fe adsorption on 3d-TM-doped (Nb0.5Mo0.5)C and (Ti0.5Mo0.5)C (TM ¼ Ti, V, Cr, Mn, Co and Ni) to reveal the influence of these alloying elements on the subsequent Fe nucleation. 2. Calculation method and details The Cambridge serial total energy package (CASTEP) code [31,32], which is based on density functional theory (DFT), was used for all
Wads ¼ EFe þ Esurface EFeþsurface
(1)
where Esurface and EFe are the total energy of composite carbide surfaces and a single Fe atom, respectively. EFeþsurface is the total energy of carbide surfaces adsorbing Fe atom. 3. Results and discussion Fig. 2. Supercell structure of Fe adsorption on 3d-TM-doped 2 2 (Nb0.5Mo0.5)C(001) surface (a), top view of the adsorption system (b). The black, brown, blue, pink, and red spheres are 3d-TM, C, Nb, Mo, and Fe atoms, respectively. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)
3.1. Bulk and surface properties of NbC and TiC To make sure the accuracy of our calculation methods, we carried out a series of calculations on the properties of NbC and TiC, whose crystal
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Fig. 3. Adsorption energy of Fe on the (001) surface of (a) ðTi1x Mox ÞC; (b) ðTi1x Vx ÞC; (c) ðTi1x Nbx ÞC. For each adsorption system, the largest adsorption energy at a given composition is connected with a solid line. T, M, and N represent Ti, Mo, and Nb, respectively.
Nb, compared with those of Fe atom on the TiC, which implies that the addition of these alloying elements in the TiC lattice is in favor of Fe nucleation. Our calculations further support the experimental observation that the grain size of both ferrite and austenite in the Mo-added steels is smaller than that in the Mo-free steels [42]. Moreover, the nucleation capacity of ðTi1x Mox ÞC and ðTi1x Vx ÞC is superior to that of ðTi1x Nbx ÞC. For the three adsorption systems (Fig. 3), the largest Wads values are found at a composition of ðTi0:5 Mo0:5 ÞC, ðTi0:25 V0:75 ÞC; and ðTi0:25 Nb0:75 Þ, which are 6.43 eV, 6.12 eV, and 6.04 eV, respectively. In particular, compared with the Fe@TiC system, the Fe@ðTi0:5 Mo0:5 ÞC system with the MMTT structure exhibits a maximum increase of 0.61 eV in the Wads value. In addition, the Fe–C bond length (1.694 Å) of the Fe@ðTi0:5 Mo0:5 ÞC system is smaller than that of Fe@TiC (1.705 Å). This confirms that ðTi0:5 Mo0:5 ÞC has the strongest Fe absorption ability, which is further supported by the previous study [43] that the Fe–(Ti0.5Mo0.5)C interface has the lowest interfacial energy and thus (Ti0.5Mo0.5)C can be the effective heterogeneous nucleus of ferrite. When the Nb atoms in NbC are partly replaced by Mo or V atoms, most Nb-based complex carbides exhibit larger Fe adsorption capacity compared with pure NbC, as shown in Fig. 4(a-b). However, the adsorption energies of Fe on ðNb1x Tix ÞC complex carbides are all decreased [Fig. 4(c)]. The largest Wads values are also found at a composition of ðNb0:5 Mo0:5 ÞC and ðNb0:25 V0:75 ÞC for ðNb1x Mox ÞC andðNb1x Vx ÞC composite carbides. The calculated results agree well with the experimental results that the replacement of Nb by Mo in NbC will reduce nucleation barrier of NbC, and thus enhance the
structure is NaCl type with FM3M space groups. The calculated bulk properties (including lattice constant, volume, and bulk modulus) and surface energies are listed in Table 1. The corresponding experimental data and other calculated values are also listed in Table 1. It can be seen that the calculated lattice constant a and bulk modulus B of TiC are 4.332 Å and 250 GPa, respectively, which are 0.07% and 3.33% larger than those of the experimental ones. Meanwhile, the surface energy of TiC(001) obtained in this work is 1.69 J/m2, which matches well with the calculated result of Medvedeva [25]. The GGA-determined bulk and surface properties of NbC are also in good agreement with the experimental ones. Therefore, the calculation method is accurate enough to be used in subsequent calculations. 3.2. Fe adsorption on (A1-xmx)C surface 3.2.1. Adsorption energy To explore the behavior of Fe adsorption on different composite carbides, we systemically calculated the adsorption energies of Fe on the (001) surface of Ti-based and Nb-based composite carbides (Figs. 3 and 4). For each adsorption system, the energetically favorable structures corresponding to the largest adsorption energy are connected with a solid line. The Wads values of Fe on pure transition metal carbides, including TiC, MoC, VC, and NbC, are also given in the figures. As displayed in Fig. 3, the Wads values of Fe on most of Ti-based carbides are significantly increased after the introduction of Mo, V, and 32
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Fig. 4. Adsorption energy of Fe on the (001) surface of (a) ðNb1x Mox ÞC; (b) ðNb1x Vx ÞC; (c) ðNb1x Tix ÞC. For each adsorption system, the largest adsorption energy at a given composition is connected with a solid line. N, M, and T are Nb, Mo, and Ti, respectively.
adsorption energies are 6.12, 6.43, 6.68, 6.33, and 5.97 eV for the Fe@(Ti1-xVx)C, Fe@(Ti1-xMox)C, Fe@(Nb1-xMox)C, Fe@(Nb1-xVx)C, and Fe@(Ti1-xNbx)C configurations, respectively. It is obvious that the addition of Mo by 50% in TiC and NbC will lead to the increase of adsorption energy by 10.48% and 10.60%, respectively. Based on these findings, the Fe–C bond length of Fe@ðTi0:5 Mo0:5 ÞC and Fe@ðNb0:5 Mo0:5 ÞC systems was calculated to be 1.694 and 1.675 Å, which are shorter than that of the others. Therefore, the two adsorption systems are further studied, and the details are presented in the following section.
nucleation of precipitates [44] and refine the prior austenite grain size in Nb–Mo steel [45,46]. Fig. 5 displays the largest adsorption energies and the corresponding Fe–C bond length for those five adsorption systems. The maximum
Table 2 Mulliken charge analysis for the Fe and surficial atoms in different carbides. Adsorbate
Species
s
P
d
Total
Charge (e)
TiC
Fe C Ti Fe C Mo Fe C Nb Fe C Mo
0.63 1.51 2.26 0.54 1.46 2.35 0.56 1.47 2.37 0.53 1.47 2.37
.48 3.16 6.48 .47 3.13 6.33 .48 3.19 6.27 .48 3.08 6.37
6.87 0.00 2.61 6.87 0.00 4.86 6.89 0.00 3.80 6.85 0.00 4.84
7.98 4.67 11.34 7.88 4.59 13.54 7.94 4.67 12.44 7.86 4.55 13.58
0.02 0.67 0.66 0.12 0.59 0.46 0.06 0.67 0.56 0.14 0.55 0.42
(Ti0.5Mo0.5)C
NbC
Fig. 5. The largest adsorption energies and the corresponding Fe–C bond length among the Fe@(A1-xmx)C systems. N, T, and M denote Nb, Ti, and Mo, respectively.
(Nb0.5Mo0.5)C
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Fig. 6. PDOS of surface atoms before and after Fe adsorption on the (Nb0.5Mo0.5)C(001) surface. PDOS of Fe atom (a) and C atom (b) before Fe adsorption, PDOS of Fe atom (c) and C atom (d) after Fe adsorption. The dotted line represents the Fermi level.
Fig. 8. PDOS of surface atoms. PDOS of free (Ti0.5Mo0.5)C(001) surface (a), Cr-doped (Ti0.5Mo0.5)C(001) surface (b), and Mn-doped (Ti0.5Mo0.5)C(001) surface (c). The dotted line represents the Fermi level.
3.2.2. Analysis of Mulliken charge and partial density of state Milliken population and partial density of state (PDOS) can be used to analyze the electronic structure and chemical bonding characteristics of adsorption structures. The atomic charges of absorbed Fe and surficial atoms (including C, Ti, Nb, and Mo) are listed in Table 2. When Fe atom is absorbed on TiC, (Ti0.5Mo0.5)C, NbC, and (Nb0.5Mo0.5)C, the lost charges of Fe atom are 0.02e, 0.12e, 0.06e, 0.14e, respectively. Compared with Fe@TiC and Fe@NbC systems, the number of charges transferred from surficial atoms in Fe@(Nb0.5Mo0.5)C and Fe@(Ti0.5Mo0.5)C systems decreases, whereas the number of charges transferred from Fe atom is increased. This suggests that the interactions between Fe, C, and Mo are enhanced due to the increase of the coordination number for the Fe atom. Moreover, the Fe adsorption ability for these carbides follows the order:
Fig. 7. Adsorption energy of Fe adsorption on the (001) surface of (Nb0.5Mo0.5)C and (Ti0.5Mo0.5)C covered with 3d transition metal. 34
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atom does not show obvious change compared with that before Fe adsorption. The reason is that the radius of Fe atom is larger than that of C atom, and therefore, the electronic orbitals of C are difficult to be polarized. This suggests that the large adsorption ability of (Nb0.5Mo0.5)C can ensure the stability of adsorbed iron. Moreover, the obvious hybridization between Fe-d orbital and C-s orbital can be found in the ranges of 7.5 eV to 2.3 eV [Fig. 6c and d)], which results in the formation of strong covalent bonding. This further explains why the (Nb0.5Mo0.5)C system has the highest Fe adsorption capacity. 3.3. Fe adsorption on the 3d-TM-doped (A0.5Mo0.5)C surface Fig. 7 gives the adsorption energies of Fe adatom on the (Nb0.5Mo0.5)C(001) and (Ti0.5Mo0.5)C(001) surface covered with 3d TM (TM ¼ Ti, V, Cr, Mn, Co, and Ni). The Wads values of 3d-TM-doped systems are all larger than those of the clean ones, as the coordination number of the adsorbed Fe atom is increased due to the formation of Fe–Mo, Fe–TM, and Fe–C bonds. Furthermore, the (Cr, Mn)-doped surfaces have the largest Wads compared with the others among the two adsorption systems, which indicates that the initial layer on the (001) surface of (Nb0.5Mo0.5)C or (Ti0.5Mo0.5)C may contain Cr and Mn atoms. This also reveals that the introduction of Cr and Mn on (Nb0.5Mo0.5)C and (Ti0.5Mo0.5)C surfaces can enhance the binding strength between Fe and the surfaces, and thus it obviously improves the subsequent Fe adsorption. Moreover, the segregation of 3d alloying elements in the Fe/(Nb0.5Mo0.5)C and Fe/(Ti0.5Mo0.5)C interfaces may result in additional hardening through preventing the movement of dislocations [47]. The PDOSs of surface atoms on both (Ti0.5Mo0.5)C(001) surface and (Nb0.5Mo0.5)C(001) surface with/without (Cr, Mn) dopant after Fe adsorption are presented in Fig. 8 and Fig. 9, respectively. For the Fe@(Ti0.5Mo0.5)C system (Fig. 5a), the orbital hybridization between Fe-3d and C-2p in the ranges of 7.5 eV to 2.3 eV suggests that the Fe–C covalent bonding is formed. Moreover, the obvious interaction between Fe-3d and Mo-3d orbital is observed from 2.5 eV to 2.3 eV, which leads to the formation of metallic bonds. When Cr and Mn are introduced in the Fe@(Ti0.5Mo0.5)C system (Fig. 5b–c), the PDOS values of C atom near 5 eV are increased, whereas those of Fe atom in the vicinity of Femi energy is decreased compared with the clean surface. This indicates that partial charges of Fe atom transfer to C atom, which results in the formation of strong chemical bonding. In addition, the heights of PDOS curves for Cr and Mn atoms are larger than those of Mo atom in the range of 2.5 eV to 2.5 eV, which indicates that the bonding strength between Fe and Cr/Mn atoms is larger than that of Fe and Mo atoms. Similarly, the PDOS of the Fe @ (Nb0.5Mo0.5)C system without and with Cr or Mn introduction shows the same change tendencies as those of the Fe@(Ti0.5Mo0.5)C system (Fig. 6a–c). All those analyzes further explain why the Cr and Mn atom on the (001) surface of (Ti0.5Mo0.5)C and (Nb0.5Mo0.5)C can enhance the subsequent nucleation potential. Fig. 9. PDOS of surface atoms. PDOS of free (Nb0.5Mo0.5)C(001) surface (a), Cr-doped (Nb0.5Mo0.5)C(001) surface (b), and Mn-doped (Nb0.5Mo0.5)C(001) surface (c). The dotted line represents the Fermi level.
4. Conclusions The first-principles method was performed to study Fe adsorption on the (001) surface of (A1-xmx)C (A ¼ Nb, Ti, m ¼ Mo, V) composite carbides to reveal the initialization of Fe nucleation and the influence of composition and structure of these carbides on Fe adsorption behavior. In addition, we discussed the Mulliken charge and partial density of states in this work. The results show that the calculated bulk and surface properties of TiC and NbC are consistent with experimental and other calculated results. The replacement of Ti (Nb) by Mo or V in the TiC (NbC) lattice favors Fe nucleation, which matches well with the experimental observation that grain size of steels can be refined by (Ti, Mo)C and (Nb, Mo)C. The nucleation capacity of ðTi1x Mox ÞC and ðTi1x Vx ÞC is superior to that of ðTi1x Nbx ÞC. Moreover, the largest adsorption energy is predicted for Fe on the (001) surface of (Nb0.5Mo0.5)C complex
(Nb0.5Mo0.5)C > (Ti0.5Mo0.5)C > NbC > TiC, which is in good agreement with the results of Wads. The PDOSs of surface atoms in the most stable adsorption configuration [Fe@(Nb0.5Mo0.5)C] are presented in Fig. 6. Before Fe adsorption on the (Nb0.5Mo0.5)C surface, the energy bands of C atom are located in the range of 14.35 eV to 2.33 eV. In addition, there is a single peak at 3.5 eV for the Fe-p orbital, and the centers of Fe-s and Fe-d orbitals correspond to the Fermi level. After Fe adsorption on the surface, all the orbitals of Fe atom shift to the lower energy level, and the peaks of these orbitals are significantly decreased. Meanwhile, the peak located at 3.5 eV for the Fe-p orbital disappears rapidly. The PDOS of surficial C
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carbides due to the formation of strong Fe–C and Fe–Mo bonding, which indicates that this complex carbide has the high nucleation potential at the early stage of solidification. In addition, the analysis of Fe adsorption on 3d-TM-doped (Nb0.5Mo0.5)C and (Ti0.5Mo0.5)C systems (TM ¼ Ti, V, Cr, Mn, Co and Ni) suggests that Cr and Mn have significant influence on the initial stage of nucleation. The relatively large adsorption energy of Fe on (Cr, Mn)-doped (A0.5Mo0.5)C is the result of the orbital hybridization between Fe, Cr, and Mn atoms in the range of 2.5 eV to 2.5 eV.
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Acknowledgments The authors gratefully acknowledge financial support by the National Natural Science Foundation of China (Grant No. 51174100 and 51564017) and Natural Science Foundation of Jiangxi Province, China (Grant No. 20171ACB21042). This work was carried out in the National Supercomputing Center in Shenzhen. References [1] L.I. Johansson, Electronic and structural properties of transition-metal carbide and nitride surfaces, Surf. Sci. Rep. 21 (1995) 177–250. [2] A. Arya, E.A. Carter, Structure, bonding, and adhesion at the TiC(100)/Fe(110) interface from first principles, J. Chem. Phys. 118 (2003) 8982–8996. [3] Y. Liu, Y. Jiang, R. Zhou, J. Feng, First principles study the stability and mechanical properties of MC (M ¼ Ti, V, Zr, Nb, Hf and Ta) compounds, J. Alloy. Comp. 582 (2014) 500–504. [4] L. Wu, Y. Wang, Z. Yan, J. Zhang, F. Xiao, B. Liao, The phase stability and mechanical properties of Nb–C system: using first-principles calculations and nanoindentation, J. Alloy. Comp. 561 (2013) 220–227. [5] G.K. Tirumalasetty, C.M. Fang, J. Jansen, T. Yokosawa, M.F.J. Boeije, J. Sietsma, M.A. Van Huis, H.W. Zandbergen, Structural tale of two novel (Cr, Mn)C carbides in steel, Acta Mater. 78 (2014) 161–172. [6] Z. Wang, H. Zhang, C. Guo, Z. Leng, Z. Yang, X. Sun, C. Yao, Z. Zhang, F. Jiang, Evolution of (Ti, Mo)C particles in austenite of a Ti–Mo-bearing steel, Mater. Des. 109 (2016) 361–366. [7] J. Guo, L. Liu, S. Liu, Y. Zhou, X. Qi, X. Ren, Q. Yang, Stability of eutectic carbide in Fe-Cr-Mo-W-V-C alloy by first-principles calculation, Mater. Des. 106 (2016) 355–362. [8] A. Nagao, M.L. Martin, M. Dadfarnia, P. Sofronis, I.M. Robertson, The effect of nanosized (Ti,Mo)C precipitates on hydrogen embrittlement of tempered lath martensitic steel, Acta Mater. 74 (2014) 244–254. [9] J. Yang, J. Huang, D. Fan, S. Chen, X. Zhao, Comparative investigation on Re(La,Ce) AlO3(100)/γ-Fe(100) interfaces: a first-principles calculation, Appl. Surf. Sci. 384 (2016) 207–216. [10] H.H. Xiong, H.H. Zhang, H.N. Zhang, Y. Zhou, Effects of alloying elements x (x ¼ Zr, V, Cr, Mn, Mo, W, Nb, Y) on ferrite/TiC heterogeneous nucleation interface: firstprinciples study, J. Iron Steel Res. Int. 24 (2017) 328–334. [11] J. Yang, P. Zhang, Y. Zhou, J. Guo, X. Ren, Y. Yang, Q. Yang, First-principles study on ferrite/TiC heterogeneous nucleation interface, J. Alloy. Comp. 556 (2013) 160–166. [12] H. Sawada, S. Taniguchi, K. Kawakami, T. Ozaki, First-principles study of interface structure and energy of Fe/NbC, Modell Simul. Mater. Sci. Eng 21 (2013) 045012–045025. [13] J.C. Li, H.Q. Song, J.W. Wang, J. Shen, Atomic study of semi-coherent interfacial structure at Fe[110]/TMC[001] (TM ¼ V, Nb and Ta) interfaces, Adv. Mater. Res. 1081 (2015) 232–236. [14] Y. Li, Y. Gao, B. Xiao, T. Min, S. Ma, D. Yi, Theoretical calculations on the adhesion, stability, electronic structure, and bonding of Fe/WC interface, Appl. Surf. Sci. 257 (2011) 5671–5678. [15] J.H. Jang, C.H. Lee, Y.U. Heo, D.W. Suh, Stability of (Ti, M)C (M ¼ Nb, V, Mo and W) carbide in steels using first-principles calculations, Acta Mater. 60 (2012) 208–217. [16] D.H.R. Fors, S.a.E. Johansson, M.V.G. Petisme, G. Wahnstr€ om, Theoretical investigation of moderate misfit and interface energetics in the Fe/VN system, Comp. Mater. Sci. 50 (2010) 550–559. [17] A. Arya, E.A. Carter, Structure, bonding, and adhesion at the ZrC(100)/Fe(110) interface from first principles, Surf. Sci. 560 (2004) 103–120. [18] K. K adas, O. Eriksson, N.V. Skorodumova, Highly anisotropic sliding at TiN/Fe interfaces: a first principles study, J. Appl. Phys. 108 (2010) 113511–113516. [19] C. Wang, Y. Dai, H. Gao, X. Ruan, J. Wang, B. Sun, Ab initio molecular dynamics study of Fe adsorption on TiN (001) surface, Mater. Trans. 51 (2010) 2005–2008.
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Journal of Physics and Chemistry of Solids journal homepage: www.elsevier.com/locate/jpcs
Investigation of iron adsorption on composite transition metal carbides in steel by first-principles calculation Hui-Hui Xiong a, b, *, Lei Gan a, Zhi-Fang Tong a, Heng-Hua Zhang b, Yang Zhou a a b
School of Metallurgy and Chemical Engineering, Jiangxi University of Science and Technology, Ganzhou, 341000, China School of Materials Science and Engineering, Shanghai University, Shanghai 200072, China
A R T I C L E I N F O
A B S T R A C T
Keywords: Adsorption energy Composite transition metal carbides First-principles calculation Iron
The nucleation potential of transition metal (TM) carbides formed in steel can be predicted by the behavior of iron adsorption on their surface. Therefore, Fe adsorption on the (001) surface of (A1-xmx)C (A ¼ Nb, Ti, m ¼ Mo, V) was investigated by the first-principles method to reveal the initialization of Fe nucleation. The Mulliken population and partial density of state (PDOS) were also calculated and analyzed in this work. The results show that Fe adsorption depends on the composition and configuration of the composite carbides. The adsorption energy (Wads) of Fe on most of (A1-xmx)C is larger than that of Fe on pure TiC or NbC. The maximum Wads is found for Fe on (Nb0.5Mo0.5)C complex carbide, indicating that this carbide has the high nucleation capacity at early stage. The Fe adsorption could be improved by the segregation of Cr and Mn atoms on the surfaces of (Nb0.5Mo0.5) C and (Ti0.5Mo0.5)C. The PDOS analysis of (Cr, Mn)-doped systems further explains the strong interactions between Fe and Cr or Mn atoms.
1. Introduction Because of their excellent yield strength and toughness, high-strength low-alloy (HSLA) steels have been widely used in many fields, such as high-pressure vessels, ships, railways, and energy transportation [1–5]. The mechanical properties of HSLA steels can be controlled through dispersion strengthening and grain refinement [6]. Grain refinement can be achieved by the heterogeneous nucleation of ferrite and austenite on the transition metal (TM) carbides [7,8]. Actually, the interfacial energy between carbides and matrix can be used to evaluate the nucleation potential for various carbides [9,10]. For example, Yang et al. [11] investigated the electronic, structural, and interfacial properties of the Fe–TiC interface by first-principles calculations, and found that ferrite heterogeneous nucleation preferably occurred on the C-termination interface. Similarly, the first-principles method was also used to study the Fe–NbC [12,13], Fe–WC [14,15], Fe–VN [16], Fe–ZrC [17], Fe–TiN [18,19] interfaces, and their interfacial properties and bonding characteristics were revealed. In addition, the interfacial energies of coherent and semicoherent fcc Fe/MX and bcc Fe/MX (M ¼ Ti, Zr, Hf, V, Nb, Ta, X ¼ C, N) were explored using the first-principles approach [20–22], which confirmed that NbC has the largest nucleation potential. It is reported that heterogeneous nucleation during the early stage of solidification is an adsorption process [23,24], and the larger adsorption
ability of Fe atoms on the precipitate surface is associated with a higher nucleation potential of particles. At present, first-principles calculations have been considerably applied to research the metal atom adsorption on particle surfaces, which can provide the atomic and electronic structures of the adsorption system. Wang et al. [19] used density functional theory (DFT) simulations to study the adsorption of Fe on the TiN(001) surface, and the heterogeneous nucleation mechanism of Fe on TiN precipitate was revealed. Furthermore, the iron adsorption on the (001) surface of TM carbides and nitrides was calculated using the first-principles method, and the nucleation tendency and potential of these precipitates in steel were confirmed [25]. Besides the pure carbides, the addition of alloying elements also could result in the formation of composite carbides in steel, such as (Ti, Mo)C [26], (Ti, V)C [27], and (Nb, Mo)C [28]. Those particles can lead to grain refinement and thus improve mechanical properties of steel. However, the theoretical research of Fe adsorption on composite carbide surfaces has not been previously reported in the literature. In this article, first-principles calculations about Fe adsorption on the possible (001) surfaces of composite carbides (A1-xmx)C (A ¼ Nb or Ti, m ¼ Mo, V) were performed to explore their nucleation behaviors. The electronic structure and bonding characteristics of those adsorption structures were also analyzed. Moreover, the segregation of alloying elements on (A1-xmx)C surfaces may affect the Fe adsorption, as is the case
* Corresponding author. School of Metallurgy and Chemical Engineering, Jiangxi University of Science and Technology, Ganzhou, 341000, China. E-mail address: [email protected] (H.-H. Xiong). https://doi.org/10.1016/j.jpcs.2018.01.013 Received 11 September 2017; Received in revised form 9 January 2018; Accepted 10 January 2018 Available online 10 January 2018 0022-3697/© 2018 Elsevier Ltd. All rights reserved.
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Journal of Physics and Chemistry of Solids 116 (2018) 30–36 Table 1 Calculated lattice constants “a,” volume “V0,” bulk modulus “B,” and surface energy “γs” [(001) surface] of NbC and TiC compared with experimental results and other references. Phases
Method
a ¼ b ¼ c (Å)
V0 (Å3)
B (GPa)
γs (J/m2)
TiC
GGAthis work GGA [36] Expt. [37] GGAthis work GGA-PBE [38] Exp. [39]
4.332 4.331 4.329 4.480 4.493 4.470
81.3 81.2 81.1 89.9
250 248 242 301 307 311 [40]
1.69 1.60 [25]
NbC
89.3
1.49 1.42 [25] 1.55 [41]
the calculations in this work. The ultra-soft pseudopotential method [33] was used to describe the interactions between ionic core and valence electrons. The valence electrons of the atoms chosen were Nb 4s24p64d45s1, Ti 3s23p63d24s2, and C 2s22p2, respectively. Generalized gradient approximation (GGA) of Perdew–Burke–Ernzerh of(PBE) functional [34] was used to treat the exchange–correlation interactions. The Brillouin zone was sampled with the Monkhorst–Pack k-point grid. The cutoff energy was selected as 400 eV and the k-point sampling was set as 8 8 8 for the bulk and 8 8 1 for the surfaces, respectively. The geometry optimization was performed using the Broyden–Fletcher–Goldfarb–Shanno (BFGS) algorithm [35] to achieve relaxation of atoms fully. The convergence parameters used in the calculations were as follows: total energy tolerance, 1.0 105 eV/atom; maximum force tolerance, 0.03 eV/Å; and maximal displacement, 1.0 104 nm. Lekakh et al. [25] have demonstrated that the optimal adsorption position for Fe on TMC(001) is the C-top site instead of the TM-top site or bridge site. Therefore, the Fe adsorption on only the C-top site of TMC(001) was considered in this work. First, we established the model of Fe adsorption on complex carbides with different configurations of (A1-xmx)C. Taking the Fe adsorption on the 2 1 (Nb1-xmx)C(001) surface (Fig. 1) for example, each adsorption model consists of eight atomic layers with four atoms in each layer that corresponds to the Fe monolayer (ML) covering of 0.25ML. The atomic structures of (Nb1-xmx)C (x ¼ 0, 0.25, 0.50, and 1) with different stacking sequences are shown in Fig. 1 (b)-(d). In Fig. 1 (a), Fe adsorption on the NbC(001) surface is defined as “Fe@NbC” (where A@B means A adsorption on B) and N and m represent Nb and alloying elements (e.g., Mo, V, and Ti), respectively. It is reported that Fe adsorption can be affected by the segregation of alloying elements on TM carbide surfaces [25]. Therefore, we also studied iron adsorption on the (A1-xmx)C(001) surface covered with 3d TM(TM ¼ Ti, V, Cr, Mn, Co, and Ni) to understand how these substitutional atoms influence the Fe nucleation. The (Nb0.5Mo0.5)C and (Ti0.5Mo0.5)C complexes, having the relatively large Fe adsorption ability (see the “Adsorption Energy” section), were chosen to investigate the influences of 3d TM on Fe adsorption. Fig. 2 shows the supercell structure of Fe adsorption on the 3d-TM-doped 2 2 (Nb0.5Mo0.5)C(001) surface; each adsorption model is composed of eight atomic layers with one 3d atom substituting an Mo atom in the first layer. Here the nonmagnetic iron was considered due to the simulation of the initial process. The adsorption energy (Wads) of Fe on complex carbide surfaces is derived according to the following equation:
Fig. 1. (a) Supercell model of Fe adsorption on NbC(001) surface. Atomic structures of (b) ðNb0:75 m0:25 ÞC, (c) ðNb0:5 m0:5 ÞC, (d) ðNb0:25 m0:75 ÞC, where N and m represent Nb and alloying elements (e.g., Mo, V, and Ti). The brown, blue, and red spheres are C, Nb, and Fe atoms, respectively. The stacking sequence of (Nb1-xmx)C is shown from the top to the bottom. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)
with Ni alloys with Ni3Al precipitate [29,30]. Therefore, we also discuss the Fe adsorption on 3d-TM-doped (Nb0.5Mo0.5)C and (Ti0.5Mo0.5)C (TM ¼ Ti, V, Cr, Mn, Co and Ni) to reveal the influence of these alloying elements on the subsequent Fe nucleation. 2. Calculation method and details The Cambridge serial total energy package (CASTEP) code [31,32], which is based on density functional theory (DFT), was used for all
Wads ¼ EFe þ Esurface EFeþsurface
(1)
where Esurface and EFe are the total energy of composite carbide surfaces and a single Fe atom, respectively. EFeþsurface is the total energy of carbide surfaces adsorbing Fe atom. 3. Results and discussion Fig. 2. Supercell structure of Fe adsorption on 3d-TM-doped 2 2 (Nb0.5Mo0.5)C(001) surface (a), top view of the adsorption system (b). The black, brown, blue, pink, and red spheres are 3d-TM, C, Nb, Mo, and Fe atoms, respectively. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)
3.1. Bulk and surface properties of NbC and TiC To make sure the accuracy of our calculation methods, we carried out a series of calculations on the properties of NbC and TiC, whose crystal
31
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Journal of Physics and Chemistry of Solids 116 (2018) 30–36
Fig. 3. Adsorption energy of Fe on the (001) surface of (a) ðTi1x Mox ÞC; (b) ðTi1x Vx ÞC; (c) ðTi1x Nbx ÞC. For each adsorption system, the largest adsorption energy at a given composition is connected with a solid line. T, M, and N represent Ti, Mo, and Nb, respectively.
Nb, compared with those of Fe atom on the TiC, which implies that the addition of these alloying elements in the TiC lattice is in favor of Fe nucleation. Our calculations further support the experimental observation that the grain size of both ferrite and austenite in the Mo-added steels is smaller than that in the Mo-free steels [42]. Moreover, the nucleation capacity of ðTi1x Mox ÞC and ðTi1x Vx ÞC is superior to that of ðTi1x Nbx ÞC. For the three adsorption systems (Fig. 3), the largest Wads values are found at a composition of ðTi0:5 Mo0:5 ÞC, ðTi0:25 V0:75 ÞC; and ðTi0:25 Nb0:75 Þ, which are 6.43 eV, 6.12 eV, and 6.04 eV, respectively. In particular, compared with the Fe@TiC system, the Fe@ðTi0:5 Mo0:5 ÞC system with the MMTT structure exhibits a maximum increase of 0.61 eV in the Wads value. In addition, the Fe–C bond length (1.694 Å) of the Fe@ðTi0:5 Mo0:5 ÞC system is smaller than that of Fe@TiC (1.705 Å). This confirms that ðTi0:5 Mo0:5 ÞC has the strongest Fe absorption ability, which is further supported by the previous study [43] that the Fe–(Ti0.5Mo0.5)C interface has the lowest interfacial energy and thus (Ti0.5Mo0.5)C can be the effective heterogeneous nucleus of ferrite. When the Nb atoms in NbC are partly replaced by Mo or V atoms, most Nb-based complex carbides exhibit larger Fe adsorption capacity compared with pure NbC, as shown in Fig. 4(a-b). However, the adsorption energies of Fe on ðNb1x Tix ÞC complex carbides are all decreased [Fig. 4(c)]. The largest Wads values are also found at a composition of ðNb0:5 Mo0:5 ÞC and ðNb0:25 V0:75 ÞC for ðNb1x Mox ÞC andðNb1x Vx ÞC composite carbides. The calculated results agree well with the experimental results that the replacement of Nb by Mo in NbC will reduce nucleation barrier of NbC, and thus enhance the
structure is NaCl type with FM3M space groups. The calculated bulk properties (including lattice constant, volume, and bulk modulus) and surface energies are listed in Table 1. The corresponding experimental data and other calculated values are also listed in Table 1. It can be seen that the calculated lattice constant a and bulk modulus B of TiC are 4.332 Å and 250 GPa, respectively, which are 0.07% and 3.33% larger than those of the experimental ones. Meanwhile, the surface energy of TiC(001) obtained in this work is 1.69 J/m2, which matches well with the calculated result of Medvedeva [25]. The GGA-determined bulk and surface properties of NbC are also in good agreement with the experimental ones. Therefore, the calculation method is accurate enough to be used in subsequent calculations. 3.2. Fe adsorption on (A1-xmx)C surface 3.2.1. Adsorption energy To explore the behavior of Fe adsorption on different composite carbides, we systemically calculated the adsorption energies of Fe on the (001) surface of Ti-based and Nb-based composite carbides (Figs. 3 and 4). For each adsorption system, the energetically favorable structures corresponding to the largest adsorption energy are connected with a solid line. The Wads values of Fe on pure transition metal carbides, including TiC, MoC, VC, and NbC, are also given in the figures. As displayed in Fig. 3, the Wads values of Fe on most of Ti-based carbides are significantly increased after the introduction of Mo, V, and 32
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Journal of Physics and Chemistry of Solids 116 (2018) 30–36
Fig. 4. Adsorption energy of Fe on the (001) surface of (a) ðNb1x Mox ÞC; (b) ðNb1x Vx ÞC; (c) ðNb1x Tix ÞC. For each adsorption system, the largest adsorption energy at a given composition is connected with a solid line. N, M, and T are Nb, Mo, and Ti, respectively.
adsorption energies are 6.12, 6.43, 6.68, 6.33, and 5.97 eV for the Fe@(Ti1-xVx)C, Fe@(Ti1-xMox)C, Fe@(Nb1-xMox)C, Fe@(Nb1-xVx)C, and Fe@(Ti1-xNbx)C configurations, respectively. It is obvious that the addition of Mo by 50% in TiC and NbC will lead to the increase of adsorption energy by 10.48% and 10.60%, respectively. Based on these findings, the Fe–C bond length of Fe@ðTi0:5 Mo0:5 ÞC and Fe@ðNb0:5 Mo0:5 ÞC systems was calculated to be 1.694 and 1.675 Å, which are shorter than that of the others. Therefore, the two adsorption systems are further studied, and the details are presented in the following section.
nucleation of precipitates [44] and refine the prior austenite grain size in Nb–Mo steel [45,46]. Fig. 5 displays the largest adsorption energies and the corresponding Fe–C bond length for those five adsorption systems. The maximum
Table 2 Mulliken charge analysis for the Fe and surficial atoms in different carbides. Adsorbate
Species
s
P
d
Total
Charge (e)
TiC
Fe C Ti Fe C Mo Fe C Nb Fe C Mo
0.63 1.51 2.26 0.54 1.46 2.35 0.56 1.47 2.37 0.53 1.47 2.37
.48 3.16 6.48 .47 3.13 6.33 .48 3.19 6.27 .48 3.08 6.37
6.87 0.00 2.61 6.87 0.00 4.86 6.89 0.00 3.80 6.85 0.00 4.84
7.98 4.67 11.34 7.88 4.59 13.54 7.94 4.67 12.44 7.86 4.55 13.58
0.02 0.67 0.66 0.12 0.59 0.46 0.06 0.67 0.56 0.14 0.55 0.42
(Ti0.5Mo0.5)C
NbC
Fig. 5. The largest adsorption energies and the corresponding Fe–C bond length among the Fe@(A1-xmx)C systems. N, T, and M denote Nb, Ti, and Mo, respectively.
(Nb0.5Mo0.5)C
33
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Journal of Physics and Chemistry of Solids 116 (2018) 30–36
Fig. 6. PDOS of surface atoms before and after Fe adsorption on the (Nb0.5Mo0.5)C(001) surface. PDOS of Fe atom (a) and C atom (b) before Fe adsorption, PDOS of Fe atom (c) and C atom (d) after Fe adsorption. The dotted line represents the Fermi level.
Fig. 8. PDOS of surface atoms. PDOS of free (Ti0.5Mo0.5)C(001) surface (a), Cr-doped (Ti0.5Mo0.5)C(001) surface (b), and Mn-doped (Ti0.5Mo0.5)C(001) surface (c). The dotted line represents the Fermi level.
3.2.2. Analysis of Mulliken charge and partial density of state Milliken population and partial density of state (PDOS) can be used to analyze the electronic structure and chemical bonding characteristics of adsorption structures. The atomic charges of absorbed Fe and surficial atoms (including C, Ti, Nb, and Mo) are listed in Table 2. When Fe atom is absorbed on TiC, (Ti0.5Mo0.5)C, NbC, and (Nb0.5Mo0.5)C, the lost charges of Fe atom are 0.02e, 0.12e, 0.06e, 0.14e, respectively. Compared with Fe@TiC and Fe@NbC systems, the number of charges transferred from surficial atoms in Fe@(Nb0.5Mo0.5)C and Fe@(Ti0.5Mo0.5)C systems decreases, whereas the number of charges transferred from Fe atom is increased. This suggests that the interactions between Fe, C, and Mo are enhanced due to the increase of the coordination number for the Fe atom. Moreover, the Fe adsorption ability for these carbides follows the order:
Fig. 7. Adsorption energy of Fe adsorption on the (001) surface of (Nb0.5Mo0.5)C and (Ti0.5Mo0.5)C covered with 3d transition metal. 34
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atom does not show obvious change compared with that before Fe adsorption. The reason is that the radius of Fe atom is larger than that of C atom, and therefore, the electronic orbitals of C are difficult to be polarized. This suggests that the large adsorption ability of (Nb0.5Mo0.5)C can ensure the stability of adsorbed iron. Moreover, the obvious hybridization between Fe-d orbital and C-s orbital can be found in the ranges of 7.5 eV to 2.3 eV [Fig. 6c and d)], which results in the formation of strong covalent bonding. This further explains why the (Nb0.5Mo0.5)C system has the highest Fe adsorption capacity. 3.3. Fe adsorption on the 3d-TM-doped (A0.5Mo0.5)C surface Fig. 7 gives the adsorption energies of Fe adatom on the (Nb0.5Mo0.5)C(001) and (Ti0.5Mo0.5)C(001) surface covered with 3d TM (TM ¼ Ti, V, Cr, Mn, Co, and Ni). The Wads values of 3d-TM-doped systems are all larger than those of the clean ones, as the coordination number of the adsorbed Fe atom is increased due to the formation of Fe–Mo, Fe–TM, and Fe–C bonds. Furthermore, the (Cr, Mn)-doped surfaces have the largest Wads compared with the others among the two adsorption systems, which indicates that the initial layer on the (001) surface of (Nb0.5Mo0.5)C or (Ti0.5Mo0.5)C may contain Cr and Mn atoms. This also reveals that the introduction of Cr and Mn on (Nb0.5Mo0.5)C and (Ti0.5Mo0.5)C surfaces can enhance the binding strength between Fe and the surfaces, and thus it obviously improves the subsequent Fe adsorption. Moreover, the segregation of 3d alloying elements in the Fe/(Nb0.5Mo0.5)C and Fe/(Ti0.5Mo0.5)C interfaces may result in additional hardening through preventing the movement of dislocations [47]. The PDOSs of surface atoms on both (Ti0.5Mo0.5)C(001) surface and (Nb0.5Mo0.5)C(001) surface with/without (Cr, Mn) dopant after Fe adsorption are presented in Fig. 8 and Fig. 9, respectively. For the Fe@(Ti0.5Mo0.5)C system (Fig. 5a), the orbital hybridization between Fe-3d and C-2p in the ranges of 7.5 eV to 2.3 eV suggests that the Fe–C covalent bonding is formed. Moreover, the obvious interaction between Fe-3d and Mo-3d orbital is observed from 2.5 eV to 2.3 eV, which leads to the formation of metallic bonds. When Cr and Mn are introduced in the Fe@(Ti0.5Mo0.5)C system (Fig. 5b–c), the PDOS values of C atom near 5 eV are increased, whereas those of Fe atom in the vicinity of Femi energy is decreased compared with the clean surface. This indicates that partial charges of Fe atom transfer to C atom, which results in the formation of strong chemical bonding. In addition, the heights of PDOS curves for Cr and Mn atoms are larger than those of Mo atom in the range of 2.5 eV to 2.5 eV, which indicates that the bonding strength between Fe and Cr/Mn atoms is larger than that of Fe and Mo atoms. Similarly, the PDOS of the Fe @ (Nb0.5Mo0.5)C system without and with Cr or Mn introduction shows the same change tendencies as those of the Fe@(Ti0.5Mo0.5)C system (Fig. 6a–c). All those analyzes further explain why the Cr and Mn atom on the (001) surface of (Ti0.5Mo0.5)C and (Nb0.5Mo0.5)C can enhance the subsequent nucleation potential. Fig. 9. PDOS of surface atoms. PDOS of free (Nb0.5Mo0.5)C(001) surface (a), Cr-doped (Nb0.5Mo0.5)C(001) surface (b), and Mn-doped (Nb0.5Mo0.5)C(001) surface (c). The dotted line represents the Fermi level.
4. Conclusions The first-principles method was performed to study Fe adsorption on the (001) surface of (A1-xmx)C (A ¼ Nb, Ti, m ¼ Mo, V) composite carbides to reveal the initialization of Fe nucleation and the influence of composition and structure of these carbides on Fe adsorption behavior. In addition, we discussed the Mulliken charge and partial density of states in this work. The results show that the calculated bulk and surface properties of TiC and NbC are consistent with experimental and other calculated results. The replacement of Ti (Nb) by Mo or V in the TiC (NbC) lattice favors Fe nucleation, which matches well with the experimental observation that grain size of steels can be refined by (Ti, Mo)C and (Nb, Mo)C. The nucleation capacity of ðTi1x Mox ÞC and ðTi1x Vx ÞC is superior to that of ðTi1x Nbx ÞC. Moreover, the largest adsorption energy is predicted for Fe on the (001) surface of (Nb0.5Mo0.5)C complex
(Nb0.5Mo0.5)C > (Ti0.5Mo0.5)C > NbC > TiC, which is in good agreement with the results of Wads. The PDOSs of surface atoms in the most stable adsorption configuration [Fe@(Nb0.5Mo0.5)C] are presented in Fig. 6. Before Fe adsorption on the (Nb0.5Mo0.5)C surface, the energy bands of C atom are located in the range of 14.35 eV to 2.33 eV. In addition, there is a single peak at 3.5 eV for the Fe-p orbital, and the centers of Fe-s and Fe-d orbitals correspond to the Fermi level. After Fe adsorption on the surface, all the orbitals of Fe atom shift to the lower energy level, and the peaks of these orbitals are significantly decreased. Meanwhile, the peak located at 3.5 eV for the Fe-p orbital disappears rapidly. The PDOS of surficial C
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carbides due to the formation of strong Fe–C and Fe–Mo bonding, which indicates that this complex carbide has the high nucleation potential at the early stage of solidification. In addition, the analysis of Fe adsorption on 3d-TM-doped (Nb0.5Mo0.5)C and (Ti0.5Mo0.5)C systems (TM ¼ Ti, V, Cr, Mn, Co and Ni) suggests that Cr and Mn have significant influence on the initial stage of nucleation. The relatively large adsorption energy of Fe on (Cr, Mn)-doped (A0.5Mo0.5)C is the result of the orbital hybridization between Fe, Cr, and Mn atoms in the range of 2.5 eV to 2.5 eV.
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