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First principles study on surface structure and stability of alloyed cementite doped with Cr
Materials Letters 100 (2013) 170–172
Contents lists available at SciVerse ScienceDirect
Materials Letters journal homepage: www.elsevier.com/locate/matlet
First principles study on surface structure and stability of alloyed cementite doped with Cr Yang Gao a, Zhiqing Lv a, Shuhua Sun a,b, Minggui Qu a, Zhongping Shi a, Ronghua Zhang a, Wantang Fu a,n a b
State Key Laboratory of Metastable Materials Science and Technology, Yanshan University, Qinhuangdao 066004, China College of Science, Yanshan University, Qinhuangdao 066004, China
a r t i c l e i n f o
a b s t r a c t
Article history: Received 12 December 2012 Accepted 25 February 2013 Available online 7 March 2013
First-principles calculations were carried out to investigate the surface structure and stability of orthorhombic cementite (y-Fe3C) and alloyed cementite doped with Cr (Fe2CrC), based on densityfunctional theory (DFT). The influence of Cr-doping on the surface stability of the cementite was analyzed and predicted. The results show that at a temperature of 0 K and under a pressure of 0 GPa, the surface stability of both Fe3C and Fe2CrC gradually decreased from (001) and (010) to (100), with each Fe2CrC surface being less stable than the corresponding Fe3C surface. Cr-doping can weaken the strength of the Fe–C bond in the cementite, and stronger surface localized Fe–C bonds may be one of the main reasons for greater surface stability. & 2013 Elsevier B.V. All rights reserved.
Keywords: Metals and alloys Surfaces Structure and stability First principles Bond strength Simulation and modeling
1. Introduction As one of the essential phases in carbon steels and white cast iron, cementite plays a critical role in their strength and toughness [1–3]. Some alloying elements (such as Cr or Mn) can appear in the cementite phase during heat treatment or hot working, and influence the structure, characteristics, morphology and growth kinetics of cementite [4–6]. There are many theoretical and experimental studies that have been reported on the crystal structure, magnetism, formation enthalpy and other properties of the bulk cementite [7–9]. The present group has also studied the electronic structure and formation enthalpy of (Fe, M)3C (M ¼Cr/Mn/Co/Ni), and concluded that Cr/Mn doping can enhance the stability of cementite, and Co/Ni doping is opposite [10,11]. However, cementite stability is not only related to the crystal structure and stability of the bulk phase, but is also closely related to the surface properties and interfaces in the steels [2,3,7–17]. Chiou et al. [12] calculated the stability of several Fe3C surfaces using DFT, and predicted that the Fe3C (001) surface is the most stable while the Fe3C (100) surface is the least stable, and that the surface energies of cementite are lower than those of all pure Fe. However, so far there have been very few reports on the surface properties of alloyed cementite. In particular the influence of Crdoping on the surface structure and stability of cementite is not very clear.
n
Corresponding author. Tel.: þ86 335 8074036; fax: þ 86 335 8057068. E-mail address: [email protected] (W. Fu).
0167-577X/$ - see front matter & 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.matlet.2013.02.095
In the present work, the structure and stability of several lowindex surfaces for alloyed cementite doped with Cr (Fe2CrC) are calculated using DFT, and are compared with a corresponding Fe3C surface, in order to establish the relationship between cementite surface stability before and after being doped with alloying elements, and to provide a theoretical basis for further studies on homophase (such as grain boundaries) and heterophase (such as cementite–ferrite) interfaces.
2. Crystal structure and calculation details Cementite (y-Fe3C) has an orthorhombic structure and a space group of Pnma (S.G. No. 62) with four formula units (Z ¼4) per cell, where eight iron atoms are in ‘‘general’’ positions (Feg), and four iron atoms in ‘‘special’’ positions (Fes) and four carbon atoms are in the interstices [18,19]. Fes (Feg) atoms in cementite are replaced by Cr, and the alloyed cementite Fe2CrC (FeCr2C) is formed. All calculations were carried out with CASTEP based on DFT [20,21] at a temperature of 0 K and pressure of 0 GPa. Electron exchange and correlation were approximated using the Perdew– Burke–Ernzerhof (PBE) scheme of generalized gradient approximation (GGA) [7,10–12]. The Vanderbilt Ultrasoft pseudopotentials (USPP) [22] were used to describe the electron–ion interaction. For the first Brillouin zone sampling, the Monkhorst–Pack Scheme [23] was adopted. The kinetic energy cutoff of 330 eV and a 5 4 6 mesh of k-points were used in the calculations of Fe3C and Fe2CrC bulk cell [10,11].
Y. Gao et al. / Materials Letters 100 (2013) 170–172
The three most common cementite surfaces among the orientation relationships between cementite and ferrite [14–17] were cleaved from relaxed Fe3C and Fe2CrC bulk cells: (001), (010) and (100). The three surfaces had stoichiometric layers corresponding to the three bulk unit cells [12]. One bulk unit cell is four Fe3C (Fe2CrC) layers for (001) and (100) surfaces, and two Fe6C2 (Fe4Cr2C2) layers for the (010) surface. A vacuum slab thickness of the surface was built equivalent to the corresponding slab thickness [12,24]. The kinetic energy cutoff of 330 eV and k-point meshes of 5 4 1, 1 6 5, and 1 4 6 for the (001), (010), and (100) surfaces were adopted respectively. The convergence criteria for geometry optimization were set to ultra-fine quality, which means the tolerance for SCF, energy, maximum force and maximum displacement was 5 10 7 eV/atom, 5 10 6 eV/ ˚ respectively. atom, 0.01 eV/A˚ and 5 10 4 A,
3. Results and analysis Bulk cementite: In order to verify the reliability of our calculation method, the lattice parameters, cohesive energy and formation enthalpy of bulk Fe3C and Fe2CrC were calculated, and were compared with the experimental and other calculated values. The calculated lattice parameters (4.9969, 6.7023, and 4.4439) of bulk Fe3C coincide well with the experimental values (5.0875, 6.7484, and 4.5219) [5], and the deviation is less than 1.8%. The deviation is less than 0.7% between the calculated Fe2CrC lattice parameters (5.0153, 6.8416, and 4.3817) and other theoretical values (5.0201, 6.8606, and 4.3907) [10]. Thus it can be seen that the optimized crystal structures of the surfaces are sufficiently precise. According to the equation (2) in Ref. [10], cohesive energy of Fe2CrC and Fe3C were calculated. The calculated values ( 38.569 eV for Fe2CrC, and 37.683 eV for Fe3C) agree well with other theoretical predictions ( 38.640 eV for Fe2CrC, and 37.608 eV for Fe3C) [6,10]. Hence the calculated surface stability of cementite and alloyed cementite should be effective and reliable using the above method. Cementite surface: Surface structural relaxation: In order to analyze the influence of Cr-doping on the structure and stability of the cementite surface, several properties of Fe3C and Fe2CrC surfaces were calculated, and the results are listed in Table 1. With the purpose of directly comparing the stability of Fe3C and Fe2CrC surfaces, the surface energy is calculated by Esurf ¼ ðEslab NEbulk Þ=2A. Here, N is the number of bulk cementite (Fe3C or Fe2CrC) units in the slab, Ebulk and Eslab are the total energy of bulk cementite and the slab respectively, and A is the surface area of the slab. From the surface energy (Esurf) listed in Table 1, it can be found that both Fe3C and Fe2CrC surface stabilities gradually decrease from (001), and (010) to (100). And the Esurf of each Fe2CrC surface is larger than that of the corresponding Fe3C surface, which indicates that the surface of Fe2CrC is less stable than the corresponding Fe3C surface. In addition, the stability of the Fe2CrC (001) surface is greater than that of the Fe3C (100) surface, and similar to that of Fe3C (010) surface.
171
After surface relaxation, atomic binding characterization shows different findings. The (001) and (100) surface C atoms of Fe3C and Fe2CrC are all 5-coordinate, while the coordination number of the (010) surface C atoms is 6, because the (010) surface is Fe-terminated and does not possess exposed C atoms. The statistically analytical results of the surface M–C (M ¼Fe/ Cr) bonds are listed in Table 1. As shown in Table 1, for Fe3C and Fe2CrC surfaces respectively, the (001) surface average Fe–C bond length is the shortest, while the (100) surface mean Fe–C bond length is the longest, even longer than that of the bulk-like layer ˚ For the Fe2CrC surface, the Fe–C bond is the shortest (about 2 A). and the Cr–C bond is the longest in the most stable (001) surface, while the least stable (100) surface is the opposite. The mean Fe– C bond length in Fe2CrC surface is longer than that in the corresponding Fe3C surface, which indicates that Cr-doping weakens the Fe–C bond. The Cr–C bonds are stronger than the Fe–C bonds in the Fe2CrC surface, and thus the stronger surface localized Fe–C bond may be one of the main reasons for greater surface stability. Surface electronic structure: Fig. 1 shows the partial densities of states (PDOSs) for bulk Fe2CrC (Fe8Cr4C4) and its (001), (010) and (100) surface outer layer (Fe8Cr4C4). No band gap near the Fermi level indicates that the Fe2CrC bulk cell and surface have a metallic characteristic. As shown in Fig. 1, the lowest valence band, mostly composed of C 2s, presents some differences. The lowest valence band of the (010) surface is similar to bulk Fe2CrC and ranges from 14.5 to 10.5 eV, while that of the (001) and (100) surfaces separates into two parts: for the (001) surface the first one ranges from 14.5 to 11.6 eV and the second one ranges from 11.6 to 10.0 eV; for the (100) surface the first one is from 14.5 to 11.3 eV and the second one is from 11.3 to 9.7 eV. It can be concluded that the exposed C atom in the (001) and (100) surfaces is the origin of that separation. And the expansion of the lowest valence band in the (001) and (100) surfaces results in the phenomenon that the empty band width between the lower and upper valence bands decreases. The empty band width follows the order of (010)4(001) 4(100), which in turn determines the ionicity order of (010) 4(001)4(100). Fig. 2 shows the electron density differences maps of the Fe3C and Fe2CrC (001) surface atoms. As shown in Fig. 2, the red regions (lost electron) of the Fe3C (001) surface Fe and C atoms are larger than those of the corresponding Fe2CrC surface atoms, which means that the Fe3C (001) surface Fe and C atoms contribute more electrons to the bonds. For the other two surfaces, the regularities are analogous to the (001) surface.
4. Conclusions First-principles calculations were carried out to investigate the surface structure and the stabilities of orthorhombic cementite and alloyed cementite (Fe2CrC) with DFT. The comparison of the Fe2CrC surface structure and electronic characteristics with Fe3C reveals that the surface stability of both Fe3C and Fe2CrC gradually decreases from (001) and (010) to (100), and the surface of
Table 1 Surfaces properties of Fe3C and Fe2CrC. Fe3C
Surface properties
2
Esurf (J/m ) ˚ Surfaces mean bond length (A)
Fe–C Cr–C
Fe2CrC
(001)
(010)
(100)
(001)
(010)
(100)
2.472 1.867 –
2.802 1.968 –
2.979 2.012 —
2.801 1.876 2.045
2.993 1.980 1.996
3.026 2.057 1.890
172
Y. Gao et al. / Materials Letters 100 (2013) 170–172
Fig. 1. PDOSs of bulk Fe2CrC and its three surface outer layers.
Fig. 2. Electron density difference map of Fe3C and Fe2CrC (001) surface outermost layer atoms from 0.212 (blue) to 0.174 (red) e A˚ 3 (a) Fe3C; and (b) Fe2CrC, setting the slice parallel to the surface. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Fe2CrC is less stable than the corresponding Fe3C surface. Crdoping can weaken the Fe–C bond strength of cementite. The Cr– C bond is stronger than the Fe–C bond in Fe2CrC surfaces, and thus a stronger surface localized Fe–C bond may be one of the main reasons for the greater surface stability.
Acknowledgment This work was supported by the Research Fund for the Doctoral Program of Higher Education of China (No. 20101333110005) and the Natural Science Foundation of China (Nos. 51171161 and 51101137). References [1] Sun SH, Xiong Y, Zhao J, Lv ZQ, Li Y, Zhao DL, et al. Scripta Mater 2005;53:137–40. [2] Hono K, Ohnuma M, Murayama M, Nishida S, Yoshie A, Takahashi. T. Scripta Mater 2001;44:977–83. [3] Zhang XD, Godfrey A, Hansen N, Huang XX, Liu W, Liu. Q. Mater Charact 2010;61:65–72.
[4] Lv ZQ, Sun SH, Zhang ZH, Qv MG, Jiang P, Fu. WT. Mater Sci Eng A 2008;489:107–12. [5] Umemoto M, Liu ZG, Masuyama K, Tsuchiya. K. Scripta Mater 2001;45:391–7. [6] Zhou CT, Xiao B, Feng J, Xing JD, Xie XJ, Chen YH, et al. Comput Mater Sci 2009;45:986–92. [7] Lv ZQ, Zhang FC, Sun SH, Wang ZH, Jiang P, Zhang WH, et al. Comput Mater Sci 2008;44:690–4. [8] Haglund J, Grimvall G, Jarlborg. T. Phys Rev B 1991;44:2914. [9] Ledbetter H. Mater Sci Eng A 2010;527:2657–61. [10] Lv ZQ, Fu WT, Sun SH, Bai XH, Gao Y, Wang ZH, et al. J Magn Magn Mater 2011;323:915–9. [11] Wang CX, Lv ZQ, Fu WT, Li Y, Sun SH, Wang B. Solid State Sci 2011;13:1658–63. [12] Chiou WC, Carter EA. Surf Sci 2003;530:88–100. [13] Ohmori Y, Jung YC, Nakai K, Shioiri. H. Acta Mater 2001;49:3149–62. [14] Bagaryatskii. YA. Dokl Akad Nauk SSSR 1950;73:1161. [15] Isaichev IV. Zh Tekh Fiz 1947;17:835. [16] Pitch W. Acta Metall 1962;10:79. [17] Petch NJ. Acta Crystallogr 1953;6:96. [18] Herbstein FH, Smuts. J. Acta.Crystallogr 1964;17:1331. [19] Fasiska EJ, Jeffrey GA. Acta.Crystallogr 1965;19:463. [20] Hohenberg P, Kohn W. Phys Rev B 1964;136:864. [21] Kohn W, Sham LJ. Phys Rev A 1965;140:1133. [22] Vanderbilt D. Phys Rev B 1990;41:7892. [23] Monkhorst HJ, Pack JD. Phys Rev B 1976;13:5188. [24] Materials Studio Online Help. Accelrys Software Inc; 2002.
Contents lists available at SciVerse ScienceDirect
Materials Letters journal homepage: www.elsevier.com/locate/matlet
First principles study on surface structure and stability of alloyed cementite doped with Cr Yang Gao a, Zhiqing Lv a, Shuhua Sun a,b, Minggui Qu a, Zhongping Shi a, Ronghua Zhang a, Wantang Fu a,n a b
State Key Laboratory of Metastable Materials Science and Technology, Yanshan University, Qinhuangdao 066004, China College of Science, Yanshan University, Qinhuangdao 066004, China
a r t i c l e i n f o
a b s t r a c t
Article history: Received 12 December 2012 Accepted 25 February 2013 Available online 7 March 2013
First-principles calculations were carried out to investigate the surface structure and stability of orthorhombic cementite (y-Fe3C) and alloyed cementite doped with Cr (Fe2CrC), based on densityfunctional theory (DFT). The influence of Cr-doping on the surface stability of the cementite was analyzed and predicted. The results show that at a temperature of 0 K and under a pressure of 0 GPa, the surface stability of both Fe3C and Fe2CrC gradually decreased from (001) and (010) to (100), with each Fe2CrC surface being less stable than the corresponding Fe3C surface. Cr-doping can weaken the strength of the Fe–C bond in the cementite, and stronger surface localized Fe–C bonds may be one of the main reasons for greater surface stability. & 2013 Elsevier B.V. All rights reserved.
Keywords: Metals and alloys Surfaces Structure and stability First principles Bond strength Simulation and modeling
1. Introduction As one of the essential phases in carbon steels and white cast iron, cementite plays a critical role in their strength and toughness [1–3]. Some alloying elements (such as Cr or Mn) can appear in the cementite phase during heat treatment or hot working, and influence the structure, characteristics, morphology and growth kinetics of cementite [4–6]. There are many theoretical and experimental studies that have been reported on the crystal structure, magnetism, formation enthalpy and other properties of the bulk cementite [7–9]. The present group has also studied the electronic structure and formation enthalpy of (Fe, M)3C (M ¼Cr/Mn/Co/Ni), and concluded that Cr/Mn doping can enhance the stability of cementite, and Co/Ni doping is opposite [10,11]. However, cementite stability is not only related to the crystal structure and stability of the bulk phase, but is also closely related to the surface properties and interfaces in the steels [2,3,7–17]. Chiou et al. [12] calculated the stability of several Fe3C surfaces using DFT, and predicted that the Fe3C (001) surface is the most stable while the Fe3C (100) surface is the least stable, and that the surface energies of cementite are lower than those of all pure Fe. However, so far there have been very few reports on the surface properties of alloyed cementite. In particular the influence of Crdoping on the surface structure and stability of cementite is not very clear.
n
Corresponding author. Tel.: þ86 335 8074036; fax: þ 86 335 8057068. E-mail address: [email protected] (W. Fu).
0167-577X/$ - see front matter & 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.matlet.2013.02.095
In the present work, the structure and stability of several lowindex surfaces for alloyed cementite doped with Cr (Fe2CrC) are calculated using DFT, and are compared with a corresponding Fe3C surface, in order to establish the relationship between cementite surface stability before and after being doped with alloying elements, and to provide a theoretical basis for further studies on homophase (such as grain boundaries) and heterophase (such as cementite–ferrite) interfaces.
2. Crystal structure and calculation details Cementite (y-Fe3C) has an orthorhombic structure and a space group of Pnma (S.G. No. 62) with four formula units (Z ¼4) per cell, where eight iron atoms are in ‘‘general’’ positions (Feg), and four iron atoms in ‘‘special’’ positions (Fes) and four carbon atoms are in the interstices [18,19]. Fes (Feg) atoms in cementite are replaced by Cr, and the alloyed cementite Fe2CrC (FeCr2C) is formed. All calculations were carried out with CASTEP based on DFT [20,21] at a temperature of 0 K and pressure of 0 GPa. Electron exchange and correlation were approximated using the Perdew– Burke–Ernzerhof (PBE) scheme of generalized gradient approximation (GGA) [7,10–12]. The Vanderbilt Ultrasoft pseudopotentials (USPP) [22] were used to describe the electron–ion interaction. For the first Brillouin zone sampling, the Monkhorst–Pack Scheme [23] was adopted. The kinetic energy cutoff of 330 eV and a 5 4 6 mesh of k-points were used in the calculations of Fe3C and Fe2CrC bulk cell [10,11].
Y. Gao et al. / Materials Letters 100 (2013) 170–172
The three most common cementite surfaces among the orientation relationships between cementite and ferrite [14–17] were cleaved from relaxed Fe3C and Fe2CrC bulk cells: (001), (010) and (100). The three surfaces had stoichiometric layers corresponding to the three bulk unit cells [12]. One bulk unit cell is four Fe3C (Fe2CrC) layers for (001) and (100) surfaces, and two Fe6C2 (Fe4Cr2C2) layers for the (010) surface. A vacuum slab thickness of the surface was built equivalent to the corresponding slab thickness [12,24]. The kinetic energy cutoff of 330 eV and k-point meshes of 5 4 1, 1 6 5, and 1 4 6 for the (001), (010), and (100) surfaces were adopted respectively. The convergence criteria for geometry optimization were set to ultra-fine quality, which means the tolerance for SCF, energy, maximum force and maximum displacement was 5 10 7 eV/atom, 5 10 6 eV/ ˚ respectively. atom, 0.01 eV/A˚ and 5 10 4 A,
3. Results and analysis Bulk cementite: In order to verify the reliability of our calculation method, the lattice parameters, cohesive energy and formation enthalpy of bulk Fe3C and Fe2CrC were calculated, and were compared with the experimental and other calculated values. The calculated lattice parameters (4.9969, 6.7023, and 4.4439) of bulk Fe3C coincide well with the experimental values (5.0875, 6.7484, and 4.5219) [5], and the deviation is less than 1.8%. The deviation is less than 0.7% between the calculated Fe2CrC lattice parameters (5.0153, 6.8416, and 4.3817) and other theoretical values (5.0201, 6.8606, and 4.3907) [10]. Thus it can be seen that the optimized crystal structures of the surfaces are sufficiently precise. According to the equation (2) in Ref. [10], cohesive energy of Fe2CrC and Fe3C were calculated. The calculated values ( 38.569 eV for Fe2CrC, and 37.683 eV for Fe3C) agree well with other theoretical predictions ( 38.640 eV for Fe2CrC, and 37.608 eV for Fe3C) [6,10]. Hence the calculated surface stability of cementite and alloyed cementite should be effective and reliable using the above method. Cementite surface: Surface structural relaxation: In order to analyze the influence of Cr-doping on the structure and stability of the cementite surface, several properties of Fe3C and Fe2CrC surfaces were calculated, and the results are listed in Table 1. With the purpose of directly comparing the stability of Fe3C and Fe2CrC surfaces, the surface energy is calculated by Esurf ¼ ðEslab NEbulk Þ=2A. Here, N is the number of bulk cementite (Fe3C or Fe2CrC) units in the slab, Ebulk and Eslab are the total energy of bulk cementite and the slab respectively, and A is the surface area of the slab. From the surface energy (Esurf) listed in Table 1, it can be found that both Fe3C and Fe2CrC surface stabilities gradually decrease from (001), and (010) to (100). And the Esurf of each Fe2CrC surface is larger than that of the corresponding Fe3C surface, which indicates that the surface of Fe2CrC is less stable than the corresponding Fe3C surface. In addition, the stability of the Fe2CrC (001) surface is greater than that of the Fe3C (100) surface, and similar to that of Fe3C (010) surface.
171
After surface relaxation, atomic binding characterization shows different findings. The (001) and (100) surface C atoms of Fe3C and Fe2CrC are all 5-coordinate, while the coordination number of the (010) surface C atoms is 6, because the (010) surface is Fe-terminated and does not possess exposed C atoms. The statistically analytical results of the surface M–C (M ¼Fe/ Cr) bonds are listed in Table 1. As shown in Table 1, for Fe3C and Fe2CrC surfaces respectively, the (001) surface average Fe–C bond length is the shortest, while the (100) surface mean Fe–C bond length is the longest, even longer than that of the bulk-like layer ˚ For the Fe2CrC surface, the Fe–C bond is the shortest (about 2 A). and the Cr–C bond is the longest in the most stable (001) surface, while the least stable (100) surface is the opposite. The mean Fe– C bond length in Fe2CrC surface is longer than that in the corresponding Fe3C surface, which indicates that Cr-doping weakens the Fe–C bond. The Cr–C bonds are stronger than the Fe–C bonds in the Fe2CrC surface, and thus the stronger surface localized Fe–C bond may be one of the main reasons for greater surface stability. Surface electronic structure: Fig. 1 shows the partial densities of states (PDOSs) for bulk Fe2CrC (Fe8Cr4C4) and its (001), (010) and (100) surface outer layer (Fe8Cr4C4). No band gap near the Fermi level indicates that the Fe2CrC bulk cell and surface have a metallic characteristic. As shown in Fig. 1, the lowest valence band, mostly composed of C 2s, presents some differences. The lowest valence band of the (010) surface is similar to bulk Fe2CrC and ranges from 14.5 to 10.5 eV, while that of the (001) and (100) surfaces separates into two parts: for the (001) surface the first one ranges from 14.5 to 11.6 eV and the second one ranges from 11.6 to 10.0 eV; for the (100) surface the first one is from 14.5 to 11.3 eV and the second one is from 11.3 to 9.7 eV. It can be concluded that the exposed C atom in the (001) and (100) surfaces is the origin of that separation. And the expansion of the lowest valence band in the (001) and (100) surfaces results in the phenomenon that the empty band width between the lower and upper valence bands decreases. The empty band width follows the order of (010)4(001) 4(100), which in turn determines the ionicity order of (010) 4(001)4(100). Fig. 2 shows the electron density differences maps of the Fe3C and Fe2CrC (001) surface atoms. As shown in Fig. 2, the red regions (lost electron) of the Fe3C (001) surface Fe and C atoms are larger than those of the corresponding Fe2CrC surface atoms, which means that the Fe3C (001) surface Fe and C atoms contribute more electrons to the bonds. For the other two surfaces, the regularities are analogous to the (001) surface.
4. Conclusions First-principles calculations were carried out to investigate the surface structure and the stabilities of orthorhombic cementite and alloyed cementite (Fe2CrC) with DFT. The comparison of the Fe2CrC surface structure and electronic characteristics with Fe3C reveals that the surface stability of both Fe3C and Fe2CrC gradually decreases from (001) and (010) to (100), and the surface of
Table 1 Surfaces properties of Fe3C and Fe2CrC. Fe3C
Surface properties
2
Esurf (J/m ) ˚ Surfaces mean bond length (A)
Fe–C Cr–C
Fe2CrC
(001)
(010)
(100)
(001)
(010)
(100)
2.472 1.867 –
2.802 1.968 –
2.979 2.012 —
2.801 1.876 2.045
2.993 1.980 1.996
3.026 2.057 1.890
172
Y. Gao et al. / Materials Letters 100 (2013) 170–172
Fig. 1. PDOSs of bulk Fe2CrC and its three surface outer layers.
Fig. 2. Electron density difference map of Fe3C and Fe2CrC (001) surface outermost layer atoms from 0.212 (blue) to 0.174 (red) e A˚ 3 (a) Fe3C; and (b) Fe2CrC, setting the slice parallel to the surface. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Fe2CrC is less stable than the corresponding Fe3C surface. Crdoping can weaken the Fe–C bond strength of cementite. The Cr– C bond is stronger than the Fe–C bond in Fe2CrC surfaces, and thus a stronger surface localized Fe–C bond may be one of the main reasons for the greater surface stability.
Acknowledgment This work was supported by the Research Fund for the Doctoral Program of Higher Education of China (No. 20101333110005) and the Natural Science Foundation of China (Nos. 51171161 and 51101137). References [1] Sun SH, Xiong Y, Zhao J, Lv ZQ, Li Y, Zhao DL, et al. Scripta Mater 2005;53:137–40. [2] Hono K, Ohnuma M, Murayama M, Nishida S, Yoshie A, Takahashi. T. Scripta Mater 2001;44:977–83. [3] Zhang XD, Godfrey A, Hansen N, Huang XX, Liu W, Liu. Q. Mater Charact 2010;61:65–72.
[4] Lv ZQ, Sun SH, Zhang ZH, Qv MG, Jiang P, Fu. WT. Mater Sci Eng A 2008;489:107–12. [5] Umemoto M, Liu ZG, Masuyama K, Tsuchiya. K. Scripta Mater 2001;45:391–7. [6] Zhou CT, Xiao B, Feng J, Xing JD, Xie XJ, Chen YH, et al. Comput Mater Sci 2009;45:986–92. [7] Lv ZQ, Zhang FC, Sun SH, Wang ZH, Jiang P, Zhang WH, et al. Comput Mater Sci 2008;44:690–4. [8] Haglund J, Grimvall G, Jarlborg. T. Phys Rev B 1991;44:2914. [9] Ledbetter H. Mater Sci Eng A 2010;527:2657–61. [10] Lv ZQ, Fu WT, Sun SH, Bai XH, Gao Y, Wang ZH, et al. J Magn Magn Mater 2011;323:915–9. [11] Wang CX, Lv ZQ, Fu WT, Li Y, Sun SH, Wang B. Solid State Sci 2011;13:1658–63. [12] Chiou WC, Carter EA. Surf Sci 2003;530:88–100. [13] Ohmori Y, Jung YC, Nakai K, Shioiri. H. Acta Mater 2001;49:3149–62. [14] Bagaryatskii. YA. Dokl Akad Nauk SSSR 1950;73:1161. [15] Isaichev IV. Zh Tekh Fiz 1947;17:835. [16] Pitch W. Acta Metall 1962;10:79. [17] Petch NJ. Acta Crystallogr 1953;6:96. [18] Herbstein FH, Smuts. J. Acta.Crystallogr 1964;17:1331. [19] Fasiska EJ, Jeffrey GA. Acta.Crystallogr 1965;19:463. [20] Hohenberg P, Kohn W. Phys Rev B 1964;136:864. [21] Kohn W, Sham LJ. Phys Rev A 1965;140:1133. [22] Vanderbilt D. Phys Rev B 1990;41:7892. [23] Monkhorst HJ, Pack JD. Phys Rev B 1976;13:5188. [24] Materials Studio Online Help. Accelrys Software Inc; 2002.