- Email: [email protected]
Ab initio study of the structural and electronic properties of Nb2AlC
Computational Condensed Matter 6 (2016) 1e4
Contents lists available at ScienceDirect
Computational Condensed Matter journal homepage: http://ees.elsevier.com/cocom/default.asp
Ab initio study of the structural and electronic properties of Nb2AlC Ai-Jiao Xu a, *, Wen-Wu Zhong a, Xin Zhang b a b
College of Physics and Electronic Engineering, Taizhou University, Taizhou, 317000, PR China Ningbo Institute of Materials Technology and Engineering, Chinese Academy of Science, Ningbo, 315201, PR China
a r t i c l e i n f o
a b s t r a c t
Article history: Received 22 December 2015 Received in revised form 14 March 2016 Accepted 20 March 2016 Available online 22 March 2016
The structural and electronic properties of Nb2AlC have been studied using the ab initio pseudopotential approach based on density functional theory. The internal coordinates of Nb atom is determined to be (1/ 3, 2/3, 0.089). The equilibrium lattice parameters are computed to be a ¼ 3.119 Å and c ¼ 13.92 Å, in good agreement with experimental results. The band structure and density of states reveal that Nb2AlC is an electronic conductor. Both Nb 4d and Al 3p contribute to the electronic properties. Partial density of state indicates that a strong hybridization of Nb 4d and C 2p states. The charge density distribution shows that the Nb and C atoms form a strong NbeCeNb covalently bonded chain. © 2016 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
Keywords: Nb2AlC Crystal structure Electronic structure Ab initio
1. Introduction Nb2AlC is a ternary compound of the well-known MAX phases, which has been successfully fabricated by hot isostatically pressing [1], hot pressing [2] and magnetron sputtering [3], respectively. Nb2AlC has the space group P63/mmc with lattice parameters of a ¼ 3.10 Å and c ¼ 13.8 Å and its crystal structure is shown in Fig. 1. The bulk properties of Nb2AlC have been well studied. Similar to metals, Nb2AlC has good thermal conductivity of 22 W m1 K1 and electrical conductivity of 3.45 106 S m1 at room temperature [4]. Nb2AlC has a low Vickers hardness of ~4.5 GPa, which renders it a soft and machinable ceramics compared with traditional hard ceramics such as TiC, Al2O3 and Si3N4. Similar to ceramics, Nb2AlC has a comparative low density of 6.5 g/cm3 [5] and a high Young's modulus of 294 GPa. The four-point bending strength and fracture toughness were reported to be 443 MPa, and 5.9 MPa m1/2, respectively [2]. Moreover, Nb2AlC was reported to oxidize in air at 650 C by forming Nb oxides and NbAlO4 with a subparabolic oxidation kinetics [6]. Manoun [7] studied the compression behavior of Nb2AlC and found no phase transformation up to 50 G Pa. Salient properties make Nb2AlC a potential structuralfunctional material for high-temperature applications. Density functional-theory has been extensively used to investigate MAX phases, such as Ti3SiC2 [8e14], Ti3AlC2 [15e19], Ti2AlC
* Corresponding author. E-mail address: [email protected] (A.-J. Xu).
[20e30] and Ta4AlC3 [31e38]. For Nb2AlC, Sun et al. [24] calculated the elastic properties, including the bulk and shear moduli, Young's modulus and Poisson's ratio using ab initio calculations. Pressure effects on the structural and elastic properties of Nb2AlC were studied by Medkour et al. using ab initio calculations [39]. The basal-slipping behavior was also investigated theoretically by analyzing the stressestrain dependence that NbeAl bonds break during deformation, while the NbeC bond length decreases by 4.1% [40]. Although many physical properties of Nb2AlC have been studied systematically, the above mentioned theoretical calculations are not very comprehensive. In this work, we studied the internal coordinates, the lattice parameter and the electronic structure in Nb2AlC to get a better understanding of it. Our theoretically computed results are in good agreement with available experimental data. 2. Computation details For the ground-state electronic structure calculations within the density functional theory we used the standard CASTEP code [41], which employs the plane-wave pseudopotential method. The s, p valence orbitals of C, the s, p orbitals of Al as well as the s, p, and d orbitals of Nb were included in the calculation of partial density of states. One of the main features of CASTEP code is the internal coordinates can be automatically relaxed so that the crystal structure with the minimum energy can be obtained. For the calculation of the internal atom coordinates and the lattice parameters, the plane-wave energy cutoff and the Brillouin zone sampling were set
http://dx.doi.org/10.1016/j.cocom.2016.03.002 2352-2143/© 2016 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
2
A.-J. Xu et al. / Computational Condensed Matter 6 (2016) 1e4
Fig. 1. Crystal structure of Nb2AlC.
at 700 eV and 14 14 6 MonkhorstePack [42] special k-point meshes, respectively. Interactions of electrons with ion cores were represented by the Vanderbilit-type ultrasoft pseudopotential [43]. The electronic exchange-correlation energy was estimated according to Perdew-Wang generalized-gradient approximation (GGA-PW91) [44]. The Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm [45] was used to minimize the total energy and internal forces. The tolerances for geometry optimization were set as the difference in total energy being within 5 106 eV/atom, the maximum ionic Hellmann-Feynman force being within 0.01 eV/Å, the maximum stress being within 0.02 GPa and the maximum ionic displacement being within 5 104 Å. 3. Results and discussion Previous studies did not report the internal coordinate of Nb2AlC [24,39,40], while it is a fundamental parameter for many properties calculations. Our calculation was performed by optimizing both the internal coordinate and unit cell. In Nb2AlC, the position of the Nb atom is not fixed by the group symmetry and in this work, the calculated fractional coordinate of Nb atom is (1/3, 2/
3, 0.089). The calculated lattice parameter together with experimental values was listed in Table 1. From the table, we can see that our results are in good agreement with previous reported data. The deviation of lattice parameters is 0.38% for a and 0.22% for c compared with the experimental values reported by Salama. Moreover, we also calculated the bond length at the equilibrium atomic configuration, which is important for the following discussion of Nb2AlC. The calculated bond length of NbeC is 2.18 Å, which is close to those of 211 MAX compounds, such as TieC bond (2.12 Å) inTi2CdC [46]. The bond length of NbeAl is 3.92 Å, much longer than that of NbeC. If the difference in atomic size between C and Al is ignored, the longer bond length of NbeAl indicates that the bonding between them is comparatively weaker. For a better understanding of the tribological property of Nb2AlC, it is necessary to recall the hexagonal graphite, despite of many differences in their properties. Graphite is the most studied material with layered stacking planes of carbon atoms. The nearest distance of CeC within a plane is 1.42 Å, while that of interplanar CeC is around 3.35 Å [47]. Such crystal structure makes the interplanar bonding weaker than the planar bonding. As a result, graphite exhibits a low coefficient of friction and excellent lubricative properties due to the interplanar lower shear strength. Nb2AlC and hexagonal graphite share a lot in common on crystal structure. The structure of Nb2AlC can be described as near close-packed Nb layers interleaved with pure Al layers, with C atoms filling the octahedral sites between the Nb layers. The layers are bonded mainly by the weak NbeAl bonding. Therefore, it is concluded that Nb2AlC may possess a low coefficient of friction because of the relatively weak bonding. The computed density of Nb2AlC is 6.361 g/cm3 and it agrees well with the experimental value (6.474 g/cm3) found in the JCPDS data file and previous reported data (6.34 g/cm3) [48]. Based on the optimized cell configuration, the band structure was calculated and obtained. Fig. 2 shows the band structure along the high-symmetry lines of the Brillouin zone. It can be assessed that there is no gap at the vicinity of the Fermi level, whereas there is an overlapping of bonding and anti bonding states. As a result, Nb2AlC will exhibit metallic properties, much similar to Cr2AlC [49] and Ti2AlC [21]. The band structure demonstrates a strongly anisotropic feature with less c-axis energy dispersion, indicating the conductivity for single-crystal Nb2AlC is also anisotropic, i.e. the electrical conductivity along the c axis is lower than that in the ab plane. To better evaluate the nature of the chemical bonding, the electronic structure of Nb2AlC was studied. The calculated total density of states (TDOS) and partial density of states (PDOS) for Nb2AlC are presented in Fig. 3. The TDOS at the Fermi level is 3.40 states/(eV cell), which is much smaller than 6.46 states/(eV cell) for Cr2AlC, the maximum TDOS measured for MAX phases so far [23]. The zero gap and finite value at EF reveal the existence of metallic bonding in Nb2AlC. It is observed that the lowest valence bands from approximately 56.1 to 54.3 eV of the TDOS are formed by the Nb 5s states. The higher valence bands from about 32.5 to 30.2 eV are formed by Nb 4p with a small amount of C 2p states. The highest valence bands from 12.2 eV to 10.3 eV are formed
Table 1 Comparison of the calculated and experimental lattice parameter for Nb2AlC. Lattice parameters a (Å) 3.107 3.103 3.108 3.119
References c (Å)
expt. calc. calc. calc.
13.89 13.83 13.97 13.92
c/a expt. calc. calc. calc.
4.47 4.45 4.49 4.46
[1] [48] [48] This work
A.-J. Xu et al. / Computational Condensed Matter 6 (2016) 1e4
3
8
Energy (eV)
4 0 -4 -8 -12 -16
G A
H K
G
M L
H
Fig. 2. Calculated band structure along the high symmetry direction in the first Brillouin zone.
Fig. 4. Valence electron density of a slice of the ð1120Þ plane in a 2 2 1 supercell.
electronegative than Nb. The electron cloud of Al hardly overlaps with that of NbeCeNb chains, indicating relatively weak bonding between them, which may account for the low friction coefficient. These results are in agreement with the previous results on the strong MeC bonds, and weak MeA bonds [50,52].
Fig. 3. Total and partial density of states for Nb2AlC.
almost entirely from the C 2s states. The valence bands in the range from 7.2 to 3.2 eV are dominated by the highly hybridized Nd 4d and C 2p states, indicating a strong covalent interaction. The d-p interaction stabilizes the crystal structure and thus is the driving bonding force. From 3.0 to 0.8 eV, the bands are related to the weak hybridized Nb 4d and Al 3p states, which is in agreement with the long distance of NbeAl bond as discussed previously. At around the EF, the DOS mainly originates from Nb 4d with less contribution from Al 3p and C does not contribute to the DOS, therefore, Nb 4d electrons should mainly be involved in the conduction properties. These results are consistent with previous reports on MAX phases [50,51]. The conduction bands are provided by the antibonding Nb 4d states and less contribution from Al 3p states. In order to further understand the bonding behavior of Nb2AlC, we have calculated the charge density. Fig. 4 shows the charge density distribution for a slice of the ð1120Þ plane in a 2 2 1 supercell. The figure clearly shows that Nb and C form an NbeCeNb covalently bonded chain, which are interleaved and mirrored by Al atomic plane. The figure clearly shows that Nb and C form an NbeCeNb covalently bonded chain, which are interleaved and mirrored by Al atomic plane. The charge density is pulled from Nb atoms toward C atoms, which is due to the difference in the electronegativities of Nb and C. According to Pauling rule, C is more
4. Conclusion We have studied the structural and electronic properties of Nb2AlC using ab initio calculations. The calculated equilibrium lattice parameters agree with the available experimental results. The band structure indicates that Nb2AlC is an electronic conductor, and that the chemical bonding is anisotropic. TDOS and PDOS show a strong hybridization of Nb 4d and C 2p and a weak hybridization of N 4d and Al 3p. Strong NbeCeNb covalent bond chains have been identified. References [1] I. Salama, T. El-Raghy, M.W. Barsoum, J. Alloys Compd. 347 (2002) 271. [2] W. Zhang, N. Travitzky, C.F. Hu, Y.C. Zhou, P. Greil, J. Am. Ceram. Soc. 92 (2009) 2396. [3] T.H. Scabarozi, J. Roche, A. Rosenfeld, S.H. Lim, L. Salamanca-Riba, G. Yong, I. Takeuchi, M.W. Barsoum, J.D. Hettinger, S.E. Lofland, Thin Solid Films 517 (2009) 2920. [4] M.W. Barsoum, I. Salama, T. El-Raghy, J. Golczewski, W.D. Porter, H. Wang, H.J. Seifert, F. Aldinger, Metall. Mater. Trans. A Phys. Metall. Mater. Sci. 33 (2002) 2775. [5] M.W. Barsoum, Prog. Solid State Chem. 28 (2000) 201. [6] I. Salama, T. El-Raghy, M.W. Barsoum, J. Electrochem. Soc. 150 (2003) C152. [7] B. Manoun, R.P. Gulve, S.K. Saxena, S. Gupta, M.W. Barsoum, C.S. Zha, Phys. Rev. B 73 (2006) 024100. [8] R. Ahuja, O. Eriksson, J.M. Wills, B. Johansson, Appl. Phys. Lett. 76 (2000) 2226. [9] Y. Du, J.C. Schuster, H.J. Seifert, F. Aldinger, J. Am. Ceram. Soc. 83 (2000) 197. [10] Z.M. Sun, Y.C. Zhou, J. Mater. Chem. 10 (2000) 343. [11] B. Holm, R. Ahuja, B. Johansson, Appl. Phys. Lett. 79 (2001) 1450. [12] D.W. Shi, Y.C. Zhou, J. Mater. Sci. Technol. 18 (2002) 146.
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A.-J. Xu et al. / Computational Condensed Matter 6 (2016) 1e4 J.Y. Wang, Y.C. Zhou, J. Phys. Condes. Matter 15 (2003) 1983. R. Ahuja, Z. Sun, W. Luo, High. Press. Res. 26 (2006) 127. A.L. Ivanovskii, N.I. Medvedeva, M. Commun. 9 (1999) 36. X.H. Wang, Y.C. Zhou, J. Mater. Sci. Technol. 26 (2010) 385. Z.J. Lin, M.S. Li, Y.C. Zhou, J. Mater. Sci. Technol. 23 (2007) 145. X.M. Min, R. Yi, J. Wuhan Univ. Technol. 22 (2007) 27. H.Z. Zhang, S.Q. Wang, Acta Mater. 55 (2007) 4645. Z.M. Sun, R. Ahuja, S. Li, J.M. Schneider, Appl. Phys. Lett. 83 (2003) 899. Y.C. Zhou, Z.M. Sun, Phys. Rev. B 61 (2000) 12570. G. Hug, E. Fries, Phys. Rev. B 65 (2002) 113104. S.E. Lofland, J.D. Hettinger, K. Harrell, P. Finkel, S. Gupta, M.W. Barsoum, G. Hug, Appl. Phys. Lett. 84 (2004) 508. Z.M. Sun, S. Li, R. Ahuja, J.M. Schneider, Solid State Commun. 129 (2004) 589. Z.M. Sun, D. Music, R. Ahuja, S. Li, J.M. Schneider, Phys. Rev. B 70 (2004) 092102. Z.M. Sun, D. Music, R. Ahuja, J.M. Schneider, J. Phys. Condes. Matter 17 (2005) 7169. T. Liao, J.Y. Wang, Y.C. Zhou, J. Phys. Condes. Matter 18 (2006) 6183. T. Liao, J.Y. Wang, Y.C. Zhou, Phys. Rev. B 73 (2006) 214109. J.Y. Wang, Y.C. Zhou, T. Liao, J. Zhang, Z.J. Lin, Scr. Mater. 58 (2008) 227. Y.L. Du, Z.M. Sun, H. Hashimoto, Phys. B 405 (2010) 720. Z.J. Lin, M.J. Zhuo, Y.C. Zhou, M.S. Li, J.Y. Wang, J. Am. Ceram. Soc. 89 (2006) 3765. Y.L. Du, Z.M. Sun, H. Hashimoto, W.B. Tian, Mater. Trans. 49 (2008) 1934. Y.L. Du, Z.M. Sun, H. Hashimoto, W.B. Tian, Solid State Commun. 147 (2008) 246.
[34] Y.L. Du, Z.M. Sun, H. Hashimoto, W.B. Tian, Solid State Commun. 145 (2008) 461. [35] W. Lu, X.H. Deng, H. Wang, H.T. Huang, L.L. He, J. Mater. Res. 23 (2008) 2350. [36] J.Y. Wang, J.M. Wang, Y.C. Zhou, Z.J. Lin, C.F. Hu, Scr. Mater. 58 (2008) 1043. [37] Y.L. Bai, X.D. He, Y.B. Li, C.C. Zhu, M.W. Li, Solid State Commun. 149 (2009) 2156. [38] X.H. Deng, B.B. Fan, W. Lu, Solid State Commun. 149 (2009) 441. [39] Y. Medkour, A. Roumili, D. Maouche, Eur. Phys. J. Appl. Phys. 44 (2008) 125. [40] D. Music, Z.M. Sun, A.A. Voevodin, J.M. Schneider, J. Phys. Condes. Matter 18 (2006) 4389. [41] M.D. Segall, P.J.D. Lindan, M.J. Probert, C.J. Pickard, P.J. Hasnip, S.J. Clark, M.C. Payne, J. Phys. Condes. Matter 14 (2002) 2717. [42] H.J. Monkhorst, J.D. Pack, Phys. Rev. B 13 (1976) 5188. [43] D. Vanderbilt, Phys. Rev. B 41 (1990) 7892. [44] J.P. Perdew, J.A. Cherary, S.H. Vosko, K.A. Jackson, M.R. Pederson, D.J. Singh, C. Fiolhais, Phys. Rev. B 46 (1992) 6671. [45] B.G. Pfrommer, M. Cote, S.G. Louie, M.L. Cohen, J. Comput. Phys. 131 (1997) 133. [46] Y.L. Bai, X.D. He, M.W. Li, Y. Sun, C.C. Zhu, Y.B. Li, Solid State Sci. 12 (2010) 144. [47] J.C. Charlier, X. Gonze, J.P. Michenaud, Carbon 32 (1994) 289. [48] J.D. Hettinger, S.E. Lofland, P. Finkel, Phys. Rev. B 72 (2005) 115120. [49] Z.J. Lin, Y.C. Zhou, M.S. Li, J. Mater. Sci. Technol. 23 (2007) 721. [50] J.Y. Wang, Y.C. Zhou, Phys. Rev. B 69 (2004) 214111. [51] Y. Medkour, A. Bouhemadou, A. Roumili, Solid State Commun. 148 (2008) 459. [52] M. Ramzan, S. Lebegue, R. Ahuja, Appl. Phys. Lett. 98 (2011) 021902.
Contents lists available at ScienceDirect
Computational Condensed Matter journal homepage: http://ees.elsevier.com/cocom/default.asp
Ab initio study of the structural and electronic properties of Nb2AlC Ai-Jiao Xu a, *, Wen-Wu Zhong a, Xin Zhang b a b
College of Physics and Electronic Engineering, Taizhou University, Taizhou, 317000, PR China Ningbo Institute of Materials Technology and Engineering, Chinese Academy of Science, Ningbo, 315201, PR China
a r t i c l e i n f o
a b s t r a c t
Article history: Received 22 December 2015 Received in revised form 14 March 2016 Accepted 20 March 2016 Available online 22 March 2016
The structural and electronic properties of Nb2AlC have been studied using the ab initio pseudopotential approach based on density functional theory. The internal coordinates of Nb atom is determined to be (1/ 3, 2/3, 0.089). The equilibrium lattice parameters are computed to be a ¼ 3.119 Å and c ¼ 13.92 Å, in good agreement with experimental results. The band structure and density of states reveal that Nb2AlC is an electronic conductor. Both Nb 4d and Al 3p contribute to the electronic properties. Partial density of state indicates that a strong hybridization of Nb 4d and C 2p states. The charge density distribution shows that the Nb and C atoms form a strong NbeCeNb covalently bonded chain. © 2016 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
Keywords: Nb2AlC Crystal structure Electronic structure Ab initio
1. Introduction Nb2AlC is a ternary compound of the well-known MAX phases, which has been successfully fabricated by hot isostatically pressing [1], hot pressing [2] and magnetron sputtering [3], respectively. Nb2AlC has the space group P63/mmc with lattice parameters of a ¼ 3.10 Å and c ¼ 13.8 Å and its crystal structure is shown in Fig. 1. The bulk properties of Nb2AlC have been well studied. Similar to metals, Nb2AlC has good thermal conductivity of 22 W m1 K1 and electrical conductivity of 3.45 106 S m1 at room temperature [4]. Nb2AlC has a low Vickers hardness of ~4.5 GPa, which renders it a soft and machinable ceramics compared with traditional hard ceramics such as TiC, Al2O3 and Si3N4. Similar to ceramics, Nb2AlC has a comparative low density of 6.5 g/cm3 [5] and a high Young's modulus of 294 GPa. The four-point bending strength and fracture toughness were reported to be 443 MPa, and 5.9 MPa m1/2, respectively [2]. Moreover, Nb2AlC was reported to oxidize in air at 650 C by forming Nb oxides and NbAlO4 with a subparabolic oxidation kinetics [6]. Manoun [7] studied the compression behavior of Nb2AlC and found no phase transformation up to 50 G Pa. Salient properties make Nb2AlC a potential structuralfunctional material for high-temperature applications. Density functional-theory has been extensively used to investigate MAX phases, such as Ti3SiC2 [8e14], Ti3AlC2 [15e19], Ti2AlC
* Corresponding author. E-mail address: [email protected] (A.-J. Xu).
[20e30] and Ta4AlC3 [31e38]. For Nb2AlC, Sun et al. [24] calculated the elastic properties, including the bulk and shear moduli, Young's modulus and Poisson's ratio using ab initio calculations. Pressure effects on the structural and elastic properties of Nb2AlC were studied by Medkour et al. using ab initio calculations [39]. The basal-slipping behavior was also investigated theoretically by analyzing the stressestrain dependence that NbeAl bonds break during deformation, while the NbeC bond length decreases by 4.1% [40]. Although many physical properties of Nb2AlC have been studied systematically, the above mentioned theoretical calculations are not very comprehensive. In this work, we studied the internal coordinates, the lattice parameter and the electronic structure in Nb2AlC to get a better understanding of it. Our theoretically computed results are in good agreement with available experimental data. 2. Computation details For the ground-state electronic structure calculations within the density functional theory we used the standard CASTEP code [41], which employs the plane-wave pseudopotential method. The s, p valence orbitals of C, the s, p orbitals of Al as well as the s, p, and d orbitals of Nb were included in the calculation of partial density of states. One of the main features of CASTEP code is the internal coordinates can be automatically relaxed so that the crystal structure with the minimum energy can be obtained. For the calculation of the internal atom coordinates and the lattice parameters, the plane-wave energy cutoff and the Brillouin zone sampling were set
http://dx.doi.org/10.1016/j.cocom.2016.03.002 2352-2143/© 2016 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
2
A.-J. Xu et al. / Computational Condensed Matter 6 (2016) 1e4
Fig. 1. Crystal structure of Nb2AlC.
at 700 eV and 14 14 6 MonkhorstePack [42] special k-point meshes, respectively. Interactions of electrons with ion cores were represented by the Vanderbilit-type ultrasoft pseudopotential [43]. The electronic exchange-correlation energy was estimated according to Perdew-Wang generalized-gradient approximation (GGA-PW91) [44]. The Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm [45] was used to minimize the total energy and internal forces. The tolerances for geometry optimization were set as the difference in total energy being within 5 106 eV/atom, the maximum ionic Hellmann-Feynman force being within 0.01 eV/Å, the maximum stress being within 0.02 GPa and the maximum ionic displacement being within 5 104 Å. 3. Results and discussion Previous studies did not report the internal coordinate of Nb2AlC [24,39,40], while it is a fundamental parameter for many properties calculations. Our calculation was performed by optimizing both the internal coordinate and unit cell. In Nb2AlC, the position of the Nb atom is not fixed by the group symmetry and in this work, the calculated fractional coordinate of Nb atom is (1/3, 2/
3, 0.089). The calculated lattice parameter together with experimental values was listed in Table 1. From the table, we can see that our results are in good agreement with previous reported data. The deviation of lattice parameters is 0.38% for a and 0.22% for c compared with the experimental values reported by Salama. Moreover, we also calculated the bond length at the equilibrium atomic configuration, which is important for the following discussion of Nb2AlC. The calculated bond length of NbeC is 2.18 Å, which is close to those of 211 MAX compounds, such as TieC bond (2.12 Å) inTi2CdC [46]. The bond length of NbeAl is 3.92 Å, much longer than that of NbeC. If the difference in atomic size between C and Al is ignored, the longer bond length of NbeAl indicates that the bonding between them is comparatively weaker. For a better understanding of the tribological property of Nb2AlC, it is necessary to recall the hexagonal graphite, despite of many differences in their properties. Graphite is the most studied material with layered stacking planes of carbon atoms. The nearest distance of CeC within a plane is 1.42 Å, while that of interplanar CeC is around 3.35 Å [47]. Such crystal structure makes the interplanar bonding weaker than the planar bonding. As a result, graphite exhibits a low coefficient of friction and excellent lubricative properties due to the interplanar lower shear strength. Nb2AlC and hexagonal graphite share a lot in common on crystal structure. The structure of Nb2AlC can be described as near close-packed Nb layers interleaved with pure Al layers, with C atoms filling the octahedral sites between the Nb layers. The layers are bonded mainly by the weak NbeAl bonding. Therefore, it is concluded that Nb2AlC may possess a low coefficient of friction because of the relatively weak bonding. The computed density of Nb2AlC is 6.361 g/cm3 and it agrees well with the experimental value (6.474 g/cm3) found in the JCPDS data file and previous reported data (6.34 g/cm3) [48]. Based on the optimized cell configuration, the band structure was calculated and obtained. Fig. 2 shows the band structure along the high-symmetry lines of the Brillouin zone. It can be assessed that there is no gap at the vicinity of the Fermi level, whereas there is an overlapping of bonding and anti bonding states. As a result, Nb2AlC will exhibit metallic properties, much similar to Cr2AlC [49] and Ti2AlC [21]. The band structure demonstrates a strongly anisotropic feature with less c-axis energy dispersion, indicating the conductivity for single-crystal Nb2AlC is also anisotropic, i.e. the electrical conductivity along the c axis is lower than that in the ab plane. To better evaluate the nature of the chemical bonding, the electronic structure of Nb2AlC was studied. The calculated total density of states (TDOS) and partial density of states (PDOS) for Nb2AlC are presented in Fig. 3. The TDOS at the Fermi level is 3.40 states/(eV cell), which is much smaller than 6.46 states/(eV cell) for Cr2AlC, the maximum TDOS measured for MAX phases so far [23]. The zero gap and finite value at EF reveal the existence of metallic bonding in Nb2AlC. It is observed that the lowest valence bands from approximately 56.1 to 54.3 eV of the TDOS are formed by the Nb 5s states. The higher valence bands from about 32.5 to 30.2 eV are formed by Nb 4p with a small amount of C 2p states. The highest valence bands from 12.2 eV to 10.3 eV are formed
Table 1 Comparison of the calculated and experimental lattice parameter for Nb2AlC. Lattice parameters a (Å) 3.107 3.103 3.108 3.119
References c (Å)
expt. calc. calc. calc.
13.89 13.83 13.97 13.92
c/a expt. calc. calc. calc.
4.47 4.45 4.49 4.46
[1] [48] [48] This work
A.-J. Xu et al. / Computational Condensed Matter 6 (2016) 1e4
3
8
Energy (eV)
4 0 -4 -8 -12 -16
G A
H K
G
M L
H
Fig. 2. Calculated band structure along the high symmetry direction in the first Brillouin zone.
Fig. 4. Valence electron density of a slice of the ð1120Þ plane in a 2 2 1 supercell.
electronegative than Nb. The electron cloud of Al hardly overlaps with that of NbeCeNb chains, indicating relatively weak bonding between them, which may account for the low friction coefficient. These results are in agreement with the previous results on the strong MeC bonds, and weak MeA bonds [50,52].
Fig. 3. Total and partial density of states for Nb2AlC.
almost entirely from the C 2s states. The valence bands in the range from 7.2 to 3.2 eV are dominated by the highly hybridized Nd 4d and C 2p states, indicating a strong covalent interaction. The d-p interaction stabilizes the crystal structure and thus is the driving bonding force. From 3.0 to 0.8 eV, the bands are related to the weak hybridized Nb 4d and Al 3p states, which is in agreement with the long distance of NbeAl bond as discussed previously. At around the EF, the DOS mainly originates from Nb 4d with less contribution from Al 3p and C does not contribute to the DOS, therefore, Nb 4d electrons should mainly be involved in the conduction properties. These results are consistent with previous reports on MAX phases [50,51]. The conduction bands are provided by the antibonding Nb 4d states and less contribution from Al 3p states. In order to further understand the bonding behavior of Nb2AlC, we have calculated the charge density. Fig. 4 shows the charge density distribution for a slice of the ð1120Þ plane in a 2 2 1 supercell. The figure clearly shows that Nb and C form an NbeCeNb covalently bonded chain, which are interleaved and mirrored by Al atomic plane. The figure clearly shows that Nb and C form an NbeCeNb covalently bonded chain, which are interleaved and mirrored by Al atomic plane. The charge density is pulled from Nb atoms toward C atoms, which is due to the difference in the electronegativities of Nb and C. According to Pauling rule, C is more
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