- Email: [email protected]
First-principles study on the structure, elastic and electronic properties of hexagonal HfPtAl under pressure
Solid State Communications 152 (2012) 462–465
Contents lists available at SciVerse ScienceDirect
Solid State Communications journal homepage: www.elsevier.com/locate/ssc
First-principles study on the structure, elastic and electronic properties of hexagonal HfPtAl under pressure Haizhou Wang, Yongzhong Zhan ∗ , Mingjun Pang Laboratory of Nonferrous Metal Materials and New Processing Technology, Ministry of Education, Guangxi University, Nanning, Guangxi 530004, People’s Republic of China
article
info
Article history: Received 2 November 2011 Received in revised form 31 December 2011 Accepted 4 January 2012 by E.V. Sampathkumaran Available online 10 January 2012 Keywords: A. Metals D. Electronic band structure D. Mechanical properties
abstract We have investigated the structure, elastic and electronic properties in hexagonal HfPtAl by a firstprinciples ultrasoft pseudopotential of the plane wave within the density functional theory (DFT) plus the generalized gradient approximation (GGA) in the scheme of Perdew–Burke–Ernzerhof (PBE). All properties are calculated as a function of external pressure. The results of structural parameters have a good agreement with reported experiments and can predict the properties under pressure well. The hexagonal HfPtAl is mechanically stable and behaves in a ductile manner. The TDOS is occupied by Pt-d, Hf-d and Al-p. © 2012 Elsevier Ltd. All rights reserved.
1. Introduction ′
The intermetallics compounds in the T − T − X (T = Ti, Zr, ′ Hf; T = Ag, Au, Pt, Pd; X = Al, Ga) system has been widely investigated [1]. Among them, HfPtAl (HfRhSn structure type) has attracted a lot of research interest due to its promising physical and chemical properties [2–9]. The Hf atoms are surrounded by 15 neighbors, for the Pt atoms coordination polyhedra are trigonal prisms with additional atoms, and the Al atoms are in a 12-vertex ′ polyhedron [1]. The T elements are so expensive it is impossible to experimentally study these compounds on a large scale. However, advances in the accuracy and efficiency of first-principles calculation provide a new way. For a material with a high melting point that can be used as a bonding layer between thermal barrier coatings and turbine blades in internal combustion engines, a detailed investigation under a series of pressures is necessary because pressures can effectively influence the physical properties of the material. This effect has been proved to be very important for the understanding of the material’s behaviors in different external conditions. Nowadays high pressures are usually applied to small samples to study the effects and mechanisms, in a controlled manner, using devices like the diamond anvil cell. The calculations have allowed comprehensive studies on those samples under simulated uniform hydrostatic pressure [10]. Based on the importance of HfPtAl ternary compound, their properties including the
∗
Corresponding author. Tel.: +86 771 3272311; fax: +86 771 3233530. E-mail address: [email protected] (H. Wang).
0038-1098/$ – see front matter © 2012 Elsevier Ltd. All rights reserved. doi:10.1016/j.ssc.2012.01.006
structure, elastic, electronic, stability and various other properties should be thoroughly researched and discussed. It is known that the structure, elastic and electronic properties of the material under pressure are closely related to transport properties, hardness, compressibility and other characteristics. We can directly obtain some important information of the HfPtAl crystal for related materials design, by analyzing the above-mentioned aspects. However, up to now the effects of pressure on the structure and mechanical properties of this compound have not been calculated or measured. 2. Calculation details Limited experimental information can be found on the structure of HfPtAl [1]. Theoretical calculations in this work were performed using the plane-wave pseudopotential method [11] within the framework of density functional theory (DFT) implemented in the Cambridge serial total energy package code [12]. The generalized gradient approximation (GGA) in the scheme of Perdew– Burke–Ernzerhof (PBE) [13] is used for the exchange-correlation function. The parameters including 290 eV plane-wave cutoff energy, 4 × 4 × 4 Monkhorst–Pack k-points [14], as well as the difference of total energy within 0.00125 eV/cell, maximum ionic displacement within 100 eV/Å, maximum ionic displacement within 100 Å, and maximum stress within 100 GPa, were applied. Detailed and systematic research on the structure, elastic, and electronic (including band structure and density of state) properties of the HfPtAl ternary compound in pressures from 0 to 20 GPa with a step of 2 GPa was then performed.
H. Wang et al. / Solid State Communications 152 (2012) 462–465
463
in good agreement with the reported experimental ones, 7.0912, 7.0912 and 7.1127 Å [1]. In order to further estimate the structure change with pressure, the complete geometry optimization for the lattice cell was performed in the pressure range from 0 GPa up to 20 GPa with a step of 2 GPa. As bulk modulus B0 is an important parameter to reveal the hardness of alloys, the obtained Birch–Murnaghan equation of state (EOS) [16] derived by calculating cell volumes at different pressure was used: P =
Fig. 1. Calculated bulk modulus (B), shear modulus (G), Young’s modulus (E) and Poisson’s ratio (ν ) for hexagonal HfPtAl from 0 to 20 GPa.
3. Results and discussions 3.1. Structural properties The atomic configurations used to generate the ultrasoft pseudopotentials are 3s2 3p1 for Al, 5d9 6d1 for Pt, and 5d2 6s2 for Hf, respectively. The HfPtAl compound has a hexagonal structure with space group P62c (No. 190). The Al atoms occupy the 6g sites (0.2538, 0, 0), the Hf atoms occupy the 6h sites (0.4119, 0.3902, 0.25), some Pt atoms occupy the 2b sites (0, 0, 0.25) and the other Pt atoms occupy the 4f sites (0.3333, 0.6667, 0.0282), respectively. The structural relaxation was conducted by using the Broyden–Fletcher–Goldfarb–Shanno minimization [15], modified to take into account the total energy in addition to the gradients. The calculated optimized equilibrium lattice constants at 0 GPa are 7.1834, 7.1834, and 7.2041 Å for a, b, and c direction, which are
(a) 0 GPa.
3 2
B0 (x
− 37
−x
− 53
3
) 1 + (B0 − 4)(x ′
4
− 23
− 1) .
(1)
In the equation, x stands for V /V0 and P stands for pressure. Fitting parameters are the bulk modulus (B0 ) and its pressure derivative (B′0 ). The calculated values of B0 and B′0 are 167.8087 GPa and 4.5757, respectively. 3.2. Elastic properties Elastic properties can provide a link between the mechanical and dynamic information concerning the nature of the forces operating in solids, especially for the stability and stiffness of materials. We calculated the elastic constants (Cij ), bulk modulus (B), shear modulus (G), Young’s modulus (E), and Poisson’s ratio (ν ) for HfPtAl. For the hexagonal crystals, there are five independent elastic constants C11 , C12 , C13 , C33 , and C44 . The obtained C11 , C12 , C13 , C33 and C44 are 258.207, 109.623, 144.81, 189.687 and 102.915, respectively, when pressure is 0. Five distortions involving C33 , C44 , C11 + C12 , C11 − C12 , and (2C11 + 2C12 + 4C13 + C33 ) were employed to determine all the elastic constants [17,18]. According to the born stability conditions for hexagonal structure 2 (C11 > 0, C44 > 0, C11 > |C12 |, (C11 + 2C12 )C33 > 2C13 [19]), this compound is mechanically stable due to these criteria being satisfied [20]. The BH and GH were determined using the Voigt–Reuss–Hill (VRH) averaging scheme [21]. The BH , GH , E and
(b) 10 GPa.
(c) 20 GPa. Fig. 2. Band structure of HfPtAl under 0 GPa (a), 10 GPa (b) and 20 GPa (c) uniform hydrostatic pressure.
464
H. Wang et al. / Solid State Communications 152 (2012) 462–465
(a) 0 GPa.
(b) 10 GPa.
(c) 20 GPa. Fig. 3. TDOS and PDOS of HfPtAl under 0 GPa (a), 10 GPa (b) and 20 GPa (c) uniform hydrostatic pressure.
ν are 166.441, 68.583, 180.902 and 0.3189, respectively, at 0 pressure. It is observed that C11 and C33 for hexagonal HfPtAl ternary compound are larger than the other constants, meaning that HfPtAl is incompressible under uniaxial stress along the x or y axes. The calculated results of BH , GH , E and ν from 0 GPa up to 20 GPa with a step of 2 GPa are presented in Fig. 1. It is obvious that all of them increase with increasing pressure. The result BH > GH shows that the parameter limiting the stability of hexagonal HfPtAl is the shear modulus [22]. The bulk modulus (BH ) at zero pressure is in good agreement with that obtained through the fit to a Birch–Murnaghan EOS (B0 ) which means that the approach of the calculation is reliable. Moreover, it is described as ductile because of Pugh’s definition (according to the B/G) [23]. Otherwise, Poisson’s ratio ν provides more information about the characteristics of the bonding forces than any other elastic constants [24]. The ν value of hexagonal HfPtAl is in the range of 0.25–0.5 on 0 GPa, indicating that the interatomic forces are a central force [25]. 3.3. Electronic properties In Fig. 2, the calculated band structure of HfPtAl under 0, 10, and 20 GPa uniform hydrostatic pressures are displayed. As the changes in the cell volume are controlled by pressure, the differences among them reveal that external pressure has certain influence on band structure. The valence and conduction bands overlap considerably and there is no bandgap at the Fermi level. Thus HfPtAl ternary compound will exhibit metallic property in this pressure range. The Fermi level of HfPtAl lies above the valence
band maximum near the G point. It leads to some additional occupation of bonding states near to Fermi level. With the increase of pressure, the energy bands become more dispersive and the hybridization among Hf-d, Pt-d, Al-p and Pt-p increases. The energy bands of HfPtAl overlap greatly with the pressure increases, which leads to stronger metallization in the compound. We also calculated its total density of states (TDOS) and partial density of states (PDOS) under 0, 10 and 20 GPa uniform hydrostatic pressure, as displayed in Fig. 3. The tetrahedron Blöchl method [26] with corrections was used for the calculation of the TDOS and the PDOS under the optimized structures. The calculated Fermi level was 7.526, 7.363 and 7.319 eV for 0, 10 and 20 GPa, respectively. At metallization pressure, the bands overlap and the Fermi level is mainly dominated by Hf-d state. The higher the external pressure, the smaller the values of Fermi level in the HfPtAl compound that are obtained. Unfortunately, there are no experimental results for comparison and the present theoretically obtained results could be suggestions for future work. The shapes and values of TDOS are similar. Between −6 and −3 eV, it is mostly occupied by the Pt-d state. Near to −5 eV, it is a hybridization of Al-p and Pt-p states. Between −2 and 2 eV, it is mostly occupied by the Hf-d state. From −2 eV to Fermi level, it is a hybridization of Alp and Pt-p states. The other states only have a limited contribution. With pressure increasing, the value of the Pt-d state between −6 and −5 eV increases while the value of the Hf-d state between 1 and 1.5 eV decreases. In other words, as pressure increases, the contribution of Pt atoms goes up while the contribution of Hf atoms decreases.
H. Wang et al. / Solid State Communications 152 (2012) 462–465
Special attention is paid to the bonding states near the Fermi level. The Fermi level of HfPtAl lies above the valence band maximum near the G point. It leads to some additional occupation of bonding states near Fermi level. In HfPtAl, with atomic number increasing, fewer valence electrons are present in the unit cell and the Fermi level decreases. It is also shown that the initially unoccupied valence band near H point shifts downward and is located below the Fermi level in HfPtAl. The above results determine that the improvement of cohesive properties originates dominantly from the occupation of Hf–Al covalent bonding. 4. Conclusions In summary, we have shown the structure, elastic and electronic properties of HfPtAl under hydrostatic pressure using the DFT and GGA approaches. The structural parameters from the GGA–PBE method agree well with reported experiments. The calculated elastic properties show that hexagonal HfPtAl is mechanically stable and behaves in a ductile manner. External pressure has a little influence on electronic properties at least up to 20 GPa. As pressure increases, the contribution of Pt atoms goes up while that of Hf atoms decreases. Acknowledgments This work was supported by the National Natural Science Foundation of China (51161002), Guangxi Natural Science Foundation (2011GXNSFA018017) and the Guangxi Science and Technology Development Project (1114003-1).
465
References [1] Y. Verbovytsky, K. Ła¸tka, J. Alloys Compd. 431 (2007) 130. [2] T.D. Hatchard, J.E. Harlow, D.A. Stevens, G.C. Liu, R.J. Sanderson, N. van der Bosch, J.R. Dahn, G.M. Haugen, G.D. Vernstrom, R.T. Atanasoski, Electrochim. Acta (2011) doi:10.1016/j.electacta.2011.05.059. [3] C. Li, S. Ranganathan, A. Inoue, Acta Mater. 49 (2001) 1903. [4] K.M. Carling, W. Glover, H. Gunaydin, T.A. Mitchell, E.A. Carter, Surf. Sci. 600 (2006) 2079. [5] A. Kovács, P.B. Barna, J.L. Lábár, Thin Solid Films 433 (2003) 78. [6] D.E. Kim, V.R. Manga, S.N. Prins, Z.K. Liu, CALPHAD 35 (2011) 20. [7] H. Hallem, B. Forbord, K. Marthinsen, Mate. Sci. Eng. A 387 (2004) 940. [8] G.S.E. Antipas, C. Lekakou, P. Tsakiropoulos, Mater. Charact. 62 (2011) 402. [9] A. Campos, B. Gagea, S. Moreno, P. Jacobs, R. Molina, Appl. Catal. A 345 (2008) 112. [10] S. Dong, H. Zhao, Appl. Phys. Lett. 98 (2011) 182501. [11] D. Vanderbilt, Phys. Rev. B 41 (1990) 7892. [12] M.D. Segall, P.J.D. Lindan, M.J. Probert, C.J. Pickard, P.J. Hasnip, S.J. Clark, M.C. Payne, J. Phys.: Condens. Matter 14 (2002) 2717. [13] B. Hammer, L.B. Hansen, J.K. Norskov, Phys. Rev. B 59 (1999) 7413. [14] H.J. Monkhorst, J.D. Pack, Phys. Rev. B 13 (1976) 5188. [15] B.G. Pfrommer, M. Côté, S.G. Louie, M.L. Cohen, J. Comput. Phys. 131 (1997) 233. [16] F. Birch, J. Geophys. Res. 83 (1978) 1257. [17] F. Jona, P.M. Marcus, Phys. Rev. B 66 (2002) 094104. [18] L. Fast, J.M. Wills, B. Johansson, O. Eriksson, Phys. Rev. B 51 (1995) 17431. [19] C. Höglund, J. Birch, B. Alling, J. Bareño, Z. Czigány, P.O.Å Persson, G. Wingqvist, A. Zukauskaite, L. Hultman, Appl. Phys. Lett. 107 (2010) 123515. [20] Z. Wu, E. Zhao, H. Xiang, X. Hao, X. Liu, J. Meng, Phys. Rev. B 76 (2007) 054115. [21] R. Hill, Proc. Phys. Soc. London 65 (1953) 350. [22] Q.J. Liu, Z.T. Liu, L.P. Feng, H. Tian, Comput. Mater. Sci. 50 (2011) 2822. [23] S.F. Pugh, Philos. Mag 45 (1954) 823. [24] B. Mayer, H. Anton, E. Bott, M. Methfessel, J. Sticht, P.C. Schmidt, Intermetallics 11 (2003) 23. [25] H.Z. Fu, D.H. Li, F. Peng, T. Gao, X.L. Cheng, Comput. Mater. Sci. 44 (2008) 774. [26] P.E. Blöchl, O. Jepsen, O.K. Andersen, Phys. Rev. B 49 (1994) 16223.
Contents lists available at SciVerse ScienceDirect
Solid State Communications journal homepage: www.elsevier.com/locate/ssc
First-principles study on the structure, elastic and electronic properties of hexagonal HfPtAl under pressure Haizhou Wang, Yongzhong Zhan ∗ , Mingjun Pang Laboratory of Nonferrous Metal Materials and New Processing Technology, Ministry of Education, Guangxi University, Nanning, Guangxi 530004, People’s Republic of China
article
info
Article history: Received 2 November 2011 Received in revised form 31 December 2011 Accepted 4 January 2012 by E.V. Sampathkumaran Available online 10 January 2012 Keywords: A. Metals D. Electronic band structure D. Mechanical properties
abstract We have investigated the structure, elastic and electronic properties in hexagonal HfPtAl by a firstprinciples ultrasoft pseudopotential of the plane wave within the density functional theory (DFT) plus the generalized gradient approximation (GGA) in the scheme of Perdew–Burke–Ernzerhof (PBE). All properties are calculated as a function of external pressure. The results of structural parameters have a good agreement with reported experiments and can predict the properties under pressure well. The hexagonal HfPtAl is mechanically stable and behaves in a ductile manner. The TDOS is occupied by Pt-d, Hf-d and Al-p. © 2012 Elsevier Ltd. All rights reserved.
1. Introduction ′
The intermetallics compounds in the T − T − X (T = Ti, Zr, ′ Hf; T = Ag, Au, Pt, Pd; X = Al, Ga) system has been widely investigated [1]. Among them, HfPtAl (HfRhSn structure type) has attracted a lot of research interest due to its promising physical and chemical properties [2–9]. The Hf atoms are surrounded by 15 neighbors, for the Pt atoms coordination polyhedra are trigonal prisms with additional atoms, and the Al atoms are in a 12-vertex ′ polyhedron [1]. The T elements are so expensive it is impossible to experimentally study these compounds on a large scale. However, advances in the accuracy and efficiency of first-principles calculation provide a new way. For a material with a high melting point that can be used as a bonding layer between thermal barrier coatings and turbine blades in internal combustion engines, a detailed investigation under a series of pressures is necessary because pressures can effectively influence the physical properties of the material. This effect has been proved to be very important for the understanding of the material’s behaviors in different external conditions. Nowadays high pressures are usually applied to small samples to study the effects and mechanisms, in a controlled manner, using devices like the diamond anvil cell. The calculations have allowed comprehensive studies on those samples under simulated uniform hydrostatic pressure [10]. Based on the importance of HfPtAl ternary compound, their properties including the
∗
Corresponding author. Tel.: +86 771 3272311; fax: +86 771 3233530. E-mail address: [email protected] (H. Wang).
0038-1098/$ – see front matter © 2012 Elsevier Ltd. All rights reserved. doi:10.1016/j.ssc.2012.01.006
structure, elastic, electronic, stability and various other properties should be thoroughly researched and discussed. It is known that the structure, elastic and electronic properties of the material under pressure are closely related to transport properties, hardness, compressibility and other characteristics. We can directly obtain some important information of the HfPtAl crystal for related materials design, by analyzing the above-mentioned aspects. However, up to now the effects of pressure on the structure and mechanical properties of this compound have not been calculated or measured. 2. Calculation details Limited experimental information can be found on the structure of HfPtAl [1]. Theoretical calculations in this work were performed using the plane-wave pseudopotential method [11] within the framework of density functional theory (DFT) implemented in the Cambridge serial total energy package code [12]. The generalized gradient approximation (GGA) in the scheme of Perdew– Burke–Ernzerhof (PBE) [13] is used for the exchange-correlation function. The parameters including 290 eV plane-wave cutoff energy, 4 × 4 × 4 Monkhorst–Pack k-points [14], as well as the difference of total energy within 0.00125 eV/cell, maximum ionic displacement within 100 eV/Å, maximum ionic displacement within 100 Å, and maximum stress within 100 GPa, were applied. Detailed and systematic research on the structure, elastic, and electronic (including band structure and density of state) properties of the HfPtAl ternary compound in pressures from 0 to 20 GPa with a step of 2 GPa was then performed.
H. Wang et al. / Solid State Communications 152 (2012) 462–465
463
in good agreement with the reported experimental ones, 7.0912, 7.0912 and 7.1127 Å [1]. In order to further estimate the structure change with pressure, the complete geometry optimization for the lattice cell was performed in the pressure range from 0 GPa up to 20 GPa with a step of 2 GPa. As bulk modulus B0 is an important parameter to reveal the hardness of alloys, the obtained Birch–Murnaghan equation of state (EOS) [16] derived by calculating cell volumes at different pressure was used: P =
Fig. 1. Calculated bulk modulus (B), shear modulus (G), Young’s modulus (E) and Poisson’s ratio (ν ) for hexagonal HfPtAl from 0 to 20 GPa.
3. Results and discussions 3.1. Structural properties The atomic configurations used to generate the ultrasoft pseudopotentials are 3s2 3p1 for Al, 5d9 6d1 for Pt, and 5d2 6s2 for Hf, respectively. The HfPtAl compound has a hexagonal structure with space group P62c (No. 190). The Al atoms occupy the 6g sites (0.2538, 0, 0), the Hf atoms occupy the 6h sites (0.4119, 0.3902, 0.25), some Pt atoms occupy the 2b sites (0, 0, 0.25) and the other Pt atoms occupy the 4f sites (0.3333, 0.6667, 0.0282), respectively. The structural relaxation was conducted by using the Broyden–Fletcher–Goldfarb–Shanno minimization [15], modified to take into account the total energy in addition to the gradients. The calculated optimized equilibrium lattice constants at 0 GPa are 7.1834, 7.1834, and 7.2041 Å for a, b, and c direction, which are
(a) 0 GPa.
3 2
B0 (x
− 37
−x
− 53
3
) 1 + (B0 − 4)(x ′
4
− 23
− 1) .
(1)
In the equation, x stands for V /V0 and P stands for pressure. Fitting parameters are the bulk modulus (B0 ) and its pressure derivative (B′0 ). The calculated values of B0 and B′0 are 167.8087 GPa and 4.5757, respectively. 3.2. Elastic properties Elastic properties can provide a link between the mechanical and dynamic information concerning the nature of the forces operating in solids, especially for the stability and stiffness of materials. We calculated the elastic constants (Cij ), bulk modulus (B), shear modulus (G), Young’s modulus (E), and Poisson’s ratio (ν ) for HfPtAl. For the hexagonal crystals, there are five independent elastic constants C11 , C12 , C13 , C33 , and C44 . The obtained C11 , C12 , C13 , C33 and C44 are 258.207, 109.623, 144.81, 189.687 and 102.915, respectively, when pressure is 0. Five distortions involving C33 , C44 , C11 + C12 , C11 − C12 , and (2C11 + 2C12 + 4C13 + C33 ) were employed to determine all the elastic constants [17,18]. According to the born stability conditions for hexagonal structure 2 (C11 > 0, C44 > 0, C11 > |C12 |, (C11 + 2C12 )C33 > 2C13 [19]), this compound is mechanically stable due to these criteria being satisfied [20]. The BH and GH were determined using the Voigt–Reuss–Hill (VRH) averaging scheme [21]. The BH , GH , E and
(b) 10 GPa.
(c) 20 GPa. Fig. 2. Band structure of HfPtAl under 0 GPa (a), 10 GPa (b) and 20 GPa (c) uniform hydrostatic pressure.
464
H. Wang et al. / Solid State Communications 152 (2012) 462–465
(a) 0 GPa.
(b) 10 GPa.
(c) 20 GPa. Fig. 3. TDOS and PDOS of HfPtAl under 0 GPa (a), 10 GPa (b) and 20 GPa (c) uniform hydrostatic pressure.
ν are 166.441, 68.583, 180.902 and 0.3189, respectively, at 0 pressure. It is observed that C11 and C33 for hexagonal HfPtAl ternary compound are larger than the other constants, meaning that HfPtAl is incompressible under uniaxial stress along the x or y axes. The calculated results of BH , GH , E and ν from 0 GPa up to 20 GPa with a step of 2 GPa are presented in Fig. 1. It is obvious that all of them increase with increasing pressure. The result BH > GH shows that the parameter limiting the stability of hexagonal HfPtAl is the shear modulus [22]. The bulk modulus (BH ) at zero pressure is in good agreement with that obtained through the fit to a Birch–Murnaghan EOS (B0 ) which means that the approach of the calculation is reliable. Moreover, it is described as ductile because of Pugh’s definition (according to the B/G) [23]. Otherwise, Poisson’s ratio ν provides more information about the characteristics of the bonding forces than any other elastic constants [24]. The ν value of hexagonal HfPtAl is in the range of 0.25–0.5 on 0 GPa, indicating that the interatomic forces are a central force [25]. 3.3. Electronic properties In Fig. 2, the calculated band structure of HfPtAl under 0, 10, and 20 GPa uniform hydrostatic pressures are displayed. As the changes in the cell volume are controlled by pressure, the differences among them reveal that external pressure has certain influence on band structure. The valence and conduction bands overlap considerably and there is no bandgap at the Fermi level. Thus HfPtAl ternary compound will exhibit metallic property in this pressure range. The Fermi level of HfPtAl lies above the valence
band maximum near the G point. It leads to some additional occupation of bonding states near to Fermi level. With the increase of pressure, the energy bands become more dispersive and the hybridization among Hf-d, Pt-d, Al-p and Pt-p increases. The energy bands of HfPtAl overlap greatly with the pressure increases, which leads to stronger metallization in the compound. We also calculated its total density of states (TDOS) and partial density of states (PDOS) under 0, 10 and 20 GPa uniform hydrostatic pressure, as displayed in Fig. 3. The tetrahedron Blöchl method [26] with corrections was used for the calculation of the TDOS and the PDOS under the optimized structures. The calculated Fermi level was 7.526, 7.363 and 7.319 eV for 0, 10 and 20 GPa, respectively. At metallization pressure, the bands overlap and the Fermi level is mainly dominated by Hf-d state. The higher the external pressure, the smaller the values of Fermi level in the HfPtAl compound that are obtained. Unfortunately, there are no experimental results for comparison and the present theoretically obtained results could be suggestions for future work. The shapes and values of TDOS are similar. Between −6 and −3 eV, it is mostly occupied by the Pt-d state. Near to −5 eV, it is a hybridization of Al-p and Pt-p states. Between −2 and 2 eV, it is mostly occupied by the Hf-d state. From −2 eV to Fermi level, it is a hybridization of Alp and Pt-p states. The other states only have a limited contribution. With pressure increasing, the value of the Pt-d state between −6 and −5 eV increases while the value of the Hf-d state between 1 and 1.5 eV decreases. In other words, as pressure increases, the contribution of Pt atoms goes up while the contribution of Hf atoms decreases.
H. Wang et al. / Solid State Communications 152 (2012) 462–465
Special attention is paid to the bonding states near the Fermi level. The Fermi level of HfPtAl lies above the valence band maximum near the G point. It leads to some additional occupation of bonding states near Fermi level. In HfPtAl, with atomic number increasing, fewer valence electrons are present in the unit cell and the Fermi level decreases. It is also shown that the initially unoccupied valence band near H point shifts downward and is located below the Fermi level in HfPtAl. The above results determine that the improvement of cohesive properties originates dominantly from the occupation of Hf–Al covalent bonding. 4. Conclusions In summary, we have shown the structure, elastic and electronic properties of HfPtAl under hydrostatic pressure using the DFT and GGA approaches. The structural parameters from the GGA–PBE method agree well with reported experiments. The calculated elastic properties show that hexagonal HfPtAl is mechanically stable and behaves in a ductile manner. External pressure has a little influence on electronic properties at least up to 20 GPa. As pressure increases, the contribution of Pt atoms goes up while that of Hf atoms decreases. Acknowledgments This work was supported by the National Natural Science Foundation of China (51161002), Guangxi Natural Science Foundation (2011GXNSFA018017) and the Guangxi Science and Technology Development Project (1114003-1).
465
References [1] Y. Verbovytsky, K. Ła¸tka, J. Alloys Compd. 431 (2007) 130. [2] T.D. Hatchard, J.E. Harlow, D.A. Stevens, G.C. Liu, R.J. Sanderson, N. van der Bosch, J.R. Dahn, G.M. Haugen, G.D. Vernstrom, R.T. Atanasoski, Electrochim. Acta (2011) doi:10.1016/j.electacta.2011.05.059. [3] C. Li, S. Ranganathan, A. Inoue, Acta Mater. 49 (2001) 1903. [4] K.M. Carling, W. Glover, H. Gunaydin, T.A. Mitchell, E.A. Carter, Surf. Sci. 600 (2006) 2079. [5] A. Kovács, P.B. Barna, J.L. Lábár, Thin Solid Films 433 (2003) 78. [6] D.E. Kim, V.R. Manga, S.N. Prins, Z.K. Liu, CALPHAD 35 (2011) 20. [7] H. Hallem, B. Forbord, K. Marthinsen, Mate. Sci. Eng. A 387 (2004) 940. [8] G.S.E. Antipas, C. Lekakou, P. Tsakiropoulos, Mater. Charact. 62 (2011) 402. [9] A. Campos, B. Gagea, S. Moreno, P. Jacobs, R. Molina, Appl. Catal. A 345 (2008) 112. [10] S. Dong, H. Zhao, Appl. Phys. Lett. 98 (2011) 182501. [11] D. Vanderbilt, Phys. Rev. B 41 (1990) 7892. [12] M.D. Segall, P.J.D. Lindan, M.J. Probert, C.J. Pickard, P.J. Hasnip, S.J. Clark, M.C. Payne, J. Phys.: Condens. Matter 14 (2002) 2717. [13] B. Hammer, L.B. Hansen, J.K. Norskov, Phys. Rev. B 59 (1999) 7413. [14] H.J. Monkhorst, J.D. Pack, Phys. Rev. B 13 (1976) 5188. [15] B.G. Pfrommer, M. Côté, S.G. Louie, M.L. Cohen, J. Comput. Phys. 131 (1997) 233. [16] F. Birch, J. Geophys. Res. 83 (1978) 1257. [17] F. Jona, P.M. Marcus, Phys. Rev. B 66 (2002) 094104. [18] L. Fast, J.M. Wills, B. Johansson, O. Eriksson, Phys. Rev. B 51 (1995) 17431. [19] C. Höglund, J. Birch, B. Alling, J. Bareño, Z. Czigány, P.O.Å Persson, G. Wingqvist, A. Zukauskaite, L. Hultman, Appl. Phys. Lett. 107 (2010) 123515. [20] Z. Wu, E. Zhao, H. Xiang, X. Hao, X. Liu, J. Meng, Phys. Rev. B 76 (2007) 054115. [21] R. Hill, Proc. Phys. Soc. London 65 (1953) 350. [22] Q.J. Liu, Z.T. Liu, L.P. Feng, H. Tian, Comput. Mater. Sci. 50 (2011) 2822. [23] S.F. Pugh, Philos. Mag 45 (1954) 823. [24] B. Mayer, H. Anton, E. Bott, M. Methfessel, J. Sticht, P.C. Schmidt, Intermetallics 11 (2003) 23. [25] H.Z. Fu, D.H. Li, F. Peng, T. Gao, X.L. Cheng, Comput. Mater. Sci. 44 (2008) 774. [26] P.E. Blöchl, O. Jepsen, O.K. Andersen, Phys. Rev. B 49 (1994) 16223.