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First-principles study of the crystal structures and electronic properties of LaNi4.5M0.5 (M = Al, Mn, Fe, Co)
Computational Materials Science 69 (2013) 520–526
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First-principles study of the crystal structures and electronic properties of LaNi4.5M0.5 (M = Al, Mn, Fe, Co) Chuanyu Zhang a,⇑, Yiliang Liu b, Xiaofeng Zhao a, Min Yan a, Tao Gao c a
Department of Applied Physics, Chengdu University of Technology, Chengdu 610059, China College of Electrical and Information Engineering, Southwest University for Nationalities, Chengdu 610041, China c Institute of Atomic and Molecular Physics, Sichuan University, Chengdu 610065, China b
a r t i c l e
i n f o
Article history: Received 8 August 2012 Received in revised form 9 November 2012 Accepted 11 November 2012 Available online 24 January 2013 Keywords: First-principles theory Crystal structure Electronic structure
a b s t r a c t The structure, stability and electronic properties of the different B-site partial substituted derivatives LaNi4.5M0.5 (M = Al, Mn, Fe, Co) have been investigated by means of the density functional theory using the full-potential linearized augmented plane wave (FLAPW) method with the generalized gradient approximation (GGA). The optimized results indicate that all of Al, Mn, Fe, Co atoms prefer to substitute Ni atoms in the 3g sites. Due to the different radius of elements, the cell volume would increase with the doping Ni (3g) atoms. And the sequence of volume is LaNi4.5Al0.5 > LaNi4.5Mn0.5 > LaNi4.5Fe0.5 > LaNi4.5 Co0.5 > LaNi5, which is in agreement with the experimental result. The calculated data of formation and cohesive energies indicate that LaNi4.5Mn0.5 has the stablest structure among five alloys. Based on the analysis of the density of states and charge density, the interactions of Mn–Ni, Fe–Ni, Co–Ni atoms are greatly stronger compared to the Ni–Ni interaction, while the interaction of Al–Ni atoms is weakened. Based on the formation energy of hydrogen atom in LaNi4.5M0.5H0.5, the sequence of bounding hydrogen atoms is LaNi4.5Mn0.5 > LaNi4.5Fe0.5 > LaNi4.5Co0.5 > LaNi4.5Al0.5 > LaNi5. Ó 2012 Elsevier B.V. All rights reserved.
1. Introduction The intermetallic compound LaNi5 is known to store large quantity of hydrogen since the early 1970s [1–6]. Meanwhile, LaNi5 is of great importance for hydrogen storage applications, such as negative electrode materials, hydrogen purification and recovery devices [7–9]. Nevertheless, hydrogen absorption and desorption cycling has two main physical and irreversible consequences: pulverization and defect generation [10–14]. Generally, the wide ranges of pseudo-binary substitutions yield important changes in the related LaNi5 hydride properties. In order to modify the overall properties of the host material LaNi5, the effects of partial substitution of Ni with other metals have been studied extensively. Al, Mn, Fe and Co elements are most commonly used among the substituted metals. The functions of all these substitutions are as follows: the partial substitutions at the Ni with Al can commendably improve the cycling performance and reduce the plateau pressure of the P–C–T curve [15–17]; the partial substitutions at the Ni with Mn can reduce the plateau pressure of hydrogen without reduction of hydrogen storage capacity [18]; the partial substitutions at the Ni with Fe can efficiently increase the hydrogen storage capacity [19]; the partial substitutions
⇑ Corresponding author. Tel.: +86 28 84078267; fax: +86 28 85415508. E-mail address: [email protected] (C. Zhang). 0927-0256/$ - see front matter Ó 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.commatsci.2012.11.023
at the Ni with Co can significantly extend the cycle life [15,20]. In recent years, many references in La–Ni–M system have been published between the experimental results [19,21–28] and theoretical investigations [29–32]. However, most of previous works were carried out to investigate the hydrogenation behavior of single doped or co-doped LaNi5 type alloys. Little comparative studies of LaNi5xM0.5 (M = Al, Mn, Fe, Co, etc.) have been reported so far. On the experimental front, the electrochemical performance of LaNi4.7M0.3 (M = Ni, Co, Mn, Al) alloys were rapidly evaluated by means of a powder microelectrode technique [21]. Hydrogen desorption kinetics of hydrides of LaNi4.5Al0.5, LaNi4.5Mn0.5 and LaNi2.5M2.5 were studied by a volumetric method [27]. Magnetic properties of the LaNi4.5M0.5 (M = Fe, Co, Mn, Cu, Cr, Si) and their hydride compounds have been studied by magnetization measurement using a VSM [28]. In order to clarify the mechanism of formation of lattice strain in hydriding and dehydriding, peak broadening in X-ray powder diffraction (XRD) profiles of LaNi4.5M0.5 (M = Fe, Co, Mn) alloys was investigated [33]. In the theoretical research, the effect of Ni substitutions by group IVA (Si, Ge, Sn) elements on the electronic properties of LaNi5 and its hydrides have been studied using ab initio band structure calculations [32]. A more systematic investigation of the crystal structure and electronic properties of B-site partial substituted LaNi5 alloys is necessary for a better understanding of the substitution effects. In this paper, the steady structures and corresponding cell parameters of LaNi4.5M0.5 (M = Al, Mn, Fe, Co) were obtained by
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modeling and optimizing. The cohesive and formation energies are estimated to forecast the stability of the system. And the densities of states, electronic densities are calculated to analyze the effects on the electronic properties of the host alloy due to the substitution of Ni atoms. Finally, the formation energy of hydrogen atom in LaNi4.5M0.5H0.5 (M = Al, Mn, Fe, Co) is calculated to discuss the bounding hydrogen capacity of the system.
Table 1 The primitive occupation sites of two models of LaNi4.5M0.5 (M = Al, Mn, Fe, Co). Structure
Model
LaNi4.5Al0.5
Model Model Model Model Model Model Model Model
LaNi4.5Mn0.5 LaNi4.5Fe0.5 LaNi4.5Co0.5
2. Computational methods In this article, we employ the all-electron full-potential linearized augmented plane wave (FLAPW) method [34], which is among the most accurate methods for performing electronic structure calculations for crystals. The FLAPW method is the ab initio method for solving the Kohn–Sham equations for the ground state density, total energy, and eigenvalues of a many electron system by introducing a basis set. First, many-electron problem of a crystal is translated into single-electron problem, which is translated into Kohn–Sham equation. Second, Kohn–Sham equation can be solved by introducing linearized augmented plane wave basis functions, and the generalized gradient approximation (GGA) developed by Perdew et al. [35] is used to solve the electron exchange–correlation energy function. Third, the unit cell is divided into two regions: (1) non-overlapping atomic spheres and (2) an interstitial region. Therefore, two different types of basis set are used: the plane wave basis set is adopted inside atomic sphere; a plane wave expansion is adopted in the interstitial region. Then, the solution to the Kohn–Sham equations is expanded in this combined basis set of LAPW’s according to the linear variation method. Finally, the potential is also expanded in self-consistent-field cycle. The FLAPW calculations are performed using the WIEN2K package [36]. In the course of calculation, the muffin-tin radii Rmt of La, Ni, M (M = Al, Mn, Fe, Co) atoms are taken to be 0.95, 0.95 and 0.95 Å, respectively. The size of the basis set is given by the product Rmt Kmax = 7.0, where Kmax is the largest reciprocal space wave vector in the basis set. The charge density and the potentials are expanded into lattice harmonics up to L = 6 inside the spheres and a Fourier series in the interstitial region. The value of Gmax = 14 is used, which may limit the LM expansion. The separation energy between inner electrons and covalence electrons is 108.8 eV in the calculation of exchange correlation energy. Electronic configuration of covalence electrons are La-5d16s2, Ni-3d84s2, Al-3s23p1, Mn3d54s2, Fe-3d64s2, Co-3d74s2, respectively. Self-consistency is achieved by demanding the convergence of total energy smaller than 104 eV/cell. To ensure convergence for the Brillouin zone (BZ) integration, 1000 k-points in the irreducible wedge of the first BZ of the hexagonal lattice is chosen in course of calculation. Owing to the spin–orbit coupling having little effect on the equilibrium geometric structure and electronic structure of LaNi5 alloy [37], the spin polarization is neglected in the SCF cycles. LaNi5 is known to be described in the hexagonal CaCu5 structure, space group P6/mmm, where the La atoms occupy the (1a) sites and Ni atoms occupy (2c) and (3g) Wyckoff sites [38,39]. For LaNi4.5Al0.5, the previous research shows that Al atoms predominantly occupy 3g sites and the CaCu5 structure is retained until x 6 1.3 for alloys LaNi5xAlx [31,40–42]. For LaNi4.5Co0.5, Co prefers to occupy the 3g sites in the LaNi5-type structure [43]. And the Neutron diffraction study indicates that the occupancy numbers of Co in LaNi4Co are 23% at the 2c site and 77% at the 3g site [44]. For LaNi4.5Fe0.5, Fe can be substituted for Ni inLaNi5xFex up to x = 1.2. Ni is replaced by Fe at both the 2c and 3g sites [45]. For LaNi4.5Mn0.5, the micro-arrangement of Mn atom in LaNi5xMnx was rarely reported. Based on all these, two calculated models of LaNi4.5M0.5 (M = Al, Mn, Fe, Co) employing double-unit cell of LaNi5 along c-axis are designed by replacing one Ni atom
1 2 1 2 1 2 1 2
Site of M atom
x
y
z
3g 2c 3g 2c 3g 2c 3g 2c
1/2 2/3 1/2 2/3 1/2 2/3 1/2 2/3
1/2 1/3 1/2 1/3 1/2 1/3 1/2 1/3
3/4 1/2 3/4 1/2 3/4 1/2 3/4 1/2
in the 2c and 3g site with M atom, respectively, as shown in Table 1. To see the expanded crystal structure, the model 1 of LaNi4.5Co0.5 is shown in Fig. 1.
3. Results and discussion 3.1. Crystal structure of LaNi4.5M0.5 (M = Al, Mn, Fe, Co) To obtain the stable structure, each model of LaNi4.5M0.5 (M = Al, Mn, Fe, Co) has been optimized in both the volume and c/a ratio, respectively. Analysis of X-ray diffraction patterns confirmed that LaNi5xMx (M = Al, Mn, Fe, Co) crystallize in the hexagonal CaCu5-type structure [19]. So the symmetry of the alloy is lowered into space group H in course of calculation. The optimization is truncated when M atom could reach relaxation in the unit cell. All these optimized results and the reference data are listed in Table 2. As can be seen from Table 2, the optimized results in LaNi4.5M0.5 (M = Al, Mn, Fe, Co) indicate that the total energy of each model 1 is lower than that of each model 2. And the calculated cell parameters are very close to those experimental values measured in Refs. [33,47,48]. It means that each model 1 is the most favorable structure among all the models of LaNi4.5M0.5 (M = Al, Mn, Fe, Co). Therefore, we can draw a conclusion that Al, Mn, Fe and Co atoms prefer to substitute Ni atoms of 3g sites, which is in agreement with the experimental data obtained by neutron power diffraction technique [44,47]. Because the double cell model is adopted, both
Fig. 1. Crystal structure of LaN4.5Co0.5.
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Table 2 The optimized results of LaNi4.5M0.5 (M = Ni, Al, Mn, Fe, Co). V (Å3)
Structure
Model
a (Å)
c (Å)
c/a
Et (eV)
LaNi5
Expt. [46] Calc. [31]
5.018 4.992
3.982 3.961
0.793 0.793
437967.25
85.48
LaNi4.5Al0.5
Model 1 Model 2 Expt. [47]
5.043 5.107 5.038
8.019 7.883 4.018
0.795
841174.27 841174.03
176.63 178.06
LaNi4.5Mn0.5
Model 1 Model 2 Expt. [33]
5.012 5.0295 5.052
7.935 7.953 4.018
0.791
866082.37 866082.24
172.61 174.17
LaNi4.5Fe0.5
Model 1 Model 2 Expt. [33]
5.002 5.017 5.037
7.919 7.895 4.00
0.791
869187.29 869187.12
171.63 172.14
LaNi4.5Co0.5
Model 1 Model 2 Expt. [48]
4.992 5.001 5.022
7.950 7.919 3.981
0.796
872470.00 872469.88
171.54 171.56
lattice constant c and total volume are twice over the data of the unit cell. In addition, the lattice parameters of model 1 are less than the corresponding experimental results. The reason for the discrepancy may be the temperature dependence [49]. Compared with the calculated data of LaNi5 [31], the cell volumes of LaNi4.5M0.5 (M = Al, Mn, Fe, Co) slightly expand, which could induce the trend of the increase of lattice parameters a and c except LaNi4.5Fe0.5. The lattice parameter c slightly decreases for LaNi4.5Fe0.5. Namely the total volume sequence is LaNi4.5Al0.5 > LaNi4.5Mn0.5 > LaNi4.5 Fe0.5 > LaNi4.5Co0.5 > LaNi5, which results from the difference of atom radius. Compared with 1.62 Å of Ni atom, the atom radius of Al, Mn, Fe, Co is 1.82, 1.79, 1.72, 1.67 Å, respectively. Lattice expansion has a certain influence on platform pressure in P–C isotherm curves. Generally, the larger volume expansion is, the lower platform pressure is. According to the system volume, the platform pressure is LaNi4.5Al0.5 < LaNi4.5Mn0.5 < LaNi4.5Fe0.5 < LaNi4.5Co0.5 < LaNi5, which is in well agreement with the experimental result [46,50]. Furthermore, the ratio of c/a in LaNi4.5M0.5 (M = Ni, Al, Mn, Fe, Co) is 0.793, 0.795, 0.791, 0.791, 0.796. Therefore, LaNi4.5M0.5 (M = Mn, Fe) systems change more anisotropic in contrast with LaNi5, while the LaNi4.5M0.5 (M = Al, Co) compounds were observed less anisotropic, which is one of reasons that improve the anti-pulverization characteristics of the system with the substitution of Al, Co atoms. 3.2. Cohesive and formation energies of LaNi4.5M0.5 (M = Ni, Al, Mn, Fe, Co) Generally, the stability of the system can be discussed using the cohesive energy and formation energy. The cohesive energies Ecoh of LaNi4.5M0.5 (M = Al, Mn, Fe, Co) composed of the metals La, Ni and M are obtained by [42]
Ecoh ¼
1 ½Ei ðLaÞ þ 4:5Ei ðNiÞ þ 0:5Ei ðMÞ Et ðLaNi4:5 M0:5 Þ 6
ð1Þ
where Et(LaNi4.5M0.5) refers to the total energy of the intermetallic compound at equilibrium, and Ei(La), Ei(Ni) and Ei(M) are the total energies of the pure atomic constituents. Simple cubic model is adopted to calculate the total energy of single atom constituent. The formation energies DH of LaNi4.5M0.5 composed of the metals La, Ni and M can be calculated by [42]
DH ¼ Et ðLaNi4:5 M0:5 Þ ½Et ðLaÞ þ 4:5Et ðNiÞ þ 0:5Et ðMÞ
ð2Þ
where Et(La), Et(Ni) and Et(M) are the total energies of the solid elemental constituents. The space group of La and Ni elements are P63/ mmc and Fm3m, while the crystal structure of M (M = Al, Mn, Fe, Co) is Fm3m, I-43 m, Im3m and P63/mmc, respectively.
Table 3 summarizes the ab initio formation and cohesive energies including the corresponding experimental values as well as the total energies of La, Ni, M and LaNi4.5M0.5 (M = Ni, Al, Mn, Fe, Co). The comparison for LaNi5 shows that the ab initio data of the formation energy is in good agreement with the experimental result [51]. As is known, when either the formation energy is more negative or the cohesive energy is more positive, an alloy is more stable. It can be seen in Table 3 that LaNi4.5Mn0.5 alloy has the most negative formation energy and the most positive cohesive energy, which indicates that the stability of LaNi4.5Mn0.5 is the best among five alloys. According to the data of formation energies, the stability sequence of the alloy is LaNi4.5Mn0.5 > LaNi4.5Co0.5 > LaNi4.5 Al0.5 > LaNi5 > LaNi4.5Fe0.5. However, the calculated cohesive energies follow a different trend, LaNi4.5Mn0.5 > LaNi4.5Fe0.5 > LaNi4.5Co0.5 > LaNi5 > LaNi4.5Al0.5. Actually, this discrepancy between DH and Ecoh on forecasting the system stability originates from their respective different physical significance. The formation energy expresses the change of enthalpy that accompanies the formation of one mole of the compound. We know that, the free energy of formation DG could suggest the stability of phases. At zero temperature, because there is no entropy contribution, the DG is derived by the formation enthalpy [52]. In other words, the formation energy could be used to determine the phase stability of the compounds. In addition, the cohesive energy is energy required to separate atoms to infinite distance with no more interaction. It is a measure of the strength of the force which binds atoms together in the solid state that is correlative with the structural stability at the ground state [42]. Generally, the crystal structure, bond type and bond strength would change during the formation of an intermetallic phase from its components. It is clearly shown in Table 3 that the DH of LaNi4.5M0.5 (M = Ni, Al, Mn, Fe, Co) changes obvious compared to Ecoh, which demonstrates that DH is related to changes of not only binding strength but also to the crystal structures with the variety of components in a system [42]. 3.3. Electronic structures of LaNi4.5M0.5 (M = Al, Mn, Fe, Co)
3.3.1. Analysis of densities of states To discuss the effect of the substitutions at the Ni site on the electronic structure, the total densities of states (TDOSs) are plotted in Fig. 2 for LaNi4.5M0.5 (M = Al, Mn, Fe, Co). Owing to employing the double cell model of LaNi5, the TDOS are twice over the data of the unit cell. And the Fermi energy EF has been taken as the energy zero in every figure. Fermi energies of LaNi4.5M0.5 (M = Al, Mn, Fe, Co) are about 10.05, 10.44, 10.40 and 10.34 eV.
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Table 3 The calculated total energy (Et and Ei) of elemental solids (La, Ni, and M), pure atoms (La, Ni, and M) and LaNi4.5M0.5, cohesive energy (Ecoh), formation energy (DH) of LaNi4.5M0.5 (M = Ni, Al, Mn, Fe, Co). Atom
La
Ni
Al
Mn
Fe
Co
Ei (eV) Et (eV) Structure Ecoh (eV) DH (mJ/mol) Expt. [51]
231130.65 231135.40 LaNi5 5.72 171.77 159.1 ± 8.3
41360.45 41366.01 LaNi4.5Al0.5 5.65 222.92
6600.98 6604.71 LaNi4.5Mn0.5 5.90 546.75
31506.07 31506.08 LaNi4.5Fe0.5 5.87 150.71
34611.44 34619.23 LaNi4.5Co0.5 5.81 364.08
37894.86 37897.51
Table 4 The formation energy of hydrogen atom and total energy of LaNi4.5M0.5H0.5 (M = Ni, Al, Mn, Fe, Co). Structure
LaNi5H0.5
LaNi4.5Al0.5H0.5
LaNi4.5Mn0.5H0.5
LaNi4.5Fe0.5H0.5
LaNi4.5Co0.5H0.5
Et (eV) Ecoh (eV)
437985.53 4.69
841194.63 6.77
866103.39 7.43
869208.30 7.42
872490.95 7.36
Fig. 2. The total densities of states (TDOSs) of LaNi4.5M0.5 (M = Al, Mn, Fe, Co).
The difference of fermi energy is due to the different number of valence electrons with the substitution of M for Ni atoms and the charge transfer from valence band to conduction band. As can be seen from Fig. 2, the TDOS is composed of both bonding and non-bonding area. Part of DOS is across the Fermi level region, which shows that this system still puts up the metallic character with the substitution of Ni atoms. The width of valence band for LaNi4.5M0.5 (M = Al, Mn, Fe, Co) is 8.81, 8.34, 8.12, 8.09 eV, respectively. Compared with the width 8.17 eV of valence band for LaNi5 system, the valence bands of LaNi4.5M0.5 (M = Al, Mn) become wider, and that of LaNi4.5Al0.5 has the maximum width. This is due to the contribution of the Al s and p sub-bands, which are located near the bottom of the total valence bands [43,53]. The bonding states are formed by the interaction between the hybridization orbital of atom s, p, d and f orbital. In order to give a qualitative characteristics of electronic structure in these alloy, the partial density of states (PDOSs) plots for La, Ni, and M
Fig. 3. The partial densities of states (PDOSs) of LaNi4.5M0.5 (M = Al, Mn, Fe, Co).
(M = Al, Mn, Fe, Co) atoms are given in Fig. 3. Compared with LaNi5 [39], the occupied part of valence bands in higher energy region is still dominated by the Ni (2c)-d and Ni (3g)-d states, and the occupied part of valence bands in lower energy region is dominated by the La-4p states. The occupied states near EF are dominated by the Ni-3d states and M-3d states (M = Mn, Fe, Co) with non-negligible bonding contributions of the La-5d states and Al-s,p states. Furthermore, the M (M = Al, Mn, Fe, Co) atoms cause reconstruction of the starting LaNi5 band structure and change of the value of DOS at the Fermi level. The DOS (EF) for LaNi4.5M0.5 (M = Al, Mn, Fe, Co) is equal to about 11.63, 23.22, 17.4, 18.74 states/ (eV f.u.). As is clearly seen in Figs. 2 and 3, the TDOS at EF is mostly composed of Ni (2c)-d, Ni (3g)-d and M (M = Mn, Fe, Co)-d states, which provide almost equal contributions to it. The PDOS of M( = Al, Mn, Fe, Co) at EF is equal to 0.05, 6.65, 3.67, 2.98 states/ (eV atom.), which would result from the different number of
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(a)
(b)
(c)
(d)
(e)
Fig. 4. The electron densities on the (0 0 0 4) plane: (a) LaNi5; (b) LaNi4.5Al0.5; (c) LaNi4.5Mn0.5; (d) LaNi4.5Fe0.5; (e) LaNi4.5Co0.5.
valence electrons. And the Mn, Fe, Co atoms supplies 9, 8, 7 valence electrons, whereas the Al atom 3 valence electrons. As also can be seen from Fig. 3, Ni-d states and M-d states at EF have strong interactions, which would reduce the TDOS at EF. Therefore, the sequence of TDOS (EF) is LaNi4.5Mn0.5 > LaNi4.5Co0.5 > LaNi4.5Fe0.5, which indicate that the interaction between Ni-d and M-d states is LaNi4.5Fe0.5 > LaNi4.5Co0.5 > LaNi4.5Mn0.5. According to the electronic-specific heat coefficient [54]
c¼
p
2
3
2
kB nðEF Þ
ð3Þ
Compared to 17.6 mJ/mol K2 of LaNi5 [31], the electronic-specific heat coefficient of LaNi4.5Al0.5 deceases to 13.7 mJ/mol K2, while c of LaNi4.5M0.5 (M = Mn, Fe, Co) increases to 27.4, 20.5, 22.1 mJ/mol K2, respectively. This might indicate that the stability of this system would be changed with the substitution of M atoms.
3.3.2. Charge distributions To further study the interactions among La, Ni (3g), Ni (2c) and M atoms, contour maps of the electron densities on two planes are shown in Fig. 4a–e and Fig. 5a–d: one is the (0 0 0 4) plane
C. Zhang et al. / Computational Materials Science 69 (2013) 520–526
(a)
(b)
(c)
(d)
525
0Þ plane of (a) LaNi4.5Al0.5; (b) LaNi4.5Mn0.5; (c) LaNi4.5Fe0.5; (d) LaNi4.5Co0.5. Fig. 5. Charge densities in the ð1 1 2
containing the Ni (3g)–Ni (3g) and Ni (3g)-M interactions, the other 0) plane containing the La–Ni (2c), Ni (3g)–Ni (2c) and M– is (1 1 2 Ni (2c) interactions for LaNi4.5M0.5 (M = Al, Mn, Fe, Co). As is evidently shown from Fig. 4a–e and Fig. 5a–d, the valence electrons intensively diffuse in the unit cell, and the highest density charge resides in the immediate vicinity of the nuclei. In contrast, there are relatively low electron densities in the interstitial area, and interstitial charges are well delocalized, which indicates that the metallic bonding is formed in the interstitial area; but no clear directional bonds can be seen [54,55]. It is clearly seen from Fig. 4a–e, the electron densities (0.32 e/Å3) between Ni (3g) atom and Ni (3g) atom for LaNi5 is greatly higher than the corresponding value 0.25 e/Å3 between Al atom and Ni (3g) atom for LaNi4.5Al0.5. It indicates that the alloy strengthens the anti-pulverization characteristics with the substitution of Al atoms [30]. In addition, the electron densities between Ni (3g) atom and Mn, Fe, Co atom is 0.325, 0.33, 0.33 e/Å3 for LaNi4.5M0.5 (M = Mn, Fe, Co), respectively. It is shown that the interactions between atoms of the system are slightly reinforced with the substitution of Mn, Fe, Co atoms, which is in consistence with the analysis of DOS. It can be clearly observed from Fig. 5a that the electron densities (0.32 e/Å3) of Ni (3g)–Ni (2c) are much higher than the corresponding value 0.2 e/Å3 of La–Ni (2c), which shows that the interaction between Ni (3g) and Ni (2c) atoms is much stronger than that between La and Ni (2c) atoms. The result is consistent with the previous analysis. In contrast, the charge densities between the Al and Ni (2c) atoms is about 0.27 e/Å3. It is further
testified here that the Al–Ni interaction is certain to be still weaker compared to the Ni–Ni interaction. From Fig. 5b–d, the electron densities between Mn, Fe, Co and Ni (2c) atom is 0.35, 0.355, 0.355 e/Å3, which is slightly higher than the corresponding value 0.34 e/Å3 of Ni (3g)–Ni (2c) atoms. It is further confirmed that the interactions of Mn–Ni, Fe–Ni, Co–Ni atoms are greatly stronger compared to the Ni–Ni interaction, which is in well agreement with the experimental results [19]. As is also seen from Fig. 5b–d that the electron densities (0.21 e/Å3) of La–Ni (2c) is slightly larger than 0.2 e/Å3 for LaNi4.5Al0.5, which is caused by the expansion and distortion of the lattice. 3.4. The bounding hydrogen capacity of LaNi4.5M0.5 (M = Al, Mn, Fe, Co) To discuss the bounding hydrogen capacity of LaNi4.5M0.5 system, the formation energy of hydrogen atom in LaNi4.5M0.5H0.5 (M = Al, Mn, Fe, Co) was calculated. As is known, more positive of the formation energy, stronger capacity of the system to bound hydrogen atom. The formation energy of hydrogen atom in LaNi4.5M0.5H0.5 (M = Al, Mn, Fe, Co) is obtained by
Ecoh ¼ Et ðLa2 Ni9 MÞ þ Ei ðHÞ Et ðLa2 Ni9 MHÞ
ð4Þ
where Et(La2Ni9M) and Et(La2Ni9MH) refer to the total energy of the intermetallic compound at equilibrium. For La2Ni9MH, we employ hypothetical unit cells by doubling the unit cell of LaNi4.5M0.5 along the c-axis and placing one hydrogen atom at the 6 m site. And the
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total energies of LaNi4.5M0.5H0.5 have been made by optimizing the cell parameters and internal coordinates. Ei(H) is the total energy of single hydrogen atom by building simple cubic model. The formation energy of hydrogen atom and total energy for LaNi4.5M0.5H0.5 (M = Al, Mn, Fe, Co) are listed in Table 4. The total energy of single hydrogen atom is 13.59 eV, and the total energies of LaNi4.5M0.5 are used in Table 2. As can be seen from Table 4, the formation energy of hydorgen atom in LaNi5H0.5 is 4.69 eV, while it increases to 6.77, 7.43, 7.42 and 7.36 eV for LaNi4.5M0.5H0.5 (M = Al, Mn, Fe, Co), respectively. This indicates that the partial substitutions at the Ni with M could enhance the bounding hydrogen capacity of the system. Therefore, the formation energy of hydrogen atom is LaNi4.5Mn0.5H0.5 > LaNi4.5Fe0.5H0.5 > LaNi4.5Co0.5H0.5 > LaNi4.5Al0.5H0.5 > LaNi5H0.5, which indicate that the bounding hydrogen capacity of the system is LaNi4.5Mn0.5 > LaNi4.5Fe0.5 > LaNi4.5Co0.5 > LaNi4.5Al0.5 > LaNi5. 4. Conclusions The crystal structures, stability and electronic structures of LaNi4.5M0.5 (M = Al, Mn, Fe, Co) have been systematically investigated by first-principles calculations. The optimized results indicate that M (M = Al, Mn, Fe, Co) atoms prefer to substitute Ni atoms of 3g sites. The total volume sequence is LaNi4.5Al0.5 > LaNi4.5Mn0.5 > LaNi4.5Fe0.5 > LaNi4.5Co0.5 > LaNi5, which is consistent with the experimental data. According to the radio of c/a, LaNi4.5Al0.5 and LaNi4.5Co0.5 alloys were observed less anisotropic, which is a probable reasons to improve the anti-pulverization characteristics of the host alloy with the substitution of Al, Co atoms. The stability of LaNi4.5M0.5 (M = Al, Mn, Fe, Co) alloys is studied by calculating the formation and cohesive energies. According to the data of negative formation energy, the stability sequence is LaNi4.5Mn0.5 > LaNi4.5Co0.5 > LaNi4.5Al0.5 > LaNi5 > LaNi4.5Fe0.5. While the results of cohesive energy show the different trend. From the plots of density of states, the valence band of LaNi4.5 Al0.5 becomes broad, which are dominated by the Al-s, p states. For LaNi4.5M0.5 (M = Mn, Fe, Co), Ni-3d states and M-d states at EF have strong interactions, and the interaction between Ni-d and M-d states is LaNi4.5Fe0.5 > LaNi4.5Co0.5 > LaNi4.5Mn0.5. According to the formation energy of hydrogen atom in LaNi4.5M0.5H0.5 (M = Al, Mn, Fe, Co), the bounding hydrogen capacity of the system is LaNi4.5Co0.5 > LaNi4.5Fe0.5 > LaNi4.5Mn0.5 > LaNi4.5Al0.5. Acknowledgements This research was supported by the Program of National Natural Science Foundation of China under Grant No. 11104022 and Cultivating Programme of Middle-aged backbone teachers of Chengdu University of Technology. We acknowledge Project supported by the Scientific Research Foundation of the Education Department of Sichuan Province, China (Grant Nos. 11ZB036 and 11ZB266). References [1] J.H.N. Van Vucht, F.A. Kuijpers, H.C.A.M. Bruning, Philips Res. Rep. 25 (1970) 133–140. [2] B. Joseph, B. Schiavo, J. Alloys Compd. 480 (2009) 912–916. [3] T. Kaneko, A. Tezuka, H. Ogawa, T. Ikeshoji, Phys. Rev. B 81 (2010) 184302. [4] A. Tezuka, H. Wang, H. Ogawa, T. Ikeshoji, Phys. Rev. B 81 (2010) 134304. [5] C.Y. Zhang, X.F. Zhao, L.J. Tang, T. Gao, Physica B 406 (2011) 3436–3441. [6] J. Payá, A. Freni, J.M. Corberán, V. Compañ, J. New Mat. Electrochem. Syst. 15 (2012) 293–300. [7] J.J.G. Willems, K.H.J. Buschow, J. Less-Common Met. 129 (1987) 13–30. [8] E.D. Snijder, G.F. Versteeg, W.P.M. van Swaaij, Chem. Eng. Sci. 48 (1993) 2429– 2441. [9] A. Anani, A. Visintin, K. Petrov, S. Srinivasan, J.J. Reilly, J.R. Johnson, J. Power Sources 47 (1994) 261–275.
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First-principles study of the crystal structures and electronic properties of LaNi4.5M0.5 (M = Al, Mn, Fe, Co) Chuanyu Zhang a,⇑, Yiliang Liu b, Xiaofeng Zhao a, Min Yan a, Tao Gao c a
Department of Applied Physics, Chengdu University of Technology, Chengdu 610059, China College of Electrical and Information Engineering, Southwest University for Nationalities, Chengdu 610041, China c Institute of Atomic and Molecular Physics, Sichuan University, Chengdu 610065, China b
a r t i c l e
i n f o
Article history: Received 8 August 2012 Received in revised form 9 November 2012 Accepted 11 November 2012 Available online 24 January 2013 Keywords: First-principles theory Crystal structure Electronic structure
a b s t r a c t The structure, stability and electronic properties of the different B-site partial substituted derivatives LaNi4.5M0.5 (M = Al, Mn, Fe, Co) have been investigated by means of the density functional theory using the full-potential linearized augmented plane wave (FLAPW) method with the generalized gradient approximation (GGA). The optimized results indicate that all of Al, Mn, Fe, Co atoms prefer to substitute Ni atoms in the 3g sites. Due to the different radius of elements, the cell volume would increase with the doping Ni (3g) atoms. And the sequence of volume is LaNi4.5Al0.5 > LaNi4.5Mn0.5 > LaNi4.5Fe0.5 > LaNi4.5 Co0.5 > LaNi5, which is in agreement with the experimental result. The calculated data of formation and cohesive energies indicate that LaNi4.5Mn0.5 has the stablest structure among five alloys. Based on the analysis of the density of states and charge density, the interactions of Mn–Ni, Fe–Ni, Co–Ni atoms are greatly stronger compared to the Ni–Ni interaction, while the interaction of Al–Ni atoms is weakened. Based on the formation energy of hydrogen atom in LaNi4.5M0.5H0.5, the sequence of bounding hydrogen atoms is LaNi4.5Mn0.5 > LaNi4.5Fe0.5 > LaNi4.5Co0.5 > LaNi4.5Al0.5 > LaNi5. Ó 2012 Elsevier B.V. All rights reserved.
1. Introduction The intermetallic compound LaNi5 is known to store large quantity of hydrogen since the early 1970s [1–6]. Meanwhile, LaNi5 is of great importance for hydrogen storage applications, such as negative electrode materials, hydrogen purification and recovery devices [7–9]. Nevertheless, hydrogen absorption and desorption cycling has two main physical and irreversible consequences: pulverization and defect generation [10–14]. Generally, the wide ranges of pseudo-binary substitutions yield important changes in the related LaNi5 hydride properties. In order to modify the overall properties of the host material LaNi5, the effects of partial substitution of Ni with other metals have been studied extensively. Al, Mn, Fe and Co elements are most commonly used among the substituted metals. The functions of all these substitutions are as follows: the partial substitutions at the Ni with Al can commendably improve the cycling performance and reduce the plateau pressure of the P–C–T curve [15–17]; the partial substitutions at the Ni with Mn can reduce the plateau pressure of hydrogen without reduction of hydrogen storage capacity [18]; the partial substitutions at the Ni with Fe can efficiently increase the hydrogen storage capacity [19]; the partial substitutions
⇑ Corresponding author. Tel.: +86 28 84078267; fax: +86 28 85415508. E-mail address: [email protected] (C. Zhang). 0927-0256/$ - see front matter Ó 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.commatsci.2012.11.023
at the Ni with Co can significantly extend the cycle life [15,20]. In recent years, many references in La–Ni–M system have been published between the experimental results [19,21–28] and theoretical investigations [29–32]. However, most of previous works were carried out to investigate the hydrogenation behavior of single doped or co-doped LaNi5 type alloys. Little comparative studies of LaNi5xM0.5 (M = Al, Mn, Fe, Co, etc.) have been reported so far. On the experimental front, the electrochemical performance of LaNi4.7M0.3 (M = Ni, Co, Mn, Al) alloys were rapidly evaluated by means of a powder microelectrode technique [21]. Hydrogen desorption kinetics of hydrides of LaNi4.5Al0.5, LaNi4.5Mn0.5 and LaNi2.5M2.5 were studied by a volumetric method [27]. Magnetic properties of the LaNi4.5M0.5 (M = Fe, Co, Mn, Cu, Cr, Si) and their hydride compounds have been studied by magnetization measurement using a VSM [28]. In order to clarify the mechanism of formation of lattice strain in hydriding and dehydriding, peak broadening in X-ray powder diffraction (XRD) profiles of LaNi4.5M0.5 (M = Fe, Co, Mn) alloys was investigated [33]. In the theoretical research, the effect of Ni substitutions by group IVA (Si, Ge, Sn) elements on the electronic properties of LaNi5 and its hydrides have been studied using ab initio band structure calculations [32]. A more systematic investigation of the crystal structure and electronic properties of B-site partial substituted LaNi5 alloys is necessary for a better understanding of the substitution effects. In this paper, the steady structures and corresponding cell parameters of LaNi4.5M0.5 (M = Al, Mn, Fe, Co) were obtained by
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modeling and optimizing. The cohesive and formation energies are estimated to forecast the stability of the system. And the densities of states, electronic densities are calculated to analyze the effects on the electronic properties of the host alloy due to the substitution of Ni atoms. Finally, the formation energy of hydrogen atom in LaNi4.5M0.5H0.5 (M = Al, Mn, Fe, Co) is calculated to discuss the bounding hydrogen capacity of the system.
Table 1 The primitive occupation sites of two models of LaNi4.5M0.5 (M = Al, Mn, Fe, Co). Structure
Model
LaNi4.5Al0.5
Model Model Model Model Model Model Model Model
LaNi4.5Mn0.5 LaNi4.5Fe0.5 LaNi4.5Co0.5
2. Computational methods In this article, we employ the all-electron full-potential linearized augmented plane wave (FLAPW) method [34], which is among the most accurate methods for performing electronic structure calculations for crystals. The FLAPW method is the ab initio method for solving the Kohn–Sham equations for the ground state density, total energy, and eigenvalues of a many electron system by introducing a basis set. First, many-electron problem of a crystal is translated into single-electron problem, which is translated into Kohn–Sham equation. Second, Kohn–Sham equation can be solved by introducing linearized augmented plane wave basis functions, and the generalized gradient approximation (GGA) developed by Perdew et al. [35] is used to solve the electron exchange–correlation energy function. Third, the unit cell is divided into two regions: (1) non-overlapping atomic spheres and (2) an interstitial region. Therefore, two different types of basis set are used: the plane wave basis set is adopted inside atomic sphere; a plane wave expansion is adopted in the interstitial region. Then, the solution to the Kohn–Sham equations is expanded in this combined basis set of LAPW’s according to the linear variation method. Finally, the potential is also expanded in self-consistent-field cycle. The FLAPW calculations are performed using the WIEN2K package [36]. In the course of calculation, the muffin-tin radii Rmt of La, Ni, M (M = Al, Mn, Fe, Co) atoms are taken to be 0.95, 0.95 and 0.95 Å, respectively. The size of the basis set is given by the product Rmt Kmax = 7.0, where Kmax is the largest reciprocal space wave vector in the basis set. The charge density and the potentials are expanded into lattice harmonics up to L = 6 inside the spheres and a Fourier series in the interstitial region. The value of Gmax = 14 is used, which may limit the LM expansion. The separation energy between inner electrons and covalence electrons is 108.8 eV in the calculation of exchange correlation energy. Electronic configuration of covalence electrons are La-5d16s2, Ni-3d84s2, Al-3s23p1, Mn3d54s2, Fe-3d64s2, Co-3d74s2, respectively. Self-consistency is achieved by demanding the convergence of total energy smaller than 104 eV/cell. To ensure convergence for the Brillouin zone (BZ) integration, 1000 k-points in the irreducible wedge of the first BZ of the hexagonal lattice is chosen in course of calculation. Owing to the spin–orbit coupling having little effect on the equilibrium geometric structure and electronic structure of LaNi5 alloy [37], the spin polarization is neglected in the SCF cycles. LaNi5 is known to be described in the hexagonal CaCu5 structure, space group P6/mmm, where the La atoms occupy the (1a) sites and Ni atoms occupy (2c) and (3g) Wyckoff sites [38,39]. For LaNi4.5Al0.5, the previous research shows that Al atoms predominantly occupy 3g sites and the CaCu5 structure is retained until x 6 1.3 for alloys LaNi5xAlx [31,40–42]. For LaNi4.5Co0.5, Co prefers to occupy the 3g sites in the LaNi5-type structure [43]. And the Neutron diffraction study indicates that the occupancy numbers of Co in LaNi4Co are 23% at the 2c site and 77% at the 3g site [44]. For LaNi4.5Fe0.5, Fe can be substituted for Ni inLaNi5xFex up to x = 1.2. Ni is replaced by Fe at both the 2c and 3g sites [45]. For LaNi4.5Mn0.5, the micro-arrangement of Mn atom in LaNi5xMnx was rarely reported. Based on all these, two calculated models of LaNi4.5M0.5 (M = Al, Mn, Fe, Co) employing double-unit cell of LaNi5 along c-axis are designed by replacing one Ni atom
1 2 1 2 1 2 1 2
Site of M atom
x
y
z
3g 2c 3g 2c 3g 2c 3g 2c
1/2 2/3 1/2 2/3 1/2 2/3 1/2 2/3
1/2 1/3 1/2 1/3 1/2 1/3 1/2 1/3
3/4 1/2 3/4 1/2 3/4 1/2 3/4 1/2
in the 2c and 3g site with M atom, respectively, as shown in Table 1. To see the expanded crystal structure, the model 1 of LaNi4.5Co0.5 is shown in Fig. 1.
3. Results and discussion 3.1. Crystal structure of LaNi4.5M0.5 (M = Al, Mn, Fe, Co) To obtain the stable structure, each model of LaNi4.5M0.5 (M = Al, Mn, Fe, Co) has been optimized in both the volume and c/a ratio, respectively. Analysis of X-ray diffraction patterns confirmed that LaNi5xMx (M = Al, Mn, Fe, Co) crystallize in the hexagonal CaCu5-type structure [19]. So the symmetry of the alloy is lowered into space group H in course of calculation. The optimization is truncated when M atom could reach relaxation in the unit cell. All these optimized results and the reference data are listed in Table 2. As can be seen from Table 2, the optimized results in LaNi4.5M0.5 (M = Al, Mn, Fe, Co) indicate that the total energy of each model 1 is lower than that of each model 2. And the calculated cell parameters are very close to those experimental values measured in Refs. [33,47,48]. It means that each model 1 is the most favorable structure among all the models of LaNi4.5M0.5 (M = Al, Mn, Fe, Co). Therefore, we can draw a conclusion that Al, Mn, Fe and Co atoms prefer to substitute Ni atoms of 3g sites, which is in agreement with the experimental data obtained by neutron power diffraction technique [44,47]. Because the double cell model is adopted, both
Fig. 1. Crystal structure of LaN4.5Co0.5.
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Table 2 The optimized results of LaNi4.5M0.5 (M = Ni, Al, Mn, Fe, Co). V (Å3)
Structure
Model
a (Å)
c (Å)
c/a
Et (eV)
LaNi5
Expt. [46] Calc. [31]
5.018 4.992
3.982 3.961
0.793 0.793
437967.25
85.48
LaNi4.5Al0.5
Model 1 Model 2 Expt. [47]
5.043 5.107 5.038
8.019 7.883 4.018
0.795
841174.27 841174.03
176.63 178.06
LaNi4.5Mn0.5
Model 1 Model 2 Expt. [33]
5.012 5.0295 5.052
7.935 7.953 4.018
0.791
866082.37 866082.24
172.61 174.17
LaNi4.5Fe0.5
Model 1 Model 2 Expt. [33]
5.002 5.017 5.037
7.919 7.895 4.00
0.791
869187.29 869187.12
171.63 172.14
LaNi4.5Co0.5
Model 1 Model 2 Expt. [48]
4.992 5.001 5.022
7.950 7.919 3.981
0.796
872470.00 872469.88
171.54 171.56
lattice constant c and total volume are twice over the data of the unit cell. In addition, the lattice parameters of model 1 are less than the corresponding experimental results. The reason for the discrepancy may be the temperature dependence [49]. Compared with the calculated data of LaNi5 [31], the cell volumes of LaNi4.5M0.5 (M = Al, Mn, Fe, Co) slightly expand, which could induce the trend of the increase of lattice parameters a and c except LaNi4.5Fe0.5. The lattice parameter c slightly decreases for LaNi4.5Fe0.5. Namely the total volume sequence is LaNi4.5Al0.5 > LaNi4.5Mn0.5 > LaNi4.5 Fe0.5 > LaNi4.5Co0.5 > LaNi5, which results from the difference of atom radius. Compared with 1.62 Å of Ni atom, the atom radius of Al, Mn, Fe, Co is 1.82, 1.79, 1.72, 1.67 Å, respectively. Lattice expansion has a certain influence on platform pressure in P–C isotherm curves. Generally, the larger volume expansion is, the lower platform pressure is. According to the system volume, the platform pressure is LaNi4.5Al0.5 < LaNi4.5Mn0.5 < LaNi4.5Fe0.5 < LaNi4.5Co0.5 < LaNi5, which is in well agreement with the experimental result [46,50]. Furthermore, the ratio of c/a in LaNi4.5M0.5 (M = Ni, Al, Mn, Fe, Co) is 0.793, 0.795, 0.791, 0.791, 0.796. Therefore, LaNi4.5M0.5 (M = Mn, Fe) systems change more anisotropic in contrast with LaNi5, while the LaNi4.5M0.5 (M = Al, Co) compounds were observed less anisotropic, which is one of reasons that improve the anti-pulverization characteristics of the system with the substitution of Al, Co atoms. 3.2. Cohesive and formation energies of LaNi4.5M0.5 (M = Ni, Al, Mn, Fe, Co) Generally, the stability of the system can be discussed using the cohesive energy and formation energy. The cohesive energies Ecoh of LaNi4.5M0.5 (M = Al, Mn, Fe, Co) composed of the metals La, Ni and M are obtained by [42]
Ecoh ¼
1 ½Ei ðLaÞ þ 4:5Ei ðNiÞ þ 0:5Ei ðMÞ Et ðLaNi4:5 M0:5 Þ 6
ð1Þ
where Et(LaNi4.5M0.5) refers to the total energy of the intermetallic compound at equilibrium, and Ei(La), Ei(Ni) and Ei(M) are the total energies of the pure atomic constituents. Simple cubic model is adopted to calculate the total energy of single atom constituent. The formation energies DH of LaNi4.5M0.5 composed of the metals La, Ni and M can be calculated by [42]
DH ¼ Et ðLaNi4:5 M0:5 Þ ½Et ðLaÞ þ 4:5Et ðNiÞ þ 0:5Et ðMÞ
ð2Þ
where Et(La), Et(Ni) and Et(M) are the total energies of the solid elemental constituents. The space group of La and Ni elements are P63/ mmc and Fm3m, while the crystal structure of M (M = Al, Mn, Fe, Co) is Fm3m, I-43 m, Im3m and P63/mmc, respectively.
Table 3 summarizes the ab initio formation and cohesive energies including the corresponding experimental values as well as the total energies of La, Ni, M and LaNi4.5M0.5 (M = Ni, Al, Mn, Fe, Co). The comparison for LaNi5 shows that the ab initio data of the formation energy is in good agreement with the experimental result [51]. As is known, when either the formation energy is more negative or the cohesive energy is more positive, an alloy is more stable. It can be seen in Table 3 that LaNi4.5Mn0.5 alloy has the most negative formation energy and the most positive cohesive energy, which indicates that the stability of LaNi4.5Mn0.5 is the best among five alloys. According to the data of formation energies, the stability sequence of the alloy is LaNi4.5Mn0.5 > LaNi4.5Co0.5 > LaNi4.5 Al0.5 > LaNi5 > LaNi4.5Fe0.5. However, the calculated cohesive energies follow a different trend, LaNi4.5Mn0.5 > LaNi4.5Fe0.5 > LaNi4.5Co0.5 > LaNi5 > LaNi4.5Al0.5. Actually, this discrepancy between DH and Ecoh on forecasting the system stability originates from their respective different physical significance. The formation energy expresses the change of enthalpy that accompanies the formation of one mole of the compound. We know that, the free energy of formation DG could suggest the stability of phases. At zero temperature, because there is no entropy contribution, the DG is derived by the formation enthalpy [52]. In other words, the formation energy could be used to determine the phase stability of the compounds. In addition, the cohesive energy is energy required to separate atoms to infinite distance with no more interaction. It is a measure of the strength of the force which binds atoms together in the solid state that is correlative with the structural stability at the ground state [42]. Generally, the crystal structure, bond type and bond strength would change during the formation of an intermetallic phase from its components. It is clearly shown in Table 3 that the DH of LaNi4.5M0.5 (M = Ni, Al, Mn, Fe, Co) changes obvious compared to Ecoh, which demonstrates that DH is related to changes of not only binding strength but also to the crystal structures with the variety of components in a system [42]. 3.3. Electronic structures of LaNi4.5M0.5 (M = Al, Mn, Fe, Co)
3.3.1. Analysis of densities of states To discuss the effect of the substitutions at the Ni site on the electronic structure, the total densities of states (TDOSs) are plotted in Fig. 2 for LaNi4.5M0.5 (M = Al, Mn, Fe, Co). Owing to employing the double cell model of LaNi5, the TDOS are twice over the data of the unit cell. And the Fermi energy EF has been taken as the energy zero in every figure. Fermi energies of LaNi4.5M0.5 (M = Al, Mn, Fe, Co) are about 10.05, 10.44, 10.40 and 10.34 eV.
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Table 3 The calculated total energy (Et and Ei) of elemental solids (La, Ni, and M), pure atoms (La, Ni, and M) and LaNi4.5M0.5, cohesive energy (Ecoh), formation energy (DH) of LaNi4.5M0.5 (M = Ni, Al, Mn, Fe, Co). Atom
La
Ni
Al
Mn
Fe
Co
Ei (eV) Et (eV) Structure Ecoh (eV) DH (mJ/mol) Expt. [51]
231130.65 231135.40 LaNi5 5.72 171.77 159.1 ± 8.3
41360.45 41366.01 LaNi4.5Al0.5 5.65 222.92
6600.98 6604.71 LaNi4.5Mn0.5 5.90 546.75
31506.07 31506.08 LaNi4.5Fe0.5 5.87 150.71
34611.44 34619.23 LaNi4.5Co0.5 5.81 364.08
37894.86 37897.51
Table 4 The formation energy of hydrogen atom and total energy of LaNi4.5M0.5H0.5 (M = Ni, Al, Mn, Fe, Co). Structure
LaNi5H0.5
LaNi4.5Al0.5H0.5
LaNi4.5Mn0.5H0.5
LaNi4.5Fe0.5H0.5
LaNi4.5Co0.5H0.5
Et (eV) Ecoh (eV)
437985.53 4.69
841194.63 6.77
866103.39 7.43
869208.30 7.42
872490.95 7.36
Fig. 2. The total densities of states (TDOSs) of LaNi4.5M0.5 (M = Al, Mn, Fe, Co).
The difference of fermi energy is due to the different number of valence electrons with the substitution of M for Ni atoms and the charge transfer from valence band to conduction band. As can be seen from Fig. 2, the TDOS is composed of both bonding and non-bonding area. Part of DOS is across the Fermi level region, which shows that this system still puts up the metallic character with the substitution of Ni atoms. The width of valence band for LaNi4.5M0.5 (M = Al, Mn, Fe, Co) is 8.81, 8.34, 8.12, 8.09 eV, respectively. Compared with the width 8.17 eV of valence band for LaNi5 system, the valence bands of LaNi4.5M0.5 (M = Al, Mn) become wider, and that of LaNi4.5Al0.5 has the maximum width. This is due to the contribution of the Al s and p sub-bands, which are located near the bottom of the total valence bands [43,53]. The bonding states are formed by the interaction between the hybridization orbital of atom s, p, d and f orbital. In order to give a qualitative characteristics of electronic structure in these alloy, the partial density of states (PDOSs) plots for La, Ni, and M
Fig. 3. The partial densities of states (PDOSs) of LaNi4.5M0.5 (M = Al, Mn, Fe, Co).
(M = Al, Mn, Fe, Co) atoms are given in Fig. 3. Compared with LaNi5 [39], the occupied part of valence bands in higher energy region is still dominated by the Ni (2c)-d and Ni (3g)-d states, and the occupied part of valence bands in lower energy region is dominated by the La-4p states. The occupied states near EF are dominated by the Ni-3d states and M-3d states (M = Mn, Fe, Co) with non-negligible bonding contributions of the La-5d states and Al-s,p states. Furthermore, the M (M = Al, Mn, Fe, Co) atoms cause reconstruction of the starting LaNi5 band structure and change of the value of DOS at the Fermi level. The DOS (EF) for LaNi4.5M0.5 (M = Al, Mn, Fe, Co) is equal to about 11.63, 23.22, 17.4, 18.74 states/ (eV f.u.). As is clearly seen in Figs. 2 and 3, the TDOS at EF is mostly composed of Ni (2c)-d, Ni (3g)-d and M (M = Mn, Fe, Co)-d states, which provide almost equal contributions to it. The PDOS of M( = Al, Mn, Fe, Co) at EF is equal to 0.05, 6.65, 3.67, 2.98 states/ (eV atom.), which would result from the different number of
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(a)
(b)
(c)
(d)
(e)
Fig. 4. The electron densities on the (0 0 0 4) plane: (a) LaNi5; (b) LaNi4.5Al0.5; (c) LaNi4.5Mn0.5; (d) LaNi4.5Fe0.5; (e) LaNi4.5Co0.5.
valence electrons. And the Mn, Fe, Co atoms supplies 9, 8, 7 valence electrons, whereas the Al atom 3 valence electrons. As also can be seen from Fig. 3, Ni-d states and M-d states at EF have strong interactions, which would reduce the TDOS at EF. Therefore, the sequence of TDOS (EF) is LaNi4.5Mn0.5 > LaNi4.5Co0.5 > LaNi4.5Fe0.5, which indicate that the interaction between Ni-d and M-d states is LaNi4.5Fe0.5 > LaNi4.5Co0.5 > LaNi4.5Mn0.5. According to the electronic-specific heat coefficient [54]
c¼
p
2
3
2
kB nðEF Þ
ð3Þ
Compared to 17.6 mJ/mol K2 of LaNi5 [31], the electronic-specific heat coefficient of LaNi4.5Al0.5 deceases to 13.7 mJ/mol K2, while c of LaNi4.5M0.5 (M = Mn, Fe, Co) increases to 27.4, 20.5, 22.1 mJ/mol K2, respectively. This might indicate that the stability of this system would be changed with the substitution of M atoms.
3.3.2. Charge distributions To further study the interactions among La, Ni (3g), Ni (2c) and M atoms, contour maps of the electron densities on two planes are shown in Fig. 4a–e and Fig. 5a–d: one is the (0 0 0 4) plane
C. Zhang et al. / Computational Materials Science 69 (2013) 520–526
(a)
(b)
(c)
(d)
525
0Þ plane of (a) LaNi4.5Al0.5; (b) LaNi4.5Mn0.5; (c) LaNi4.5Fe0.5; (d) LaNi4.5Co0.5. Fig. 5. Charge densities in the ð1 1 2
containing the Ni (3g)–Ni (3g) and Ni (3g)-M interactions, the other 0) plane containing the La–Ni (2c), Ni (3g)–Ni (2c) and M– is (1 1 2 Ni (2c) interactions for LaNi4.5M0.5 (M = Al, Mn, Fe, Co). As is evidently shown from Fig. 4a–e and Fig. 5a–d, the valence electrons intensively diffuse in the unit cell, and the highest density charge resides in the immediate vicinity of the nuclei. In contrast, there are relatively low electron densities in the interstitial area, and interstitial charges are well delocalized, which indicates that the metallic bonding is formed in the interstitial area; but no clear directional bonds can be seen [54,55]. It is clearly seen from Fig. 4a–e, the electron densities (0.32 e/Å3) between Ni (3g) atom and Ni (3g) atom for LaNi5 is greatly higher than the corresponding value 0.25 e/Å3 between Al atom and Ni (3g) atom for LaNi4.5Al0.5. It indicates that the alloy strengthens the anti-pulverization characteristics with the substitution of Al atoms [30]. In addition, the electron densities between Ni (3g) atom and Mn, Fe, Co atom is 0.325, 0.33, 0.33 e/Å3 for LaNi4.5M0.5 (M = Mn, Fe, Co), respectively. It is shown that the interactions between atoms of the system are slightly reinforced with the substitution of Mn, Fe, Co atoms, which is in consistence with the analysis of DOS. It can be clearly observed from Fig. 5a that the electron densities (0.32 e/Å3) of Ni (3g)–Ni (2c) are much higher than the corresponding value 0.2 e/Å3 of La–Ni (2c), which shows that the interaction between Ni (3g) and Ni (2c) atoms is much stronger than that between La and Ni (2c) atoms. The result is consistent with the previous analysis. In contrast, the charge densities between the Al and Ni (2c) atoms is about 0.27 e/Å3. It is further
testified here that the Al–Ni interaction is certain to be still weaker compared to the Ni–Ni interaction. From Fig. 5b–d, the electron densities between Mn, Fe, Co and Ni (2c) atom is 0.35, 0.355, 0.355 e/Å3, which is slightly higher than the corresponding value 0.34 e/Å3 of Ni (3g)–Ni (2c) atoms. It is further confirmed that the interactions of Mn–Ni, Fe–Ni, Co–Ni atoms are greatly stronger compared to the Ni–Ni interaction, which is in well agreement with the experimental results [19]. As is also seen from Fig. 5b–d that the electron densities (0.21 e/Å3) of La–Ni (2c) is slightly larger than 0.2 e/Å3 for LaNi4.5Al0.5, which is caused by the expansion and distortion of the lattice. 3.4. The bounding hydrogen capacity of LaNi4.5M0.5 (M = Al, Mn, Fe, Co) To discuss the bounding hydrogen capacity of LaNi4.5M0.5 system, the formation energy of hydrogen atom in LaNi4.5M0.5H0.5 (M = Al, Mn, Fe, Co) was calculated. As is known, more positive of the formation energy, stronger capacity of the system to bound hydrogen atom. The formation energy of hydrogen atom in LaNi4.5M0.5H0.5 (M = Al, Mn, Fe, Co) is obtained by
Ecoh ¼ Et ðLa2 Ni9 MÞ þ Ei ðHÞ Et ðLa2 Ni9 MHÞ
ð4Þ
where Et(La2Ni9M) and Et(La2Ni9MH) refer to the total energy of the intermetallic compound at equilibrium. For La2Ni9MH, we employ hypothetical unit cells by doubling the unit cell of LaNi4.5M0.5 along the c-axis and placing one hydrogen atom at the 6 m site. And the
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total energies of LaNi4.5M0.5H0.5 have been made by optimizing the cell parameters and internal coordinates. Ei(H) is the total energy of single hydrogen atom by building simple cubic model. The formation energy of hydrogen atom and total energy for LaNi4.5M0.5H0.5 (M = Al, Mn, Fe, Co) are listed in Table 4. The total energy of single hydrogen atom is 13.59 eV, and the total energies of LaNi4.5M0.5 are used in Table 2. As can be seen from Table 4, the formation energy of hydorgen atom in LaNi5H0.5 is 4.69 eV, while it increases to 6.77, 7.43, 7.42 and 7.36 eV for LaNi4.5M0.5H0.5 (M = Al, Mn, Fe, Co), respectively. This indicates that the partial substitutions at the Ni with M could enhance the bounding hydrogen capacity of the system. Therefore, the formation energy of hydrogen atom is LaNi4.5Mn0.5H0.5 > LaNi4.5Fe0.5H0.5 > LaNi4.5Co0.5H0.5 > LaNi4.5Al0.5H0.5 > LaNi5H0.5, which indicate that the bounding hydrogen capacity of the system is LaNi4.5Mn0.5 > LaNi4.5Fe0.5 > LaNi4.5Co0.5 > LaNi4.5Al0.5 > LaNi5. 4. Conclusions The crystal structures, stability and electronic structures of LaNi4.5M0.5 (M = Al, Mn, Fe, Co) have been systematically investigated by first-principles calculations. The optimized results indicate that M (M = Al, Mn, Fe, Co) atoms prefer to substitute Ni atoms of 3g sites. The total volume sequence is LaNi4.5Al0.5 > LaNi4.5Mn0.5 > LaNi4.5Fe0.5 > LaNi4.5Co0.5 > LaNi5, which is consistent with the experimental data. According to the radio of c/a, LaNi4.5Al0.5 and LaNi4.5Co0.5 alloys were observed less anisotropic, which is a probable reasons to improve the anti-pulverization characteristics of the host alloy with the substitution of Al, Co atoms. The stability of LaNi4.5M0.5 (M = Al, Mn, Fe, Co) alloys is studied by calculating the formation and cohesive energies. According to the data of negative formation energy, the stability sequence is LaNi4.5Mn0.5 > LaNi4.5Co0.5 > LaNi4.5Al0.5 > LaNi5 > LaNi4.5Fe0.5. While the results of cohesive energy show the different trend. From the plots of density of states, the valence band of LaNi4.5 Al0.5 becomes broad, which are dominated by the Al-s, p states. For LaNi4.5M0.5 (M = Mn, Fe, Co), Ni-3d states and M-d states at EF have strong interactions, and the interaction between Ni-d and M-d states is LaNi4.5Fe0.5 > LaNi4.5Co0.5 > LaNi4.5Mn0.5. According to the formation energy of hydrogen atom in LaNi4.5M0.5H0.5 (M = Al, Mn, Fe, Co), the bounding hydrogen capacity of the system is LaNi4.5Co0.5 > LaNi4.5Fe0.5 > LaNi4.5Mn0.5 > LaNi4.5Al0.5. Acknowledgements This research was supported by the Program of National Natural Science Foundation of China under Grant No. 11104022 and Cultivating Programme of Middle-aged backbone teachers of Chengdu University of Technology. We acknowledge Project supported by the Scientific Research Foundation of the Education Department of Sichuan Province, China (Grant Nos. 11ZB036 and 11ZB266). References [1] J.H.N. Van Vucht, F.A. Kuijpers, H.C.A.M. Bruning, Philips Res. Rep. 25 (1970) 133–140. [2] B. Joseph, B. Schiavo, J. Alloys Compd. 480 (2009) 912–916. [3] T. Kaneko, A. Tezuka, H. Ogawa, T. Ikeshoji, Phys. Rev. B 81 (2010) 184302. [4] A. Tezuka, H. Wang, H. Ogawa, T. Ikeshoji, Phys. Rev. B 81 (2010) 134304. [5] C.Y. Zhang, X.F. Zhao, L.J. Tang, T. Gao, Physica B 406 (2011) 3436–3441. [6] J. Payá, A. Freni, J.M. Corberán, V. Compañ, J. New Mat. Electrochem. Syst. 15 (2012) 293–300. [7] J.J.G. Willems, K.H.J. Buschow, J. Less-Common Met. 129 (1987) 13–30. [8] E.D. Snijder, G.F. Versteeg, W.P.M. van Swaaij, Chem. Eng. Sci. 48 (1993) 2429– 2441. [9] A. Anani, A. Visintin, K. Petrov, S. Srinivasan, J.J. Reilly, J.R. Johnson, J. Power Sources 47 (1994) 261–275.
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