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Hydrogen Storage in AB2 Laves Phase (A ) Zr, Ti; B ) Ni, Mn, Cr, V): Binding Energy and Electronic Structure S. B. Gesari,*,† M. E. Pronsato,† A. Visintin,‡ and A. Juan† Departamento de Fı´sica, UniVersidad Nacional del Sur, AV. Alem 1253, 8000 Bahı´a Blanca, Argentina, and Instituto de InVestigaciones Fisicoquı´micas Teo´ricas y Aplicadas (INIFTA), Facultad de Ciencias Exactas, UNLP, CCT La Plata-CONICET, (1900), La Plata, Argentina ReceiVed: June 30, 2010; ReVised Manuscript ReceiVed: August 6, 2010
Theoretical studies on the total energy, electronic structure, and bonding of the Zr0.9Ti0.1NiMn0.5Cr0.25V0.25 alloy and its hydrides were performed using density functional theory calculations. This alloy crystallizes in the C14 Laves phase. To determine the equilibrium structural parameters for this compound, we performed lattice constants optimization. The optimized c/a ratio was found in good agreement with experimental data. When hydrogen is introduced in the AB2 matrix, there are different sites to localize it with a variety of local environments. We found that A2B2 sites are preferentially occupied. After hydrogenation, the volume of the alloy increases, whereas the binding energy remains practically the same up to 3.5 H/FU, indicating little interaction among hydrogen atoms. The electronic structure of AB2 and AB2H3.5 phases is also analyzed. 1. Introduction Rechargeable nickel-metal hydride (Ni/MH) batteries have been popularly marketed since 1990. Ni/MH batteries are now extensively used in portable electronic devices and hybrid electric vehicles.1,2 The performance of a Ni/MH battery is strongly determined by the nature of the metal hydride anode. Most binary metal hydrides (metal-hydrogen phases) cannot be directly used for hydrogen storage because they are too stable to desorb hydrogen under usual battery operating conditions. One type of electrode, known as AB2 or Laves phases, consists of A ) Mg, Zr, and Ti in combination with B ) Ni, V, Cr, and Mn. Compositional substitution of metallic elements in ZrMn2, ZrCr2, and ZrV2 Laves phases has been shown to enhance hydrogen absorbing/desorbing kinetics and electrochemical capacity. Zirconium metal is extensively used as the main component of AB2 alloys for battery applications.3-7 An improvement of the hydrogen absorption behavior has been reported in the literature by Ovshinky et al.8 on multicomponent alloys containing Zr, Ti, V, Cr, Ni, etc., who proposed that electrochemical activity was improved due to compositional and structural disorder. Elements, such as Ti, V, and Zr, can increase the number of hydrogen atoms stored per metal atoms. Other elements change the metal-hydrogen bond strength (V, Mn, Zr). Ni and Mn provide catalytic properties, whereas Cr improves surface properties. Later on,9,10 this improvement was also attributed to the effect of the secondary phases that changes its electrochemical characteristics.11-13 Hydrogen effects on the chemical bonding, electronic structure, and magnetic properties within Laves phases have been studied by DFT calculations by different authors.14-18 Theoretical studies of Laves phases’ structural stabilities were reported in refs 19-22. * To whom correspondence should be addressed. E-mail: sbgesari@ criba.edu.ar. † Universidad Nacional del Sur. ‡ Instituto de Investigaciones Fisicoquı´micas Teo´ricas y Aplicadas (INIFTA), Facultad de Ciencias Exactas, UNLP, CCT La Plata-CONICET.
In this study, we report the theoretical results for the total energy and the electronic structure of the Zr0.9Ti0.1NiMn0.5Cr0.25V0.25 alloy and its hydrides. Our calculations for the lattice parameters of the alloy are compared with the previous experimental data and XRD measurements.23 Several tetrahedral sites for the H location are analyzed, and the binding energy and the volume per unit cell are calculated at different H concentrations. Analysis of the density of states (DOS) of AB2 and AB2H3.5 phases is also performed and related with the bonding characteristics. 2. Crystal Structure Laves phases, which form the largest group of intermetallics, have the ideal composition AB2. An intermetallic compound is classified as a Laves phase purely on the basis of the geometry of the crystal structure.24 The Laves phases crystallize in three structure types, which are named after the representatives cubic MgCu2 (C15), hexagonal MgZn2 (C14), and hexagonal MgNi2 (C36).25-27 The A metal is generally an electropositive metal, such as an alkali metal, alkaline earth, lanthanide, actinide, or early transition metal, whereas the B metal is generally a less electropositive transition metal (e.g., from group VII or VIII) or noble metal.28 The Laves phases constitute a subset of socalled Frank-Kasper phases. These phases are all tetrahedrally close-packed (TCP) because all of the interstices (holes) are tetrahedral, in contrast with the traditional close-packed structures (face-centered cubic and hexagonal close-packed) adopted by monatomic solids and alloys with atoms of approximately equal size, where both tetrahedral and octahedral holes are present.28 The compound described in this paper is isostructural with the hexagonal Laves phase MgZn2. The structure contains four formula units per unit cell, ideal c/a ) 8/3, and belongs to the space group P63/mmc (D46h).29 The A sublattice defines a hexagonal diamond net, as shown in Figure 1. The B sublattice is composed of B4 tetrahedra alternatively sharing vertices and faces along the c axis, thereby forming chains of apically fused trigonal bipyramids. These chains are linked together by vertex sharing in the ab plane. In this structure, the A atoms are defined
10.1021/jp106036v 2010 American Chemical Society Published on Web 09/07/2010
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Figure 3. Unit cell of the hexagonal Laves phase and the three types of tetrahedral interstices that are present: B4, AB3, and A2B2.
Figure 1. Laves-phase AB2 structure type MgZn2. (a) A and B sublattices and the structure projected along the [110] direction. This view emphasizes the connectivity of B4 tetrahedra and B5 trigonal bipyramids. The small circles denote B atoms (white circles are B(I)type and gray circles are B(II)-type atoms); large circles denote A atoms. (b) Top view of A and B sublattices and the complete structure. A ) Zr, Ti; B ) Ni, Mn, Cr, V.
Figure 2. Coordination polyhedra of the (a) A-, (b) B(I)-, and (c) B(II)type atoms in the hexagonal Laves phase. The A atoms have a coordination number of 16 [3B(I) + 9B(II) + 4A]. The B(I) atoms have an environment of 6A + 6B(II), and the B(II) atoms have an environment of 6A + 4B(II) + 2B(I).28
as interstitials in the B sublattice. For the C14 hexagonal structure, tetrahedral units are built up from two crystallographically distinct B(I) and B(II) atoms, with a 1:3 ratio, and are connected by B(I) vertex sharing and by triangle B(II)-B(II)-B(II) face sharing;30 see Figure 1. Figure 2 shows the local environment of the C14 system. The A atoms lie at the centers of tetracapped truncated tetrahedra with a coordination number of 16 (12B + 4A). This is known as the Friauf polyhedron.27 The B(I) atoms lie at the center of distorted icosahedra composed of six A and six B atoms, with the A atoms defining a nonplanar hexagon in either the chair or the boat conformation. Figure 3 shows the unit cell of the hexagonal Laves phase that has three types of available tetrahedral interstices: B4, AB3, and A2B2. In the C14 structure, there are 12 equivalent A2B2 sites, 4 equivalent AB3 sites, and 1 B4 site per formula unit. The B4 tetrahedra are generally distorted.28 In a previous experimental study, Peretti et al.23 have reported the hydrogen absorption behavior of the Zr0.9Ti0.1NiMn0.5CrxV0.5-x alloy (with 0 e x e 0.5) by volumetric and electrochemical techniques. They found a high hydrogen storage capacity expressed as hydrogen atoms per formula unit (H/FU
∼ 3.6) and a steep slope rather than a horizontal plateau corresponding to the two-phase equilibrium. Discharge capacities of about 340 mAh/g were found for high Cr/V content ratios, whereas the high-rate dischargeability significantly decreases on increasing the Cr content in the alloy. The hydrogen absorption characteristics of Zr1-xTixCrNi alloys with x ranging between 0.1 and 0.4 were also studied. It was found that the equilibrium pressures for Zr0.9Ti0.1CrNi are substantially higher than those for the ZrCrNi alloy without substitutions, while maintaining a reasonable good hydrogen storage capacity. The Zr0.9Ti0.1CrNi alloy electrodes exhibit the highest discharge capacities and the best performances during fast charge-discharge cycling.31 In the present work, we choose x ) 0.25 in Zr0.9Ti0.1NiMn0.5CrxV0.5-x for the Cr/V concentration as an alloy model for hydrogen absorption. That structure crystallizes in the C14 Laves phase. Rietveld crystal structural refinement indicates that, in the C14 structure, Zr and Ti are randomly mixed at the A sites, Ni atoms prefer to occupy the B(I) sites,32 and V, Cr, Mn, and the remaining Ni are randomly distributed in the B(II) sites.30 As a result, a variety of local environments with different nearest-neighbor configurations are created that distort the bond length and bond angle and modify both the size of the interstitial volume and the hydrogen-bond strength. Neutron diffraction and X-ray studies32-35 show that the C14 structure of the intermetallic compound remains after deuteration. 3. Computational Method and Model The present results were obtained with self-consistent density functional theory (DFT) calculations using the Vienna Ab initio Simulation package (VASP).36 This package uses a plane-wave basis and a periodic supercell method. Potentials within the projector-augmented wave method (PAW)37 and the generalized gradient approximation (GGA) with the Perdew-BurkeErnzerhof functional (PBE)38,39 were used. Lattice parameters were determined by minimizing the total energy of the cell using a conjugated-gradient algorithm to relax the ions.40 A 3 × 3 × 3 Monkhorst-Pack k-point grid for sampling the Brillouin zone was considered. No significant change in energy was observed performing calculations with larger sets of k-points. A plane-wave cutoff energy of 500 eV was chosen to ensure full converge. Using the total energy values extracted from the geometry optimization results, we have computed the hydrogen binding energy, EB, which we define as follows
EB )
n 1 (E ) - (EAB2) - EH2(g) n AB2Hn 2
[
]
where the first term on the right-hand side is the total energy of the supercell AB2 with n hydrogen atoms, the second term is the
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Gesari et al. TABLE 1: Calculated and Experimental Values of the Lattice Constants a and c for the Zr0.9Ti0.1NiMn0.5Cr0.25V0.25 Alloy
Figure 4. Configuration 1 is for the 48-atom supercell. Other configurations (2-5) were modeled from configuration 1 by interchanging A-type atoms or B-type atoms: configuration 2, between Mn and V; configuration 3, between Mn and Cr; configuration 4, between V and Mn; configuration 5, between Zr and Ti.
total energy of the supercell AB2 without hydrogen, and the third term is half the total energy of the hydrogen molecule. The first two terms are calculated with the same parameters, and the third is calculated locating a H2 molecule in a 10 Å cubic cell. The Zr0.9Ti0.1NiMn0.5Cr0.25V0.25 alloy was modeled by a large supercell (2a, 2b, c, with 48 atoms) to ensure the desired composition. This supercell contains 14 Zr, 2 Ti, 16 Ni, 8 Mn, 4 Cr, and 4 V atoms. The use of a large supercell to model the alloy provides numerous system configurations that describe the same composition. Keeping those atoms that belong to the A or B subnets, we generated several random configurations interchanging Zr by Ti (A) and Ni, Mn, Cr, or V among them (B). We present here the five most stable configurations (see Figure 4). 4. Results and Discussion Lattice parameters were calculated after geometry optimization of the structure. The optimizations were carried out in two steps. First, the cell volume was allowed to relax keeping the cell shape and relative atomic positions fixed, and then, in a second step, ions were allowed to relax within the cell. Table 1 presents the experimental and calculated lattice parameters. The values are slightly underestimated with respect to experimental values;23 however, the dispersion is less than 2%, demonstrating the accuracy of the method. The use of LDAPAW PP does not improve these results. Table 1 shows the metal-metal first neighbors distances for the five different studied configurations, all in agreement with our selected composition. The total energies for such configurations were calculated, finding differences not larger than 0.31 eV, which represent less than 0.1% of each other (see Table 2).
config
a [Å]
∆a/a, %
c [Å]
∆c/c, %
1 2 3 4 5 exptl23
4.9146 4.9191 4.9137 4.9163 4.9129 4.995
1.61 1.52 1.62 1.57 1.64
8.0404 8.0476 8.0388 8.0431 8.0376 8.150
1.35 1.25 1.36 1.31 1.38
These findings agree with the random distribution, previously suggested by experimental data.30,33 Configuration 5 (the most stable) was selected to study the hydrogen absorption. 4.1. Hydrides. To find the hydrogen absorption sites, we have first considered the system containing only one H atom in the supercell. The hexagonal Laves-phase structure has three types of tetrahedral sites suitable for hydrogen occupation, as mentioned before (see Figure 3). We have carried out total energy calculations for the H atom located at those three different sites, each with a different environment, finding that the sites with a higher content of the B component (B4) are the less favorable for hydrogen location. In all cases, the absolute value of the binding energy (EB) is substantially larger (more stable) for A2B2 sites than that for B4 sites (see Table 3), as expected from the largest interstitial hole size formed by two A atoms and two B atoms and the higher content of the A component in the tetrahedron. The B4 site is the smallest, and hydrogen is weakly bound to it. The first neighbor distance hydrogen-metal (A or B) atoms are also shown in Table 3. Some experimental results from different authors32-35,41,42 indicate that the A2B2 sites are preferentially occupied and that their occupancy factors are related to the trend for deuterium to fill the tetrahedron constituted by atoms with a high hydrogen affinity (A type atoms). In most of Laves-phase hydrides AB2Hx, H atoms occupy only the A2B2 sites at low and intermediate hydrogen concentrations (up to ≈2.5).43 Fruchart et al.44 found that, in ZrV2, within the range of stoichiometry used, both Zr2V2 and ZrV3 sites are occupied by deuterium with the relative occupancies depending on the total absorption. In ZrCr2, only the Zr2Cr2 site is progressively filled until the formula approaches ZrCr2D3.5, near the experimental limit of absorption, at which point, a minor amount of deuterium may enter ZrCr3 sites. On the other hand, we have investigated the storage capacity of the alloy by calculating the hydrogen binding energy as we incorporate additional H atoms to the system. For each H atom added, a full geometry optimization was carried out, letting the lattice relax. We have found that the binding energy decreases less than 10% when additional hydrogen concentrations are considered, reaching a value of -0.98 eV at 3.5 H/FU This is an indication of a low interaction among hydrogen atoms in the unit cell. The results are shown in Figure 5. Many of the Laves-phase alloys exhibit excellent hydrogen sorption properties. Although theoretically they can absorb up to 6 H/FU, for the C14 and C15 structured compounds, it cannot be used for practical applications because it has a too high stability.45 In these Laves phases, the highest demonstrated hydrogen occupancy is ZrV2H5.3; however, this alloy is not suitable for battery applications.13 The pressure-composition isotherm (PCT) curves, corresponding to the hydrogen absorption of the Zr0.9Ti0.1NiMn0.5Cr0.25V0.25 alloy, show that the alloy is progressively filled until the formula approaches AB2H3.6,23 in accordance with reported values for similar alloys.31,46-49
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TABLE 2: Metal-Metal First Neighbors Distances, Energy for Each Configuration, and Relative Energy to Emin (config 5) distances (Å) config
Ti-Ti
Zr-Zr
V-V
Cr-Cr
Ti-V
Ti-Cr
Ti-Mn
Ti-Zr
Ti-Ni
E (eV)
∆E
1 2 3 4 5
9.20 9.22 9.19 9.23 2.79
2.92 2.93 2.91 2.94 2.92
2.55 4.29 2.54 2.56 2.56
4.99 5.00 2.38 4.94 4.98
2.82 5.85 2.82 2.86 2.90
2.76 2.78 2.76 2.81 2.70
2.77 2.78 2.77 2.80 2.67
2.89 2.91 2.89 2.94 4.76
2.80 2.81 2.81 2.80 2.71
-379.96 -379.85 -379.88 -379.86 -380.16
0.20 0.31 0.28 0.30
TABLE 3: Binding Energy (EB), EB Relative to the EB min (∆E), H-M Distances (First Neighbor to H) for H in Tetrahedral Sites, and OP for a Representative Metal-Metal Bond with and without H
The computed cell volume presents a significant change after hydrogenation (increase in 29% for AB2H3.5); see Figure 5. Several authors have reported in the case of hydrogenation that the volume of the AB2-Hn alloy with n between 3 and 4 increases by 15-25%.17,32,35 4.2. Electronic Structure. Figure 6 shows the total DOS for Zr0.9Ti0.1NiMn0.5Cr0.25V0.25 (AB2) and AB2H3.5 and the projected DOS for H in AB2H3.5. The DOS is dominated by a 6 eV wide d-band complex, which is structured into a number of subbands. The region of -7 to 1 eV (see Figure 6b,c) contains the H 1s states. Normally, introduction of hydrogen modifies the electronic structure of the host alloy by creation of metal-hydrogen bonding states, shift of the Fermi level, and change in the width of bands and/or modification of the lattice symmetry. One common feature in the electronic structures of these hydrides is the occurrence of the H states at the bottom
Figure 5. Calculated hydrogen binding energy and change of the volume with the hydrogenation of the unit cell (%) versus the number of hydrogen atoms per formula unit.
of the valence band.15 Including the additional bonding H s states in the energy range of -7 to 1 eV not only changed the corresponding portion of the DOS but also systematically shifted the EF (15%) (compare panel a with panels b and c in Figure 6). Similar results were found by other authors for similar phases.14,15,17,18 Additional qualitative calculations with the YAeHMOP program50 allow us to compute the changes in the overlap population (OP) between metal atoms before and after hydrogenation. From the analysis of the OP for different bonds in the unit cell, we can conclude that all the metal-metal bonds are weakened when hydrogen is present (see Table 3). 5. Conclusions The computed lattice parameters in AB2 (A ) Zr, Ti; B ) Ni, Mn, Cr, V) Laves-phase compounds are in good agreement with the experimental values. The dispersion is less than 2%. The calculated total energies for different configurations present differences lower than 0.1%. These results support the idea of a random distribution in the alloy components.
Figure 6. (a) Total DOS for the AB2 alloy. (b) Total DOS for the AB2H3.5. (c) Projected DOS for H in AB2H3.5.
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The computed absolute value of the hydrogen binding energy decreases as the number of A-type atoms that form the tetrahedral site decreases, and simultaneously, the hole sizes decrease. EB decreases in the order A2B2 > AB3 > B4, the Zr2Mn2 environment being the most favorable. The B4 site is 6 times less favorable than A2B2; however, hydrogen location is still possible. When the hydrogen concentration increases, the binding energy remains practically the same up to 3.5 H/FU. It is indicative of a little interaction among H’s. After hydrogenation, the volume increases up to 29% for AB2H3.5. Hydrogen modifies the bonding characteristics of the metals, reducing its overlap population, which is indicative of a detrimental effect in metal-metal bonding in favor of A-H or B-H bonding. Hydrogen is an embrittling element for the alloy. Acknowledgment. The authors are grateful for the financial support from PIP-CONICET 2009, SGCyT-UNS, PICTR 656, PICT 560, and PIP 2009. A.J., A.V., and M.E.P. are members of CONICET. We also thank Prof. Eitel Peltzer y Blanca for useful discussions. References and Notes (1) Chai, Y. J.; Zhao, M. S.; Wang, N. Mater. Sci. Eng. 2008, 147, 47–51. (2) Visintin, A.; Wang, C.; Baricuatro, J. H.; Soriaga, M. P. In Electrochemical Hydrogen Storage, Handbook of Sustainable Energy; Lee, W. H., Cho, V. G., Eds.; Nova Science Publishers, Inc.: Hauppauge, NY, 2009; Chapter 16, p 225. (3) Harris, J. H.; Curtin, W. A.; Tenhover, M. A. Phys. ReV. B 1987, 36, 5784–5797. (4) Gebert, A.; Ismail, N.; Wolff, U.; Uhlemann, M.; Eckert, J.; Schultz, L. Intermetallics 2002, 10, 1207–1213. (5) Zander, D.; Leptien, H.; Ko¨ster, U.; Eliaz, N.; Eliezer, D. J. NonCryst. Solids 1999, 250, 893–897. (6) Xiao, X.; Shoushi, F.; Guoming, W.; Qin, H.; Yuanda, D. J. Alloys Compd. 2004, 376, 145–148. (7) Bulyk, I.; Basaraba, Y. B.; Trostianchyn, A. M. J. Alloys Compd. 2004, 376, 95–104. (8) Ovshinsky, S. R.; Fetcenko, M. A.; Ross, J. Science 1993, 269, 176–181. (9) Visintin, A.; Peretti, H. A.; Ruiz, F.; Corso, H. L.; Triaca, W. E. J. Alloys Compd. 2007, 428, 244–251. (10) Young, K.; Fetcenko, M. A.; Li, F.; Ouchi, T.; Koch, J. J. Alloys Compd. 2009, 468, 482–492. (11) Ruiz, F. C.; Castro, E. B.; Peretti, H. A.; Visintin, A. Int. J. Hydrogen Energy, in press. (12) Fujitani, S.; Yonezu, I.; Saito, T.; Furukawa, N.; Akiba, E.; Hayakawa, H.; Ono, S. J. Less-Common Met. 1991, 172-174, 220–230. (13) Young, R. C.; Ovshinsky, S. R.; Huang, B.; Chao, B. S.; Li, Y. Mater. Res. Soc. Symp. Proc. 2000, 575, 187–192. (14) Al Alam, A. F.; Matar, S. F.; Ouı¨ni, N.; Nakhl, M. Prog. Solid State Chem. 2008, 36, 192–212. (15) Yartys, V. A.; Vajeeston, P.; Riabov, A. B.; Ravindran, P.; Denys, R. V.; Maehlen, J. P.; Delaplane, R. G.; Fjellvåg, H. Z. Kristallogr. 2008, 223, 674–689. (16) Herbst, J. F.; Hector, L. G. J. Alloys Compd. 2007, 446-447, 188– 194.
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JP106036V
