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Hydrogen desorption energies of Aluminum hydride (AlnH3n) clusters
ARTICLE IN PRESS Physica B 405 (2010) 3075–3081
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Hydrogen desorption energies of Aluminum hydride (AlnH3n) clusters Krishna Gandhi n, Deepesh Kumar Dixit, Brajesh Kumar Dixit Department of Physics, Bipin Behari PG College, Outside Sainyer Gate, Jhansi-284001, Uttar Pradesh, India
a r t i c l e in fo
abstract
Article history: Received 22 February 2010 Received in revised form 10 April 2010 Accepted 13 April 2010
Hydrogen desorption energies are considered an important factor in the selection of hydrogen storage materials. Among metal hydrides, aluminum hydride seems to be a promising material for hydrogen storage. We report the theoretical calculations of the hydrogen desorption energies of AlnH3n (n ¼1, 2, 3y) clusters based on Density Functional Theory (DFT). Except for very small clusters, desorption energy is seen to steadily decrease with cluster size n and reach a value of 0.19 eV per H2 for n ¼20, showing that for large cluster sizes approximating bulk behavior, aluminum hydride tends to be unstable. But AlnH3n clusters of sizes n ¼8–16 have desorption energies in the range 0.6–0.4 eV per H2, which is suitable for hydrogen storage application. & 2010 Elsevier B.V. All rights reserved.
Keywords: Aluminum hydride Hydrogen storage AlnH3n clusters Desorption energy DFT
1. Introduction Hydrogen, the most abundant element in the universe, constituting roughly 75% of universe’s elemental mass, has great potential as an energy source [1]. Unlike petroleum, it can easily be generated from renewable energy sources. It is also nonpolluting, and forms water as a harmless byproduct during use. Like electricity, hydrogen is an energy carrier and must be produced from another substance. But, unlike electricity, large quantities of hydrogen can easily be stored for use in future. So it can be used as a future fuel [2]. For the last one or two decades there has been intense research on hydrogen storage materials. One mechanism of adsorption of hydrogen in a solid is physi-sorption on the surface. In this process H2 molecules are bonded to a surface by van der Waals forces. In the other mechanism, atomic hydrogen can be chemisorbed on the surface by forming a covalent bond. Chemi-sorbed hydrogen has a binding energy of more than 2–3 eV, compared to approximately 0.1 eV for physi-sorbed hydrogen [3]. One important category of hydrogen storage materials is metal hydrides [2,4–9]. The reaction between hydrogen and a metal can be expressed by the following reaction. MeðsÞ þ ðx=2ÞH2 ðgÞ-MeHx ðsÞ þ DH
ð1Þ
where DH is released as heat during the reaction. Metal hydrides of practical interest are products of exothermic reactions. Basically the search is for such materials that desorb or release n
Corresponding author. Tel.: + 91 9415057538; +91 5102330085. E-mail address: [email protected] (K. Gandhi).
0921-4526/$ - see front matter & 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.physb.2010.04.069
hydrogen in large amounts when heated to 100–200 1C [10]. While the above reaction may seem quite feasible based on thermo-dynamic considerations, it can be very misleading from a kinetic point of view. The mechanisms of hydride formation as well as hydrogen desorption have a high degree of complexity. Among metal hydrides, alanes are considered most suitable for hydrogen storage [2,11,12]. Aluminum hydride, AlH3, is the most well-known alane. It is a fascinating material that has recently attracted attention for its potential as a hydrogen storage medium for low temperature fuel cells. AlH3 is a very good medium for onboard automotive hydrogen storage, since it contains 10.1% by wt. hydrogen with a density of 1.48 g/ml. Brower et al. [13] noted the existence of at least 7 phases, namely a, a0 , b, g, d, e and z of AlH3, all of which are thermodynamically unstable. At room temperature they are usually meta stable and do not decompose rapidly. The decomposition of AlH3 occurs in a single step, as shown below: AlH3 ðsÞ-AlðsÞ þð3=2ÞH2 ðgÞ
ð2Þ
Experiments have shown that the size of the metal hydride particles have a substantial effect on both the thermodynamics and the reaction kinetics of hydrogen sorption and desorption. It has been reported that the reduction of particle size to nano dimensions resulted in lowering of the desorption temperature and improving the reaction kinetics [14–22]. There are basically two reasons for this. First, the surface-to-volume ratio increases when the particle size goes down and this helps in improving the physi- and chemi-sorption and desorption rates, as these are basically surface phenomena. Second, due to the formation of defects, the material becomes more amorphous and less crystalline when it is converted to smaller dimensions and this affects
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the thermodynamics. Thus hydrogen storage in nano-sized metal hydrides is being increasingly explored by experimentalists. This motivated us to undertake theoretical calculations of hydrogen desorption energies in nano-size aluminum hydride clusters.
2. Theory and calculations With the objective of studying the systematics of hydrogen desorption energies, we performed calculations on AlnH3n clusters based on density functional theory (DFT) [23,24]. The Vienna abinitio simulation package (VASP) [25,26] was used with ultra soft PW91 pseudo potentials [27] to calculate the G-point total energies of the clusters. The generalized gradient approximation (GGA) [28,29] was used for the exchange-correlation energy
functional. Geometry optimisation was achieved by starting from random geometries which were annealed at 300 1K to obtain a large number of energy configurations for both Al and AlH3 clusters self-consistently, subject to energy difference o0.0001 eV and atomic forces o0.01 a.u. between successive iterations. These were then subjected to slow cooling down to 0 1K to get the binding energies for the lowest-energy configurations. 3. Results and discussions 3.1. Cluster size, geometries and binding energies for Aln and AlnH3n clusters In this section we discuss the lowest-energy structures, the energetics and the bonding trends in Aln and AlnH3n clusters. First
Table 1 Ground state geometries of the Aln and AlnH3n clusters. Size
Aluminum cluster (Aln)
Size in nm
Aluminum hydride cluster (AlnH3n)
Size in nm
0.17
1 2
0.25
0.36
3
0.25
0.43
4
0.36
0.66
6
0.53
0.99
8
0.54
1.0
10
1.18
1.35
12
1.17
1.43
14
1.26
1.5
16
1.14
1.59
20
1.15
1.59
ARTICLE IN PRESS K. Gandhi et al. / Physica B 405 (2010) 3075–3081
3.5
3077
4.5 4
3
3.5 3 Energy [eV]
Energy [eV.]
2.5 2 1.5
2.5 2 1.5 1
1
0.5
0.5
0 0
0
2
4
6
8
10
12
14
16
18
-0.5
20
2
4
6
10
12
14
16
12
14
16
Cluster Size
Cluster Size 14
13.4
12 Energy [eV]
13.2 13 Energy [eV.]
8
12.8
10 8 6 4
12.6 2 12.4 12.2
0 -2 0
2
4
6
8
10
12
14
16
18
20
Cluster Size Fig. 1. (a) Binding Energy per Al Atom: Aln Clusters and (b) Binding Energy per Al Atom: AlnH3n Clusters.
we discuss the evolution of the geometries. The geometries of the Aln clusters and AlnH3n clusters, where n ¼1, 2, 3, 4, 6, 8, 10, 12, 14, 16 and 20, are shown in Table 1. It also shows the linear dimensions of the clusters which go up to 1.15 and 1.59 nanometers, respectively for Al20 and Al20H60. The Aln cluster symmetries obtained by us are broadly similar to the geometries reported earlier, except in the case of Al4 for which we obtained a geometry corresponding to a tetrahedron [30,31]. The Aln clusters exhibit symmetries even for higher cluster sizes whereas, in the case of AlnH3n, we do not observe much symmetry for higher clusters. We further observe that in the case of AlnH3n clusters, Al–Al bonds are weaker compared to Al–H bonds. In other words, the introduction of H2 in Al cages basically ruptures Al–Al bonds and causes (AlH4) complexes to form. This could be one of the reasons for the breakdown of symmetry in higher AlnH3n clusters. Another interesting feature of AlnH3n clusters is that here the basic nature of bonding is Al–H–Al, that is, hydrogen atoms mediate the Al–Al bonds. In addition to Al–H–Al bonds which are in majority, we find instances of Al–2H–Al bonds also. This feature of AlH3 has been previously reported in literature in both experimental and theoretical studies [32–34] of bulk AlH3. Here also, we observe these two different types of bonds of AlH3. For both Aln and AlnH3n clusters, binding energy per Al atom are plotted in Figs. 1(a) and (b), and second energy differences DEn ¼ (2En En En + )/2 in Figs. 2(a) and (b). Interestingly, Aln and
2
4
6
8
10
Cluster Size Fig. 2. (a) Second Energy Difference: Aln Clusters and (b) Second Energy Difference: AlnH3n Clusters.
AlnH3n clusters show similarities in second energy difference curves, whereas the binding energy per Al atom curves are quite different. The binding energies range from 0.0 to 3.0 eV for pure Aln whereas the range is from 12.4 to 13.4 eV for AlnH3n. The pure Aln binding energies obtained by us are in agreement with those reported by M. Wang et al. [31]. The Aln clusters tend to show stability at cluster sizes n ¼3, 8 and 12, whereas AlnH3n clusters display stability at n ¼2, 8 and 12.
3.2. Bond lengths/strengths and desorption energy trends in Aln and AlnH3n clusters Now we consider the average bond lengths of Al–Al and Al–H bonds [see Figs. 3(a), (b) and 4]. We find that, for a given n, when we go from Aln cluster to AlnH3n cluster, the average Al–Al bondlength increases substantially. In the case of cluster size 8, a stable cluster, the increase is from 3.64 to 4.82 A˚ which means that hydrogen sorption causes Aln clusters to expand in volume. We also observe that in AlnH3n clusters, for the same cluster size 8, the average Al–H bond length, 4.64 A˚ is less than the Al–Al bond length 4.82 A˚ (Fig. 4). On the whole, we can say that when the clusters are hydrided, substantial increases in volume occur. Further, we see from Figs. 3(a) and (b) that for Aln clusters the average Al–Al bond-length shows a saturation-like behavior of a rapid rise followed by a leveling off with increasing n. That is, an increase in the number of Al atoms n in the Aln cluster does not
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1.6
5
1.4 1.2 Energy [eV]
Bond length [Ans.]
4.5
4
3.5
1 0.8 0.6 0.4
3
0.2 2.5
2
4
6
8
10
12
14
16
18
20
0
0
2
4
Cluster Size
Bond length [Ans.]
Aln H3n -Aln þ ð3=2ÞnH2
5
14
16
18
20
ð3Þ
We obtained the desorption energy as equal to the reaction enthalpy DH ¼ EðAln Þ þ ð3=2ÞnEðH2 ÞEðAln H3n Þ =n ð4Þ
4 3
2
4
6
8
10
12
14
16
18
20
Cluster Size Fig. 3. (a) Average Al–Al bond length: Aln Clusters and (b) Average Al–Al bond length: AlnH3n Clusters
8 7 Bond length [Ans.]
12
to aid the formation of (AlH4) complexes seen in the AlnH3n cluster geometries. The hydrogen desorption energies were calculated by us for the desorption reaction
6
6 5 4 3 2
0
10
Fig. 5. Desorption Energy without ZPE correction: AlnH3n.
7
1
8
Cluster Size
8
2
6
2
4
6
8
10
12
14
16
18
20
Cluster Size
where the energies E are the total energies at 0 1K, obtained directly from the calculations. The desorption energies are plotted against cluster size in Fig. 5. In our calculations we have not included the Zero Point Energy (ZPE) corrections arising due to the rotational and vibrational contributions to the binding energy at 0 1K, as we were more interested in the analysis of the systematics as a function of cluster size. For very small clusters no8, there is a significant lowering of desorption energy with increasing cluster size. Beyond size 8, the desorption energy decreases more slowly and steadily and at size n¼20, at and beyond which bulk properties are expected, we have a value of about 0.19 eV per H2 (18.33 kJ/ mol per H2) as desorption energy. This compares reasonably well with the experimental results of a - and g - AlH3 phases respectively of 11.4 and 7.1 kJ/mol per H2 [34,35] and previously reported theoretical values of 9.2 and 10.8 kJ/mol per H2 [13] for bulk AlH3. Our results are also broadly in agreement with the theoretical calculations of C.Wolverton et al. who obtained for bulk AlH3, a value of 8.4 kJ/mol H2 of desorption energy using DFT with VASP [36]. From Fig. 5 we also see that in AlnH3n, for the cluster sizes in the range 8–16, the desorption energies are in the range 0.6–0.4 eV per H2, which is quite desirable from the point of hydrogen storage application [37]. We also see that a comparison of Figs. 1(a) and 5 reveals that the binding energy per Al atom of Aln clusters and the desorption energies of AlnH3n clusters show an inverse relationship. This negative correlation can arise because, the more bound a pure metal cluster is, the less bound are the hydrogen atoms attached to the metal cluster.
Fig. 4. Average Al–H bond length In AlnH3n Clusters.
3.3. Density of states result in a corresponding increase in its volume. On the other hand, for AlnH3n, there is a near linear increase of Al–Al bond length with increasing n. This also shows that when hydrided, Aln clusters break-up, because of the formation of (AlH4) complexes. The Al–H bonds are stronger than the Al–Al bonds and this seems
The total density of states curves are shown in Table 2 with the Fermi energy levels fixed at 0 eV. There is a systematic difference between the curves for the Aln clusters and those for the AlnH3n clusters. In the case of Aln clusters we observe a distributed pattern of fewer number of peaks at lower energies, whereas in
ARTICLE IN PRESS K. Gandhi et al. / Physica B 405 (2010) 3075–3081
Table 2 Total Density of States Curves for Aln and AlnH3n, Fermi level is set to 0 eV. Size 1
2
3
4
6
8
Aluminum Cluster (Aln)
Aluminum hydride Cluster (AlnH3n)
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Table 2 (continued ) Size
Aluminum Cluster (Aln)
Aluminum hydride Cluster (AlnH3n)
10
12
14
16
20
the case of AlnH3n clusters, we see a more complicated DOS with the higher bands separated from the Fermi level by gaps of the order of 5 eV. Within each category the variations in DOS when going from small clusters to big ones show the following trends: Aln Clusters (a) In the case of Aln clusters, the number of peaks and their separations in DOS show variations. For cluster sizes less than 12, the number of peaks is relatively smaller, whereas for larger sizes the number of peaks is large with less clear separation between them. (b) The position of the bands on both sides of the Fermi level with energy gaps of the order of 1 eV or less shows a tendency to metallic character (c) There is a gradual lowering of the first occupied band with increasing cluster size. AlnH3n Clusters (a) The number of peaks in the DOS does not appear to correlate to the cluster size. At around 5 eV higher bands are seen which may be due to hydrogen-metal bonds, as they are totally absent in pure Aln clusters. (b) The presence of the higher bands beyond Fermi level, after gaps of the order of 5 eV,
shows nonmetallic character. For cluster sizes 14, 16 and 20 there appears to be a slight band spread across the Fermi level, accompanied by smaller band gaps. This perhaps shows some tendency to semiconductor behavior for these cluster sizes. (c) The first occupied band, in this case also, is gradually shifted to more negative energies, as is to be expected.
4. Conclusions The following are the important conclusions of our discussion. (i) When Aln clusters are hydrided to their optimum stoichiometric levels, there is a significant loosening of the tightly bound Aln cages (ii) The average Al–Al bond length is more than the average Al–H bond length in tightly bound AlnH3n clusters. That is, Al–H bond is stronger compared to Al–Al bond and this seems to aid the formation of (AlH4) complexes. (iii) There appears to be a
ARTICLE IN PRESS K. Gandhi et al. / Physica B 405 (2010) 3075–3081
negative correlation between the binding energies of Aln clusters and the desorption energies of AlnH3n clusters. (iv) Except for very small clusters, desorption energy steadily decreases with cluster size n and reaches a value of 0.19 eV per H2 for n¼20, showing that for large cluster sizes approximating bulk behavior, aluminum hydride tends to be unstable (v) The AlnH3n clusters of sizes n ¼8–16 have desorption energies in the range 0.6–0.4 eV per H2 which is quite suitable for hydrogen storage application. (vi) DOS curves show metallic tendencies in Aln clusters and nonmetallic to semiconductor trends in AlnH3n clusters. Acknowledgement The authors are grateful to Prof. D.G. Kanhere, Department of Physics, University of Pune, India for making available the computational facilities and providing access to the VASP package. References [1] David, Palmer, November 13, 1997. Hydrogen in the Universe. NASA. Retrieved on-02-05 (2008). [2] A. Zuttel, Mater. Today (Sept) (2003) 24. ¨ [3] Zuttel, S. Orimo, MRS Bull. (September) (2002) 705. [4] L. Zhou, Renew. Sustain Energy Rev. 9 (2005) 395. ¨ [5] L. Schlapbach, A. Zuttel, Nature 414 (2001) 353. [6] L. Zhou, Y. Zhou, Y. Sun, Int. J. Hydrogen Energy 31 (2) (2006) 259. [7] W. Grochala, P.P. Edwards, Chem. Rev. 104 (2004) 1283. [8] U. Eberle, G. Arnold, R.V. Helmholt, J. Power Sources 154 (2) (2006) 456.
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[9] T. Vegge, L.S. Hedegaard-Jensen, J. Bonde, T.R. Munter, J.K. Norskov, J. Alloys Compd. 386 (2005) 1. [10] M. Au, Mater. Sci. Eng. B—Solid State Mater. Adv. Technol. 117 (2005) 37. [11] G. Liang, J. Alloys Compd. 370 (2004) 123. [12] W. Oelerich, T. Klassen, R. Bormann, Mater. Trans. 42 (2001) 1588. [13] J. Huot, G. Liang, R. Schulz, J. Alloys Compd. 353 (2003) L12. [14] W. Oelerich, T. Klassen, R. Bormann, J. Alloys Compd. 315 (2001) 237. [15] J. Huot, I.P. Swainson, R. Schulz, J. Alloys Compd. 292 (1999) 292. [16] X.L. Wang, S. Suda, J. Alloys Compd. 231 (1995) 380. [17] G. Liang, J. Huot, S. Boily, R. Schulz, J. Alloys Compd. 305 (2000) 239. [18] M. Latroche, J. Phys. Chem. Solids 65 (2004) 517. [19] Sakintuna, et al., Int. J. Hydrogen Energy 32 (2007) 1121. [20] Bogdanovic, M. Schwickardi, J. Alloys Compd. 253 (1997) 1. [21] B. Bogdanovic, G. Sandrock,Catalyzed, MRS Bull. 27 (2002) 712. [22] Jia-An Yan Yan Wang, M.Y. Chou, Phys. Rev. B 77 (2008) 014101. [23] P. Hohenberg, W. Kohn, Phys. Rev. 136 (1964) B864. [24] W. Kohn, L.J. Sham, Self-Consistent Equations Including Exchange and Correlation Effects 14 (0) (1965) A1133. [25] G. Kresse, J. Furthmuller, Comput. Mater. Sci. 6 (1996) 15. [26] G. Kresse, J. Furthmuller, Phys. Rev. B 54 (1996) 11169. [27] Vanderbilt, Phys. Rev. B 41 (1990) 7892. [28] J.P. Perdew, Y. wang, Phys. Rev. Lett. 66 (1991) 508. [29] J.P. Perdew, K. burke, M. Ernzerhof, Phys. Rev. Lett. 77 (1996) 3865. [30] R.R. Zope and Baruah, Phys. Rev. A 64, 053202. [31] M. Wang, X. Huang, Z. Du, Y. Li, Chem. Phys. Lett. 480 (2009) 258. [32] V.A. Yartys, R.V. Denys, J.P. Maehlen, C. Frommen, M. Fichtner, B.M. Bulychev, H. Emerich, Inorg. Chem. 46 (2007) 1051. [33] H.W. Brinks, C. Browns, C.M. Jensen, J. Graetz, J.J. Reilly, B.C. Hauback, J. Alloys Compd. 441 (2007) 364. [34] J. Graetz, J.J. Reilly, J. Phys. Chem. B 109 (2005) 22181. [35] J. Graetz, J.J. Reilly, Alloys Compd. 424 (2006) 262. [36] C. Wolverton, V. Ozolins, M. Asta, Phys. Rev. B 69 (2004) 144109. ¨ [37] B. Schuth, Bogdanovic, M. Felderhoff, Chem. Commun. Cambridge 20 (2004) 2249.
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Physica B journal homepage: www.elsevier.com/locate/physb
Hydrogen desorption energies of Aluminum hydride (AlnH3n) clusters Krishna Gandhi n, Deepesh Kumar Dixit, Brajesh Kumar Dixit Department of Physics, Bipin Behari PG College, Outside Sainyer Gate, Jhansi-284001, Uttar Pradesh, India
a r t i c l e in fo
abstract
Article history: Received 22 February 2010 Received in revised form 10 April 2010 Accepted 13 April 2010
Hydrogen desorption energies are considered an important factor in the selection of hydrogen storage materials. Among metal hydrides, aluminum hydride seems to be a promising material for hydrogen storage. We report the theoretical calculations of the hydrogen desorption energies of AlnH3n (n ¼1, 2, 3y) clusters based on Density Functional Theory (DFT). Except for very small clusters, desorption energy is seen to steadily decrease with cluster size n and reach a value of 0.19 eV per H2 for n ¼20, showing that for large cluster sizes approximating bulk behavior, aluminum hydride tends to be unstable. But AlnH3n clusters of sizes n ¼8–16 have desorption energies in the range 0.6–0.4 eV per H2, which is suitable for hydrogen storage application. & 2010 Elsevier B.V. All rights reserved.
Keywords: Aluminum hydride Hydrogen storage AlnH3n clusters Desorption energy DFT
1. Introduction Hydrogen, the most abundant element in the universe, constituting roughly 75% of universe’s elemental mass, has great potential as an energy source [1]. Unlike petroleum, it can easily be generated from renewable energy sources. It is also nonpolluting, and forms water as a harmless byproduct during use. Like electricity, hydrogen is an energy carrier and must be produced from another substance. But, unlike electricity, large quantities of hydrogen can easily be stored for use in future. So it can be used as a future fuel [2]. For the last one or two decades there has been intense research on hydrogen storage materials. One mechanism of adsorption of hydrogen in a solid is physi-sorption on the surface. In this process H2 molecules are bonded to a surface by van der Waals forces. In the other mechanism, atomic hydrogen can be chemisorbed on the surface by forming a covalent bond. Chemi-sorbed hydrogen has a binding energy of more than 2–3 eV, compared to approximately 0.1 eV for physi-sorbed hydrogen [3]. One important category of hydrogen storage materials is metal hydrides [2,4–9]. The reaction between hydrogen and a metal can be expressed by the following reaction. MeðsÞ þ ðx=2ÞH2 ðgÞ-MeHx ðsÞ þ DH
ð1Þ
where DH is released as heat during the reaction. Metal hydrides of practical interest are products of exothermic reactions. Basically the search is for such materials that desorb or release n
Corresponding author. Tel.: + 91 9415057538; +91 5102330085. E-mail address: [email protected] (K. Gandhi).
0921-4526/$ - see front matter & 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.physb.2010.04.069
hydrogen in large amounts when heated to 100–200 1C [10]. While the above reaction may seem quite feasible based on thermo-dynamic considerations, it can be very misleading from a kinetic point of view. The mechanisms of hydride formation as well as hydrogen desorption have a high degree of complexity. Among metal hydrides, alanes are considered most suitable for hydrogen storage [2,11,12]. Aluminum hydride, AlH3, is the most well-known alane. It is a fascinating material that has recently attracted attention for its potential as a hydrogen storage medium for low temperature fuel cells. AlH3 is a very good medium for onboard automotive hydrogen storage, since it contains 10.1% by wt. hydrogen with a density of 1.48 g/ml. Brower et al. [13] noted the existence of at least 7 phases, namely a, a0 , b, g, d, e and z of AlH3, all of which are thermodynamically unstable. At room temperature they are usually meta stable and do not decompose rapidly. The decomposition of AlH3 occurs in a single step, as shown below: AlH3 ðsÞ-AlðsÞ þð3=2ÞH2 ðgÞ
ð2Þ
Experiments have shown that the size of the metal hydride particles have a substantial effect on both the thermodynamics and the reaction kinetics of hydrogen sorption and desorption. It has been reported that the reduction of particle size to nano dimensions resulted in lowering of the desorption temperature and improving the reaction kinetics [14–22]. There are basically two reasons for this. First, the surface-to-volume ratio increases when the particle size goes down and this helps in improving the physi- and chemi-sorption and desorption rates, as these are basically surface phenomena. Second, due to the formation of defects, the material becomes more amorphous and less crystalline when it is converted to smaller dimensions and this affects
ARTICLE IN PRESS 3076
K. Gandhi et al. / Physica B 405 (2010) 3075–3081
the thermodynamics. Thus hydrogen storage in nano-sized metal hydrides is being increasingly explored by experimentalists. This motivated us to undertake theoretical calculations of hydrogen desorption energies in nano-size aluminum hydride clusters.
2. Theory and calculations With the objective of studying the systematics of hydrogen desorption energies, we performed calculations on AlnH3n clusters based on density functional theory (DFT) [23,24]. The Vienna abinitio simulation package (VASP) [25,26] was used with ultra soft PW91 pseudo potentials [27] to calculate the G-point total energies of the clusters. The generalized gradient approximation (GGA) [28,29] was used for the exchange-correlation energy
functional. Geometry optimisation was achieved by starting from random geometries which were annealed at 300 1K to obtain a large number of energy configurations for both Al and AlH3 clusters self-consistently, subject to energy difference o0.0001 eV and atomic forces o0.01 a.u. between successive iterations. These were then subjected to slow cooling down to 0 1K to get the binding energies for the lowest-energy configurations. 3. Results and discussions 3.1. Cluster size, geometries and binding energies for Aln and AlnH3n clusters In this section we discuss the lowest-energy structures, the energetics and the bonding trends in Aln and AlnH3n clusters. First
Table 1 Ground state geometries of the Aln and AlnH3n clusters. Size
Aluminum cluster (Aln)
Size in nm
Aluminum hydride cluster (AlnH3n)
Size in nm
0.17
1 2
0.25
0.36
3
0.25
0.43
4
0.36
0.66
6
0.53
0.99
8
0.54
1.0
10
1.18
1.35
12
1.17
1.43
14
1.26
1.5
16
1.14
1.59
20
1.15
1.59
ARTICLE IN PRESS K. Gandhi et al. / Physica B 405 (2010) 3075–3081
3.5
3077
4.5 4
3
3.5 3 Energy [eV]
Energy [eV.]
2.5 2 1.5
2.5 2 1.5 1
1
0.5
0.5
0 0
0
2
4
6
8
10
12
14
16
18
-0.5
20
2
4
6
10
12
14
16
12
14
16
Cluster Size
Cluster Size 14
13.4
12 Energy [eV]
13.2 13 Energy [eV.]
8
12.8
10 8 6 4
12.6 2 12.4 12.2
0 -2 0
2
4
6
8
10
12
14
16
18
20
Cluster Size Fig. 1. (a) Binding Energy per Al Atom: Aln Clusters and (b) Binding Energy per Al Atom: AlnH3n Clusters.
we discuss the evolution of the geometries. The geometries of the Aln clusters and AlnH3n clusters, where n ¼1, 2, 3, 4, 6, 8, 10, 12, 14, 16 and 20, are shown in Table 1. It also shows the linear dimensions of the clusters which go up to 1.15 and 1.59 nanometers, respectively for Al20 and Al20H60. The Aln cluster symmetries obtained by us are broadly similar to the geometries reported earlier, except in the case of Al4 for which we obtained a geometry corresponding to a tetrahedron [30,31]. The Aln clusters exhibit symmetries even for higher cluster sizes whereas, in the case of AlnH3n, we do not observe much symmetry for higher clusters. We further observe that in the case of AlnH3n clusters, Al–Al bonds are weaker compared to Al–H bonds. In other words, the introduction of H2 in Al cages basically ruptures Al–Al bonds and causes (AlH4) complexes to form. This could be one of the reasons for the breakdown of symmetry in higher AlnH3n clusters. Another interesting feature of AlnH3n clusters is that here the basic nature of bonding is Al–H–Al, that is, hydrogen atoms mediate the Al–Al bonds. In addition to Al–H–Al bonds which are in majority, we find instances of Al–2H–Al bonds also. This feature of AlH3 has been previously reported in literature in both experimental and theoretical studies [32–34] of bulk AlH3. Here also, we observe these two different types of bonds of AlH3. For both Aln and AlnH3n clusters, binding energy per Al atom are plotted in Figs. 1(a) and (b), and second energy differences DEn ¼ (2En En En + )/2 in Figs. 2(a) and (b). Interestingly, Aln and
2
4
6
8
10
Cluster Size Fig. 2. (a) Second Energy Difference: Aln Clusters and (b) Second Energy Difference: AlnH3n Clusters.
AlnH3n clusters show similarities in second energy difference curves, whereas the binding energy per Al atom curves are quite different. The binding energies range from 0.0 to 3.0 eV for pure Aln whereas the range is from 12.4 to 13.4 eV for AlnH3n. The pure Aln binding energies obtained by us are in agreement with those reported by M. Wang et al. [31]. The Aln clusters tend to show stability at cluster sizes n ¼3, 8 and 12, whereas AlnH3n clusters display stability at n ¼2, 8 and 12.
3.2. Bond lengths/strengths and desorption energy trends in Aln and AlnH3n clusters Now we consider the average bond lengths of Al–Al and Al–H bonds [see Figs. 3(a), (b) and 4]. We find that, for a given n, when we go from Aln cluster to AlnH3n cluster, the average Al–Al bondlength increases substantially. In the case of cluster size 8, a stable cluster, the increase is from 3.64 to 4.82 A˚ which means that hydrogen sorption causes Aln clusters to expand in volume. We also observe that in AlnH3n clusters, for the same cluster size 8, the average Al–H bond length, 4.64 A˚ is less than the Al–Al bond length 4.82 A˚ (Fig. 4). On the whole, we can say that when the clusters are hydrided, substantial increases in volume occur. Further, we see from Figs. 3(a) and (b) that for Aln clusters the average Al–Al bond-length shows a saturation-like behavior of a rapid rise followed by a leveling off with increasing n. That is, an increase in the number of Al atoms n in the Aln cluster does not
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1.6
5
1.4 1.2 Energy [eV]
Bond length [Ans.]
4.5
4
3.5
1 0.8 0.6 0.4
3
0.2 2.5
2
4
6
8
10
12
14
16
18
20
0
0
2
4
Cluster Size
Bond length [Ans.]
Aln H3n -Aln þ ð3=2ÞnH2
5
14
16
18
20
ð3Þ
We obtained the desorption energy as equal to the reaction enthalpy DH ¼ EðAln Þ þ ð3=2ÞnEðH2 ÞEðAln H3n Þ =n ð4Þ
4 3
2
4
6
8
10
12
14
16
18
20
Cluster Size Fig. 3. (a) Average Al–Al bond length: Aln Clusters and (b) Average Al–Al bond length: AlnH3n Clusters
8 7 Bond length [Ans.]
12
to aid the formation of (AlH4) complexes seen in the AlnH3n cluster geometries. The hydrogen desorption energies were calculated by us for the desorption reaction
6
6 5 4 3 2
0
10
Fig. 5. Desorption Energy without ZPE correction: AlnH3n.
7
1
8
Cluster Size
8
2
6
2
4
6
8
10
12
14
16
18
20
Cluster Size
where the energies E are the total energies at 0 1K, obtained directly from the calculations. The desorption energies are plotted against cluster size in Fig. 5. In our calculations we have not included the Zero Point Energy (ZPE) corrections arising due to the rotational and vibrational contributions to the binding energy at 0 1K, as we were more interested in the analysis of the systematics as a function of cluster size. For very small clusters no8, there is a significant lowering of desorption energy with increasing cluster size. Beyond size 8, the desorption energy decreases more slowly and steadily and at size n¼20, at and beyond which bulk properties are expected, we have a value of about 0.19 eV per H2 (18.33 kJ/ mol per H2) as desorption energy. This compares reasonably well with the experimental results of a - and g - AlH3 phases respectively of 11.4 and 7.1 kJ/mol per H2 [34,35] and previously reported theoretical values of 9.2 and 10.8 kJ/mol per H2 [13] for bulk AlH3. Our results are also broadly in agreement with the theoretical calculations of C.Wolverton et al. who obtained for bulk AlH3, a value of 8.4 kJ/mol H2 of desorption energy using DFT with VASP [36]. From Fig. 5 we also see that in AlnH3n, for the cluster sizes in the range 8–16, the desorption energies are in the range 0.6–0.4 eV per H2, which is quite desirable from the point of hydrogen storage application [37]. We also see that a comparison of Figs. 1(a) and 5 reveals that the binding energy per Al atom of Aln clusters and the desorption energies of AlnH3n clusters show an inverse relationship. This negative correlation can arise because, the more bound a pure metal cluster is, the less bound are the hydrogen atoms attached to the metal cluster.
Fig. 4. Average Al–H bond length In AlnH3n Clusters.
3.3. Density of states result in a corresponding increase in its volume. On the other hand, for AlnH3n, there is a near linear increase of Al–Al bond length with increasing n. This also shows that when hydrided, Aln clusters break-up, because of the formation of (AlH4) complexes. The Al–H bonds are stronger than the Al–Al bonds and this seems
The total density of states curves are shown in Table 2 with the Fermi energy levels fixed at 0 eV. There is a systematic difference between the curves for the Aln clusters and those for the AlnH3n clusters. In the case of Aln clusters we observe a distributed pattern of fewer number of peaks at lower energies, whereas in
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Table 2 Total Density of States Curves for Aln and AlnH3n, Fermi level is set to 0 eV. Size 1
2
3
4
6
8
Aluminum Cluster (Aln)
Aluminum hydride Cluster (AlnH3n)
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Table 2 (continued ) Size
Aluminum Cluster (Aln)
Aluminum hydride Cluster (AlnH3n)
10
12
14
16
20
the case of AlnH3n clusters, we see a more complicated DOS with the higher bands separated from the Fermi level by gaps of the order of 5 eV. Within each category the variations in DOS when going from small clusters to big ones show the following trends: Aln Clusters (a) In the case of Aln clusters, the number of peaks and their separations in DOS show variations. For cluster sizes less than 12, the number of peaks is relatively smaller, whereas for larger sizes the number of peaks is large with less clear separation between them. (b) The position of the bands on both sides of the Fermi level with energy gaps of the order of 1 eV or less shows a tendency to metallic character (c) There is a gradual lowering of the first occupied band with increasing cluster size. AlnH3n Clusters (a) The number of peaks in the DOS does not appear to correlate to the cluster size. At around 5 eV higher bands are seen which may be due to hydrogen-metal bonds, as they are totally absent in pure Aln clusters. (b) The presence of the higher bands beyond Fermi level, after gaps of the order of 5 eV,
shows nonmetallic character. For cluster sizes 14, 16 and 20 there appears to be a slight band spread across the Fermi level, accompanied by smaller band gaps. This perhaps shows some tendency to semiconductor behavior for these cluster sizes. (c) The first occupied band, in this case also, is gradually shifted to more negative energies, as is to be expected.
4. Conclusions The following are the important conclusions of our discussion. (i) When Aln clusters are hydrided to their optimum stoichiometric levels, there is a significant loosening of the tightly bound Aln cages (ii) The average Al–Al bond length is more than the average Al–H bond length in tightly bound AlnH3n clusters. That is, Al–H bond is stronger compared to Al–Al bond and this seems to aid the formation of (AlH4) complexes. (iii) There appears to be a
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negative correlation between the binding energies of Aln clusters and the desorption energies of AlnH3n clusters. (iv) Except for very small clusters, desorption energy steadily decreases with cluster size n and reaches a value of 0.19 eV per H2 for n¼20, showing that for large cluster sizes approximating bulk behavior, aluminum hydride tends to be unstable (v) The AlnH3n clusters of sizes n ¼8–16 have desorption energies in the range 0.6–0.4 eV per H2 which is quite suitable for hydrogen storage application. (vi) DOS curves show metallic tendencies in Aln clusters and nonmetallic to semiconductor trends in AlnH3n clusters. Acknowledgement The authors are grateful to Prof. D.G. Kanhere, Department of Physics, University of Pune, India for making available the computational facilities and providing access to the VASP package. References [1] David, Palmer, November 13, 1997. Hydrogen in the Universe. NASA. Retrieved on-02-05 (2008). [2] A. Zuttel, Mater. Today (Sept) (2003) 24. ¨ [3] Zuttel, S. Orimo, MRS Bull. (September) (2002) 705. [4] L. Zhou, Renew. Sustain Energy Rev. 9 (2005) 395. ¨ [5] L. Schlapbach, A. Zuttel, Nature 414 (2001) 353. [6] L. Zhou, Y. Zhou, Y. Sun, Int. J. Hydrogen Energy 31 (2) (2006) 259. [7] W. Grochala, P.P. Edwards, Chem. Rev. 104 (2004) 1283. [8] U. Eberle, G. Arnold, R.V. Helmholt, J. Power Sources 154 (2) (2006) 456.
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