J. Phys. Chem. C 2010, 114, 16849–16854
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Reaction Intermediates during the Dehydrogenation of Metal Borohydrides: A Cluster Perspective Sa Li,* Mary Willis, and P. Jena Physics Department, Virginia Commonwealth UniVersity, Richmond, Virginia 23284-2000 ReceiVed: July 16, 2010; ReVised Manuscript ReceiVed: August 25, 2010
Complex light metal hydrides such as alanates, amides, and borohydrides have among the highest hydrogen storage capacities of any materials investigated thus far. However, their use in the transportation industry is plagued by poor thermodynamics and kinetics as well as lack of reversibility at ambient pressure and temperature. To achieve a fundamental understanding of the properties of these materials, considerable efforts have been made to study the reaction intermediates as hydrogen continues to desorb. Recent experiments1 have confirmed the formation of [B12H12]2- complexes during the dehydrogenation of metal tetrahydroborates. We show that the existence of these complexes can be understood by studying the stability of borane clusters and their interaction with metal atoms. We further examine the possibility that other reaction intermediates with different B and H stoichiometry may be present during the dehydrogenation process. Study of the interaction of boron-hydrogen complexes with various metal cations also permits us to illustrate which of the metal borohydrides may be better suited for hydrogen storage. The results are obtained from first principles cluster calculations using density functional theory. I. Introduction In recent years, there has been considerable interest in studying materials issues associated with a new hydrogen economy. Among these, developing hydrogen storage materials suitable for automotive applications is the key for a successful transition from an oil to a hydrogen economy.2 This is a difficult challenge as the storage materials must meet stringent requirements for gravimetric and volumetric density as well as be able to operate at ambient thermodynamic conditions. Complex light metal hydrides such as alanates,3 amides,4 and borohydrides5 not only meet the gravimetric density requirements, but, unlike many nanostructured materials that also meet this requirement, the synthesis of these hydrides is not complicated and is costeffective. Unfortunately, the strong bonds with which hydrogen is held in these materials do not allow the complex hydrides to operate at ambient conditions. Considerable efforts, therefore, have been made to understand the nature of these bonds, and how catalysts and destabilization mechanisms can help to lower the operating pressure and temperature. In this regard, understanding the intermediate products as hydrogen desorbs from these materials has been an important line of study. For example, the release of hydrogen from M(BH4)n has been thought to follow the following reaction paths depending on whether the final product is stable binary hydride (MHx) or an elemental metal (M).6
M(BH4)n f MHx + nB + [2n - x/2]H2
(1)
M(BH4)n f M + nB + (2n)H2
(2)
Here, n is the valence of the metal atom M. In reality, hydrogen desorption from MBH4 takes place in more complicated ways due to the appearance of intermediate phases. * To whom correspondence should be addressed. E-mail:
[email protected].
Using a synergistic approach involving first principles calculations of phase stability and Raman spectroscopy measurements, Orimo and co-workers1,7 found that the decomposition of LiBH4 occurs via formation of one or more polyhedral borane phases (i.e., Li2B12H12 and perhaps similar BnHn containing compounds) prior to forming elemental B and LiH as the final products. However, it is not clear from this experiment what these other BnHn complexes are. Recently, Bowman and co-workers6 used the solid-state NMR method to study the reaction intermediates formed during the decomposition reactions of various metal borohydride systems containing Li, Mg, and Sc metals and identified [B12H12]2- to be the most probable candidate. The existence of Li2B12H12,8-12 Na2B12H12,10 MgB12H12,13-15 and CaB12H1216 has also been determined during the decompositions of various borohydrides by others. Theoretical studies on intermediate phase of decomposition of metal borohydride were initiated by Ohba et al.;7 the monoclinic Li2B12H12 intermediate phase was found to be most stable among LiB3H8 and Li2BnHn (n ) 5-12). Later on, a cubic structure with a pseudoface-center symmetry was suggested for Li2B12H12.8 Thermodynamical calculations17 on LiBH4, Mg(BH4)2, Ca(BH4)2 showed that hydrogen release from LiBH4 and Mg(BH4)2 proceeds via intermediate Li2B12H12 and MgB12H12 phases, whereas for Ca borohydride two competing reaction pathways (into CaB6 and CaH2, and into CaB12H12 and CaH2) are found to have nearly equal free energies. Note that these intermediate phases containing [B12H12]2- species are undesirable with respect to reaction reversibility.9 Thus, these studies pose two important questions: First, are there other intermediate phases besides B12H122- species that are present during dehydrogenation? Second, can these intermediate borane phases be made less stable through use of different metal cations, such as Na+, Mg2+, Ca2+, and Sc2+? In this article, we have addressed these issues using a cluster approach. Borane clusters with BnHn stoichiometry have been known for a long time. The relationship of borane (BnHn) geometries
10.1021/jp106638u 2010 American Chemical Society Published on Web 09/14/2010
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to their electronic structures was originally given by Wade18 using an empirical approach. This was later formalized by Mingos19 using molecular orbital theory. The best known form of the Wade-Mingos rule applies to closo-boranes with stoichiometry, [BnHn]2-. The rule states that the stability of these complexes requires (2n + 1) valence electron pairs. Of these, n pairs are required by the B-H terminal bonds, leaving n + 1 electron pairs for cage bonding. Thus, a [BnHn]2-cluster has the geometry of a polyhedron with n vertices. A classic example of this rule is given by the remarkable stability of the [B12H12]2- cluster. Here, the 12 B atoms form the vertices of an icosahedron, whereas the 12 H atoms are radially bonded. Twelve pairs of electrons are occupied by the 12 terminal B-H bonds, whereas the (n + 1) ) 13 pairs of electrons stabilize the cage structure. The [B12H12]2- cluster can be counterbalanced by either a divalent cation such as Mg or two alkali metal atoms such Li and Na. Consequently, Mg2+[B12H12]2- and Li22+[B12H12]2form very stable compounds and hence are seen as the intermediate reaction products during the dehydrogenation of metal borohydrides. However, according to the Wade-Mingos rule, a large number of such BnHn boranes (n g 5) are possible. The relative stability of neutral hypercloso hydrides BnHn- (n ) 5-13, 16, 19, 22) and the boron hydride radical monoanion BnHn- (n ) 5-13) have been studied.20 Among them, the superior stability of neutral B12H12 was confirmed. They also pointed out the unusual stability of neutral B13H13. Nguyen et al.21 have studied closo boron hydride BnHn2(n ) 5-12) dianions, the B3H8- and B11H14- anions, and the B5H9 and B10H14 neutral species. They found that B12H122is the most stable species, followed by B11H14-. Hofmann et al.22 showed that a new four-center two-electron bond exists in [B6H7]-. Here, the B atoms occupy the vertices of an octahedron and six H atoms are radially bonded to these B atoms. The remaining H atom caps one of the triangular faces and two electrons are shared by three B and one H atom. [B6H7]- forms a stable salt. The question then remains: Is it possible that there are other intermediate reaction products with different B and H stoichiometry and different charge states that could exist during the dehydrogenation reaction of borohydrides? In this article, we have studied these possibilities. Using density functional theory, we have calculated the relative stability of a number of BnHm clusters in neutral and anionic forms with varying composition and their interaction with Li, Na, Mg, and Ca. We show that compounds containing [B12H12]2- complexes are indeed the most stable species, although other less stable compounds may be present during the dehydrogenation of metal-borohydrides. We identify these possible compounds. In the following, we present a brief discussion of our computational procedure and results. II. Computational Procedure Using density functional theory (DFT)23 and the B3LYP24-26 hybrid exchange-correlation functional, we have calculated the equilibrium geometries of Li, Na, Mg and Ca atoms interacting with BnHm complexes. All calculations are performed with the program package Gaussian 03.27 The geometries of clusters were fully optimized without any symmetry constraint at the B3LYP/6-311G+(d) level. The energies and forces at every atom site were converged to 1 × 10-6 eV and 1 × 10-2 eV/Å, respectively. Vibrational frequencies for the lowest energy structures were calculated.
Li et al.
Figure 1. Geometries of (a) B6H62-, (b) B10H102-, and (c) B12H122clusters.
No imaginary frequencies were found, indicating that the structures are dynamically stable. III. Results and Discussion We first discuss the geometry and stability of BnHn2- (n ) 6, 10, 12) dianions and compare these with the results of Schleyer and co-workers.20 Interaction of these borane clusters with Li, Na, Mg, and Ca are then studied and compared with those obtained from calculations on crystalline Li2BnHn7. We show that studies on clusters can provide the same understanding as those obtained from crystal calculations. With this success, the calculations are extended to study the relative stability of Na2BnHn, MgBnHn, and CaBnHn clusters for n ) 6, 10, and 12 as well as the interaction of metal atoms with monoanions of certain BnHm clusters. The results allow us to predict other possible reaction intermediates during dehydrogenation of Li, Na, Mg, and Ca borohydrides. A. [BnHn]2- Clusters and Their Interaction with Li, Na, Mg, and Ca. In Figure 1, we show the equilibrium geometries of BnHn2- clusters. As discussed before, the equilibrium geometries of neutral BnHn clusters are distorted polyhedra with n number of vertices. As a pair of electrons is attached, the polyhedral structures of BnHn2- clusters become more symmetrical, but remain similar to those of their neutrals. The average B-H and B-B distances for BnHn2- clusters with n ) 6, 10, and 12 are given in Table 1. The binding energies per atom, EB ) -[E(BnHn) - nE(B) - nE(H)]/n, of BnHn (n ) 6, 10, 12) clusters are given in Table 2. Note that the binding energies increase as cluster size increases. However, a more interesting quantity to consider is the energy gain when two electrons are added to further stabilize the skeletal structure, namely,
∆E2 ) -[E(BnH2n ) - E(BnHn)]
(3)
It is clear that B12H122- gains the greatest amount of energy and hence is the most stable among the BnHn2- clusters studied. This stability is also reflected in the energy gap between the highest occupied and lowest unoccupied (HOMO-LUMO) energy levels. In Figure 2, we show the equilibrium geometries of Li2BnHn and MgBnHn clusters. Li2B6H6 cluster has the same D3d point group symmetry as previous calculations.28 The equilibrium geometries of Na2BnHn and CaBnHn clusters are similar to those of Li2BnHn and MgBnHn, respectively. The average distances between B-H and B-B atoms in Li2BnHn, Na2BnHn, MgBnHn, and CaB12H12 clusters are given in Table 1. These agree well with those given above for the bare BnHn2- clusters (n ) 6, 10, and 12). This suggests that the bonding between metal atoms and BnHn clusters is ionic and results from the charge transfer from the metal atoms to the
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TABLE 1: Point Group, Average B-B, Average B-H, and Shortest M-B Bond Distances (Å) in (BnHn)2- (n ) 6, 10, 12), (BnHm)- (n ) 4 or 6, m ) 7), Mx(BnHn) (M ) Li, Na, Mg, or Ca, x ) 1 or 2), and M(BnHm) (M ) Li, Na) are Listed 2-
(B6H6) (B10H10)2(B12H12)2(B4H7)(B6H7)Li2B6H6 Li2B10H10 Li2B12H12 LiB4H7 LiB6H7 Na2B6H6 Na2B10H10 Na2B12H12 NaB4H7 NaB6H7 MgB6H6 MgB10H10 MgB12H12 CaB6H6 CaB10H10 CaB12H12
point group
B-B
B-H
M-B
Oh D4d Ih Cs C3V D3d C2 D3d C1 C3V D3d C2 D3d C1 C3V C3V Cs C3V C3V Cs C3V
1.74 1.79 1.79 1.79 1.76 1.73 1.78 1.78 1.76 1.76 1.73 1.78 1.78 1.77 1.76 1.76 1.79 1.79 1.73 1.77 1.78
1.24 1.22 1.22 1.25 1.28 1.22 1.21 1.21 1.25 1.28 1.22 1.21 1.21 1.28 1.28 1.21 1.22 1.22 1.21 1.20 1.20
2.17 2.16 2.19 2.10 2.17 2.50 2.50 2.55 2.52 2.54 2.23 2.19 2.21 2.41 2.42 2.48
Figure 2. Geometries of Mx(BnHn) clusters (M ) Li or Mg, x ) 1 or 2 and n ) 6, 10, or 12).
borane clusters. We note that Ohba et al.7 have calculated the lattice parameters of Li2BnHn (n ) 5-12) by optimizing the crystal structures of these compounds. The structures of the BnHn clusters as well as the B-H and B-B distances obtained here are similar to those in their corresponding crystal structures. In addition, the binding energies, δE between the metal atoms and the borane clusters,
δE ) -[E(Li2BnHn) - 2E(Li) - E(BnHn)]
(4)
for n ) 6, 10, 12, given in Table 2 increase with n. This is again in agreement with the calculations of Li2BnHn crystals as a function of n. We also note from Table 2 that the HOMO-LUMO gap of Li2B12H12 is 5.83 eV, which agrees well with the 5.6 eV band gap calculated by Ohba et al.7 for the Li2B12H12 crystal. From the HOMO and LUMO of Li2B12H12 in parts a and b of Figure 3 we can see that the B p-orbitals contribute to the HOMO, while the Li s-orbital contributes mostly to LUMO. The above results show that the cluster approach can be used to provide an understanding of the relative stability of various intermediate phases that could form during dehydrogenation of metal borohydrides. This is particularly useful when the crystal structures of the intermediate phases are not known. We now discuss the results of Na2BnHn, MgBnHn, and CaBnHn (n ) 6, 10, and 12). Even though there are calculations on Na2BnHn,10 MgBnHn,17 and CaBnHn16,17 (n ) 12) crystal struc-
Figure 3. (a) HOMO of Li2B12H12, (b) the LUMO of Li2B12H12, (c) the HOMO of MgB12H12, and (d) the LUMO of MgB12H12.
tures, systematic calculations on other crystal phases with n ) 6 and 10 do not exist. We note from Table 2 that energy gain, δE and HOMO-LUMO gaps for these systems are still large, although a little smaller than those of Li2BnHn. This is understandable because Na, being a larger ion than Li, is farther removed from the BnHn cage and hence leads to a weaker ionic bond. MgBnHn, on the other hand, shows a larger deviation. The energy gain in MgB10H10 is less than that in MgB6H6, which
TABLE 2: Binding Energy per Atom, Energy Gains due to Successive Attachment of Electron to BnHn Neutral Cluster (∆E), and HOMO-LUMO Gaps of BnHn Clustersa B nH n
E(BnHn) - E(BnHn-)
E(BnHn-) - E(BnHn2-)
(BnHn)2-
Li2(BnHn)
Na2(BnHn)
Mg(BnHn)
Ca(BnHn)
n
EB
∆E
∆E
∆gap
δE
∆gap
δE
∆gap
δE
∆gap
δE
∆gap
6 10 12
3.81 4.00 4.05
3.03 3.70 4.61
-1.78 -0.55 0.90
2.72 3.61 5.08
6.80 7.37 9.3
4.76 4.94 5.83
5.34 5.92 7.83
3.66 3.98 4.89
1.76 1.61 3.29
2.45 1.59 2.37
3.60 3.89 5.50
2.71 2.60 4.25
a
Also given are binding energies (δE) of BnHn clusters attached to Li, Na, Mg, and Ca, as defined in eq 4, and corresponding HOMO-LUMO gaps (∆gap). All units are in eV.
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TABLE 3: Average Energy (eV) of BnHnc (n ) 6, 10, 12) Clusters Relative to B6H6c Clustera
B6 H6 B10H10 B12H12
Neutral (c ) 0)
Anion (c ) -1)
Dianion (c ) -2)
present work
earlier work20
present work
earlier work20
present work
earlier work20
0.0 0.37 0.47
0.0 0.37 0.47
0.0 0.23 0.35
0.0 0.23 0.39
0.0 0.48 0.72
0.0 0.48 0.72
Average energy: AE ) 1/6(B6H6c) - 1/n(BnHnc), where n is the number of vertices and c is the charge. a
TABLE 4: Binding Energy per Atom, Energy Gains due to Attachment of One Electron (∆E), and HOMO-LUMO Gaps of BnHm Clustersa BnHm E(BnHm) - E(BnHm-) BnHm-
Li(BnHm)
Na(BnHn) δE
n,m
EB
∆E
∆gap
δE
4, 7 6, 7
3.40 3.73
2.23 3.86
4.41 5.36
2.88 4.89 2.12 3.93 4.10 5.36 3.44 4.47
∆gap
∆gap
a Also given are binding energies (δE, see eq 4) of BnHm clusters attached to Li and Na and corresponding HOMO-LUMO gaps (∆gap). All units are in eV.
Figure 4. Geometries of (a) B4H7-, (b) B4H7, (c) B6H7, and (d) B6H7 clusters.
reverses the trend that binding energy increases with the cluster size as seen in the alkali systems. In contrast, Ca, which is also a divalent cation, presents the same trend as Li- and Na-based systems, namely, binding energy increases with the cluster size. More importantly, the HOMO-LUMO gaps (shown in parts c and d of Figure 3) for the Mg-based systems are much smaller than those of their alkali counterparts and correspondingly energy gains and δE are also reduced. Even though Ca is farther away from B12H12 cage than Mg, due to lower ionization energy, Ca forms a stronger bond with B12H12 complex. Note that the Mg atom has the highest ionization energy, 7.65 eV,29 in comparison with Li (5.39 eV), Na (5.14 eV) and Ca (6.11 eV). Hence, it is more difficult for Mg to donate electrons to B12H12 cage than the metal atoms discussed above. Consequently, Mg forms the weakest bond with B12H12 unit. Because the intermediate phase, MgB12H12, is less stable compared to other Mx(BnHn) clusters (M ) Li, Na, or Ca, x ) 1 or 2), it is expected that Mg(BH4)2 may be a better hydrogen storage material than LiBH4. B. [BnHn]- Monoanionic Clusters and Their Interaction with Li and Na. McKee et al.20 have reported a systematic study of the atomic structure and stability of BnHn and BnHn- (n ) 5-13, 16, 19, 22) clusters and have shown that with the exception of B12H122-, loss of one electron from BnHn2- (n ) 5-13) is exothermic. Note that according to the Wade-Mingos rule described earlier (n + 1) electron pairs are needed to stabilize closo-borane polyhedra with n vertices. Stable cages with less than (n + 1) electron pairs are called hyperclosoboranes and BnHn- (n ) 5-11, 13) fall into this category. We have repeated the calculations for BnHn- (n ) 6, 10, and 12). We had two objectives: First, we wanted to check the accuracy of our calculation against those of McKee et al.20 Second, we wanted to see if the BnHn- monoanions can be stabilized by
Figure 5. Geometries of (a) LiB4H7, (b) LiB6H7, (c) NaB4H7, and (d) NaB6H7 clusters.
reacting these with Li and Na. If so, are M(BnHn) (M ) Li, Na, and n ) 6, 10, and 12) more stable than M2(BnHn) (M ) Li, Na, and n ) 6, 10 and 12)? If so, they can be likely candidates for intermediate phases in the dehydrogenation of metal borohydrides. We first discuss the geometry and stability of BnHn- (n ) 6, 10) clusters. The geometries given in Figure 1 agree very well with those found by McKee et al.20 We also find that B6H6and B10H10- clusters are more stable than B6H62- and B10H10 2clusters by 1.78 and 0.55 eV, respectively. We have also calculated the average energy, AE ) 1/6(B6H6c) - 1/n(BnHnc) defined by the above authors, where c is the charge. In Table 3, we compare our results with those obtained by McKee et al.20 Note that the agreement is very good and this confirms the accuracy of our computational procedure. We have next computed the equilibrium geometries of M2BnHn (M ) Li, Na, and n ) 6, 10). The results are given in Figure 2. However, we find that the binding energy of M2BnHn (M ) Li, Na, and n ) 6, 10) clusters are larger than twice that of MBnHn (M ) Li, Na, and n ) 6, 10). This shows that even though small borane monoanions for n ) 6, 10 are more stable than their dianions, they are less stable once they interact with metal atoms. Hence, we do not expect MBnHn (M ) Li, Na, and n ) 6, 10) complexes to be among the reaction intermediates as metal borohydrides dehydrogenate. C. BnHm and BnHm- Clusters and Their Interaction with Li and Na. We now examine the relative stability of monoanions of B4H7 and B6H7 and study their reactions with Li and
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Figure 6. δE and HUMO-LUMO gap for Mx(BnHn) and M(BnHm) clusters (M ) Li, Na, Mg, or Ca and x ) 1 or 2).
Na. In Figure 4, we provide the equilibrium geometries of neutral and anionic B4H7 and B6H7 clusters. We see that the geometries of neutral and negatively charged clusters are different although both maintain a tetrahedral B core. In neutral B4H7 three hydrogen atoms are bridge-bonded, whereas in the anion only one is bridge-bonded. However, both neutral and negatively charged B6H7 clusters present similar structures with the extra H atom located on the hollow site and shared by three B atoms. The binding energies, the energy gain in adding an electron and HOMO-LUMO gaps of B4H7 and B6H7 clusters are given in Table 4. These energies are defined as,
EB ) -[E(BnHm) - nE(B) - mE(H)]/(n + m)
(5)
∆E ) -[E(BnHm-) - E(BnHm)]
(6)
We note that both neutral and anionic B6H7 clusters are much more stable than B4H7. In particular, the electron affinity of B6H7 is 3.86 eV, which is larger than that of F (3.4 eV), the most electronegative element in the periodic table. We also note that the binding energies increase with increasing HOMO-LUMO gap. These characteristics are manifested when these clusters interact with Li and Na. In Figure 5, we show the geometries of MBnHm (M ) Li, Na; and n,m ) 4,7 and 6,7, respectively) clusters. We note that the distances of Li and Na atoms from their nearest B atom, namely 2.10 and 2.52 Å for MB4H7 and 2.17 and 2.54 Å for MB6H7, are similar to those found for the M2BnHn (M ) Li, Na) clusters. Thus, the bonding between BnHm and Li and Na atoms are ionic. However, MBnHm (M ) Li, Na) clusters are less stable than those containing the BnHn moiety discussed above. Hence, it is unlikely that either LiB6H7 or LiB4H7 can be an intermediate phase during the dehydrogenation of alkali metal borohydrides. IV. Summary In summary, using density functional theory we have calculated the equilibrium geometries, electronic structure, and relative stability of BnHm clusters for a range of stoichiometry, both in neutral and negatively charged form and their interactions with metal atoms such as Li, Na, Mg, and Ca. The study was motivated by recent experiments where B12H12 complexes,
attached to metal atoms, were identified as intermediate phases in the dehydrogenation reaction of metal borohydrides. Our objective was to see if other intermediate phases can exist during dehydrogenation of metal borohydrides and if suitable metal cations can be found that will make the appearance of these intermediate phases less likely. We first showed that studies on clusters can provide similar insight into the relative stability of various intermediate phases as the calculations based on crystal symmetry can. In addition, studies based on clusters can illustrate whether other intermediate products can form during the dehydrogenation process. This is particularly useful when the crystal structures of these intermediate phases are not known. We find that whereas borane clusters carrying a single negative charge are stable, they react with metal atoms more weakly than the closo-boranes (BnHn2-) and hence are not likely to form intermediate phases during the dehydrogenation of metal borohydrides. Whereas Li2B12H12, Na2B12H12, MgB12H12, and CaB12H12 are preferred intermediates during dehydrogenation of LiBH4, NaBH4, Mg(BH4)2, and Ca(BH4)2, hydriding/dehydriding process in Mg(BH4)2 may be easier than other hydrides due to the reduced stability of the MgB12H12 intermediate phase. Note that experimental finding proved that >11 wt % of hydrogen can be reversibly stored for the sample of Mg(BH4)2 after the dehydriding reaction.30 All our results are summarized in Figure 6. For Li and Na BnHm systems, we clearly see that B12H12-containing complexes form the most stable intermediate phase. However, for the magnesium borohydride system not only are there more than one possible intermediate phase, but also they are much less stable than those seen in alkali borohydrides. The HOMO-LUMO gaps of these borane complexes follow the same trend as the relative energies. We hope that this work will motivate experimentalists to search for these intermediate phases in magnesium borohydrides. Acknowledgment. This was supported by grants from the Department of Energy. This research used resources of the National Energy Research Scientific Computing Center, which is supported by the Office of Science of the U.S. Department of Energy under Contract No. DE-AC02-05CH11231. References and Notes (1) Orimo, S. I.; Nakamori, Y.; Ohba, N.; Miwa, K.; Aoki, M.; Towata, S.; Zuttel, A. Appl. Phys. Lett. 2006, 89, 021920. (2) Schlapbach, L.; Zuttel, A. Nature 2001, 414, 353.
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