Influence of Surface Reactions on Complex Hydride Reversibility - The

18270

J. Phys. Chem. C 2008, 112, 18270–18279

Influence of Surface Reactions on Complex Hydride Reversibility Bing Dai Department of Chemical Engineering, UniVersity of Pittsburgh, Pittsburgh, PennsylVania 15261

Rees B. Rankin and J. Karl Johnson* Department of Chemical Engineering, UniVersity of Pittsburgh, Pittsburgh, PennsylVania 15261, and National Energy Technology Laboratory, Pittsburgh, PennsylVania 15236

Mark D. Allendorf Sandia National Laboratories, P.O. Box 969, LiVermore, California, 94551

David S. Sholl School of Chemical and Biomolecular Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332

Nikolai A. Zarkevich and Duane D. Johnson Departments of Physics and Materials Science and Engineering, and Frederich Seitz Materials Research Laboratory, UniVersity of Illinois, Urbana-Champaign, Illinois 61801 ReceiVed: August 11, 2008; ReVised Manuscript ReceiVed: September 13, 2008

Alkali metal hexahydride alanates, M3AlH6, are known to exist for M ) Li, Na, and K. All three release hydrogen, forming MH and Al as the solid phase products. The reverse of this reaction, 6MH + 2Al + 3H2 f 2M3AlH6, occurs without a catalyst for M ) K, occurs only with a catalyst for M ) Na, and has not been observed, even with a catalyst, for M ) Li. Differences in the reactivities of the LiH, NaH, and KH surfaces may contribute to the observed differences in rehydriding. We have examined the reactivities of the lowenergy MH(100) surfaces with respect to gas phase H2, H, O, O2, and H2O in order to test this hypothesis. We have found that H2 weakly physisorbs and that H is unbound to all three MH surfaces, relative to gas phase H2. Atomic oxygen is very strongly bound to all three surfaces and O2 dissociates without a barrier at low coverage on the LiH and NaH surfaces. The KH surface is more resistant to O2 dissociation, but molecular O2 strongly binds to the surface. We have identified dissociation pathways for H2O on all three MH surfaces, which results in the formation of surface metal hydroxide and gas phase H2. The zero-point energy corrected dissociation activation energies for H2O are 23.0, 13.8, and 18.4 kJ/mol for LiH, NaH, and KH, respectively. We have performed kinetic modeling of the H2O dissociation process resulting from MH surfaces exposed to vapor phase water at room temperature and partial pressures of 0.03 bar (100% relative humidity) and 10-6 bar (1 ppm). In both cases, our modeling predicts that all three MH surfaces will be essentially completely covered with a monolayer of OH groups in less than 10 ms. We therefore conclude that there are no substantial differences in the reactivities of the MH surfaces that can account for the observed differences in their abilities to form the hexahydride alanate phase. I. Introduction The key barrier to the use of hydrogen as a transportation energy carrier is often said to be the lack of safe and efficient hydrogen storage technologies for on-board fuel cell vehicles.1,2 Complex light metal hydrides such as alanates (MAlH4, M ) Li, Na)3-10 have been investigated extensively in the past several years because of their potential as hydrogen storage materials. However, none of the materials identified thus far are acceptable for on-board hydrogen storage due to thermodynamic or kinetic issues. Recent work by a number of different groups have addressed the issue of predicting the thermodynamics of complex metal hydride systems through the use of ab initio density functional theory (DFT).4,7,8,11-19 In contrast, less theoretical work has been devoted to predicting the kinetics of metal hydride reactions.7,9,20-22

It is instructive to compare the kinetics of the Li, Na, and K alanate systems. The alanate reactions take place in two stages:

3MAlH4 h M3AlH6 + 2Al + 3H2

(1)

2M3AlH6h 6MH + 2Al + 3H2

(2)

and where M ) Li, Na, or K. When M ) K both reactions 1 and 2 are known to be fully reversible without a catalyst.23 However, KAlH4 is not a viable hydrogen storage material because the gravimetric density is too low, being only 4.3 wt % for the completed reaction. Furthermore, the heat of reaction is too high, being 68.7 kJ/mol H2, requiring a high temperature to release the hydrogen and a cooling requirement of 41.6 kW, to charge 1 kg of H2 into a tank within 10 min. Bogdanovic´ et al. reported that reactions 1 and 2 can be made to be reversible for M ) Na

10.1021/jp807162k CCC: $40.75  2008 American Chemical Society Published on Web 10/28/2008

Surface Reactions on Complex Hydride

J. Phys. Chem. C, Vol. 112, No. 46, 2008 18271

TABLE 1: Zero Temperature Heats of Reactions of Key Compounds Computed from DFT and Compared with Experimental and Tabulated Dataa heats of reactions (0 K)

PAW-PBE

/3Li3AlH6 f 2LiH + /3Al + H2 /3Na3AlH6 f 2NaH + 2/3Al + H2 2 /3K3AlH6 f 2KH + 2/3Al + H2 LiAlH4 f 1/3Li3AlH6 + 2/3Al + H2 NaAlH4 f 1/3Na3AlH6 + 2/3Al + H2 KAlH4 f 1/3K3AlH6 + 2/3Al + H2 LiH + 1/2O2 f LiOH NaH + 1/2O2 f NaOH KH + 1/2O2 f KOH 2LiH + O2 f Li2O + H2O 2NaH + O2 f Na2O + H2O 2KH + O2 f K2O + H2O LiH + H2O f LiOH + H2 2 LiOH + MgH2 f Mg(OH)2 + 2LiH

33.6 40.0 56.1 -5.3 26.8 46.9 -374.8 -353.7 -347.2 -622.7 -530.8 -462.7

2

2

2

PAW-PW91 28.7 50.8 69.4 5.1 31.9 -424.5 -600.4 -128.3 -24.8

exp

tabulated 28.950

4724 3.4650 3724 -394.3 -369.5 -366.9 -659.3 -546.9 -489.4 -155 -30

a “Tabulated” indicates that the reaction enthalpies were calculated from the formation energies of the compounds available from the NIST database,51 unless indicated otherwise. All values are given in units of kilojoules for the reaction as written. The PAW-PW91 data for the hydrides were computed using the database of Alapati et al.11,13,15,16

with the addition of a few atom percent of Ti as a catalyst.3 The catalysis of NaAlH4 with Ti has been studied extensively.24-28 We note in passing claims by one group that sodium alanate is reversible without a catalyst when ball milled in a stainless steel vial.29,30 Nevertheless, NaAlH4 is also not acceptable because it has a theoretical hydrogen capacity of only 5.6 wt %. LiAlH4 can release 7.9 wt % hydrogen and has a much more favorable heat of reaction than Na and K alanates (see Table 1). However, the rehydrogenation kinetics of this reaction is not favorable. The dehydrogenation and rehydrogenation of LiAlH4 has been investigated experimentally.31-37 Partial reversibility of reaction 2 for M ) Li has been claimed by Chen et al.,32 however, others have failed to reproduce their results under similar conditions.33 It has been claimed that tetrahydrofuran forms an adduct with LiAlH4, fostering the hydrogenation of LiH and Al to LiAlH4.34 The differences in the reversibility of reaction 2 for K, Na, and Li are striking given that all three MH compounds have the same crystal structure (with different lattice constants, of course). However the M3AlH6 phases are structurally dissimilar. Li3AlH6 has a trigonal R symmetry, whereas Na3AlH6 and K3AlH6 have the monoclinic P121/n1 symmetries. There are several possible reasons for the observed differences in reversibilities of these three systems. For example, the Li system may require very high H2 pressures. Another possibility is that differences in the melting points of the MH species contribute to differences in reversibility. Solid phase reactions are known to occur at rapid rates when one of the solid species becomes a liquid.38 On this basis, one might assume that the hydrogenation reaction in 2 might proceed at an appreciable rate when the MH phase becomes a liquid and coats the Al phase. The melting points of LiH, NaH, and KH are 962, 1073, and 633 K, respectively. The melting points of LiOH, NaOH, and KOH are 723-743, 591, and 633 K, respectively. Therefore, an alternative explanation for the lack of Li3AlH6 reversibility is that formation of a liquid hydroxide layer is necessary to achieve reasonable H2 diffusion rates to the underlying MH solid. The low melting points of NaOH and KOH enable this, but the higher melting point of LiOH prohibits it. Differences in the crystal structures of the three hexahydrides is another possible reason for the differences in the reversibilities. It is reasonable to assume for solid phase reactants that reactions take place at solid interfaces; hence, the differences in reactivity may be due to differences in the reactivity of the three different MH surfaces, specifically with the respect to

poisoning. This assumes that the Al surface is essentially the same in each of the three cases. In this paper, we examine the hypothesis that the differences in reversibility among the KH, NaH, and LiH systems is due (at least in part) to differences in the reactivities of the respective MH surfaces. We present an initial study of reactions of H, H2, O, O2, and H2O on the most stable surfaces of KH, NaH, and LiH. We view this as a first step toward understanding the kinetics of formation of these hexahydride compounds. First-principles modeling of the kinetics of solid phase reactions is an extremely difficult task. There have been very few studies of solid phase reaction kinetics of hydrogenation or dehydrogenation of metal hydrides. Most of the previous work focused on surface reaction kinetics. Vegge studied the dissociation of H2 on the Mg(0001) surface and the diffusion of atomic hydrogen into the bulk Mg phase.20 Vegge also studied Ti-catalyzed H2 desorption from NaAlH4 nanoparticles.9 Adsorption and dissociation of H2 on the Mg2Si(1j10) surface was studied by Dai et al.39 Du et al.40,41 examined the energetics of desorption of H2 from MgH2(001) and (110) surfaces along with vacancy formation energies and vacancy diffusion pathway barriers. They concluded that diffusion barriers on or near the surface are much smaller than H2 desorption barriers and hence the rate limiting step for dehydrogenation of MgH2 is the desorption of H2 from the surface. Their results only apply to the initial dehydrogenation of MgH2, since nucleation of the Mg phase was not considered. Kang et al. investigated the thermal decomposition mechanism of reactions 1 and 2 for M ) Li.7 They used simplified cluster models to mimic the reaction processes, so it is not clear how their results relate to crystalline systems or to interfacial reactions between condensed phases. Moreover, they did not discuss the reversibility of reaction 2. Larsson et al.42 have studied the energetics of dehydrogenation of MgH2 nanoclusters using DFT. They studied the impact of substitutional doping of Mg31H62 clusters with transition metals. They calculated the energetics of partial and total dehydrogenation of Mg30H62M clusters, where M is either Ti, V, Fe, or Ni, with the dopant atom being located at different positions in the cluster. These calculations account for transition metals lowering the energetics and kinetics of dehydrogenation. However, they did not explicitly calculate any dehydrogenation pathways or barriers, and hence they have not calculated any kinetic parameters.

18272 J. Phys. Chem. C, Vol. 112, No. 46, 2008

Figure 1. Calculated van’t Hoff plot for 2K3AlH6 f 6KH + 2Al + 3H2. The symbols are DFT results, and the dashed lines are ∆G ( 10 kJ/mol, the expected accuracy of our calculations.

Dai et al.

Figure 2. Calculated van’t Hoff plot for 2Na3AlH6 f 6NaH + 2Al + 3H2 adapted from the work of Alapati et al.13 (squares). The dashed lines are ∆G ( 10 kJ/mol. The triangles and circles are experimental data from two different measurement techniques.24

II. Computational Methods We have performed plane wave DFT calculations using the Vienna Ab-initio Simulation Package (VASP).43,44 We employed the Perdew-Burke-Ernzerhof generalized gradient functional (PBE)45,46 along with the projector augmented wave (PAW)47,48 method for describing ionic cores. Cutoff energies for the plane wave expansions were set to 500 or 312.5 eV for systems with or without oxygen, respectively, and to 700 eV (using PAWGGA-PW91) for calculating reaction enthalpies with higher accuracy. These energy cutoffs are sufficiently high to give wellconverged structures and total energies. We used a periodic sixlayer slab with adatoms adsorbed on one side of the slab. The calculations used either 1 × 1 or 2 × 2 surface supercells. Brillouin-zone integrations employed 6 × 6 × 1 and 4 × 4 × 1 Monkhorst-Pack49 k-point grids for 1 × 1 and 2 × 2 supercells, respectively. The slab was separated from its periodic image in the direction normal to the surface by a vacuum space of about 15 Å. Slab calculations allowed the top three surface layers to relax, holding the bottom three layers fixed in their optimized bulk positions. The positions of all unconstrained atoms were relaxed until the forces on each of the atoms were smaller than 10-2 eV/Å. The impact of dipole corrections was found to be negligible for these systems. III. Results and Discussion A. Bulk Thermodynamics. We have computed heats of reaction for several key compounds in order to assess the accuracy of the DFT methods we used. The computed heats of reaction for MAlH4, M3AlH6, MOH, and M2O (M ) Li, Na, and K) are presented in Table 1 along with experimental24,50 and tabulated51 data from the literature. We find reasonably good agreement between our calculated data and experimental data reported in the literature. The observed good agreement gives us confidence that the DFT methods we employed are sufficiently accurate for our purposes. The van’t Hoff plots from our DFT-based calculations are plotted for the decomposition reactions for K3AlH6, Na3AlH6, and Li3AlH6 in Figures 1, 2, and 3, respectively. (Alapati et al.13 have reported the van’t Hoff plot for decomposition reaction for Na3AlH6 with PAW-PW91.) Since DFT makes systematic errors in computing total energy differences because no available exchange-correlation functionals are exact,52,53 a pragmatic way to deal with this situation is to infer uncertainty estimates for our DFT results from comparisons with experimental data.

Figure 3. Calculated van’t Hoff plot for 2Li3AlH6 f 6LiH + 2Al + 3H2. The dashed lines are ∆G ( 10 kJ/mol.

Alapati et al.13 have shown that arbitrarily adding and subtracting 10 kJ/mol H2 from the DFT-generated free energy differences gives a range of pressures that encompass available experimental data. We used the same approach here for these van’t Hoff plots to estimate the equilibrium pressure of H2 as a function of temperature. B. Clean LiH, NaH, and KH Surfaces. All three metal hydrides have the same crystal structure. We have calculated the surface energies of several low Miller index surfaces of LiH, NaH, and KH in order to identify the surfaces with lowest surface energies, which would be likely to dominate the experimentally observed surfaces. The surface energy is defined as54-56

(Eslab - NhydrideEbulk hydride) Esurface ) 2A

(3)

where Nhydride is the number of formula units in the slab bulk supercell, Eslab is the calculated total energy of the slab, Ehydride is the calculated total energy per formula unit in the bulk, and A is the surface area of the slab. The factor of 2 accounts for the two sides of the slab. Calculations of the energy of the bulk structure employed 8 × 8 × 8 k-point grids. The calculated surface energies are listed in Table 2. The (100) surfaces of all three hydrides have substantially lower energies than the other surfaces calculated, and therefore, we used these surfaces for all subsequent calculations in this paper.



TABLE 2: Surface Energies (J/m2) of LiH, NaH, and KH LiH NaH KH

(100)

(110)

(121)

(111)

0.30 0.20 0.13

0.71 0.48 0.30

1.04 0.70 0.44

2.43 1.54 1.04

site

C. Adsorption of Hydrogen on LiH(100), NaH(100), and KH(100) Surfaces. We have examined the adsorption sites for atomic and molecular hydrogen on the clean MH(100) surfaces shown in Figure 4. We used both 1 × 1 and 2 × 2 supercells for atomic and molecular hydrogen adsorption calculations. The general expression for the adsorption energy per adsorbate is given as:

Eads )

Esurface+A - (Esurface - Eref) n

TABLE 3: Adsorption Energies (kJ/mol) for H2 Molecules on the Surfaces of LiH(100), NaH(100), and KH(100)a H2 H2 H2 H2 H2 H2 H2 H2 H2 a

on on on on on on on on on

LiH (1 × 1, 25% ML) LiH (2 × 2, 6.25% ML) LiH (2 × 2, 25% ML) NaH (1 × 1, 25% ML) NaH (2 × 2, 6.25% ML) NaH (2 × 2, 25% ML) KH (1 × 1, 25% ML) KH (2 × 2, 6.25% ML) KH (2 × 2, 25% ML)

A

B

C

D

-1.6 -1.7 -1.6 -2.2 -2.3 -2.2

-1.8 -1.7 -1.8 -2.4 -2.6 -2.5 -3.9 -3.8 -3.8

-1.8 -1.6 -1.9 -2.6 -2.7 -2.6 -3.9 -4.0 -3.9

-1.6 -1.4 -1.8 -2.2 -2.0 -2.3 -3.9 -3.9 -3.7

-1.9 -1.8

See Figure 4 for a definition of the sites.

(4)

where Eads is the adsorption energy, Esurface+A is the total energy of the metal hydride slab (surface) with adsorbate A, Esurface is the total energy of the surface without adsorbed species, Erefis the adsorbate gas phase reference system total energy, and n is the number of adsorbates per supercell. For A ) nH, Eref ) (n/ 2)EH2, while for A ) nH2, Eref ) nEH2, for n adsorbents. In other words, both atomic and molecular hydrogen adsorption energies are referenced to gas phase molecular hydrogen. With this definition, negative values of Eads denote adsorption that is more stable than the corresponding clean surface and gas phase H2. We do not include zero-point energy corrections in these results because the conclusions we draw from our calculations, namely that atomic hydrogen is unbound relative to gas phase H2 and that molecular hydrogen is very weakly bound through physisorption, will not change if zero-point energy corrections are added. We extensively studied the adsorption of atomic H on various sites of the MH(100) surfaces. We found that atomic H will either weakly bind to the surface at metal atop sites or will abstract an H atom from the MH surface to form a physisorbed H2 molecule on the surface. The formation of H2 molecules is much more energetically favorable than formation of surface M-H bonds; this indicates that the surface M-H bond is much weaker than the H-H bond that is formed by H atom abstraction. All of the adsorption energies for atomic hydrogen

Figure 4. Schematic top view of the metal hydride (100) surface. Letters indicate possible adsorption sites on the surface. The large dark and small light spheres represent the metal and hydrogen atoms, respectively. The white lines bound one unit cell.

Figure 5. H2 adsorption energies on LiH(100), NaH(100), and KH(100) surfaces. The inset pictures are the top and side views of optimized structures of H2 on the surfaces.

were found to be positive, meaning that atomic H adsorption is not energetically favorable relative to gas phase H2. The adsorption energies for H2 on each of the adsorption sites listed in Figure 4 are summarized in Table 3. H2 molecules weakly physisorb on the hydride surfaces, but do not chemically bind. The trends in the adsorption energies for H2 on these three metal hydride surfaces are plotted in Figure 5. The binding energies for H2 decrease (become more favorable) going from LiH to NaH to KH. The optimized structures of the H2 on the surfaces are shown as insets in the figures. We can deduce the effects due to system size and coverage from the data in Table 3. The system size effect is negligible, as observed by comparing energies for the 25% ML (monolayer) coverage cases on the 1 × 1 and 2 × 2 surfaces. Surface coverage (adsorbate-adsorbate) effects are very small, as seen by comparing energies on the same surface at different coverages. D. Adsorption of Oxygen on LiH(100), NaH(100), and KH(100) Surfaces. The adsorption energies for atomic and molecular oxygen are defined from eq 4 with Eref ) 1/2EO2 and Eref ) EO2, respectively. The adsorption energies for atomic oxygen on each of the adsorption sites we considered are summarized in Table 4. The sizes of the unit cells for the optimization are shown in parentheses, and the initial adsorption sites used here are same as the sites in Figure 4. Adsorption energies for O on the LiH(100), NaH(100), and KH(100) surfaces of the 1 × 1 unit cell are plotted in Figure 6. In contrast to H2 (see Figure 5), the Eads values are ordered as LiH < NaH < KH. The inset graphics show the most energetically favorable


Dai et al.

TABLE 4: Adsorption Energies (kJ/mol) for O Atoms on the Surfaces of LiH(100), NaH(100), and KH(100)a site O O O O O O O O O O

on on on on on on on on on on

LiH (1 × 1, 25% ML) LiH (1 × 1, 50% ML) LiH (2 × 2, 6.25% ML) LiH (2 × 2, 25% ML) NaH (1 × 1, 25% ML) NaH (2 × 2, 6.25% ML) NaH (2 × 2, 25% ML) KH (1 × 1, 25% ML) KH (2 × 2, 6.25% ML) KH (2 × 2, 25% ML)

B

B′

-370.5 -357.7 -374.4 -367.1 -364.7 -365.6 -364.2 -353.1 -353.3 -352.4

-330.0 -344.5 -313.9 -323.0 -332.9 -327.2 -321.3 -330.0 -325.3 -321.0

BB′ -361.8

-338.6

a

B and B′ represent OH groups adsorbed at B sites with the H atom pointing toward the vacuum or the bulk (second layer), respectively. See Figure 4 for a definition of the sites.

Figure 6. Atomic oxygen adsorption energies on LiH(100), NaH(100), and KH(100) surfaces. The inset pictures are the top and side views of the optimized structures.

adsorption sites for O atoms on the surfaces. Importantly, on all three hydride surfaces, optimization results in barrierless O insertion between the M-H bond to form M-O-H groups on the surface, independent of the starting configuration. The favorable energetics of M-O-H surface configurations are corroborated by the reaction enthalpies in Table 1, where we see that formation of bulk MOH is energetically much more favorable than formation of MO2 on a per formula unit MH basis. Hence, poisoning reactions would likely involve formation of MOH, as discussed in section IV. Note that O atoms can insert such that the M-O-H bond is pointing down into the bulk. These are labeled as B′ in Table 4. Note also that B′ sites are always higher in energy than B sites on the same surface. For two O atoms per unit cell (50% ML for the 1 × 1), one might also have both B and B′ sites occupied. The effect of system size for O adsorption is seen to be small (cf. 25% ML on the 1 × 1 and 2 × 2 surfaces). The effect of coverage on Eads can be seen by comparing energies for one and four O atoms on the 2 × 2 supercell (6.25% and 25% coverage, respectively). The adsorption energies for NaH and KH are very similar, indicating little adsorbate-adsorbate interaction up to 25% coverage. We do note a slight coverage effect for the LiH surface; the adsorption energies increase (become less favorable) going from 6.25% to 25% to 50% ML, indicating repulsive adsorbate-adsorbate interactions. The LiH lattice constant is smaller than for NaH and KH, which explains the lack of surface coverage effects for the latter two systems.

We have also investigated 50% coverage on both the 1 × 1 (two O atoms) and 2 × 2 (eight O atoms) LiH surfaces. Both systems converge to the same structure, shown in Figure 7. The 50% O coverage causes the first layer spacing to increase dramatically, as shown in Figure 7. The resulting structure is very similar to the LiOH crystal structure.57,58 Adsorption energies for O2 on different surfaces and at different coverages are listed in Table 5. The sizes of the unit cells for the optimization are shown in parentheses, and the initial adsorption sites used here are the same as the sites in Figure 4. We note that the adsorption energies for (1 × 1) and (2 × 2) at the same coverage are essentially identical, indicating no system size effects. However, in contrast to H, H2, and O, there appear to be significant energetic effects due to coverage. For example, the difference in Eads between O2 on site B of LiH at 6.25% and 25% coverage is 40 kJ/mol, with higher coverage giving more favorably binding. This is counterintuitive for typical electronic adsorbate-adsorbate interactions, which typically lead to decreased binding with increasing coverage. We note substantial surface reconstruction for the 25% coverage case, and this surface reconstruction may be responsible for the observed increase in the magnitude of the binding energy. The effect of coverage on the binding energy decreases in going from LiH to NaH to KH, probably because the lattice constants increase in this same order, thus increasing the distances between adsorbed O2 moieties. Figure 8 gives the structures of 25% O2 coverage on LiH(100), NaH(100), and KH(100) surfaces. Barrierless dissociation of O2 was found on the LiH and NaH surfaces. These correspond to BB and B′B′ sites for for LiH and NaH, respectively, as seen in Table 5. Dissociation results in the formation of two surface hydroxide groups, pointing toward the vacuum in the case of O2 on LiH and into the bulk on NaH. We conclude that at low coverage, O2 reacts with LiH and NaH to form surface metal hydroxide groups without a barrier. In contrast, we have not been able to observe barrierless dissociation of O2 on the KH(100) surface. We carried out a series of calculations using the nudged elastic band (NEB) method59,60 in an attempt to find a dissociation pathway for O2 on KH(100) but were unable to find a reasonable pathway. We also performed DFT molecular dynamics (DFT-MD) simulation at 600 K in order to observe dissociation of O2 on KH(100). However, O2 did not dissociate over the simulated time period of 3.75 ps. One might be tempted to conclude from our calculations that KH is more resistant to attack by O2 than LiH and NaH. There are two caveats to consider. First, the O2 moiety binds just as strongly to the KH surface as to the LiH and NaH surfaces in cases where dissociation does not occur (see Table 5). Second, the failure to locate a low-energy dissociation pathway for O2 on KH is not proof that such a pathway does not exist. It could be that O2 will readily dissociate on a different surface or at a defect site. We therefore refrain from drawing any conclusions about O2 dissociation on KH. E. H2O Adsorption on LiH(100), NaH(100), and KH(100) Surfaces. The adsorption energy of H2O on the MH surfaces is defined in eq 4 with Eref ) EH2O, the gas phase H2O total energy. When more than one water molecule was placed on the surface the adsorption energy was defined as the energy per H2O molecule, as with multiple O or O2 adsorbates. The adsorption energies for H2O on the LiH(100), NaH(100), and KH(100) surfaces are reported in Table 6. We initially put H2O on the four different adsorption sites of these surfaces shown in Figure 4. On LiH(100) H2O converges site A, independent of the starting configuration and likewise to site C



Figure 7. Optimized structures of 50% ML O coverage on the LiH(100) surface. The top and bottom rows present top and side views, respectively. B and B′ represent OH groups adsorbed at B sites (see Figure 4) pointing up (toward vacuum) and down, respectively.

TABLE 5: Adsorption Energies (kJ/mol O) for O2 Adsorption on the LiH(100), NaH(100), and KH(100) Surfacesa site O2 O2 O2 O2 O2 O2 O2 O2 O2 a

on on on on on on on on on

LiH (1 × 1, 25% ML) LiH (2 × 2, 6.25% ML) LiH (2 × 2, 25% ML) NaH (1 × 1, 25% ML) NaH (2 × 2, 6.25% ML) NaH (2 × 2, 25% ML) KH (1 × 1, 25% ML) KH (2 × 2, 6.25% ML) KH (2 × 2, 25% ML)

B -146.7 -102.3 -146.0 -137.0 -128.3 -136.9 -140.9 -137.0 -140.8

BB

TABLE 6: Adsorption Energies (kJ/mol per H2O) for H2O on the LiH(100), NaH(100), and KH(100) Surfacesa site B′B′

-371.5 -329.0


H2O H2O H2O H2O H2O H2O H2O H2O H2O H2O H2O H2O a

Figure 8. Optimized structures of O2 on the LiH(100), Na(100), and KH(100) surfaces at 6.25% ML coverage. The top and bottom rows present top and side views, respectively.

on the NaH(100) surface. There are two different final adsorption sites for H2O on the KH(100) surface. We see from the values of Eads in Table 6 that water is weakly bound to the three hydride

on on on on on on on on on on on on

LiH (1 × 1, 25% ML) LiH (2 × 2, 6.25% ML) LiH (2 × 2, 12.5% ML) LiH (2 × 2, 25% ML) NaH (1 × 1, 25% ML) NaH (2 × 2, 6.25% ML) NaH (2 × 2, 12.5% ML) NaH (2 × 2, 25% ML) KH (1 × 1, 25% ML) KH (2 × 2, 6.25% ML) KH (2 × 2, 12.5% ML) KH (2 × 2, 25% ML)

A

C

D

-33.8 -28.9 -28.9 -33.8 -42.5 -43.4 -43.4 -42.5 -59.8 -61.8 -60.8 -59.4

-50.2 -50.6


surfaces at different coverages. We see that there is very little adsorbate-adsorbate interaction for coadsorbed H2O on LiH(100) surface and almost no interaction on NaH(100) and KH(100) surfaces, in contrast to the O2 case. This is because the H2O-surface interactions are weak and involve essentially no charge transfer. The smaller size of the LiH lattice parameter is responsible for the larger adsorbate-adsorbate interactions on that surface. The most favorable adsorption energies and geometries for H2O adsorbed on LiH, NaH, and KH surfaces are plotted in Figure 9. The optimized geometries are shown inset. The H2O adsorption energies become more favorable going from LiH to NaH to KH, as was the case for H and H2 adsorption, but opposite to the trend for atomic oxygen adsorption. The geometries of adsorbed H2O on the MH surfaces are shown as insets in Figure 9. Note that in each case the water molecule adsorbs with the O atom bound to a metal atom, one H atom pointing toward a hydrogen bound to the surface, and one H atom pointing away from the surface. This particular geometry is a result of the electrostatic charges on the surface. We have computed charges on each atom of the surface from


Figure 9. H2O adsorption energies on LiH(100), NaH(100), and KH(100) surfaces. The inset pictures are the top and side views of optimized structures of H2O on the surfaces.

Bader charge analysis.61 The metal atoms in the MH surfaces have a positive charge of 0.74 to 0.82 e, depending on the metal. The hydride H atoms carry the corresponding negative charge. Water on the surface of MH has an overall charge of -0.08, -0.14, and -0.18 e, on LiH, NaH, and KH, respectively. Note that the amount of charge transfer correlates well with the binding energies given in Table 6 and Figure 9. The O atoms in water are negatively charged by about -1.3 e and the hydrogens are positively charged by about 0.6 e. Hence, the oxygen in water must be bound to the metal atom in the hydride, while the hydrogens in water are available to hydrogen bond to hydrogens in the hydride. However, geometric constraints will only allow one hydrogen on the water molecule to be in close proximity to a hydride H atom. The other hydrogen on water is forced to be close to a metal atom. The electrostatic repulsion between the water H and the hydride metal result in water orienting such that one H atom is pointing away from the surface. F. Dissociation of H2O on LiH(100), NaH(100), and KH(100) Surfaces. The dissociation pathways for H2O on the LiH, NaH, and KH surfaces have been calculated using the NEB method.59,60 The initial states for the NEB calculations were taken as the most favorable adsorption sites for physisorbed H2O (see Table 6 and Figure 9). The dissociated states, end points for the NEB calculations, were taken from results of DFTMD calculations. We performed DFT-MD calculations at 600 K starting from the optimized H2O on the hydride surfaces. We observed that H2O dissociates within a few tens of ps to form surface hydroxide groups and liberating H2 by abstracting an H atom from the MH surface. Therefore, the final states chosen for the NEB calculations consisted of coadsorbed H2 and OH on the MH surfaces. These end states are consistent with experimental observations.62 The dissociation pathways are shown in Figures 10, 11, and 12 for H2O dissociation on LiH, NaH, and KH, respectively. The calculated reaction barriers with (without) zero-point energy corrections are 23.0 (35.2), 13.8 (19.6), and 18.4 (20.9) kJ/mol, for LiH, NaH, and KH, respectively. The zero-point energy corrections were computed within the harmonic approximation63 with frequencies computed by the finite-difference method. All adsorbed atoms and atoms in the top three surface layers of the solid were included in the finite-difference frequency calculations. These calculated dissociation barriers are very smallsindicating rapid reaction rates at room temperature.

Dai et al.

Figure 10. Dissociation pathway for H2O on the LiH(100) surface.

Figure 11. Dissociation pathway for H2O on the NaH(100) surface.

Figure 12. Dissociation pathway for H2O on the KH(100) surface.

G. Microkinetic Modeling of H2O and the MH Surfaces. We can estimate the initial rates for water dissociation on the MH(100) surfaces by using the zero-point energy corrected dissociation barriers and computed forward and reverse frequency factors to construct a microkinetic model. Our model



Θfree ) 1 - ΘH2O - ΘOH

(8)

where kads denotes the adsorption coefficient for H2O on the surface, ∆EZ the zero-point corrected energy associated with event Z computed from DFT, νZ is the frequency factor for event Z, and β ) 1/kBT, where kB is the Boltzmann constant and T is the absolute temperature. kads is given by

kads )

PH2O

√2πmH OkBT

(9)

2

where PH2O and mH2O are the partial pressure and mass of water, respectively. The frequency factors were computed from20

ν)

Figure 13. Fractional coverage of OH on NaH(100) at 298 K as a function of time when exposed to (a) H2O at saturation (100% relative humidity, PH2O ) 0.0317 bar) and (b) H2O at a concentration of 1 ppm. These curves were computed from the microkinetic model given by eqs 5-8.

describes the following events: adsorption of H2O, dissociation of H2O to form H2 and M-OH, recombination of H2 and M-OH to form H2O and MH, and desorption of H2O and H2 from the MH surface. Note that we assume that H2 does not adsorb from the gas phase to any significant extent. The model can be used to quantitatively describe the poisoning of the MH surface as a function of time, temperature, and partial pressure of H2O in the gas phase. The model is given in eqs 5-8, which describe the rate of change in the fraction of surface sites covered with physisorbed H2O ΘH2O, chemisorbed OH ΘOH, and physisorbed H2 ΘH2:

d(ΘH2O) dt

) Θfreekads - ΘH2OνH2Oe-β∆EH2O ΘH2OνH2Oe-β∆EdesH2O + ΘH2ΘOHνOHe-β∆EOH (5)

d(ΘOH) ) ΘH2OνH2Oe-β∆EH2O - ΘH2ΘOHνOHe-β∆EOH (6) dt d(ΘH2) ) ΘH2OνH2Oe-β∆EH2O - ΘH2ΘHνOHe-β∆EOH dt ΘH2νH2e-β∆EdesH2 (7)

1 βh

∏in [1 - exp(-pβωiIS)] ∏in-1 [1 - exp(-pβωiTS)]

(10)

where h is the Planck constant, p is h/(2π), n is the number of vibrational modes, IS indicates the initial state, TS is the transition state, and we have explicitly indicated that the TS has one less real vibrational mode than the initial state. We have solved this system of equations at 298 K and a total pressure of 1 bar. We have used two different partial pressures of water, namely, saturation humidity (PH2O ) 0.0317 bar) and 1 ppm (10-6 bar). The solution of these equations indicates that for these conditions the MH(100) surfaces are completely transformed to MOH surfaces in times far less than 1 s, even at 1 ppm of H2O. These results are presented for the NaH(100) surface in Figure 13. The results for LiH and KH are essentially identical to those for NaH. The reason for this is that the rate of dissociation is largely controlled by arrival of H2O at the surface of the metal hydride. Hence, differences in dissociation energies play a secondary role and the rate of change of coverage of OH on the surface is, to a very good approximation, independent of the surface. The sum of the evidence from our surface reaction calculations indicates that there is no significant difference in the reactivities of the MH surfaces with respect to poisoning with either O2 or H2O. Nevertheless, thermodynamics may suggest a way to inhibit or mitigate poisoning of MH surfaces. Note that from Table 1 that the reaction

2LiOH + MgH2 ) Mg(OH)2 + 2LiH

(11)

is exothermic by 30 kJ/mol, as computed from the NIST database51 (24.8 kJ/mol from PAW-PW91). Likewise, for similar reactions of NaOH or KOH with MgH2, ∆H ) -54.8 and -57.4 kJ/mol, respectively.51 Hence, mixing MgH2 with any of the alkali MH systems studied in this work may result in sacrificial protection of the MH surfaces by selective reaction of H2O with MgH2. IV. Conclusion We used first-principles density functional theory to study the adsorption and dissociation of H2, O2, and H2O on the surfaces of alkali metal hydrides, MH, where M ) Li, Na, and K. We identified the MH(100) surfaces as having substantially lower surface energies than the other low-index surfaces we examined for all the three metal hydrides. We therefore predict that the MH(100) surface should account for a significant fraction of the exposed surface for the three MH materials. We found that dissociation of H2 on the MH surfaces is energetically unfavorable relative to H2 in the physisorbed state, by about 100 kJ/mol. This indicates that hydrogen will not react with the MH surfaces at any reasonable H2 partial pressure.

18278 J. Phys. Chem. C, Vol. 112, No. 46, 2008 We examined the adsorption of atomic and molecular oxygen on MH surfaces. Both atomic and molecular oxygen strongly bind to these surfaces. The optimized structure shows us that a full monolayer of O on the LiH surface produces a LiOH-like structure on top of the bulk LiH. We found that O2 dissociates without a barrier on LiH and NaH surfaces and binds strongly to the surface of KH as molecular O2. We have not been able to find a dissociation pathway for O2 on the KH(100) surface. However, this is not proof that O2 does not easily dissociate on other surface planes or at defect sites. Water is weakly chemisorbed on the MH surfaces but can readily dissociate due to the small activation barriers. Zeropoint energy corrections are important for H2O dissociation on the MH surfaces, with the largest corrections being for the LiH surface, as expected. Examination of Table 1 shows that MOH formation has a higher heat of reaction than MO2 on a per formula MH basis, suggesting that OH poisoning may be one key factor that inhibits rehydriding. We developed a simple kinetic model to describe the dynamic evolution of the composition of the MH(100) surfaces in the presence of water vapor. Our calculations indicate that water will rapidly react with all three of the MH surfaces to form a monolayer coverage of OH groups while generating gas phase H2. Taken together, our calculations indicate that there are not substantial differences in the MH surfaces toward poisoning with O2 or H2O. Therefore, the observed differences in the reversibility of reaction 2 cannot be described in terms of differences in the reactivities of the MH surfaces. We can speculate on factors that may play a role in the observed differences for hydrogenation of MH + Al to form M3AlH6: (1) Differences in melting points of the MH or MOH phases. KH melts at about 300-400 K lower in temperature than LiH or NaH. Similarly, LiOH has a much higher melting point than KOH or NaOH. (2) Differences in the crystal structures of the various M3AlH6 phases. Li3AlH6 has a trigonal structure, while the Na and K hexahydrides have monoclinic symmetries. (3) Excessively high pressures required for hydrogenation of LiH + Al. Our calculations predict that a pressure greater than 1.7 × 103 bar is required to reverse reaction 2 for LiH at a temperature of 100 °C (see Figure 3). (4) The lattice parameters for LiH and LiOH are such that LiOH will cover the surface of LiH with very little lattice mismatch. In contrast, lattice parameters for the other two alkali metals are quite different for the hydrides and corresponding hydroxides. It may therefore be the case that the LiOH surface perfectly passivates the LiH surface, whereas lattice mismatch for NaH/NaOH and KH/KOH allows H2 and Al to penetrate the MOH surface and react with the underlying MH material. (5) Differences in solubility of the alkali metal in bulk Al may somehow influence the reversibility of reaction 2. Lithium is known to be soluble in Al, whereas Na and K are insoluble. Testing of these hypotheses is beyond the scope of this work. Acknowledgment. This work was supported by the US DOE through the Sandia Metal Hydride Center of Excellence, with grants DE-FC3605GO15066 (Pittsburgh) and DEFC3605GO15064 (Illinois), and by the NSF through a computational grant, DMR06-0017N at NCSA. Calculations were performed at the University of Pittsburgh Center for Molecular and Materials Simulations. References and Notes (1) Choudhary, T. V.; Sivadinarayana, C.; Goodman, D. W. Chem. Eng. J. 2003, 93, 69. (2) Kruse, A.; Dinjus, E. Angew. Chem., Int. Ed. 2003, 42, 909.

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