First-Principles Investigation of Adsorption and Dissociation of

The surface energies of different low-index surfaces of Mg2Si have been examined ... Thermodynamic stability of transition metals on the Mg-terminated...
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J. Phys. Chem. C 2007, 111, 6910-6916

First-Principles Investigation of Adsorption and Dissociation of Hydrogen on Mg2Si Surfaces Bing Dai Department of Chemical Engineering, UniVersity of Pittsburgh, Pittsburgh, PennsylVania 15261

David S. Sholl Department of Chemical Engineering, Carnegie Mellon UniVersity, Pittsburgh, PennsylVania 15213, and National Energy Technology Laboratory, Pittsburgh, PennsylVania 15236

J. Karl Johnson* Department of Chemical Engineering, UniVersity of Pittsburgh, Pittsburgh, PennsylVania 15261, and National Energy Technology Laboratory, Pittsburgh, PennsylVania 15236 ReceiVed: January 19, 2007; In Final Form: March 9, 2007

Silicon can be used to destabilize MgH2 by producing Mg2Si and H2 as products. This process does not appear to be easily reversible. We have used density functional theory to investigate the adsorption and dissociation of H2 on clean and oxidized Mg2Si surfaces as a first step toward understanding the hydrogenation cycle. The surface energies of different low-index surfaces of Mg2Si have been examined and the (1h10) surface has the lowest surface energy of all the surfaces investigated. The energy barriers for hydrogen dissociation on the clean (1h10) surface along two different pathways were found to be 39.8 and 47.2 kJ/mol. Hydrogen dissociation should therefore be facile at room temperature. Oxide formation on Mg2Si(1h10) was calculated to be very exothermic. Our calculations indicate that the equilibrium coverage of oxygen on Mg2Si is 1.75 monolayer down to very low partial pressures of oxygen. Our calculations indicate that hydrogen dissociation is strongly inhibited on the oxide surface.

I. Introduction The lack of safe and efficient hydrogen storage technologies for on-board fuel cell vehicles is widely acknowledged as a key barrier to the use of hydrogen as a transportation fuel.1,2 Metal hydrides have been used for years to store hydrogen, with some hydrides capable of volumetric densities that exceed that of solid H2.3 Hydrides of period 2 and 3 metals can exhibit high gravimetric densities, but most have heats of formation that are far too large, meaning that unacceptably high temperatures are required to release the hydrogen and, just as importantly, the heat management requirements for on-board recharging are prohibitively high. Vajo and co-workers have recently demonstrated that destabilization of metal hydrides through the addition of an element or compound can substantially reduce the heat of formation of the hydride.4 Destabilization of metal hydrides has been further investigated experimentally and through density functional theory (DFT) modeling.5-31 One promising system identified by Vajo et al. involves the destabilization of MgH2 with Si through

2MgH2 + Si h Mg2Si + 2H2

(1)

This reaction scheme has a theoretical hydrogen storage capacity of 5 wt %. If used alone, MgH2 has a theoretical capacity of 7.7 wt % but a low equilibrium vapor pressure at reasonable temperatures. At 300 °C the pressure generated by MgH2 is less than 2 bar. In contrast, Vajo et al. measured a vapor pressure >7.5 bar for reaction 1 at the same temperature.4 The heats of * Address correspondence to this author. E-mail: [email protected].

reaction computed from DFT for MgH2 + Si and for MgH2 are 37.9 and 65.1 (70.6 from experiment) kJ/mol, respectively.22 Hence, the formation of Mg2Si leads to a substantial decrease in the heat of reaction. Unfortunately, reaction 1 is not as readily reversible as would be suggested by the reaction’s thermodynamics.4 The hydrogenation reaction in reaction 1 was not observed in the initial work of Vajo et al., despite experiments performed at temperatures of 150 °C and pressures up to 100 bar of H2.4 Moreover, the addition of 5 atomic % Ti did not induce rehydrogenation of Mg2Si under these conditions.4 Subsequently, Janot et al. found that the hydrogenation reaction could be observed by ball milling Mg2Si under a hydrogen atmosphere.32 The reaction kinetics of any scheme involving hydrogen storage in metal hydrides are crucial to the practical applicability of these materials. It is therefore interesting to probe the possible causes for the lack of reversibility of reaction 1. There are several possible reasons for these difficulties. One possible reason is that H2 dissociation on the Mg2Si surface could be kinetically limited. High dissociation barriers for H2 on the Mg(0001) surface are known to exist.33 Dissociation of H2 on Mg is thought to occur at defect sites. It may be that H2 dissociation is not favorable even on defect sites of Mg2Si surfaces. Another possible reason for the lack of reversibility of reaction 1 is that oxide formation on Mg2Si surfaces inhibits H2 dissociation. It is also possible that mass transport required to form separate MgH2 and Si phases might be kinetically limiting. The purpose of this paper is to investigate H2 dissociation kinetics on the clean and oxidized Mg2Si surfaces. Our goal is to assess the possibility that dissociation kinetics or oxide

10.1021/jp070469h CCC: $37.00 © 2007 American Chemical Society Published on Web 04/19/2007

Adsorption and Dissociation of H2 on Mg2Si Surfaces formation could limit hydrogenation of Mg2Si. Our calculations indicate that H2 dissociation on the clean Mg2Si surface is not kinetically limited. However, we compute that surface oxidation is energetically very favorable up to a surface coverage of 1.75 monolayer of oxygen, even at very low oxygen partial pressures. Our calculations further show that hydrogen dissociation is inhibited on the oxygen-covered Mg2Si surface. II. Computational Methods Plane wave DFT calculations with the PW91 generalized gradient approximation (GGA) functional34 were performed with the Vienna Ab initio Simulation Package (VASP).35,36 Ionic cores were described by ultrasoft pseudopotentials (USPP).37 Selected calculations were performed with both the PerdewBurke-Ernzerhof functional (PBE)38,39 and projector augmentedwave (PAW) potentials.40,41 These two approaches gave essentially the same results. All results presented below used USPP and PW91. Cutoff energies for the plane-wave expansion were set to be 250 and 495 eV for energy calculations for clean surface hydrogenation and oxidation processes, respectively. These energies are sufficiently high to give well-converged structures and total energies. The energies of the clean surfaces using these two cutoff energies are essentially the same. We used a periodic five-layer (9.1 Å thick) slab with adatoms adsorbed on one side of the slab. Most calculations used a 2 × 2 surface unit cell. Calculations for oxygen coverages of e2/3 ML (monolayer) used a 1 × 1 surface unit cell. Brillouin-zone integrations employed a 4 × 6 × 1 Monkhorst-Pack grid of k-points for all the supercells. Test calculations with seven layers gave results very similar to those computed with five layers. The slab was separated from its periodic image in the direction normal to the surface by a vacuum space of more than 15 Å. Slab calculations allowed from two to three surface layers to relax, holding the bottom three or two layers fixed in their optimized bulk positions. The optimized bulk Mg2Si lattice constant was calculated to be 6.35 Å, in good agreement with the experimental value of 6.39 Å.42 The positions of all unconstrained atoms were relaxed until the forces on each of the atoms were smaller than 10-2 eV/Å. The bond length and bond energy of molecular hydrogen calculated from our DFT approach are 0.75 Å and 4.30 eV after zero-point energy correction, in good agreement with the experimental values of 0.74 Å43 and 4.52 eV,44 respectively. The calculated zero-point energy, pωH2/2, is 0.27 eV, corresponding to a calculated vibrational frequency of ωH2 ) 4415 cm-1 for the isolated H2 molecule. This is in good agreement with the experimental value of 4395 cm-1.45 The Nudged Elastic Band (NEB) method46,47 was used to investigate the reaction pathways for H2 dissociation on the clean and oxidized surfaces. A smaller set of k-points (2 × 3 × 1) and a lower energy cutoff (200 and 396 eV for clean and oxidized surfaces, respectively) were used for NEB calculations due to their computational expense. When the energy difference between the initial state and transition state on the clean surface was recomputed by using more k-points (4 × 6 × 1) and a higher cutoff energy (250 eV), the activation barrier only differed from our original NEB result by ∼3 kJ/mol. III. Results and Discussion A. Surface Energies for Mg2Si Surfaces. We have calculated the surface energies of several low-index surfaces of Mg2Si to identify surfaces that would be likely to exist in practical experiments. The surface energy is defined as48-50

J. Phys. Chem. C, Vol. 111, No. 18, 2007 6911

Esurface )

bulk ) (Eslab - NMg2SiEMg 2Si

2A

(2)

where NMg2Si is the number of Mg2Si units in the slab supercell, bulk Eslab is the calculated total energy of the slab, EMg is the 2Si calculated total energy per Mg2Si unit in the bulk, and A is the surface area. 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-points. The surface energy computed from eq 2 is actually an average of two complementary surface terminations, which in general are not identical. Slabs 14.6, 11.0, and 9.1 Å thick were used for Mg2Si(111), Mg2Si(110), and Mg2Si(1h10), respectively. Surface layers on both sides of the slab were allowed to relax. The middle sections of each of the slabs were held fixed. The thickness of these slabs was 3.3, 3.1, and 2.3 Å, respectively. The calculated surface energies of Mg2Si(111), Mg2Si(110), and Mg2Si(1h10) are 2.59, 1.55, and 0.85 J/m 2, respectively. The complementary surfaces for Mg2Si(1h10) are identical, so the surface energy in this case is unambiguous. The other two surfaces each have one Mg-rich and one Si-rich complementary surface. Only surface terminations parallel to the surface plane were considered in our calculations, so we did not examine the possibility of redistributing atoms between the two surfaces as a means for lowering the average surface energy. We did not perform calculations for other low-index surfaces because the densities of surface atoms in the other candidate surfaces we examined were much lower than those considered above. Mg2Si(1h10) has a substantially lower energy than the other two surfaces calculated and therefore we used this surface for all subsequent calculations in this paper. B. Atomic and Molecular Hydrogen Adsorption on the Clean Mg2Si(1h10) Surface. The possible adsorption sites we examined for atomic and molecular hydrogen on clean Mg2Si(1h10) are shown in Figure 1. We also performed calculations in which we placed hydrogen atoms between the first and second layers of the Mg2Si(1h10) slab. The adsorption energies for atomic and molecular hydrogen are defined as

Eads ) Esurface+H - (Esurface - 1/2EH2)

(3)

Eads ) Esurface+H2 - (Esurface - EH2)

(4)

and

where Eads is the adsorption energy, EH2 is the total energy of H2 in the gas phase, Esurface is the total energy of the Mg2Si slab without adsorbed species, and Esurface+H and Esurface+H2 are the total energies of systems with adsorbed H and H2, respectively. 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 correction in these results. The adsorption energies of H atoms in each of the adsorption sites we considered on Mg2Si(1h10) are summarized in Table 1. Only adsorption site A (see Figure 1) is energetically favorable for H adsorption relative to gas phase H2. The adsorption energy for this site is -43.2 kJ/mol. Atoms placed initially on some sites spontaneously migrated to other sites upon optimization. No favorable binding sites (relative to H2 in the gas phase) were identified for H atoms in the second layersall adsorption energies were positive, as can be seen in Table 1. The existence of energetically unfavorable sites in the bulk of a material relative to the surface does not preclude interstitial H diffusion.51,52 However, the lack of strong binding sites for H within

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Figure 1. The top view of a 2 × 2 surface unit cell of Mg2Si(1h10). Letters indicate possible adsorption sites for atomic and molecular hydrogen on the surface.

TABLE 1: The Adsorption Energies, in kJ/mol, for H Atoms on the First and Second Layer and H2 Molecules on the First Layer of Mg2Si(1h10)a sites A-G H (1st layer) H (2nd layer) H2 (1st layer)

A

B

C

D

E

-43.2 c -3.4

13.7 34.2 -2.5

112.6 d -1.4

b 67.2 -3.2

c e

F

G

d

115.5 109.1 -2.5

a

See Figure 1 for a definition of the sites. b Converged to site C on the first layer. c Converged to site A on the first layer. d Converged to site B on the first layer. e Converged to site D on the first layer.

bulk Mg2Si may indicate that hydrogenation must take place at the surface and may not occur within the bulk. Experimental evidence supports the hypothesis that hydrogenation of the bulk Mg2Si is not favorable.53 Clemens reported experiments with multilayered structures of Pd, Mg2Si, and Mg in various configurations. One experiment consisted of a 25 nm Pd cap layer on top of a 100 nm Mg2Si layer, followed by a pure Mg layer, 200 nm thick. Exposure of the system to H2 gas resulted in hydrogenation of the pure Mg phase, but there was no evidence for hydrogenation of the Mg2Si layer, as measured by X-ray diffraction (XRD).53 This experiment clearly demonstrates that H atoms can diffuse through Mg2Si and that hydrogenation of bulk Mg2Si by diffusing atomic hydrogen does not occur to an appreciable extent. Note that the Pd cap eliminates any free Mg2Si surfaces. Table 1 also lists the calculated adsorption energies for H2 molecules on the surface. The molecules are weakly bound on all the sites. The two most favorable sites (site A and site D) were later used as initial configurations to study the dissociation of H2 on the Mg2Si(1h10) surface. It is well-known that DFT cannot give reliable energies for weakly bound systems.54-57 Therefore, the absolute energies for these physisorbed molecules are not likely to be accurate. This is not a severe difficulty for our purposes, since a change in these physisorption energies will not have a large effect on the quantity of interest to us, namely the dissociation barrier. For example, an error in the H2 binding energy of a factor of 2 would change the dissociation barrier by less than 5 kJ/mol. We also examined coadsorption of two H atoms to identify final states for H2 dissociation. Table 2 lists the adsorption energies for these coadsorption calculations. The initial and final sites identified in Table 2 indicate the initial placement of the H atoms and their final location after optimization. During the

Figure 2. The lowest energy dissociation pathway for H2 on the Mg2Si(1h10) surface and the optimized structures of the physisorbed state, the transition state, and the coadsorbed state.

optimization, the two surface layers close to H atoms are relaxed as well. Four different initial geometries converged to the same final configuration, AB, which is the most favorable configuration, having an adsorption energy of -66.0 kJ/mol. This configuration was used as the end point in the H2 dissociation study. Note that the sum of binding energies for H atoms on sites A and B from Table 1 is -29.5 kJ/mol, which is considerably less than the -66.0 kJ/mol value obtained for coadsorption on AB. The distance between the two H atoms in the AB state is 3.86 Å. The reason for the enhanced binding appears to be due to cooperative effects and can be understood by frontier orbital theory.58,59 The adsorption of an H atom at site A changes the frontier orbitals of the clean surface. The contour of the highest occupied molecular orbital is given in Figure S1 in the Supporting Information. The frontier orbitals indicate that a second H atom adsorbing on sites A′ or A′′ will have some antibonding character, while a second H on site B will only involve bonding orbitals. Thus, coadsorption on sites AA′ or AA′′ should have a binding energy smaller in magnitude than the sum of the isolated binding energies, while coadsorption on sites AB should exhibit a larger binding energy than the sum of the isolated binding energies. This is exactly what is observed (see Tables 1 and 2). The adsorption energies for configurations AA′ and AA′′ are -57.8 and -64.2 kJ/mol, respectively and are very close to the energy of AB. However, the A-A′ and A-A′′ distances are 6.35 and 4.49 Å, respectively. These distances are too large to be reasonable final configurations for dissociation, although they are presumably accessible via surface diffusion following dissociation. We note that coadsorption on sites DD′ and AD led directly to H2 formation upon optimization. C. Dissociation of H2 on Clean Mg2Si(1h 10). We have computed the dissociation pathways for H2 starting from H2 adsorbed at either site A or site D. The pathways and the energy barriers for these two initial states are similar, so we will only discuss the pathway starting from H2 at site D in some detail. The calculated dissociation pathway is plotted in Figure 2. The physisorbed, transition, and coadsorbed states are shown as insets in the figure. The initial physisorbed state is gas-like in that the H-H bond length is calculated to be 0.75 Å, which is

TABLE 2: The Adsorption Energies, in kJ/mol, for Two Coadsorbed H Atoms on the First Layer of Mg2Si(1h10) initial sites final sites Eads

AB AB -66.0

CD BA -66.0

AC AB -66.0

BD BA -66.0

DD′ AA′ -57.8

DD′′ AA -2.6

AD AA -2.6

BB′ BB′ 54.2

BC BC 103.4

AA′′ AA′′ -64.2

Adsorption and Dissociation of H2 on Mg2Si Surfaces

J. Phys. Chem. C, Vol. 111, No. 18, 2007 6913

TABLE 3: Vibrational Frequencies for Si-H and Mg-H Stretching Modes (in cm-1) Van de Walle60 SiH 4 H on Si(111) H on Mg2Si(1h10) (site B) Mg-H-Mg

2180 2080

Eads )

this work 2130 1960 1278/986

the same as the DFT optimized gas-phase bond length. The distance between the H atom and the nearest surface atom is 2.83 Å. In the transition state, the H-H bond length is 1.12 Å and the distance between the two different H atoms and the nearest surface Si atom and Mg atom is 1.94 and 1.83 Å, respectively. The coadsorbed state is the AB configuration from Table 2 and is characterized by an Si-H bond (site B) with a bond length of 1.52 Å, which is slightly longer than the Si-H bond in the SiH4 molecule of 1.49 Å.44 We calculated the stretching frequency for the Si-H bond on the Mg2Si surface to be 1960 cm-1, which is similar to the Si-H stretching frequency for H on the Si(111) surface of 2080 cm-1 computed by van de Walle.60 The Si-H stretch on the Mg2Si surface should be observable in IR spectroscopy. Vibrational frequencies calculated in this work are compared with data from the literature in Table 3. The dissociation energy barrier computed directly from the data in Figure 2 is 46.8 kJ/mol. Zero-point energy corrections, computed within the harmonic approximation,61 reduce this value to 39.8 kJ/mol. The H2 molecule and surface atoms that are allowed to relax during the optimization are used for the finite difference calculations in the zero-point energy calculations. On the basis of the framework of Transition State Theory (TST),33,62,63 the reaction rate per site for H2 dissociation can be expressed as33

r H2 )

2h2rotP

exp(-E*/kBT) 3/2

kBT(2πmkBT)

Π′i 1 - exp(-pωTS i /kBT)

(5)

where rot )7.55 meV33 is the rotational constant for H2, P is the pressure of gaseous H2, T is the absolute temperature, E* is is the the zero-point energy corrected reaction barrier, ωTS i frequency of the eigenmodes at the transition state, and m is the mass of a hydrogen molecule. The estimated reaction rate computed from eq 5 is 3.0 s-1 site-1 at 20 °C and P ) 1 bar. This estimated reaction rate indicates that H2 dissociation on the clean Mg2Si(1h10) surface should be facile at room temperature. The second dissociation pathway, starting with H2 located at site A, proceeds in a similar fashion but with a slightly higher energy barrier of 47.2 kJ/mol, after zero-point energy corrections. Taken together, these two calculations indicate that there are likely to be many pathways for molecular hydrogen dissociation on the clean Mg2Si(1h10) surface. Other surfaces or defect sites may present dissociation pathways that are even lower in energy. We can therefore conclude that dissociation of hydrogen on the clean Mg2Si surface will not cause significant kinetic limitations to the reverse reaction given in reaction 1. D. Oxygen Coverage on the Mg2Si(1h10) Surface. Another possible reason for the observed difficulty in hydrogenating Mg2Si may be that the surfaces of this material are susceptible to oxidation. To investigate this possibility, we have computed the structures and energies for various coverages of oxygen on the Mg2Si(1h10) surface. The adsorption energy is defined as

[Esurface+NO - (Esurface + NOEO2/2)]

(6)

NO

where Eads is the adsorption energy per oxygen atom, EO2 is the total energy of an O2 molecule in the gas phase, Esurface is the total energy of the Mg2Si slab without oxygen atoms, Esurface+NO is the total energy of the oxygen-covered surface, and NO is the number of oxygen atoms on the surface. Note that a single unit cell of the Mg2Si(1h10) surface contains one Si atom and two Mg atoms. We therefore define one monolayer coverage as one adatom per surface atom. Hence, one O atom per unit cell corresponds to an oxygen coverage of 1/3 ML. We optimized O atoms at 1/3 ML coverage starting from a variety of atop, bridge, and hollow adsorption sites and found four distinct minima. The structures and O adsorption energies of these minima are given in Figure S2 in the Supporting Information. Starting configurations for optimization of higher coverage sites (up to 1 ML) were obtained by combining two or three different sites from the 1/3 ML structures. The sites chosen in searching for higher coverage structures included all four stable sites plus configuration 5 from Figure S2. All possible combinations of sites were considered. At submonolayer coverages we examined all possible oxygen adsorption sites on the surface of a 1 × 1 × 5 slab. For 1 ML and higher coverages we considered adsorption on a 2 × 2 × 5 slab to allow for reconstruction of the surface. It is difficult to compute the true ground state structures for high coverages of oxygen because complex reconstructions of the surface involving large supercells may occur. We probed reconstruction of the surface in a limited way by relaxing the surface at a given oxygen coverage, then relaxing the surface with atomic hydrogen adsorbed on various sites to generate new configurations, followed by re-relaxation of the surfaces without the hydrogen atoms. This process gave rise to structures that were ∼0.10 eV/ atom lower in energy than the surfaces obtained by simple relaxation. Starting configurations for optimization of structures with >1 ML coverage were obtained by placing O atoms on selected sites that were favorable for H atom adsorption. There are many different bulk Mg2Si oxide structures.42 Most of the oxides have Mg2SiO4 stoichiometry. The common feature of all these oxide configurations is that the Si atoms are bonded to four O atoms; this is the main structural feature we observe in our optimized 1.75 ML oxide surfaces. We also observed some O atoms bonded to Mg atoms in our optimized oxide surfaces. This is perhaps not surprising given that the surface configuration of complex materials is typically more complicated than that of the bulk structure. We have plotted the adsorption energy per oxygen atom as a function of the coverage in Figure 3. We see that surface oxide formation is extremely exothermic, with 1/3 and 2/3 ML coverage being much less energetically favorable than higher coverages. The adsorption energy per atom is roughly constant for coverages from 1 to 1.75 ML, where values range from -4.43 to -4.48 eV. Increasing the coverage beyond this point, to 1.83 (11/6) ML, gives a slightly reduced binding energy of -4.21 eV. The binding energies defined above can be combined with the chemical potential for oxygen to produce a diagram showing the coverage having the lowest free energy as a function of chemical potential.64,65 The surface energy, γ, is defined as64,65

γ)

1 1 slab bulk E - NMg2SiEMg - NOEO2 + NOµO 2Si 2A 2

[

(

)]

(7)

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Figure 5. The relaxed Mg2Si surface with 1.75 ML of oxygen.

Figure 3. Adsorption energy per oxygen atom on Mg2Si(1h10) as a function of oxygen coverage.

Figure 4. Surface energy for four different oxide coverages of the Mg2Si(1h10) surface as a function of atomic oxygen chemical potential. The O2 partial pressure at 300 K is given on the top axis.

where Eslab is the DFT total energy of the oxide surface slab bulk is the total energy of the bulk Mg2Si on a per model, EMg 2Si Mg2Si unit basis, NMg2Si is the number of Mg2Si units in the slab supercell, EO2 is the total energy of a gas-phase oxygen molecule, NO is the number of oxygen atoms on the surface, and µO is the chemical potential of oxygen. Note that eq 7 reduces to eq 2 in the limit of NO ) 0 and that this energy is positive. We have plotted the surface energy as a function of the oxygen chemical potential in Figure 4. The O2 partial pressure is also plotted (top axis) in Figure 4. Treating molecular oxygen as an ideal gas, the atomic oxygen chemical potential is related to the O2 partial pressure and temperature by

()

1 p µO(T,p) ) µO(T,po) + kT ln o 2 p

(8)

If we know the temperature dependence of µO(T,po) at a particular pressure,64,65 po, we can get the temperature- and pressure-dependent chemical potential. We see that the 1.75 (7/ 4) ML coverage surface has the lowest free energy over an extremely wide range of partial pressures. The lines for the different coverages are not parallel. Although not explicitly shown in Figure 4, at extremely low partial pressures of O2 the

5/3 ML coverage surface will have a lower free energy than 7/4 ML. Likewise, at pressures higher than 105 bar O2 the 11/6 ML coverage will be lower in free energy. We note that this diagram does not include all possible realizations of oxygen on the Mg2Si surface; there may be other configurations with even lower free energy. However, our calculations clearly show that a high coverage of oxygensmore than 1 MLsis energetically very stable relative to the clean Mg2Si(1h10) surface. E. Hydrogen Dissociation on the Oxidized Mg2Si Surface. We now discuss the dissociation pathways and barrier heights for H2 dissociation on the Mg2Si(1h10) surface with two different coverages of oxygen. The Mg2Si(1h10) surface with 1.75 ML of oxygen, calculated to have the lowest energy of all the oxide structures we examined, is shown in Figure 5. It is apparent that all the Si and Mg atoms on the surface are bonded to O atoms in this structure. As a result, there are no accessible Mg or Si sites for H atom adsorption. We therefore first studied dissociation on Mg2Si(1h10) with 2/3 ML of oxygen coverage. This low coverage of oxygen is not likely to be observed according to our free energy calculations, but we performed the calculations to assess the effect of a limited amount of oxygen coverage on H2 dissociation. The most favorable adsorption site for atomic H on the 2/3 ML oxide surface is the same as that on the clean surface, namely a Mg-Mg bridge site. The adsorption energy for this site is -86.8 kJ/mol, which is larger than the energy for a H atom at that site on the clean surface. Examining this situation using Bader charge analysis,66 we found that the average charge change on the two Mg atoms bonded with a H atom before and after atomic H adsorption is -0.502e and -0.123e for 2/3 ML oxide and the clean surface, respectively. That is, there is more electron transfer from Mg atoms to the H atom on the 2/3 ML oxide surface, which makes the Mg-H-Mg bonds on the oxide surface stronger than those on the clean surface. As is the case for the clean surface, H2 molecules are weakly physisorbed on the oxide surface. We have computed the dissociation pathway for H2 on the 2/3 ML O-covered surface in a similar way to the clean surface. The dissociation pathway is shown in Figure 6. Also shown in this figure are the initial, transition, and final states. The adsorption sites for these three states are roughly the same as those for the clean surface. Thus, the reaction barrier height is 92 kJ/mol, which decreases to 80 kJ/mol after zero point energy corrections are applied. The dissociation barrier is about twice as large on the 2/3 ML surface compared with the clean surface, even though the binding sites on the oxide surface are quite similar to those observed for the clean surface. We next examine whether dissociation of H2 is possible on the 1.75 ML oxide surface. We have examined a range of different binding sites for both H2 and H atoms on this surface.

Adsorption and Dissociation of H2 on Mg2Si Surfaces

Figure 6. A dissociation pathway for H2 on the Mg2Si(1h10) surface with a coverage of 2/3 ML of oxygen.

Figure 7. A dissociation pathway for H2 on the Mg2Si(1h10) surface with a coverage of 1.75 ML of oxygen.

Only site A in Figure 5 is favorable for adsorption of atomic H relative to gas-phase H2. The adsorption energy for this site is -67.1 kJ/mol and the H atom is bound to a surface oxygen to form a surface hydroxyl group. The adsorption energy is 10.3 kJ/mol when an H atom adsorbs on site B, which is the second most energetically favorable adsorption site for an H atom. The binding energy for co-adsorption of two H atoms on sites A and B is -64.5 kJ/mol, indicating that dissociation of H2 is energetically favorable on the surface. The dissociation pathway has been computed as for the previous examples and is plotted in Figure 7. We note that dissociation of H2 on the 1.75 ML oxide surface displays two peaks. A small barrier with a height of about 52 kJ/mol (without zero-point corrections) appears first, followed by a much larger barrier, having a height of about 177 kJ/mol above the starting configuration (without zero-point corrections). The computed pathway indicates that the dissociation process on the 1.75 ML oxide surface is more complicated than on the clean surface and on the 2/3 ML oxide surface. We have calculated the vibrational frequencies for the configuration in image 5 and have found two imaginary frequencies, indicating that image 5 is not a true transition state, although there may be a transition state near this structure. Regardless of the details of this state, the overall process is dominated by the large barrier associated with image 8, which is a true transition state (one imaginary frequency). This transition state corresponds to the

J. Phys. Chem. C, Vol. 111, No. 18, 2007 6915 formation of a surface hydroxyl group. The large barrier is due to the energy required for surface rearrangement, namely the translation of a surface O atom and rotation of a SiO4 group. The end state corresponds to two H atoms coadsorbed on the oxide surface as surface hydroxyl groups. The very high activation energy required to dissociate H2 on the 1.75 ML oxygen covered Mg2Si(1h10) surface indicates that hydrogenation of the surface is highly unlikely to occur at low to moderate temperatures. The estimated reaction rate computed from TST by using eq 5 is about 1.3 × 10-24 s-1 site-1 at 20 °C. This is an extremely slow rate. Moreover, dissociation of H2 results in the formation of surface hydroxyl groups rather than Mg-H bonds. The Mg-OH and Si-OH surface structures do not appear to be compatible with formation of bulk MgH2. We therefore conclude that the very strong propensity for the Mg2Si surface to form an oxide overlayer creates a strong kinetic limitation for the overall hydrogenation pathway. According to the estimated reaction rates with TST, we can conclude that H2 dissociation is facile on the clean Mg2Si surface and effectively prohibited by oxide overlayer formation on the surface under experimental conditions. Our calculations are consistent with the experimental observation by Vajo et al. that Mg2Si cannot be hydrogenated at temperatures of 150 °C and pressures up to 100 bar of H24 and also with the experiments of Janot and co-workers,32 who showed that ball milling under hydrogen pressure was required to achieve hydrogenation of Mg2Si. IV. Conclusion We have used first-principles density functional theory to study the adsorption and dissociation of hydrogen on clean and oxidized Mg2Si surfaces. We have identified Mg2Si(1h10) as the surface with the lowest surface energy among the low-index surfaces we examined. The next most favorable surface has a surface energy that is roughly twice as large as that for the (1h10) surface. We therefore predict that this surface is likely to be observed experimentally. We have studied adsorption of H2 and H on the clean Mg2Si(1h10) surface and have identified several energetically favorable binding sites. H2 adsorbs molecularly and is weakly bound on this surface. Atomic hydrogen adsorbs strongly, having a zero-coverage binding energy of -43.2 kJ/mol. Two different dissociation pathways for H2 on the clean Mg2Si(1h10) surface have been computed. The dissociation pathways have barrier heights of 39.8 and 47.2 kJ/mol after zero-point energy corrections have been applied. The estimated reaction rate with TST is about 3.0 s-1 site-1 at 20 °C and an H2 partial pressure of 1 bar. This indicates that dissociation of H2 on the clean Mg2Si surface should be facile at room temperature. We have studied the adsorption of oxygen on the clean Mg2Si(1h10) and have found that surface oxide formation is highly exothermic relative to the clean surface and O2 in the gas phase. We predict that an oxygen coverage of 1.75 ML should be favored at room temperature over a wide range of O2 partial pressures. This means that it will be very unlikely to observe a clean Mg2Si in practice unless some kind of surface treatment (ball milling in a H2 atmosphere, for example) is used. Dissociation of H2 on the 1.75 ML oxygen covered surface is predicted to be kinetically limited, with an estimated barrier height of about 177 kJ/mol and a corresponding reaction rate that is essentially negligible. These results from our calculations are in accord with experimental results indicating that it is difficult to hydrogenate Mg2Si.4,32 Finally, we note that our calculations do not prove that oxide formation is the only reason that hydrogenation of Mg2Si is

6916 J. Phys. Chem. C, Vol. 111, No. 18, 2007 difficult. Our calculations clearly indicate that the clean Mg2Si(1h10) surface will readily hydrogenate; however, we cannot address the issue of the formation of a bulk MgH2 phase starting from the hydrogenated Mg2Si surface. Kinetic or transport issues associated with forming MgH2 and Si phases may still be problematic, even in the absence of oxygen. The experiments reported by Clemens53 support this view, as discussed above. The Pd/Mg2Si interface is believed to be oxygen free, yet no hydrogenation of Mg2Si was observed. Note, however, that no free Mg2Si surfaces existed in these multilayer experiments. The experiments of Janot et al., who show that hydrogenation of Mg2Si does take place when ball milled in a hydrogen atmosphere,32 support our claim that hydrogenation of the surface is indeed possible. Acknowledgment. We thank John Vajo, Greg Olson, and Bruce Clemens for many helpful discussions. This work was supported by the U.S. DOE, grant number DE-FC36-05GO15066, and performed in conjunction with the DOE Metal Hydride Center of Excellence. Calculations were performed at the University of Pittsburgh Center for Molecular and Materials Simulations. Supporting Information Available: The contours of the highest occupied molecular orbitals of the clean and hydrogenated Mg2Si(1h 10) surfaces (Figure S1) and top views of 1/3 ML oxygen coverage on various sites on the Mg2Si(1h10) surface (Figure S2). This material is available free of charge via the Internet at http://pubs.acs.org. 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. (3) Schlapbach, L.; Zu¨ttel, A. Nature 2001, 414, 353. (4) Vajo, J. J.; Mertens, F.; Ahn, C. C.; Bowman, R. C., Jr.; Fultz, B. J. Phys. Chem. B 2004, 108, 13977. (5) Chen, P.; Xiong, Z.; Luo, J.; Lin, J.; Tan, K. Nature 2002, 420, 302. (6) Chen, P.; Xiong, Z.; Luo, J.; Lin, J.; Tan, K. J. Phys. Chem. B 2003, 107, 10967. (7) Luo, W. J. Alloys Compd. 2004, 381, 284-287. (8) Leng, H.; Ichikawa, T.; Hino, S.; Hanada, N.; Isobe, S.; Fujii, H. J. Phys. Chem. B 2004, 108, 8763. (9) Vajo, J. J.; Skeith, S. L.; Meters, F. J. Phys. Chem. B 2005, 109, 3719. (10) Pinkerton, F. E.; Meisner, G. P.; Meyer, M. S.; Balogh, M. P.; Kundrat, M. D. J. Phys. Chem. B 2005, 109, 6-8. (11) Herbst, J. F.; Hector, L. G., Jr. Phys. ReV. B 2005, 72, 125120. (12) Aoki, M.; Miwa, K.; Noritake, T.; Kitahara, G.; Nakamori, Y.; Orimo, S.; Towata, S. Appl. Phys. A: Mater. Sci. Process. 2005, 80, 1409. (13) Nakamori, Y.; Kitahara, G.; Ninomiya, A.; Aoki, M.; Noritake, T.; Towata, S.; Orimo, S. Mater. Trans. 2005, 46, 2093-2097. (14) Ichikawa, T.; Tokoyoda, K.; Leng, H.; Fujii, H. J. Alloys Compd. 2005, 400, 245-248. (15) Ichikawa, T.; Hanada, N.; Isobe, S.; Leng, H.; Fujii, H. Mater. Trans. 2005, 46, 1. (16) Meisner, G. P.; Scullin, M. L.; Balogh, M. P.; Pinkerton, F. E.; Meyer, M. S. J. Phys. Chem. B 2006, 110, 4186. (17) Pinkerton, F. E.; Meyer, M. S.; Meisner, G. P.; Balogh, M. P. J. Phys. Chem. B 2006, 110, 7967. (18) Pinkerton, F. E.; Herbst, J. F. J. Appl. Phys. 2006, 99, 113523-5. (19) Nakamori, Y.; Ninomiya, A.; Kitahara, G.; Aoki, M.; Noritake, T.; Miwa, K.; Kojima, Y.; Orimo, S. J. Power Sources 2006, 155, 447455.

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