Hydrogen Desorption from Ti-Doped MgH2(110) Surfaces: Catalytic

Mar 16, 2012 - ... above the two hollow sites and the two BH (red) start to form H2. ..... E.; Konstanchuk , I.; Stepanov , A.; Boldyrev , V. J. Less-...
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Hydrogen Desorption from Ti-Doped MgH2(110) Surfaces: Catalytic Effect on Reaction Pathways and Kinetic Barriers Lin-Lin Wang*,† and Duane D. Johnson*,†,‡ †

Division of Materials Science and Engineering, Ames Laboratory, USDOE, Ames, IA 50011, United States Department of Materials Science and Engineering, Iowa State University, Ames, Iowa 50011, United States

‡

ABSTRACT: Transition-metal (TM) catalytic dopants are widely used in hydrogen-storage materials to increase hydrogen (H2) desorption and absorption kinetics. Using density functional theory calculations, we elucidate the catalytic effect of Ti substitutional dopant on H2 desorption from MgH2(110) surfaces. Kinetic energy barriers of H2 desorption pathways are calculated via a nudged-elastic-band method. For a Ti-doped surface, we identify a concerted mechanism involving H bulk (vacancy-mediated) diffusion to feed H2 surface desorption, arising from a synchronized diffusion of H atoms around Ti. The kinetic barrier for the Ti-doped surface is reduced by 0.41 eVa 22% drop. We also show that the catalyzed H2 desorption is mediated by a change in hydrogen coordination number of Ti, altering the associated Ti spin state.

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INTRODUCTION Among different types of hydrogen-storage materials, complex light-metal hydrides stand out by having very good volumetric and gravimetric ratios as well as a large range of thermodynamic properties.1 Recent theoretical studies have been successful in examining2 materials in the favorable thermodynamic range of 20−40 kJ/mol H2 and identifying the reaction intermediates.3,4 However, for complex light-metal hydrides, the slow kinetics in H2 desorption and absorption remains the largest obstacle1 for practical mobile application. Experimentally, it is well-known that adding transition-metal (TM) dopants in various forms as catalyst can improve H2 desorption and absorption kinetics.5−12 Yet, the exact mechanism for H2 desorption is still unclear. H2 desorption is a complicated process convoluting surface desorption, bulk diffusion, metal nucleation, and interface migration.13 Experimental data on the apparent activation barrier for H2 desorption from pure MgH2 range from 145 to 323 kJ/mol,12,14−16 a large spread which depends on how the samples were prepared and which model was used for the data analysis. The critical issue is the difficulty for experiment to determine mechanisms. Validated first-principles calculations can help to elucidate the mechanism in terms of the details in atomic processes. In this study, we take a closer look at H2 desorption from the MgH2(110) surface, a prototype lightmetal hydride. We use density functional theory17,18 (DFT) calculation to study the catalytic effect of Ti substitutional impurity on H2 desorption from the MgH2(110) surface. We apply the nudgedelastic-band (NEB) method19 with climbing image to calculate the H2 desorption kinetic barrier. Early DFT studies20,21 have shown that for pure MgH2(110), H2 desorption has a large barrier of 1.78 eV, compared to the barrier of 0.70 eV for H bulk diffusion. Early DFT studies22−24 also showed weakening © 2012 American Chemical Society

of the local metal−H bonds upon TM doping. Here we find that a single Ti substitutional impurity can effectively lower the kinetic energy barrier by 0.41 eV and the catalytic effect of Ti dopant comes from the concerted atomic processes of synchronized bulk H diffusion and H2 surface desorption. Furthermore, we find that the minimum energy pathway for H2 desorption from Ti-doped MgH2(110) surface is mediated by the change in hydrogen coordination number to Ti and the associated change in the spin state. The spin degree of freedom must be fully explored in NEB calculations to avoid local minimum.

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COMPUTATIONAL DETAILS All calculations were performed within spin-polarized DFT based on the PW91 exchange-correlation functional,25 utilizing a plane-wave basis set with the projected augmented wave method,26 as implemented in the Vienna atomic simulation package (VASP).27,28 Bulk MgH2 has a rutile structure (space group P42/mnm or Pearson tP6) and can be viewed as stacking of H−Mg−H trilayer (TL) units in the ⟨110⟩ direction (see Figure 1). The TL unit consists of H−Mg−H coplanar subunits with alternating 0° and 90° orientation, in which one chain of Mg is sandwiched between two chains of H. In total, each H is coordinated by three Mg and each Mg is coordinated by six H atoms; i.e., it has a hydrogen coordination number (HCN) of 6. The bulk lattice parameters for MgH2 calculated in DFT-PW91 with a 400 eV kinetic energy cutoff and an 8 × 8 × 12 k-point mesh are in very good agreement with experiment29 (see Table 1). Received: January 24, 2012 Revised: March 13, 2012 Published: March 16, 2012 7874

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calculate total energies, relax ionic structures, and optimize the NEB images. Total energies were converged below 2 meV/ atom with respect to the sizes of k-point mesh and vacuum spacing. For ionic relaxation, the absolute magnitude of force on each atom was reduced below 0.02 eV/Å via conjugate gradient method. In order to find the lowest-energy structure with Ti dopant, we use high-temperature molecular dynamics with steepest-descent annealing to explore efficiently different reconstructed configurations, with protocols and details provided in ref 30. For the NEB calculation, we used a spring constant of 5 eV/ Å2, 11 images, and the quick-min algorithm (as implemented by Henkelman et al.31) to find the minimum energy pathway (MEP). We found that a few hundred NEB steps are needed to converge the absolute magnitude of force on each atom below 0.05 eV/Å, giving a converged energy barrier. Separate calculation with a higher criterion of 0.02 eV/Å gives an energy barrier within 0.01 eV.

Figure 1. Bulk-terminated rutile MgH2(110) surface structure modeled with three TLs in the ⟨110⟩ direction. The surface supercell is (2 × 4) in terms of ⟨110⟩ and ⟨001⟩. Large green (small gray) spheres stand for Mg (H). The bulk rutile unit cell is shown by dashed lines.

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RESULTS AND DISCUSSION Ti Dopant Site Preference and Properties. Our study has focused on Ti as the catalytic dopant, which is one of the main impurities added to enhance H2 desorption. To study the catalytic effect on H2 desorption, we use a single Ti impurity substituting one Mg in the favored position at/near the MgH2(110) surface. Figure 2a shows the relaxed atomic structure of a pure MgH2(110) surface in both top and side views. MgH2(110) exposes alternating rows of H that are doubly bonded and stick out of the surface (sitting on bridge sites of Mg rows). The triply-bonded H stay inside the first (top surface) TL. Examples of bridging H (labeled BH) and inplane H (labeled PH) in the first TL are highlighted in Figure 2a. Also highlighted are the four Mg sites in the first and second TL, i.e., the BM, PM, SBM, and SPM. Upon relaxation, the row of BH and the Mg underneath (BM) move slightly outward (pointing to the exterior of the slab), and PH and the associated PM relax slightly inward (pointing to the interior of the slab).

Table 1. Lattice Constant (a), c/a, Internal Parameter (x), and (110) Surface Energy γ(110) for Rutile MgH2a expt. DFT-PW91 a

a (Å)

c/a

x

γ(110) (J/m2)

4.50 4.51

0.669 0.668

0.304 0.306

− 0.34

Experimental data is from ref 29.

MgH2(110) has the lowest surface energy by only breaking the Mg−H bonds between neighboring TLs. We found that the (110) surface energy is converged to 0.34 J/m2 for a symmetric slab of six TLs. To model a MgH2(110) surface for H2 desorption, we used an asymmetric slab consisting of three TLs, i.e., nine atomic layers (see Figure 1), and a 15 Å vacuum with the bottom-most TL fixed in bulk-terminated position and the top two TLs allowed to relax. The (2 × 4) surface supercell (see Figure 1) with a total of 144 atoms is large enough to consider various H2 desorption pathways around the Ti dopant. The Γ-point with a Gaussian smearing of 0.1 eV was used to

Figure 2. Structures of MgH2(110) surface (a) without a Ti dopant and (b), (c), and (d) with a Ti dopant (large red sphere). In each panel, the top (bottom) subfigure is for top (side) view of the focused regions of the surfaces. Large green (small gray) spheres stand for Mg (H). In (a), two bridge H (one in-plane H) in the first TL are labeled as BH (PH) and highlighted in red (blue), the Mg site bonded to BH (PH) in the first TL is labeled as BM (PM), and the Mg site bonded to BH (PH) in the second TL is labeled as SBM (SPM). In (b), (c), and (d), the highlighted H atoms are the same atoms in (a), and, in addition, one PH from the second TL is also highlighted in blue. The reconstructed structures in (c) and (d) have a total spin of S = 1 and 0, respectively. 7875

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distorting MgH2 rutile structure, and the change in total energy is small. Although parts c and d of Figure 2 are almost degenerate in energy, we show below that they have very different activation processes in H2 desorption due to the different bonding configurations and spin states for the Ti−H complex. We have also tried high-temperature thermal annealing when Ti is in the second TL but could not find reconstructed structures with lower energies than the structure in Figure 2b. In order for Ti to have a higher HCN than Mg to lower energy, the structure around the Ti dopant has to be distorted significantly from the rutile structure, but such large distortion always incurs a large energy cost. The open space on the top surface TL allows structural rearrangement with relatively lower energy cost than the second TL in bulk environment. Activation Processes for H2 Desorption. To study the activation process and associated kinetic barrier in H 2 desorption from Ti-doped MgH2(110), we performed NEB calculations using 11 images, with linear interpolation of positions between initial and final configurations as input. To validate our NEB calculations, we first carried out a calculation for H2 desorption from the pure MgH2(110) with the BH−PH combination. We find a kinetic energy barrier of 1.83 eV in agreement with an earlier DFT calculation20 of 1.78 eV, differing mostly due to the exchange-correlation functional used. Figure 4 shows the H2 desorption reaction pathway for the structure in Figure 2c with Ti having a HCN of 7 and S = 1. In

To find the most preferred dopant site for Ti, we considered all four Mg sites in the first and second TL (Figure 2a). Upon relaxation, Ti stays in the registry site and has a total spin (S) of 1 (or a magnetic moment of 2 μB) in all four configurations. We find that the preferred Ti substitution is at a BM site with a HCN of 6 in the first TL. As shown in Figure 2b, unlike Mg, Ti on a BM site has a significant inward relaxation. The next preferred sites are the two Mg sites in the second TL, SPM and SBM, also with an HCN of 6, being 0.20 and 0.26 eV higher than BM, respectively. With an HCN of 5, the PM site is least preferred, being 0.49 eV higher than the BM site. The open d orbitals of TM are known to bind with multiple H.32,33 A DFT study22 has shown that Nb can cause significant reconstruction when it substitutes Mg in bulk MgH2. Using high-temperature molecular dynamics with steepest-descent annealing, we find two low-energy structures, as shown in Figure 2c and d, which are 0.03 and 0.02 eV lower than the assubstituted structure in Figure 2b, respectively. Although the decrease in total energy is not large, the bonding configurations for Ti have changed significantly. Compared to Figure 2b, where Ti has a HCN of 6 and S = 1, the Ti dopant in the Figure 2c structure has a HCN of 7 and S = 1, and Ti in Figure 2d structure has a HCN of 8 and S = 0. As shown in Figure 2c, bottom panel, Ti moved inward significantly to make an additional bond with a PH (blue) in the second TL. As indicated by the Mg−Mg bonds drawn across Mg rows in the top panel of Figure 2c, the two neighboring rows of Mg in the first TL move toward Ti and form a local two-dimensional quasi-hexagonal structure. The two BH (red) tilt away from the ideal bridge sites to the threefold hollow sites of the quasi-hexagonal structure. The PH (blue) in the first TL moves inward and sits in the neighboring threefold hollow site on the opposite side of the quasihexagonal structure. (Even though the rutile (110) registry sites have been lost due to the large distortion near Ti, we still refer them as BH and PH because, as will be clear later, upon H2 desorption the two BH will come back to the bridging positions of Ti−Mg in the desorption process.) In comparison, Ti in Figure 2d has the highest HCN of 8 and S = 0 resulting from the additional bonding to the PH in the second TL on the right side. The projected densities of state on Ti 3d orbitals for the three structures in Figure 2 are plotted in Figure 3. It clearly shows that as the HCN increases, the Ti 3d-derived bands are broadened gradually and shifted to lower energy. Particularly, when HCN increases to 8 with S = 0, a t2g-derived band shifts below the Fermi level. The stabilization of Ti is at the cost of

Figure 4. H2 desorption pathway for the structure in Figure 2c with S = 1. The structures of the initial, intermediate, and final states (NEB image 3, 6, and 8 indicated by arrows) are shown in the top panel. The color and size of spheres are the same as in Figure 2.

the top panel of Figure 4, the initial (final) configuration is shown in the leftmost (rightmost) frame together with three other images from the NEB calculation, indicated by arrows. The bottom panel plots the energy change along the reaction pathway. Clearly, there are two activation steps in the reaction pathway. First, there is an outward motion of the PH (blue) in the first TL pushing the two PHs (red) up and away from the Ti, shown by image 3. Second, shown by image 6, there is the diffusion of the PH (blue) in the second TL toward the surface, and simultaneously, Ti makes an additional bond to PH in the second TL on the right side. The latter structural change has the highest energy that gives the activation barrier of 1.84 eV.

Figure 3. Projected density of state on Ti 3d orbitals for the Ti-doped structures in Figures 2b (black), 2c (red), and 2d (blue). The HCN and S are labeled accordingly. 7876

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The process completes, in and after image 8, by having the PH (blue) originated from the second TL further diffusing to the surface and finally H2 desorbing from the surface. During the whole reaction pathway, the S remains to be 1. For the overall reaction pathway, the HCN of Ti changes from 7 to 6 (due to the loss of two BH and the addition of an extra bond to PH in the second TL on the right side). However, the overall activation energy of 1.84 eV for H2 desorption is not lower than that of 1.83 eV for pure MgH2(110). In the final configuration, the Ti makes an additional bond with PH in the second TL on the right, which shows that a higher HCN may help to lower the energy of the system. For the structure in Figure 2d, which is almost degenerated with Figure 2c, Ti has a higher HCN of 8 and S = 0 and the H2 desorption reaction pathway (Figure 5) is significantly different

Importantly, then, in the state-of-the-art NEB calculation (default settings), the spin (magnetic) degrees of freedom are not fully explored for each image. Ideally, all possible spin states should be explicitly iterated for each image in each NEB step. For the current study, we find that a quick fix works well. For a second-round NEB calculation, we intermix the images 1−7 from the reaction pathway in Figure 5 and images 8−11 from that in Figure 4. The results are shown in Figure 6. Because the

Figure 6. H2 desorption pathway for the structure in Figure 2d with S changing from 0 to 1. The structures of initial, final, and other intermediate states (NEB image 3, 5, and 7 indicated by arrows) are shown in the top panel. The color and size of spheres are the same as in Figure 2. The NEB pathway from Figure 4 (Figure 5) is included as dashed (dotted) line for comparison. The square (circle) stands for the state with S = 1 (0). Figure 5. H2 desorption pathway for the structure in Figure 2d with S = 0. The structures of the initial, final, and other intermediate states (NEB image 3, 5, and 7, indicated by arrows) are shown in the top panel. The color and size of spheres are the same as in Figure 2.

images are already very close to the final structures, S associated with each image does not change. (Note, to iterate the spin states explicitly for each NEB image in each NEB step would require a rewrite and testing of the current algorithm, which is beyond the scope of the present paper.) As shown in Figure 6, before image 7, during the synchronized diffusion of the two PH (blue) of the first and second TL, the HCN of Ti remains to be 8. The high HCN gives S = 0. This has a much smaller activation energy than the scenario, in which the diffusion of the PH in the first TL is followed by the diffusion of the PH in the second TL with S = 1 (red dashed line). After reaching the transition state (image 7) with S = 0, the system prefers to have a higher S = 1 with a lowered HCN for Ti due to desorption of the H2 formed by the two BH (red). The overall activation barrier now drops to 1.42 eV. The decrease of the H2 desorption barrier by 0.41 eV (a 22% reduction) due to a single Ti dopant (2 atom % Ti) agrees with a recent experiment,12 where a decrease of ∼44 kJ/mol (or 0.46 eV, an 18% reduction) was reported for ball-milled MgH2 mixed with 1 atom % Ti. The authors noted that their H2 desorption barrier of 249 kJ/mol (2.58 eV) for pure MgH2 was high among the reported data due to the use of low-energy ball milling. Comparing the initial and final states, the two BH (red) on the hollow sites in the initial state are exactly replaced by the two PH (blue) from the first and second TL. Thus, there is a natural bulk diffusion to replenish the surface H to restart this desorption process again. That is, the diffusion of the two PH leaves two H vacancies behind that are filled quickly by bulk H

from that in Figure 4 for Ti with HCN of 6 and S = 1. The reaction pathway (lower Figure 5) also consists of two activated steps. First, as in image 3, there is a synchronized motion of the PH (blue) in the first and second TL, which has a very small (0.02 eV) activation barrier for such coordinated motion. Second, these two synchronized PH (blue), as they further diffuse toward the surface, push away the two BH (red). In image 5, the two PH (blue) are right under the two hollow sites of the quasi-hexagonal structure and two BH (red) are pushed back to the bridge sites. Then, in image 7, the two PH (blue) diffuse above the two hollow sites and the two BH (red) start to form H2. Finally, the H2 detaches from the surface, as shown in image 11. Overall, the transition-state configuration (image 7) has the highest energy and yields an activation barrier of 1.46 eV, a significant reduction from that in Figure 4 for the structure in Figure 2c. The overall change of HCN for Ti is from 8 to 6 and S remains as 0. The final state in Figure 5 has almost the same bonding configuration as that in Figure 4. But with S = 0, it is 0.5 eV higher in energy than the final state with S = 1. With a smaller HCN, Ti prefers to stay in a higher spin state. Clearly, our results indicate that the overall barrier should be even lower by switching S from 0 to 2 somewhere along the reaction pathway, which can be spontaneous because there is no magnetization sum-rule constraining such transitions.34 7877

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diffusion, controlled by an activation barrier of 0.70 eV, and then H2 desorption (with a reaction pathway detailed in Figure 6) resumes. Thus, the Ti dopant on the surface acts as a catalytic center for H2 desorption, i.e., a sink for bulk H diffusion and a source for H vacancy.

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CONCLUSION Using density functional theory methods in concert with nudged-elastic-band (NEB) calculations, we find that a single Ti substitutional dopant reduces the activation barrier for H2 desorption on MgH2(110) by 0.41 eV (from 1.83 to 1.42 eV). Indeed, the Ti catalytic dopant effect on H2 desorption is wellknown experimentally, but here we provided a detailed understanding of the mechanism(s) for activation barrier reduction and desorption. For the surface H2 desorption, we identified a cooperative mechanism involving synchronized diffusion of two H atoms around Ti and bulk diffusion into the H vacancy sites (controlled by the bulk diffusion barrier of 0.70 eV) that replenish the surface H to restart the desorption process once again (controlled by Ti-reduced barrier of 1.42 eV). The “catalytic effect” of the Ti dopant stems from the concerted motion of bulk H diffusion and H2 desorption, in which a hydrogen coordination number (HCN) of 8 is preferred by Ti with a total spin of 0 in the early H diffusion steps and, thereafter the H2 detachment, involves Ti with a total spin of 1 and a reduced HCN of 6. Importantly, to include such crossover of spin states along a reaction (minimum-energy) pathway in a NEB calculation, a careful consideration of the spin degree of freedom is needed to avoid local minimum.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected] (L.-L.W.); [email protected] (D.D.J.). Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS D.D.J. acknowledges supported by the U.S. Department of Energy, Office of Basic Energy Sciences under contracts DEFG02-03ER15476 (Chemical Sciences) and DE-AC0207CH11358 (Complex Hydrides) at the Ames Laboratory operated for the U.S. DOE by Iowa State University. We also acknowledge extensive discussion with I. M. Robertson at the University of Illinois and DOE-BES grant DEFC3605GO15064 (Sandia Metal-Hydride Center of Excellence) for support of student Jason Reich (Chemistry at Illinois) who evaluated thermodynamic size effects (to be reported elsewhere).

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REFERENCES

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