Vacancy-mediated dehydrogenation of sodium alanate

Abstract

Clarification of the mechanisms of hydrogen release and uptake in transition-metal-doped sodium alanate, NaAlH₄, a prototypical high-density complex hydride, has fundamental importance for the development of improved hydrogen-storage materials. In this and most other modern hydrogen-storage materials, H₂ release and uptake are accompanied by long-range diffusion of metal species. Using first-principles density-functional theory calculations, we have determined that the activation energy for Al mass transport via AlH₃ vacancies is Q = 85 kJ/mol·H₂, which is in excellent agreement with experimentally measured activation energies in Ti-catalyzed NaAlH₄. The activation energy for an alternate decomposition mechanism via NaH vacancies is found to be significantly higher: Q = 112 kJ/mol·H₂. Our results suggest that bulk diffusion of Al species is the rate-limiting step in the dehydrogenation of Ti-doped samples of NaAlH₄ and that the much higher activation energies measured for uncatalyzed samples are controlled by other processes, such as breaking up of AlH₄⁻ complexes, formation/dissociation of H₂ molecules, and/or nucleation of the product phases.

Introduction of environmentally friendly hydrogen-fueled vehicles requires finding a light-weight, high-density means of on-board hydrogen storage. Tanks with gaseous or liquid hydrogen are commercially impractical because of low volumetric densities of the former and low storage temperatures of the latter. Physisorption of H₂ in, for instance, carbon-based materials and metal-organic frameworks (1) offers a means of increasing storage densities, but low adsorption energies make practical applications difficult. Significant efforts have been directed toward the development of solid-state storage systems based on interstitial metal hydrides (2–6). Despite good thermodynamics and fast kinetics, these systems have serious limitations resulting from their low gravimetric storage densities, typically only a couple of percent. The field of solid-state hydrogen storage was revolutionized in 1995 by Bogdanovic and Schwickardi (4), who discovered that transition-metal-doped sodium alanate, NaAlH₄, can store H₂ reversibly via a two-step reaction that involves an intermediate Na₃AlH₆ compound:

The equilibrium temperatures for the reactions shown in Eqs. 1 and 2 at an H₂ pressure of 1 bar (1 bar = 100 kPa) are 120°C and 175°C, respectively, with a total storage capacity of 5.6 wt% H₂. The work of Bogdanovic and Schwickardi instantly doubled the reversible capacity of inexpensive hydrides and pointed to the intriguing possibility that many other complex hydrides, such as alanates, borohydrides, and amides, may be used for energy storage. Since then, numerous complex hydrides have been screened both theoretically and experimentally, and several of them have been found to have thermodynamics within the range required for on-board storage in polymer electrolyte membrane fuel-cell vehicles (7, 8). However, all these materials suffer from poor kinetics, which seriously limits their use in on-board H₂ storage systems. An in-depth understanding of the mechanisms of hydrogen release and uptake is still lacking, and NaAlH₄ continues to serve as a prototypical model system for studies of hydrogenation kinetics in complex hydrides. It is widely hoped that the lessons learned on Ti-doped sodium alanate will aid in a rational design of hydride systems with fast kinetics (9).

After more than 10 years of intensive research, open questions remain regarding the distribution of Ti in the material. Despite an early report (10), subsequent x-ray studies of Ti-doped samples (11, 12) have not demonstrated any changes in the lattice parameter of the sodium-alanate phase, which suggests that dopants are not incorporated in the bulk hydride. Theoretical first-principles calculations also indicate that Ti substitution in the bulk is energetically very costly, whereas the surface substitution is less costly but still rather unfavorable (13). Numerous experimental studies have shown that Ti is present in an amorphous solid solution with Al (14). These results leave Ti in the Al phase as the only firmly established location, even though it is often hypothesized that Ti might be present on surfaces and at interfaces between the parent and product phases in Eqs. 1 and 2 (15).

Recently, hydrogen–deuterium scrambling experiments were carried out on pure and Ti-doped NaAlH₄ (16), which revealed that some Ti had to reside at the surface, where it serves as a catalyst for the dissociation and formation of H₂ molecules. However, the study also showed that the rate of hydrogen–deuterium exchange was much faster than the rates of hydrogen release and uptake, suggesting that mass transport of heavy species (Na and/or Al) might be the rate-limiting step for the dehydrogenation of NaAlH₄ (16). It was also speculated that small amounts of Ti might somehow facilitate this process. Another recent study that used anelastic spectroscopy suggested the presence of a large number of bulk defects in materials undergoing decomposition, but the nature of these defects was not identified conclusively (17).

Dehydrogenation of Sodium Alanate.

Here, we present a first-principles Car–Parrinello molecular dynamics (CPMD) study of the kinetics of bulk diffusion in NaAlH₄, which is essential for the mass transport and microscale separation of Na and Al species, as required by Eq. 1. Using the umbrella sampling method, we obtain the activation free energies for the bulk diffusion of neutral vacancies (AlH₃ and NaH) in pure NaAlH₄. This activation energy provides the lower bound on the total activation energy of all bulk-diffusion-assisted decomposition mechanisms, unaffected by Ti doping in view of the fact that significant bulk substitution of Ti in NaAlH₄ is highly unfavorable and has not been observed. Our result for the AlH₃ vacancy-assisted diffusion agrees very well with the experimental data on Ti-doped samples, which suggests that bulk diffusion of Al species is the rate-limiting step for the dehydrogenation reaction shown in Eq. 1. Through a careful analysis of the possible reaction pathways, we are able to suggest possible scenarios for how transition metals accelerate the hydrogenation kinetics in sodium alanate.

Vacancy Formation.

We begin by considering the structure of the simplest low-energy charge-neutral defects in NaAlH₄. Fig. 1 shows the calculated structure of AlH₃ (Left) and NaH (Right) vacancy complexes obtained from short simulated annealing runs of 1 ps at 300 K, followed by conjugate gradient relaxations of the ionic positions and cell shapes. It is seen that the introduction of a metal-ion vacancy leads to a rearrangement of the coordination of the neighboring Al–H complexes. Introducing a neutral AlH₃ vacancy results in the formation of an AlH₅²⁻ moiety in NaAlH₄ (Fig. 1), bound to the vacant site by Coulomb attraction caused by local excess of Na⁺ ions. Existence of a strong Coulombic attraction between the AlH₅²⁻ complex and the vacancy implies that these defects must diffuse together (18), which requires a mechanism of changing the orientation of the vacancy–AlH₅²⁻ pair. According to our CPMD simulations, the extra hydrogen of the AlH₅²⁻ moiety is very mobile and gets exchanged with the AlH₄⁻ units surrounding the AlH₃ vacancy approximately once in every 1 ps of simulation at 400 K. This observation implies that the hydrogen ion easily diffuses around the vacancy site, facilitating the reorientation mechanism required for long-range diffusion of this complex. For the case of an NaH vacancy, two neighboring AlH₄⁻ tetrahedra start to share a vertex, forming an Al₂H₇⁻ complex to compensate for the missing H ion (see Fig. 1). Again, there is a Coulombic attraction between the Al₂H₇⁻ complex and the Na⁺ vacancy, because they create a local excess of negative and positive charge, respectively. Thus, vacancy-mediated diffusion of the Na⁺ species must be accompanied by a dynamic process that allows for the shared H ion to travel with the vacancy. It is important to note that this process does not require actual diffusion of individual H ions, only a rotation and rebonding of neighboring tetrahedra. Reorganization of H ions around an Na⁺ vacancy happens approximately once in every 4 ps of simulation at 400 K.

Fig. 1.

Relaxed structures of AlH₃ (Left) and NaH (Right) charge-neutral vacancies in NaAlH₄. Al–H complexes are shown in blue, and Na ions are shown in yellow. Empty spheres denote vacant sites, and the structure of nearby Al–H complexes is emphasized by using semitransparent polyhedra.

Vacancy Diffusion.

CPMD simulations in conjunction with the umbrella sampling technique were used to study the free-energy profiles for diffusion of both types of defects shown in Fig. 1. The free-energy barriers were determined by using potential of mean force (PMF) acting along the diffusion path obtained from a series of harmonically biased umbrella sampling simulations (see Materials and Methods). The combined PMF for the diffusion path was obtained by using the weighted histogram analysis method (19). The errors in the PMF profiles were determined from the variance of the change in the free energies along the diffusion path (20). Free-energy profiles for the diffusion of AlH₃ and NaH vacancies are shown in Fig. 2. We find that the free-energy barrier for AlH₃ vacancy diffusion (12 ± 2 kJ/mol) is significantly lower than the barrier for NaH vacancy diffusion (25 ± 2 kJ/mol). On the basis of the computed activation free energies, the diffusion of AlH₃ and NaH vacancies should, on average, take place once in every 4 and 170 ps of the simulation time at T = 400 K, respectively. Fig. 3 shows the root-mean-square displacements of Al atoms surrounding the vacancy site and distances from the center of the AlH₃ vacancy to the Al ions for a 3.5-ps-long simulation. As shown in Fig. 3, an AlH₃ vacancy diffusion attempt was made by an Al atom but was not completed successfully. The stochastic motion of the ions surrounding the AlH₃ vacancy is probably responsible for the observed recrossing of the transition state in Fig. 3, which demonstrates that direct ab initio molecular dynamics (MD) is consistent with the free-energy barriers calculated for the AlH₃ vacancy diffusion pathway by using the umbrella sampling method and underlines the difficulties associated with the estimation of the rates with direct MD simulations. In addition, these recrossing effects may modify the prefactor of the diffusion rate constants calculated here beyond the predictions of the transition-state theory (21).

Fig. 2.

Calculated free-energy profiles for the bulk diffusion of AlH₃ (Left) and NaH (Right) vacancies in NaAlH₄.

Fig. 3.

Root-mean-square displacements (RMSDs) of Al ions surrounding the vacancy site (blue, cyan, green, and purple), RMSDs of all Al atoms (red), and distances from the center of the vacancy to the surrounding aluminum atoms (gray, yellow, blue, and green).

The total activation energy for vacancy-mediated mass transport is given by the sum of the diffusion barrier (see Fig. 2) and the energy required to create the vacancies. The reactions that lead to the creation of AlH₃ and NaH vacancies in NaAlH₄ are shown in Eqs. 3 and 4. According to these reactions, the decomposition of NaAlH₄ into Na₃AlH₆, Al, and H₂ can proceed via two alternative vacancy-mediated pathways. In the first pathway, AlH₃ vacancies are introduced at the NaAlH₄–Al interface by breaking up an AlH₄ complex into bulk Al and gaseous H₂. This process can be schematically represented as follows:

where the superscript represents the type of vacancy in sodium alanate. The resulting vacancy–AlH₅²⁻ complex subsequently diffuses through the material to the NaAlH₄–Na₃AlH₆ interface, where it is annihilated and excess Na⁺ is incorporated into the growing hexahydride phase. The alternate pathway involves the creation of NaH vacancies at the NaAlH₄–Na₃AlH₆ interface according to the following reaction:

which is followed by diffusion of NaH vacancies through the bulk alanate to the NaAlH₄–Al interface and subsequent hydrogen release according to: ${\text{NaAlH}}_4^{\text{NaH}}\to {\text{NaAlH}}_4+\text{Al}+\frac{3}{2}{\text{H}}_2$. Using Eqs. 3 and 4, we find that the total enthalpy cost of creating AlH₃ and NaH vacancies is 116 and 144 kJ/mol per vacancy, respectively. We note here that other mechanisms of bulk diffusion besides those shown in Eqs. 3 and 4 are theoretically possible, and the energies of forming some of those vacancies were calculated with density-functional theory (9). We have considered several alternatives by using first-principles calculations of defect energetics and consistently found that they involve intermediate steps that are higher in energy than the simple pathways shown in Eqs. 3 and 4. For instance, it is conceivable that a pair of AlH₃ vacancies might merge into a complex defect involving two vacancies. However, we find that a pair of isolated AlH₃ vacancies is 58 kJ/mol lower in energy than the divacancy complex, which indicates that agglomeration of AlH₃ vacancies is unfavorable. Some defects, such as H vacancies, may become charged in the presence of dopants, which can donate or accept electrons. However, very high formation energies have been calculated for bulk substitution of Ti in NaAlH₄, which indicates that bulk concentration of Ti is insignificant (13). Therefore, the concentration of charged defects should also be very small and have a negligible effect on the reaction kinetics.

Vibrational Frequencies.

The vacancy-formation enthalpies quoted above include vibrational contributions computed for model gas-phase reactions (see Materials and Methods) and power spectrum obtained from MD simulations. In general, vibrational effects have been found to lower the enthalpies of H₂ release by as much as 10–20 kJ/mol H₂, because average vibrational energy of H in the complex hydride is usually higher than the sum of the zero-point and thermal energies for the H₂ molecule in the gas phase. Because the creation of an AlH₃ vacancy involves H₂ release (see Eq. 3), the effect of vibrations might be important. We have performed careful analysis to estimate the magnitude of vibrational contributions. Fig. 4 shows the power spectrum obtained from a 3.5-ps-long CPMD simulation for a supercell size of 2 × 2 × 2 of the conventional NaAlH₄ unit cell with one AlH₃ vacancy. When compared with the phonon spectra obtained from first-principles calculations (22–24) and experimental measurements (22, 24), it accurately reproduces the locations and shapes of the Al, Na, and H peaks. The hydrogen peak at ≈1750 cm⁻¹ corresponds to modes stretching HAl bonds with T₂ and A₁ symmetries. The hydrogen peak at ≈800 cm⁻¹ corresponds to bending of HAlH bond angles and rocking motions of hydrogen ions with E and T₂ symmetries. The hydrogen peak at ≈400 cm⁻¹ corresponds to rigid rotations of AlH₄ tetrahedra. The small peak that centers at ≈1250 cm⁻¹ is not present in the phonon spectrum published by Ke and Tanaka (23). This frequency significantly differs from the calculated vibrational frequencies of AlH₅²⁻ (see below). Hence, it is attributed to a combination of librational and bending modes. This peak was also proposed by Jensen and coworkers (24) to originate from the simultaneous excitations of the librational and bending modes of hydrogen via a two-phonon excitation process. Using the power spectrum in Fig. 4, we have determined that the reaction enthalpy for Eq. 1 is 24 kJ/mol H₂ at 100°C, which is in good agreement with previously published first-principles results (23, 25) but underestimates the experimental value of 37 kJ/mol H₂ (4, 11).

Fig. 4.

Calculated power spectrum of NaAlH₄ with an AlH₃ vacancy.

Conclusions

Our results are summarized in Fig. 5, which shows the calculated free-energy profiles for the dehydrogenation pathways of NaAlH₄ via the bulk vacancy mechanism. Energies are given for 1 mol of H₂. AlH₃ vacancies are created at the Al–NaAlH₄ interface with direct H₂ liberation. The energy barrier required to break apart the AlH₄⁻ anion and/or nucleate the bulk Al phase is shown schematically as a dashed blue curve in Fig. 5. Creation of an AlH₃ vacancy is endergonic by 77 kJ/mol H₂. The created AlH₃ vacancies diffuse with an activation free energy of 8 kJ/mol H₂ for each jump until they reach the NaAlH₄–Na₃AlH₆ interface, where they are annihilated by forming Na₃AlH₆. This last step is exergonic by 53 kJ/mol H₂. NaH vacancies, on the other hand, are created at the NaAlH₄–Na₃AlH₆ interface. The energy cost of creating an NaH vacancy is 96 kJ/mol H₂. Again, there might be an intermediate energy barrier associated with the nucleation of the Na₃AlH₆ phase and/or the scission of the AlH bond, which is shown as a dashed green line in Fig. 5. Once created, NaH vacancies will diffuse with a bulk activation free energy of 16 kJ/mol H₂. After reaching the Al–NaAlH₄ interface, they are annihilated by forming bulk Al and liberating H₂. This last step is exergonic by 72 kJ/mol H₂. The results provided in Fig. 5 show that the AlH₃ vacancy mechanism is energetically favored over a possible NaH vacancy mechanism for the bulk interdiffusion of Na and Al species in sodium alanate.

Fig. 5.

Proposed energy profile for the dehydrogenation pathway of NaAlH₄ via AlH₃ and NaH vacancies. AlH₃ vacancies are created at the Al–NaAlH₄ interface and diffuse toward the NaAlH₄–Na₃AlH₆ interface. NaH vacancies are created at the NaAlH₄–Na₃AlH₆ interface and diffuse toward the Al–NaAlH₄ interface, where H₂ liberation takes place. Dashed lines correspond to unknown energy barriers.

Comparison of the calculated vacancy diffusion barriers with the experimental data offers additional insight into the feasibility of AlH₃ vacancy-mediated dehydrogenation of NaAlH₄. Experimental data show that the activation enthalpies for the first step of the dehydrogenation reaction (Eq. 1) in Ti-doped samples are independent of the Ti concentration and scattered between 73 and 80 kJ/mol H₂ (26). The fact that the computed activation barrier for the decomposition of NaAlH₄ via the AlH₃ vacancy mechanism, Q = 85 ± 2 kJ/mol H₂, agrees remarkably well with the experimental activation energy data suggests that the diffusion of AlH₃ vacancies is the rate-limiting step for dehydrogenation of transition-metal-doped NaAlH₄ samples. Furthermore, we find that mass-transport processes involving diffusion of NaH vacancies have high activation energies (Q = 112 kJ/mol H₂), which is significantly above the experimentally measured data for Ti-doped samples. This high energy barrier precludes bulk Na vacancies from playing a major role in the dehydrogenation kinetics of doped samples.

Because the measured activation energy in undoped samples is ≈120 kJ/mol H₂, we conclude that other processes, not the diffusion of AlH₃ vacancies, limit the dehydrogenation rate of pure NaAlH₄. Three possibilities that can determine the height of the dashed lines shown in Fig. 5 are (i) dissociation/formation of H₂ molecules, (ii) nucleation of the product (Al and/or Na₃AlH₆) phases, and (iii) scission of the HAlH₃ bond, which is required for the creation of both types of vacancies. Because the calculation of the barriers associated with these processes is computationally prohibitive for physically realistic system sizes and geometries, we have not attempted them here. However, assuming that the effect of Ti is to facilitate one or more of the aforementioned processes, the activation barrier for the decomposition of Ti-doped NaAlH₄ will be determined by the enthalpy of introducing AlH₃ vacancy plus the diffusion barrier, which we have found to be in excellent agreement with the experimental data.

In conclusion, we have shown that first-principles calculations can be used to explore possible dehydrogenation routes for hydrogen-storage materials and provide mechanistic information about the dehydrogenation process. Our results suggest that the dehydrogenation rate of Ti-doped samples is limited by the diffusion rate of AlH₃ vacancies. The proposed roles of the Ti catalyst are (i) the catalytic scission of the H₂ bond at the surface, (ii) catalytic breaking of HAlH₃ bonds, and/or (iii) facilitation of the nucleation of the Al phase resulting from strong TiAl bonds and formation of a coherent TiAl₃ phase.

Materials and Methods

The CPMD simulations were carried out in a canonical ensemble with a time step of 6 atomic units by using the CPMD program at 400 K (27). The fictitious mass of the electrons was set to 450 atomic mass units. Ultrasoft pseudopotentials were used to describe the electronic structure of the system with density-functional theory (28). Perdew–Wang-91 generalized gradient correction was used for the exchange and correlation energy (29, 30). The planewave and electron-density cutoffs were set to 35 and 210 Rydberg, respectively. The simulations were run with a Γ-point-only sampling of the Brillouin zone for a supercell that contains 192 atoms (2 × 2 × 2 of a unit cell) with periodic boundary conditions. The converged lattice parameters a, b/a, and c/a were elongated according to the lattice expansion parameters published in ref. 22 and set to 5.04, 1.00, and 2.22 Å, respectively (22). The temperature of the MD simulations was controlled by using a Nose–Hoover thermostat (31, 32).

The diffusion of vacancies was modeled by dragging an AlH₃ unit or Na⁺ atom into the vacancy site with the umbrella sampling method (33, 34). The diffusion path for AlH₃ vacancy diffusion was described by constraining the difference in the bond lengths 1–2 and 1–3 shown in Fig. 1 Left. The diffusion path for Na⁺ atom diffusion was described by constraining the distance between 1 and 2, shown in Fig. 1 Right. The equilibration time of 1.5 ps was followed by production time of 3 to 5 ps for each window, which are separated by 0.5 Bohr along the diffusion path. To restrain the diffusion coordinates, a harmonic biasing potential with a force constant of 0.1 atomic unit was used. The activation free energies for the vacancy diffusion were determined with the potential of mean force (35) acting on the diffusion path by using the weighted histogram analysis method (19).

The formation energies of the vacancies were determined by using the VASP program (36–38). The geometries of the perfect NaAlH₄ lattice and NaAlH₄ supercell (2 × 2 × 2 of the unit cell) with a vacancy were optimized by using ultrasoft pseudopotentials with a planewave cutoff of 450 eV (1 eV = 1.602 × 10⁻¹⁹ J) by using Γ-point-only sampling. The energy of Al was determined by calculating the energy of an fcc unit cell containing 4 Al atoms with a converged lattice constant of 4.04 Å. The planewave cutoff was set to 420 eV with a Monkhorst–Pack k-points mesh of 64 × 64 × 64 (39). The energy of the H₂ molecule was calculated in the gas phase by using a cubic unit cell of 14 Å with a planewave cutoff of 350 eV. We estimated the thermal and zero-point energy corrections for the formation of vacancies and hexahydride from the structures involving vacancies with the gas-phase model reactions shown in Eqs. 5.1–5.4. We omitted the change in vibrational frequencies of Na and Al atoms. The omission of these vibrational frequencies is expected to introduce insignificant errors because the translational modes corresponding to Al and Na vibrations in NaAlH₄ and Na₃AlH₆ do not differ notably (23). The zero-point energy corrections and thermal corrections to the enthalpies for the reactions shown in Eqs. 5.1–5.4 were computed at the B3LYP/CBSB7 (40, 41) level of theory by using the GAUSSIAN03 (42) program.