Local defects enhanced dehydrogenation kinetics of the NaBH₄-added Li–Mg–N–H system

Abstract

A mechanistic understanding on the enhanced kinetics of hydrogen storage in the NaBH₄-added Mg(NH₂)₂-2LiH system is provided by carrying out experimental investigations associated with first-principles calculations. It is found that the operating temperatures for hydrogen desorption of the Mg(NH₂)₂-2LiH system are reduced by introducing NaBH₄, and the NaBH₄ species seems almost unchanged during dehydrogenation/hydrogenation process. First-principles calculations reveal that the presence of NaBH₄ in the Mg(NH₂)₂-2LiH system facilitates the formation of Mg vacancies in Mg(NH₂)₂. The appearance of Mg vacancies not only weakens the N–H bonds but also promotes the diffusion of atoms and/or ions, consequently resulting in the improvement of the reaction kinetics of hydrogen desorption/absorption of the NaBH₄-added Mg(NH₂)₂-2LiH system. This finding provides us with a deep insight into the role played by NaBH₄ in the Li–Mg–N–H system, as well as ideas for designing high-performance catalysts for metal–N–H-based hydrogen storage media.

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1. Introduction

The interest in hydrogen as an important energy vector of the future arises from its unique features of abundance, flexible convertibility from many energy sources and high environmental compatibility.¹ A safe, efficient and economical storage technology is regarded as the crucial prerequisite before hydrogen can be globally accepted as a fuel, particularly for mobile applications.² Storing hydrogen in solid-state materials is often preferred over pressurized hydrogen and liquefied hydrogen because of its high gravimetric and volumetric densities and good safety.³ The main focus of research on hydrogen storage materials is to find light weight, low cost and high capacity hydrides with favorable hydrogen absorption/desorption thermodynamics and kinetics.^4–20 In recent years, special attention has been given to those materials which are composed of hydrogen bonding to low-Z elements such as alanates,^7–10 borohydrides,^11,12amides^13–16 and their combinations.^17–20 One category of the most promising candidates seems to be combinations of amides and hydrides due to their relatively high hydrogen content, good hydrogen storage reversibility and mild operating conditions.^13–16

In 2002, Chen et al. demonstrated that lithium nitride, Li₃N could reversibly absorb/desorb 11.5 wt% hydrogen and convert finally to a LiNH₂-2LiH combination via the following two-step reaction.¹³

Li₃N + 2H₂ ⇌ Li₂NH + LiH + H₂ ⇌ LiNH₂ + 2LiH (1)

The possible driving force for hydrogen desorption from this reaction was attributed to the strong affinity between H^δ+ in the amide and H^δ− in the hydride.¹⁵ This finding stimulated an intense research interest on the N-containing compounds and opened up a new way to search for suitable hydrogen storage systems for on-board applications. Following this work, a variety of metal–N–H systems have been designed and investigated for their hydrogen storage properties.^13–20 Significantly, substituting LiNH₂ with Mg(NH₂)₂ in the LiNH₂-2LiH combination resulted in a step forward toward practical applications due to the creation of a more favorable dehydrogenation thermodynamic condition as the desorption enthalpy change was decreased from ca. 66 kJ mol⁻¹ of H₂ for LiNH₂-2LiH to ca. 44 kJ mol⁻¹ of H₂ for Mg(NH₂)₂-2LiH.¹⁴ The operating temperature predicted thermodynamically for hydrogen desorption from the Mg(NH₂)₂-2LiH system at 1 bar equilibrium hydrogen pressure was ca. 90 °C.²¹ Unfortunately, a reasonable rate of hydrogen release was only obtained experimentally at above 200 °C because of a rather high kinetic barrier.^14,15,21 Considerable efforts have been devoted to improving the dehydrogenation kinetics of the Mg(NH₂)₂-2LiH system since then.^22–24 It was found that the partial substitution of Na for Mg or Li in the Mg(NH₂)₂-2LiH system resulted in certain kinetic improvements as the peak temperature for hydrogen desorption was reduced by ∼10 °C.²² Sudik et al. even acquired a 40 °C reduction in the peak temperature by seeding the desorption product, viz., Li₂MgN₂H₂.²³ Moreover, Hu et al. reported that the addition of a small amount of LiBH₄ in the Li–Mg–N–H system led to a significant improvement in hydrogen storage properties with a two-fold increase in the average dehydrogenation rate.²⁴ However, up to now a fundamental understanding of the mechanisms for the improvement in the dehydrogenation/hydrogenation kinetics of the Mg(NH₂)₂-2LiH system is still lacking. Moreover, additional kinetic improvements are still needed to acquire a better hydrogen desorption/absorption performance to qualify this system as a practically useful hydrogen storage medium.

Recently, a three-dimensional diffusion-controlled kinetic mechanism was identified for the dehydrogenation process of the Li–Mg–N–H system.²⁵ We therefore believe that enhancement in the atomic or ionic diffusivity could be very effective for the improvement of the hydrogen desorption/absorption kinetics. It is well known that crystal defects play an important role in chemical reactions since their presence greatly expedites diffusion and mass transport in materials.²⁶ Since the compounds comprised of elemental Na (from compounds such as NaH and NaNH₂) or the BH₄⁻group (for example from LiBH₄) have been shown to enhance the dehydrogenation kinetics of the Mg(NH₂)₂-2LiH system as described above,^22,24 an improved hydrogen storage performance is expected by directly introducing NaBH₄ into the system. In the present study, we have concentrated on investigating the effects of NaBH₄ on the dehydrogenation/hydrogenation properties of the Mg(NH₂)₂-2LiH system and the corresponding mechanisms by carrying out experimental examinations associated with theoretical calculations.

2. Experimental and computational

The starting chemicals, lithium hydride (LiH, purity 98%) and sodium borohydride (NaBH₄, purity 98.5%) were purchased from Alfa Aesar and Sigma Aldrich respectively, and were used as received without any further purification. Magnesium amide (Mg(NH₂)₂) was produced in-house by reacting Mg powder (99%, Sinopharm) with ammonia at 300 °C under 7 bar ammonia pressure. Samples of Mg(NH₂)₂-2LiH-xNaBH₄ (x = 0, 0.05, 0.1, 0.2 and 0.5) mixtures were prepared by ball milling the corresponding chemicals under 78 bar of hydrogen pressure on a planetary ball mill (QM-3SP4, Nanjing) rotating at 500 rpm for 36 h. The ball-to-sample weight ratio is about 60 : 1.

Temperature dependence of hydrogen desorption behaviors of the samples was measured on a homemade temperature-programmed-desorption (TPD) system attached to an online gas chromatograph. A 50 mg sample was loaded into the tube reactor of the measurement system and then housed in a tubing furnace. Pure argon was used as the carrier gas. The temperature was raised gradually from room temperature to 270 °C at the heating rate of 2 °C min⁻¹. The quantitative measurements of hydrogen release/uptake were performed on a homemade volumetric Sieverts-type apparatus. A 200 mg sample was used in each test. Both isothermal and non-isothermal approaches were adopted. In the non-isothermal experiment, the temperature of the samples was gradually raised to 275 °C at the rate of 2 °C min⁻¹ for desorption and to 150 °C at the rate of 1 °C min⁻¹ for absorption. For isothermal dehydrogenation/hydrogenation kinetics, the samples were quickly heated to a preset temperature and kept at this temperature for the whole period of measurement.

Crystal structures of samples were determined by using an X'Pert Pro diffractometer with CuK_α radiation at 40 kV and 40 mA. Data were collected in the 2θ range of 10–90° with 0.05° step increments. A homemade container was used to keep the powder samples from air and moisture contamination. N–H and B–H vibrations in all samples were identified by a Bruker Vector 22 Fourier transform infrared spectrometer (FTIR, Germany). Each pellet sample was prepared by cold pressing a mixture of powdered samples and potassium bromide (KBr) at the weight ratio of about 1 : 30. The transmission mode was adopted with 4 cm⁻¹ scan resolution. 32 scans were made and accumulated. ¹¹B and ²³Na solid-state NMR spectra were recorded on a Bruker Avance II 300 MHz spectrometer operating at 96.3 MHz. Samples were packed in 7 mm MAS ZrO₂ rotors with a Kel-F cap in the glove box. All spectra were obtained after 1024 scans with an acquisition time of 38 ms per scan and a repetition delay time of 1 s. Chemical shifts (δ) were referenced to a 1 M aqueous solution of BF₃·OEt₂ and sodium chloride.

All calculations present in this work were performed with the CASTEP code²⁷ based on density functional theory (DFT).²⁸ The ion-electron interactions were described by using ultrasoft pseudopotentials,²⁹ and the Perdew-Wang 1991 (PW91) generalized gradient approximation (GGA)³⁰ was employed for the exchange–correlation functional. Electronic wave functions were expanded on the basis of plane waves with a well-converged cutoff energy of 340 eV. The Brillouin zone was sampled by a sum over special k-points generated with Monkhorst–Pack scheme,³¹ and set as 3 × 3 × 3 for Mg(NH₂)₂, 2 × 2 × 4 for NaBH₄, 13 × 13 × 7 for Mg, 3 × 3 × 3 for B, and Gamma-point (1 × 1 × 1) for H₂ and NH₃ molecules. To simulate the defects in a cell, the primitive cell of Mg(NH₂)₂ consisting of 112 atoms and a 2 × 2 × 1 supercell of NaBH₄ consisting of 96 atoms were adopted, and the calculations for the energies of the H₂ molecule and the NH₃ molecule were conducted on a cell of 10 × 10 × 10 Å. A finite basis set correction³² was applied in the evaluation of energy and stress, and the Pulay density-mixing scheme³³ was adopted for self-consistent field (SCF) calculations. Optimization of atomic positions and lattice parameters was performed on alternate cycles using the BFGS method³⁴ until the convergence criteria were met (maximum energy change per atom = 1.0 × 10⁻⁵ eV, maximum RMS force = 0.03 eV Å⁻¹, maximum RMS stress = 0.05 GPa and maximum RMS displacement = 1.0 × 10⁻³ Å). For the perfect crystal, all atomic positions and lattice parameters were relaxed. During the calculations for the system energy of a supercell with a point defect, the supercell dimensions were kept at the optimized lattice parameters of the perfect crystal and all atoms within the cell were allowed to relax with a SCF tolerance of 1.0 × 10⁻⁶ eV atom⁻¹. This method has been extensively used in the study of NaAlH₄.³⁵ For charged defects, a jellium background was employed to neutralize the supercells.

3. Results and discussion

3.1 Structural characterization and hydrogen storage properties

Fig. 1a shows XRD patterns of the Mg(NH₂)₂-2LiH-xNaBH₄ samples milled for 36 h. Obviously, in addition to LiH phase, the post-milled samples all exhibit some broad diffraction peaks centered around 14.6° and 29.1° (2θ), which originate from the nano-crystalline/amorphous Mg(NH₂)₂ as reported extensively before.³⁶ It is worth noting that the peak around 29.1° becomes sharper for the NaBH₄-added sample with respect to the pure sample due to the fact that the strongest diffraction peak of NaBH₄ is at about 28.9°. In particular, the NaBH₄ phase can be unambiguously identified from the peaks at 24.7°, 28.9°, 41.4°, 48.9°, 51.4°, 59.8°, and 67.9° for the samples with x = 0.5. Further FTIR examinations show that the signature N–H vibration of Mg(NH₂)₂ at 3272/3326 cm⁻¹ is observed in all the samples (Fig. 1b), indicating the existence of Mg(NH₂)₂ in the post-milled samples. In the meantime, three absorbances at 2387, 2297 and 2227 cm⁻¹ are also discernable for the NaBH₄-added samples, and they become clearer with increasing the content of NaBH₄, which locate in the typical B–H vibration range of borohydride. According to the XRD analyses, they should belong to NaBH₄. Thus, we believe that the as-milled samples are still composed of the starting chemicals, Mg(NH₂)₂, LiH and NaBH₄, without the formation of new phase.

Fig. 1 XRD patterns of the Mg(NH₂)₂-2LiH-xNaBH₄ samples milled for 36 h.

The influence of the addition of NaBH₄ on hydrogen desorption behaviors of the Mg(NH₂)₂-2LiH system was qualitatively evaluated by means of TPD. Fig. 2a shows the TPD curves of the post-milled Mg(NH₂)₂-2LiH-xNaBH₄ samples. Apparently, the addition of NaBH₄ lowers down the hydrogen desorption temperatures of the Mg(NH₂)₂-2LiH system. The sample with x = 0.1 generates the lowest operating temperature for hydrogen desorption in the present work with the starting temperature decreased to ca. 130 °C and the peak temperature to ca. 184 °C. In comparison with the pristine sample, a reduction of around 12 °C for the peak temperature of hydrogen release was attained. However, the introduction of NaBH₄ into the Mg(NH₂)₂-2LiH system decreased the hydrogen desorption amount as represented by the reduction of the peak areas. The volumetric desorption measurements gave the quantitative values as shown in Fig. 2b. It can be seen that the decrease in the amount of hydrogen desorption is dependent on the concentration of NaBH₄. The hydrogen desorbed from the pure Mg(NH₂)₂-2LiH sample amounts to 5.46 wt%, while it is only 4.28 wt% for the Mg(NH₂)₂-2LiH-0.5NaBH₄ sample, both of which are very close to the theoretical hydrogen capacities of 5.56 wt% and 4.40 wt%, respectively, with the supposition that NaBH₄ remains unchanged in the dehydrogenation process.

Fig. 2 TPD (a) and volumetric release (b) curves of the Mg(NH₂)₂-2LiH-xNaBH₄ samples.

The enhancement in the dehydrogenation kinetics induced by the addition of NaBH₄ was further characterized by isothermal hydrogen desorption examinations. Fig. 3a shows the isothermal dehydrogenation curves of the samples with and without NaBH₄ at 150 °C. It can be seen that faster desorption kinetics were achieved with the addition of NaBH₄, and the sample with x = 0.1 shows optimal dehydrogenation kinetics. Approximately 3.75 wt% of hydrogen is released from the Mg(NH₂)₂-2LiH-0.1NaBH₄ sample within 100 min at 150 °C, whereas the amount of hydrogen desorption is only ∼2.55 wt% for the pure sample under the same conditions, corresponding to 73% and 46% of hydrogen storage capacities, respectively. Analyzing the tangent slope of the linear parts of dehydrogenation curves, a ∼0.06 wt% min⁻¹ average rate was determined for the hydrogen desorption of the Mg(NH₂)₂-2LiH-0.1NaBH₄ sample, while it is only ∼0.02 wt% min⁻¹ for the pure sample. Specifically, the rate of hydrogen desorption for the Mg(NH₂)₂-2LiH-0.1NaBH₄ sample is about 3 times that of the pure sample. Taking into account the hydrogen storage capacity and the dehydrogenation rate, x = 0.1 is deemed the optimal concentration in the present study. As a consequence, the following hydrogenation examinations and the reaction mechanism analyses were focused on the Mg(NH₂)₂-2LiH-0.1NaBH₄ sample.

Fig. 3 Isothermal hydrogen desorption (a) and absorption (b) curves of the Mg(NH₂)₂-2LiH-xNaBH₄ samples.

Fig. 3b shows the isothermal hydrogenation curves of the dehydrogenated Mg(NH₂)₂-2LiH and Mg(NH₂)₂-2LiH-0.1NaBH₄ samples. At the hydrogen pressure of 105 bar and 100 °C, the dehydrogenated Mg(NH₂)₂-2LiH-0.1NaBH₄ sample exhibits a slightly faster hydrogenation rate over the pure sample, as it takes up ∼3.1 wt% hydrogen within 1000 min while only ∼2.6 wt% hydrogen is recharged into the pure sample in the same period of time. This indicates that the addition of NaBH₄ slightly improves the hydrogenation kinetics of the Mg(NH₂)₂-2LiH system as well.

Significantly, the dehydrogenation/hydrogenation kinetics of the Mg(NH₂)₂-2LiH system was enhanced with the presence of NaBH₄. To understand the role played by NaBH₄, the structural change of the Mg(NH₂)₂-2LiH-0.1NaBH₄ sample at different dehydrogenation stages is investigated by means of XRD and FTIR. The results are shown in Fig. 4. It is found that from Fig. 4a, in addition to LiH and NaBH₄, a new set of diffraction peaks assignable to the cubic Li₂MgN₂H₂ phase emerges at 18.4°, 30.7°, 42.6°, 51.1° and 60.7° with noticeable intensities in the XRD pattern of the dehydrogenated sample stopped at 180 °C.^15,22,25 As dehydrogenation stopped at 250 °C, the Li₂MgN₂H₂ phase dominates with the disappearance of the LiH phase. Moreover, it is worthy to note that NaBH₄ can be still identified in XRD profiles from the peaks at 25.1, 28.9, 41.4 and 48.9° in the dehydrogenation process although their intensities are weak. The change in the structure during dehydrogenation is further investigated by FTIR examinations as shown in Fig. 4b. It can be seen that for the dehydrogenation sample stopped at 180 °C, the peak intensity of N–H vibration of Mg(NH₂)₂ at 3272/3326 cm⁻¹ clearly decreases, and a new absorbance emerges at around 3174 cm⁻¹, which agrees well with the N–H vibration of cubic Li₂MgN₂H₂.^22,25 This indicates that Mg(NH₂)₂ was gradually consumed and a new imide product of Li₂MgN₂H₂ developed with the release of hydrogen. As the sample is heated up to 250 °C, only the absorbance at 3174 cm⁻¹ is detected for the N–H vibration while the absorbances of amide disappears completely. Interestingly enough, unlike LiBH₄,²⁴ the ternate B–H vibration of the BH₄⁻ anion in NaBH₄ remains almost unchanged relative to the post-36 h milled sample, which is in good agreement with XRD results. This implies that NaBH₄ still exists before and after dehydrogenation. However, it was found that two sharp absorbances at 3243 and 3301 cm⁻¹ emerged in the dehydrogenated Mg(NH₂)₂-2LiH-xLiBH₄ samples, which can be assigned to a new solid solution (LiNH₂)_x(LiBH₄)_1−x due to the formation of LiNH₂ upon dehydrogenation from the Mg(NH₂)₂-2LiH combination.²⁴ These facts imply that the different roles may be played by NaBH₄ and LiBH₄ in dehydrogenation process of the Mg(NH₂)₂-2LiH system.

Fig. 4 XRD patterns (a) and FTIR spectra (b) of the Mg(NH₂)₂-2LiH-0.1NaBH₄ samples at different dehydrogenation stages.

To obtain the detailed structural information of NaBH₄, solid-state NMR was conducted to characterize the chemical shift of B and Na elements in the dehydrogenation process. Fig. 5 shows the solid-state ¹¹B and ²³Na NMR spectra of the Mg(NH₂)₂-2LiH-0.1NaBH₄ sample before and after dehydrogenation. ¹¹B and ²³Na NMR spectra of NaBH₄ were also recorded as references. It is seen that the solid-state ¹¹B and ²³Na NMR spectra of NaBH₄ exhibit a symmetric single peak at −39.2 ppm and −8.2 ppm, respectively. In the case of Mg(NH₂)₂-2LiH-0.1NaBH₄, the resonance of ¹¹B is identical to that of the pure NaBH₄, viz., a symmetric transition at −39.2 ppm, which persists in the dehydrogenation process, implying that the chemical environment of B atom remains almost unchanged. It can be therefore concluded that the BH₄ ions maintain their integrity during dehydrogenation of the Mg(NH₂)₂-2LiH-0.1NaBH₄ sample. However, the resonance of ¹¹B in the Mg(NH₂)₂-2LiH-0.1LiBH₄ sample was shifted from −41 ppm to about −39 ppm after dehydrogenation, indicating a lower electron cloud density around B atom due to the formation of a new solid solution (LiNH₂)_x(LiBH₄)_1−x.²⁴ The ²³Na NMR spectrum of the post-milled Mg(NH₂)₂-2LiH-0.1NaBH₄ sample becomes broader and more asymmetric while the chemical shift seems almost unchanged as compared to that in the pure NaBH₄, indicating that the average local environment around Na nuclei is only slightly changed, viz., more disordered as reported previously.³⁷ This is possibly due to the crystal imperfection caused by the increase in defects during ball milling. In general, atoms on the surface experience surface relaxation and/or reconstruction compared with atoms in the bulk. As a consequence, the increase in number of atoms on the surface would result in less-ordered state.³⁸

Fig. 5 Solid state ¹¹B (a) and ²³Na (b) NMR spectra of NaBH₄ and the Mg(NH₂)₂-2LiH-0.1NaBH₄ samples at different dehydrogenation stages.

The dehydrogenated Mg(NH₂)₂-2LiH-0.1NaBH₄ sample was re-hydrogenated under 105 bar of hydrogen pressure. As shown in Fig. 6, it is seen that as the temperature was gradually elevated from room temperature to 150 °C, appropriately 5.0 wt% of hydrogen is recharged. The re-hydrogenated sample was then subjected to XRD and FTIR examinations (Fig. 7). Apparently, the re-hydrogenated sample consists of three species, viz., Mg(NH₂)₂, LiH and NaBH₄. The result indicates that the dehydrogenated product goes back to the starting reactants with complete hydrogen absorption.

Fig. 6 Hydrogenation curve of the dehydrogenated Mg(NH₂)₂-2LiH-0.1NaBH₄ sample with temperatures.

Fig. 7 XRD pattern (a) and FTIR spectrum (b) of the Mg(NH₂)₂-2LiH-0.1NaBH₄ sample after re-hydrogenation.

The data obtained from volumetric measurements, XRD, FTIR and NMR analyses make us believe that hydrogen storage in the Mg(NH₂)₂-2LiH-xNaBH₄ system in the temperature range of 20–250 °C originates mainly from the reaction between Mg(NH₂)₂ and LiH. The dehydrogenation/hydrogenation processes can be still described by the following reversible reaction.

Mg(NH₂)₂ + 2LiH ⇌ Li₂MgN₂H₂ + 2H₂ (2)

During the whole hydrogen storage process, the added NaBH₄ works only as a catalyst in improving the reaction kinetics and reducing the operating temperatures of dehydrogenation rather than acts as a reactant participating directly in the dehydrogenation reaction. However, Hu et al. found that a solid solution (LiNH₂)_x(LiBH₄)_1−x was formed in the dehydrogenation process of the Mg(NH₂)₂-2LiH-xLiBH₄ system by the reaction of LiBH₄ with the LiNH₂ intermediate.²⁴ This not only reduces the dehydrogenation kinetic barriers of the Li–Mg–N–H system by weakening the N–H bonds but also delivers hydrogen, viz., LiBH₄ participates in the dehydrogenation process of the Li–Mg–N–H system. The discrepancy in the roles played by LiBH₄ and NaBH₄ in the Li–Mg–N–H system urges us to study in depth the catalytic mechanisms of NaBH₄.

To quantitatively evaluate the effect of the addition of NaBH₄ on the kinetic barrier, the apparent activation energy of dehydrogenation reaction of the Mg(NH₂)₂-2LiH-0.1NaBH₄ sample was calculated with the Kissinger method.³⁹Fig. 8 shows the Kissinger plots of the Mg(NH₂)₂-2LiH and Mg(NH₂)₂-2LiH-0.1NaBH₄ samples. The apparent activation energy E_a is determined to be about 109.8 kJ mol⁻¹ for the pure sample, which is in good agreement with the previous reports.¹⁵ For the Mg(NH₂)₂-2LiH-0.1NaBH₄ sample, the E_a value is decreased to 99.0 kJ mol⁻¹, a ∼10% reduction with respect to the pure sample. This result reveals that the presence of NaBH₄ alleviates the kinetic barrier of dehydrogenation reaction of the Li–Mg–N–H, which is responsible for the reduced operating temperature for hydrogen desorption.

Fig. 8 Kissinger's plots of the Mg(NH₂)₂-2LiH and Mg(NH₂)₂-2LiH-0.1NaBH₄ samples.

As described above, an improved dehydrogenation performance was achieved by the addition of an appropriate amount of NaBH₄ yet with the NaBH₄ additive remaining unchanged before and after dehydrogenation. We believe therefore that the NaBH₄ additive should work as a catalyst in the dehydrogenation process of the Li–Mg–N–H system instead of a reactant. For understanding the catalytic mechanisms of NaBH₄, high-resolution XRD technique was employed to identify the exact structural changes in the dehydrogenation process. Fig. 9 shows three strongest reflections of the Mg(NH₂)₂ phase in the high-resolution XRD patterns of the re-hydrogenated Mg(NH₂)₂-2LiH and Mg(NH₂)₂-2LiH-0.1NaBH₄ samples at 200 °C. It is found that all of the three strongest reflections of the Mg(NH₂)₂ phase in the Mg(NH₂)₂-2LiH-0.1NaBH₄ sample slightly shift to higher angles with respect to the pure Mg(NH₂)₂-2LiH sample, indicating the subtle decrease in the lattice parameter. This phenomenon is likely to originate from the appearance of Mg vacancies and/or the substitution of Mg by smaller atoms or ions in the Mg(NH₂)₂ cell.

Fig. 9 Three strongest reflections of Mg(NH₂)₂ in the re-hydrogenated Mg(NH₂)₂-2LiH and Mg(NH₂)₂-2LiH-0.1NaBH₄ samples.

3.2 First-principles calculations

It is well known that the hydrogen storage process of the metal–N–H system always associates with the dissociation/reconstruction of the N–H bonds.^22–24 Therefore, the N–H bond strength of the amides/imides, which is affected by the presence of point defects including vacancies, interstitials, and substitutional impurities, plays a crucial role during hydrogen release/uptake. First-principles calculation is a powerful tool for understanding and predicting the structures and properties of materials, such as the properties of crystals and surfaces, band structures, optical properties, point defects, extended defects, and so on, through calculating their electronic structures.⁴⁰ It is therefore highly desirable to perform a first-principles calculation on the structures and bonding of Mg(NH₂)₂ and NaBH₄ to obtain some insights on the mechanism of formation of defects.

Mulliken population⁴¹ analyses on Mg(NH₂)₂ shows that the Mulliken effective charges (MEC) of Mg, N and H are +1.62e, −1.31e and +0.25e, respectively. In addition, the average bond overlap populations (BOP) of N–H, Mg–N and H–H bonds are calculated to be 0.75e, −0.90e and −0.15e, respectively. With the above information, we know that the bonding between N–H is strongly covalent and that between Mg–N is primarily ionic. For evaluating the covalent bond strength and understanding the stability of N–H bonds in Mg(NH₂)₂, the calculated bond length (BL) and BOP of N–H bonds for Mg(NH₂)₂ with defects free and various defects are listed in Table 1. Vacancies or substitutional atoms/ions were created by removing or replacing atoms/ions from supercells while holding the cell volume and shape fixed. This method is appropriate for materials with low defect densities.⁴² As shown in Table 1, the average BL of N–H in Mg(NH₂)₂ remains almost unchanged with the presence of various defects including the Mg vacancies and the substitution of Mg with Na. The average BOP of the N–H bond in Mg(NH₂)₂ are decreased from 0.755e to 0.747/0.736/0.722e for the Mg/Mg⁺/Mg²⁺ vacancies while it is almost unchanged for the substitution of Mg with Na. More interestingly, the minimum value of BOP of the N–H bond are decreased from 0.75e to 0.64e with the appearance of Mg vacancies, forming the bigger reduction as compared with 0.73e for the substitution of Na for Mg. As a result, we believe that the presence of Mg/Mg⁺/Mg²⁺ vacancies in Mg(NH₂)₂ plays the dominant role in weakening the N–H bond rather than the substitution of Na/Na⁺ for Mg.

Table 1 The bond overlap population (BOP) and bond length (BL) of N–H bond for Mg(NH₂)₂

Defects	Minimum values		Average values
	BOP/e	BL/Å	BOP/e	BL/Å
Defect-free	0.75	1.034	0.755	1.035
Mg vacancy	0.64	1.058	0.747	1.036
Mg^+ vacancy	0.64	1.058	0.736	1.036
Mg^2+ vacancy	0.64	1.058	0.723	1.037
Na @ Mg site	0.73	1.033	0.754	1.036
Na^+ @ Mg^+ site	0.73	1.033	0.756	1.034
Na^+ @ Mg^2+ site	0.73	1.033	0.755	1.035

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Vacancy formation energy is an important parameter for understanding the formation of vacancy in a crystal.⁴³ It is generally defined as the energy that creates a vacancy in a crystal. Further calculations were performed on the formation energies of the relevant point defects in NaBH₄ and Mg(NH₂)₂ in charged state according to eqn (3):⁴⁴

where ΔE(X^q) is the defect formation energy of X atom or ion, E_tot(X^q) is the total energy of the supercell without X atom or ion, E_tot(bulk) is the total energy of the ideal supercell, n_i is the number of atoms of i (host atoms or impurity atoms) that have been added to (n_i > 0) or removed from (n_i < 0) the supercell when the defect is created, μ_i is the corresponding chemical potential of these species, q is the charge state of the defect, and E_F is the Fermi energy which is referenced to the valence-band maximum (VBM) in the perfect crystal. Table 2 presents the formation energies of the most relevant defects in Mg(NH₂)₂ and NaBH₄. As shown in eqn (3), ΔE(X^q) is determined by atomic chemical potentials and the position of Fermi level. In the present study, the chemical potentials of B, H₂ and NH₃ are referenced to the standard states (bulk β-rhombohedral B, H₂ molecules and NH₃ molecular at T = 0 K), and the chemical potentials of Na and Mg are calculated by eqn (4) and (5), respectively.

μ_Na = μ_NaBH4 −μ_B − 2μ_H2 (4)

μ_Mg = μ_Mg(NH2)2 − 2μ_NH3 − μ_H2 (5)

The position of Fermi level varies from the maximum of the valence-band to the minimum of the conduction-band. In general, the position of Fermi level is around the mid-gap line for the intrinsic semiconductor and insulator. Thus, the Fermi level of Mg(NH₂)₂ and NaBH₄ was selected at the midpoint of the band gap. Specifically, the formation energy of a Mg atom vacancy in Mg(NH₂)₂ is about 1.92 eV, lower than that of Mg cation vacancy (Mg⁺: 3.51 eV, Mg²⁺: 5.44 eV), which implies that the formation of Mg atom vacancy is easier than that of Mg cation vacancy in Mg(NH₂)₂. However, the Na⁺ vacancy exhibits the lowest formation energy (−0.98 eV) in NaBH₄, indicating it is relatively easy to create a Na⁺ vacancy. In contrast, the formation energy of a B vacancy is highest in NaBH₄ (>3.55 eV), especially for the B³⁺ vacancy, signifying that it is rather difficult to break the B–H bond. These results are in good agreement with the experimental facts as observed by solid-state ¹¹B and ²³Na NMR in Fig. 5.

Table 2 Formation energies of the most relevant vacancies in NaBH₄ and Mg(NH₂)₂

Vacancy (X^q)	Mg(NH2)2			NaBH4
	Mg^0	Mg^+	Mg^2+	Na^0	Na^+	B^0	B^3+	BH4^0	BH4^+
ΔE(X^q) (eV)	1.92	3.51	5.44	2.46	−0.98	3.55	5.03	3.29	1.97

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It is clear that the formation of a Mg vacancy in Mg(NH₂)₂ and Na⁺ vacancy in NaBH₄ is more energetically favorable in the present study, which is possibly caused by the energetic ball-milling treatment. Subsequently, the possibility of Mg moving into Na⁺ vacancy or BH₄⁻ vacancy in NaBH₄ was estimated from the defect formation energies as listed in Table 3. The lowest defect formation energy is attained for the replacement of Mg²⁺ for Na⁺ (1.06 eV), which indicates that the migration of Mg²⁺ cation into the Na⁺ vacancies in NaBH₄ supercell is most likely to occur in the NaBH₄-doped Mg(NH₂)₂-2LiH system because of the close contact of the species at the molecular level caused by energetic milling. To further elucidate the stability of a Mg atom or cation in the matrix of NaBH₄, the overall binding energy (E_binding(X)) of the Mg atom or cation with the surrounding atoms was calculated according to the following equation:⁴⁵

where E_tot is the total energy of the whole system, E_tot(X) is the total energy of the system without X atom or ion, N_X is the number of X atoms or ions in the supercell and E(X) is the energy of an X atom. The positive or negative value denotes the unstable or stable defect state of Mg in NaBH₄. As shown in Table 3, the replacement of Mg²⁺ for Na⁺ exhibits the lowest overall binding energy of −3.83 eV, which implies that the movement of Mg²⁺ into the NaBH₄ structures by taking Na⁺ positions is thermodynamically feasible. The substitution of Mg²⁺ for Na⁺ in NaBH₄ may decrease the lattice parameters, but its structure remains almost unchanged, which is consistant with the XRD results as shown in Fig. 1, 4 and 7.

Table 3 Formation energies of Mg substituted for Na⁺ or BH₄⁻ in NaBH₄ and the overall binding energy of Mg with the matrix of NaBH₄

Defects (X^q)	NaBH4 supercell
	Mg@Na^+	Mg ^+ @Na^+	Mg^2^+ @Na^+	Mg@BH4^−	Mg ^+ @BH4^−	Mg^2^+ @BH4^−
ΔE(X^q) (eV)	4.05	2.48	1.06	5.45	6.64	7.77
E binding(Mg) (eV)	2.96	−0.51	−3.83	1.43	0.72	−0.07

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According to the above calculations, it can be seen that the formation energy for Mg vacancies in Mg(NH₂)₂ and Na⁺ vacancies in NaBH₄ is relatively low. So it is easy to create a Mg vacancy in Mg(NH₂)₂ and a Na⁺ vacancy in NaBH₄. The dispelled Mg may convert to a Mg²⁺ cation via charge transfer on the surface of Mg(NH₂)₂. Then, the substitution of Mg²⁺ for Na⁺ in NaBH₄ is energetically favorable. Moreover, the overall binding energy of Mg²⁺ with its surrounding atoms in the NaBH₄ supercell is the lowest in the present study, which implies that Mg²⁺ can stably stay at the Na⁺ position in NaBH₄. As a result, it increases Mg vacancies in Mg(NH₂)₂, and is responsible for the shrinkage in the lattice parameters of Mg(NH₂)₂ in the re-hydrogenation process as observed in Fig. 9. The increase of Mg vacancies not only weakens the N–H bonds but also promotes the diffusion of atoms and/or ions, consequently resulting in an improvement in the reaction kinetics of hydrogen desorption/absorption of the NaBH₄-added Mg(NH₂)₂-2LiH system.

4. Conclusions

The hydrogen storage properties of the NaBH₄-added Mg(NH₂)₂-2LiH system and the catalytic mechanisms of NaBH₄ on the system were systematically investigated by experimental examinations and first-principles calculations. It was found that the dehydrogenation kinetics of the Mg(NH₂)₂-2LiH system was improved by introducing NaBH₄ with a 12 °C reduction in the peak temperature of dehydrogenation of the Mg(NH₂)₂-2LiH-0.1NaBH₄ sample. Structural analyses showed that in the whole dehydrogenation process, Mg(NH₂)₂ reacted with LiH to convert to Li₂MgN₂H₂ while NaBH₄ remains almost unchanged. First-principles calculations exhibited a low formation energy for Mg vacancies in Mg(NH₂)₂ and a favorable overall binding energy of Mg²⁺ with its surrounding atoms in the NaBH₄ supercell, which facilitate the formation of Mg vacancies in the NaBH₄-doped Mg(NH₂)₂-2LiH system. The presence of Mg vacancies enhances the reaction kinetics of hydrogen desorption/absorption of the NaBH₄-added Mg(NH₂)₂-2LiH system. So the adoption of a manufacturing process which increases the crystal defects and the introduction into the system the species which weakens the N–H bonds are both effective approaches for further improving the hydrogen release/uptake kinetics of the amides/hydrides combined system used for hydrogen storage.

Acknowledgements

The authors would like to acknowledge the financial support from National Natural Science Foundation of China (Grant Nos.: 51025102, 50701040 and 50871100), from the Ministry of Science and Technology of China (Grant Nos.: 2009AA05Z106 and 2010CB631304) and from Zhejiang Innovation Program for Graduates (Grant No.: YK2009003).

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