#
Transformation Kinetics of LiBH_{4}–MgH_{2} for Hydrogen Storage

^{1}

^{2}

^{3}

^{4}

^{5}

^{*}

## Abstract

**:**

_{4}–MgH

_{2}is regarded as one of the most promising materials for hydrogen storage. Its extensive application is so far limited by its poor dehydrogenation kinetics, due to the hampered nucleation and growth process of MgB

_{2}. Nevertheless, the poor kinetics can be improved by additives. This work studied the growth process of MgB

_{2}with varying contents of 3TiCl

_{3}·AlCl

_{3}as an additive, and combined kinetic measurements, X-ray diffraction (XRD), and advanced transmission electron microscopy (TEM) to develop a structural understanding. It was found that the formation of MgB

_{2}preferentially occurs on TiB

_{2}nanoparticles. The major reason for this is that the elastic strain energy density can be reduced to ~4.7 × 10

^{7}J/m

^{3}by creating an interface between MgB

_{2}and TiB

_{2}, as opposed to ~2.9 × 10

^{8}J/m

^{3}at the original interface between MgB

_{2}and Mg. The kinetics of the MgB

_{2}growth was modeled by the Johnson–Mehl–Avrami–Kolmogorov (JMAK) equation, describing the kinetics better than other kinetic models. It is suggested that the MgB

_{2}growth rate-controlling step is changed from interface- to diffusion-controlled when the nucleation center changes from Mg to TiB

_{2}. This transition is also reflected in the change of the MgB

_{2}morphology from bar- to platelet-like. Based on our observations, we suggest that an additive content between 2.5 and 5 mol% 3TiCl

_{3}·AlCl

_{3}results in the best enhancement of the dehydrogenation kinetics.

## 1. Introduction

_{4}–MgH

_{2}is one of the promising reactive hydride composites for hydrogen storage [8,9,10]. By combining the complex metal hydride LiBH

_{4}and the metal hydride MgH

_{2}, the standard dehydrogenation enthalpy of the mixture is remarkably lowered by ~25 kJ·mol

^{−1}H

_{2}[11,12,13]. This should lead to a dehydrogenation temperature of about 170 °C, with an excellent hydrogen storage capacity of about 11.5 wt% still reserved. According to preceding studies, the dehydrogenation of LiBH

_{4}–MgH

_{2}occurs in two steps [14]. First, MgH

_{2}decomposes into H

_{2}and Mg. Then, the generated Mg reacts with LiBH

_{4}to produce MgB

_{2}and LiH, releasing the remaining H

_{2}from LiBH

_{4}. However, after the first step of the reaction, it can take more than 10 h until the second step begins, which is not acceptable for commercial utilization [15]. The long waiting time between the two reaction steps has been attributed to the sluggish nucleation process of MgB

_{2}[16]. It was later reported that this obstacle can be overcome by some transition metal additives, which notably accelerate the kinetics [14,17]. Bösenberg et al. suggested that the involvement of these additives may create more coherent nucleation sites promoting the nucleation of MgB

_{2}by lowering the interfacial strain energy [18]. This hypothesis was later experimentally validated by Jin et al., who additionally distinguished between two different MgB

_{2}morphologies by transmission electron microscopy (TEM) [19]. They considered the generation of MgB

_{2}platelets assisted by additives rather than the generation of MgB

_{2}bars based on Mg as an indication of a small interatomic misfit between the two phases, which is the origin of the improved kinetic performance. However, the additive effect on the subsequent growth process for MgB

_{2}has not been fully clarified yet. This knowledge would be another essential cornerstone of building up a comprehensive understanding of the transformation kinetics of LiBH

_{4}–MgH

_{2}.

_{3}·AlCl

_{3}additives were added to LiBH

_{4}–MgH

_{2}to study their impact on the MgB

_{2}formation after dehydrogenation using advanced TEM techniques. The applied TEM techniques include electron energy loss spectroscopy (EELS), 4D scanning transmission electron microscopy (4DSTEM) and electron tomography etc. The TEM results have been combined with the results from kinetic measurements and X-ray diffraction (XRD) for further analysis.

## 2. Results and Discussion

#### 2.1. Material Characterization by XRD and Kinetic Performance

_{3}·AlCl

_{3}additive in the as-milled state. Different peaks were detected, marking the reactants LiBH

_{4}and MgH

_{2}. In addition to this, LiCl can also be identified in the diffractogram when the additive content exceeds 2.5 mol%. This by-product is generated from the reaction between LiBH

_{4}and 3TiCl

_{3}·AlCl

_{3}during the ball milling. With 10 mol% additives, the LiCl peaks are significantly enhanced, whereas the peaks for LiBH

_{4}are greatly weakened. This happens as LiBH

_{4}is consumed by the additive [20]. For the desorbed samples, the diffraction peaks of the LiBH

_{4}and MgH

_{2}were not observed, see Figure 1b, while the peaks of LiH and MgB

_{2}appeared. This indicates that the reaction between LiBH

_{4}and MgH

_{2}proceeded with the generation of MgB

_{2}.

_{4}–MgH

_{2}is completed is to monitor the amount of hydrogen released from the material over time. As shown in Figure 1c, the more additive that was added to the system, the less hydrogen was released, which is consistent with the intensified LiCl peaks shown in Figure 1a,b. This means that less LiBH

_{4}is available for the reaction with MgH

_{2}. One anomaly is that the sample without additives only released less than 10 mol% H

_{2}, which is below the expectation of a theoretical value of 11.5 mol% H

_{2}. This can be attributed to the partial oxidation of LiBH

_{4}or/and MgH

_{2}, the low purity of the raw materials from the suppliers, or the inhomogeneous dispersion of reactants over ball milling, and so on. It is also notable that the additive improves the dehydrogenation kinetics very effectively. In contrast to the curve with respect to hydrogen release from the sample without additives, the incubation stage almost entirely disappeared with the addition of only 1 mol% 3TiCl

_{3}·AlCl

_{3}. In general, the duration of the dehydrogenation process is shortened from about 12 h without additives to about 4 h with additives. Furthermore, these curves seem to have different sigmoidal patterns, which might relate to the different MgB

_{2}growths during the reaction between LiBH

_{4}and Mg.

#### 2.2. Observation of MgB_{2} Using TEM

_{4}–MgH

_{2}prior to dehydrogenation. The corresponding diffraction pattern shows the diffraction spots representing MgH

_{2}. The missing crystallographic information for LiBH

_{4}in the diffraction pattern can presumably be attributed either to oxidation or to electron beam damage, as LiBH

_{4}is both air- and electron-beam-sensitive [21,22]. This speculation can be to some extent confirmed by Figure 2b, which shows the same region as Figure 2a, and delivers the elemental distribution of magnesium and oxygen, as obtained by local EDX. The distribution of Mg directly represents the distribution of MgH

_{2}, since Mg only exists as MgH

_{2}in this region. What’s interesting is that the MgH

_{2}grains are embedded in some of the oxygen-containing material. It is thus reasonable to assume that this material corresponds to oxidized LiBH

_{4}present in the surrounding area.

_{4}–MgH

_{2}. The diffraction pattern was taken from the corresponding 4D-STEM data stack. Accordingly, the crystals growing in the same direction are MgB

_{2}, and their growth direction is $\left[1\overline{2}10\right]$. This is in agreement with previous studies [19]. The uniform distribution of magnesium and boron recorded via STEM-EELS (Figure 2d) further proves the formation of MgB

_{2}with a bar-shaped morphology. Given the crystal structure and the rectangular bar-like morphology of MgB

_{2}, the other two directions that are vertical to $\left[1\overline{2}10\right]$ were determined to be $\left[10\overline{1}0\right]$ and $\left[0002\right]$, see Figure 2e. The disappearance of LiH may be due to electron beam damage [23].

_{3}·AlCl

_{3}was added, and then continued with the results on samples with a lower additive content. Figure 3a exhibits the desorbed LiBH

_{4}–MgH

_{2}with 10 mol% 3TiCl

_{3}·AlCl

_{3}, with the major crystal also being MgB

_{2}according to the diffraction pattern. Figure 3b displays the EDX map of Mg and Ti, showing the distribution of MgB

_{2}and Ti-containing materials. Similar to the previous observations without additives, there are parallel MgB

_{2}crystals oriented in the same direction, yet with a much smaller size. To determine the MgB

_{2}morphology in this case, STEM tomography analyses were carried out on the region shown in Figure 3a. Figure 3c displays the tomography images reconstructed from the EDX map of Mg at different angles. One exemplarily selected piece of MgB

_{2}in the yellow box marked in both Figure 3a,c was further studied; see Figure 3d. In contrast to the bar-like MgB

_{2}crystals displayed in Figure 2c,d, a regular hexagonal platelet appeared in the case of the 10 mol% additive. As illustrated in Figure 3e, given the hexagonal close-packed (hcp) crystal structure of MgB

_{2}, it can be immediately determined that this corresponds to the basal plane $\left\{0002\right\}$ [24]. The six-fold symmetrical surface planes can also be indexed. The two possible candidates for these planes are the primary prism plane $\left\{10\overline{1}0\right\}$ and the second prism plane $\left\{1\overline{2}10\right\}$, as shown in Figure 3e. According to recent studies, the bar-like MgB

_{2}crystals nucleate on Mg grains, whereas the nucleation of platelet-like MgB

_{2}occurs on TiB

_{2}nanoparticles [19]. Based on the edge-to-edge matching model [25,26,27], their respective orientation relationships and the corresponding misfits have been previously determined, which are summarized in Table 1.

_{2}can be then calculated by substituting the Miller indices of the lattice plane $\mathrm{hkil}$, the elastic constants ${\mathrm{C}}_{11}$ = 365 GPa, ${\mathrm{C}}_{12}$ = 98 GPa, ${\mathrm{C}}_{13}$ = 65 GPa, ${\mathrm{C}}_{33}$ = 203 GPa and ${\mathrm{C}}_{44}$ = 58 GPa, and the lattice constants $\mathrm{a}$ = 3.0851 Å and $\mathrm{c}$ = 3.5201 Å into Equation (1) [29,30]. The compliances ${\mathrm{S}}_{\mathrm{ij}}$ in the equation can be transferred from the elastic constants ${\mathrm{C}}_{\mathrm{lk}}$ based on the given crystal structure [31].

_{2}; see Table 2.

_{2}, the large energy density of more than 7 × 10

^{8}J/m

^{3}along the $\langle 0002\rangle $ direction explains why both MgB

_{2}bars (on Mg) and MgB

_{2}platelets (on TiB

_{2}) appeared to be rather thin in this direction. For Mg, the nucleation and growth of MgB

_{2}along the $\langle 10\overline{1}0\rangle $ direction on Mg also led to a significant amount of strain energy density of up to 3·10

^{8}J/m

^{3}. The related high strain energy at the interface may account for the primary growth along the $\langle 1\overline{2}10\rangle $ direction, which is perpendicular to the interface between MgB

_{2}and Mg, leading to the morphology of a rectangular bar. In contrast for TiB

_{2}, the nucleation of MgB

_{2}along either $\langle 10\overline{1}0\rangle $ or $\langle 1\overline{2}10\rangle $ on TiB

_{2}is equivalent from an energetic point of view, leading to a significantly smaller strain energy density of only 4.7·10

^{7}J/m

^{3}. This value is about an order of magnitude smaller than that of the corresponding growth on Mg, which explains the more isotropic morphology of the hexagonal MgB

_{2}platelets. MgB

_{2}bars are also distinct from MgB

_{2}platelets in terms of their aspect ratio, which is much larger than one, indicating that they grow predominantly in one direction.

_{2}crystals observed in both cases (with or without additives). We can understand where the parallel alignment of the MgB

_{2}bars has come from, as Mg grains are large enough to provide sufficient surface area for the nucleation of several MgB

_{2}bars on the same plane; see Figure 2b. Since the nucleation of MgB

_{2}follows a specific crystallographic orientation with respect to Mg, it is natural for the MgB

_{2}crystals nucleating on the same Mg plane to grow in the same direction. However, given the distance between two parallel MgB

_{2}platelets up to several hundred nanometers (Figure 3a), and the size of TiB

_{2}nanoparticles (Figure 3b), it is not likely for two MgB

_{2}platelets to nucleate and grow on the same TiB

_{2}nanoparticle. From this perspective, one assumption is that some TiB

_{2}nanoparticles may be attached to Mg grains in certain orientations with respect to Mg to minimize their interfacial energy during the dehydrogenation process. The nucleation of MgB

_{2}is then more likely to first occur on these attached nanoparticles. This is not only because the nucleation of MgB

_{2}based on TiB

_{2}requires less strain energy per unit volume, but also because the diffusion distance for Mg atoms is much shorter, as these TiB

_{2}nanoparticles are directly attached on the surface of Mg grains.

_{2}morphology on the additive content, samples added with lower contents of 3TiCl

_{3}·AlCl

_{3}were also studied. Figure 4a shows a STEM-HAADF image of the sample with 1 mol% additives after dehydrogenation. Again, the corresponding diffraction pattern confirms the existence of MgB

_{2}. By comparing this image with the corresponding elemental distribution of Mg, the parallel-oriented crystals of MgB

_{2}can be recognized in the agglomerate. As indicated in Figure 4a, two parallel MgB

_{2}crystals were selected for electron tomography measurements. It turns out that both pieces of MgB

_{2}have a bar-like morphology (Figure 4b). In some other regions, a MgB

_{2}morphology similar to Figure 3 can also be observed, which indicates the generation of MgB

_{2}platelets (Figure 4c). These observations indicate that the nucleation of MgB

_{2}on Mg has occurred. Besides, the nucleation of MgB

_{2}on TiB

_{2}was not as dominant as in the case of 10 mol% additives, where no more MgB

_{2}bars were observed. This also implies that there is a competition between the nucleation on Mg grains and TiB

_{2}nanoparticles for Mg and B atoms to generate MgB

_{2}bars or MgB

_{2}platelets.

_{2}bars in some areas (Figure 5a,b). After further increasing the additive content to 5 mol%, the majority of the observed MgB

_{2}crystals were platelet-like, as shown in Figure 5c,d. This can be further verified by the tomography analysis on the piece of MgB

_{2}highlighted in the yellow box in Figure 5c. These tomography images display a MgB

_{2}platelet at different angles. Based on these observations, it seems to imply a turning point in the competition between the nucleation on Mg and TiB

_{2}.

#### 2.3. Kinetic Modeling

_{3}·AlCl

_{3}are added to LiBH

_{4}–MgH

_{2}, the dehydrogenation processes of LiBH

_{4}–MgH

_{2}differ. This difference is not only reflected in the change in MgB

_{2}morphology, but also in the change in the hydrogen release rate. Regarding the additive-promoted dehydrogenation process, the shortened incubation stage that relates to the accelerated nucleation of MgB

_{2}plays an essential role, as shown in Figure 1c. In addition, the subsequent step of MgB

_{2}growth that accompanies a massive amount of hydrogen release is also crucial to the improvement of the dehydrogenation kinetics of LiBH

_{4}–MgH

_{2}. This aspect is discussed in the following.

_{2}is completed and all the released hydrogen in this case is coming from the reaction between LiBH

_{4}and Mg.

_{2}platelets are faster than those of MgB

_{2}bars. It is thus intuitive to consider a positive correlation between the hydrogen release rate and the amount of 3TiCl

_{3}·AlCl

_{3}. However, after approximately 50% of hydrogen was released, the hydrogen release rate of the sample with 10 mol% additives was smaller than that of the samples with smaller amounts of additives. One reasonable interpretation is that the mutual impingement between the generated phases becomes even more furious, as more nucleation centers of TiB

_{2}exist in the surrounding environment, which inversely decelerates the dehydrogenation process. This might also be an indication of an oversaturation of the sample with additives. Nonetheless, it is still important to study extreme cases so that the physical mechanisms behind the growth of MgB

_{2}can be distinguished and clarified.

_{2}growth for the respective samples, this equation was applied to model the process of the MgB

_{2}growth; see Equation (2) [32,33]:

_{2}phase), $\mathrm{k}$ denotes the reaction rate constant that depends on temperature and $\mathrm{n}$ refers to the Avrami exponent. The numerical value of the Avrami exponent $\mathrm{n}$ can be regarded as an indicator of the growth dimensionality for MgB

_{2}crystals and the related rate-controlling steps [32,34]. In general, $\mathrm{n}$ is equal to $\mathrm{d}/\mathrm{m}$, where d represents the dimensionality of crystal growth with the conditions that $1\le \mathrm{d}\le 2$ refers to one-dimensional growth (e.g., needle), $2\le \mathrm{d}\le 3$ refers to two-dimensional growth (e.g., platelet and sheet), and $3\le \mathrm{d}\le 4$ refers to three-dimensional growth (e.g., sphere). The value of $\mathrm{m}$ indicates the rate-controlling step for the phase transformation, with $\mathrm{m}=1$ referring to the interface-controlled growth, and $\mathrm{m}=2$ representing the diffusion-controlled growth. To determine $\mathrm{n}$ for each sample, we can rewrite Equation (2) as:

_{2}crystals, the MgB

_{2}growth was determined to be mainly two-dimensional, as the morphology extension in the third dimension along the c axis is almost negligible. The value of dimensionality $\mathrm{d}$ is therefore located between two and three. From this perspective, $\mathrm{m}=1$ and $\mathrm{m}=2$ can be assigned to the two most extreme cases: without additives ($\mathrm{n}=2.32$) and with 10 mol% additives ($\mathrm{n}=1.25$), since only one MgB

_{2}morphology exists for either case. Based on these values, the growth rate-controlling steps were determined to be mainly interface-controlled or mainly diffusion-controlled, respectively. The change in the growth rate-controlling step is also in agreement with the discussed decrease in the elastic strain energy density at the interface between MgB

_{2}and TiB

_{2}compared with that between MgB

_{2}and Mg during the formation of MgB

_{2}. For the samples with a lower additive content, where both MgB

_{2}bars and platelets were observed, it can therefore be expected that the interface-controlled and the diffusion-controlled growth may affect the dehydrogenation process simultaneously. Their Avrami exponents are thus more likely to reflect the simultaneous contribution from both growth mechanisms with varying weights for each case. This can be additionally confirmed by the decrease in their R-square values, indicating a worsened fit. When increasing the additive content up to 10 mol%, the R-square value improved again. This can be explained by the dominance of the diffusion-controlled growth, which is in agreement with the fact that only MgB

_{2}platelets have been observed in this case.

_{2}platelets becomes gradually dominant. The transition in the growth rate-controlling step is also consistent with the TEM observations, where much fewer MgB

_{2}bars were found when the additive content was increased to 5 mol%.

_{4}–MgH

_{2}over time.

## 3. Materials and Methods

#### 3.1. Material Preparations

_{2}(95% purity, Rockwood Lithium GmbH), LiBH

_{4}(95% purity, Sigma-Aldrich), and 3TiCl

_{3}·AlCl

_{3}(about 76–78% TiCl

_{3}purity, Fischer Scientific). The LiBH

_{4}–MgH

_{2}composite was mixed with a molar content of x% 3TiCl

_{3}·AlCl

_{3}(x = 0, 1, 2.5, 5 and 10). To achieve a fine mixing of the reactants and an even dispersion of the additives, the prepared material mixtures (about 3 g), namely 2LiBH

_{4}–MgH

_{2}or 2LiBH

_{4}–MgH

_{2}–3TiCl

_{3}·AlCl

_{3}, were charged into stainless steel vials with stainless steel balls in a ball to powder ratio of 20:1. The milling proceeded for 400 min using a Spex 8000M Mixer Mill. Both the powder handling and milling were performed under an argon atmosphere in a glovebox (O

_{2}, H

_{2}O < 0.5 ppm).

#### 3.2. Kinetics Measurements

^{−1}under a hydrogen atmosphere of 4 bar. After reaching the target temperature of 400 °C, the materials were kept under isothermal conditions for several hours.

#### 3.3. XRD Experiments

_{2}, H

_{2}O < 0.5 ppm).

#### 3.4. TEM Experiments

_{2}, H

_{2}O < 0.5 ppm). Sample powders were dispersed in toluene and ultra-sonicated for 1 min before being distributed on lacey carbon-coated gold TEM grids with the item number S166-A3-V (Plano GmbH). Subsequently, they were transferred under argon from the glovebox into the microscope with a vacuum transfer holder (model number 648, AMETEK Gatan Inc.).

_{4}–MgH

_{2}with 1 mol% 3TiCl

_{3}·AlCl

_{3}, from −74° to 76° for the desorbed 2LiBH

_{4}–MgH

_{2}with 5 mol% 3TiCl

_{3}·AlCl

_{3}and from −66° to 72° for the desorbed 2LiBH

_{4}–MgH

_{2}with 10 mol% 3TiCl

_{3}·AlCl

_{3}. Electron tomography combined with EDX mapping was also carried out on the desorbed 2LiBH

_{4}–MgH

_{2}with 10 mol% 3TiCl

_{3}·AlCl

_{3}with a tilt range from −66° to 69° with 3° increments. Each EDX map of Mg was constructed from 900 frames with image dimensions of 256 × 256 pixels and a dwell time of 12 µs. The alignment of the tilt series was performed in IMOD using the cross-correlation method. The aligned tilt series were then reconstructed using the algorithm of simultaneous iterative reconstruction technique (SIRT) with 100 iterations in Inspect3D (Thermo Fisher Scientific Inc.) [39]. The 3D visualization was realized using Avizo 2020.2 (Thermo Fisher Scientific Inc.).

^{7}e nm

^{−2}. STEM electron energy-loss spectroscopy (EELS) SI was acquired using a Continuum 970 HighRes imaging filter (GIF) (AMETEK Gatan Inc.) in dual-EELS mode with 13.64 ms acquisition time for each low-loss spectrum, 136.4 ms for each high-loss spectrum, 21.5 mrad convergence angle, 40 mrad collection angle, and 0.15 eV per channel energy dispersion. The EELS SI data were denoised by principal component analysis (PCA), which effectively reduces the random noise generated during signal recording [40,41].

## 4. Summary

_{4}–MgH

_{2}is controlled by the nucleation and growth of MgB

_{2}in respective orientations. The observed different MgB

_{2}morphologies can be directly correlated to the required elastic strain energy per unit volume. The nucleation of MgB

_{2}on Mg requires an energy up to 2.9 × 10

^{8}J/m

^{3}in the $\langle 10\overline{1}0\rangle $ direction, whereas it needs only 4.7·10

^{7}J/m

^{3}for the nucleation of MgB

_{2}on TiB

_{2}in the $\langle 10\overline{1}0\rangle $ or $\langle 1\overline{2}10\rangle $ directions. The formation of MgB

_{2}may occur primarily on those TiB

_{2}nanoparticles that adhere to Mg grains, which leads to the generation of parallel MgB

_{2}platelets. According to the JMAK equation parameter interpretation, the growth rate-controlling steps for MgB

_{2}bars or platelets are interface-controlled or diffusion-controlled, respectively. The change in the growth mechanism is consistent with the decreased elastic strain energy density determined for the nucleation of MgB

_{2}on TiB

_{2}and the change in the morphology of MgB

_{2}when additives were included. Based on the second dehydrogenation growth kinetics, the best additive content that accelerates the dehydrogenation process of LiBH

_{4}–MgH

_{2}the most is between 2.5 mol% and 5 mol%. However, given the consumption of LiBH

_{4}by additives, the trade-off between a reduced hydrogen storage capacity and improved kinetics also needs to be carefully considered in practice.

## Supplementary Materials

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Sample Availability

## References

- Twidell, J. Renewable Energy Resource; Routledge: London, UK, 2021. [Google Scholar]
- von Colbe, J.B.; Ares, J.R.; Barale, J.; Baricco, M.; Buckley, C.; Capurso, G.; Gallandat, N.; Grant, D.M.; Guzik, M.N.; Jacob, I.; et al. Application of hydrides in hydrogen storage and compression: Achievements, outlook and perspectives. Int. J. Hydrogen Energy
**2019**, 44, 7780–7808. [Google Scholar] [CrossRef] - Yu, X.; Tang, Z.; Sun, D.; Ouyang, L.; Zhu, M. Recent advances and remaining challenges of nanostructured materials for hydrogen storage applications. Prog. Mater. Sci.
**2017**, 88, 1–48. [Google Scholar] [CrossRef] - Pistidda, C. Solid-State Hydrogen Storage for a Decarbonized Society. Hydrogen
**2021**, 2, 428–443. [Google Scholar] [CrossRef] - Züttel, A. Hydrogen storage methods. Naturwissenschaften
**2004**, 91, 157–172. [Google Scholar] [CrossRef] [PubMed] - Rivard, E.; Trudeau, M.; Zaghib, K. Hydrogen Storage for Mobility: A Review. Materials
**2019**, 12, 1973. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Rusman, N.; Dahari, M. A review on the current progress of metal hydrides material for solid-state hydrogen storage applications. Int. J. Hydrogen Energy
**2016**, 41, 12108–12126. [Google Scholar] [CrossRef] - Milanese, C.; Jensen, T.R.; Hauback, B.C.; Pistidda, C.; Dornheim, M.; Yange, H.; Lombardoe, L.; Zuettele, A.; Filinchuk, Y.; Ngene, P.; et al. Complex hydrides for energy storage. Int. J. Hydrogen Energy
**2019**, 44, 7860–7874. [Google Scholar] [CrossRef] [Green Version] - Jepsen, J.; Milanese, C.; Puszkiel, J.; Girella, A.; Schiavo, B.; Lozano, G.A.; Capurso, G.; von Colbe, J.M.B.; Marini, A.; Kabelac, S.; et al. Fundamental Material Properties of the 2LiBH4-MgH2 Reactive Hydride Composite for Hydrogen Storage: (I) Thermodynamic and Heat Transfer Properties. Energies
**2018**, 11, 1081. [Google Scholar] [CrossRef] [Green Version] - Jepsen, J.; Milanese, C.; Puszkiel, J.; Girella, A.; Schiavo, B.; Lozano, G.A.; Capurso, G.; von Colbe, J.M.B.; Marini, A.; Kabelac, S.; et al. Fundamental Material Properties of the 2LiBH4-MgH2 Reactive Hydride Composite for Hydrogen Storage: (II) Kinetic Properties. Energies
**2018**, 11, 1170. [Google Scholar] [CrossRef] [Green Version] - Vajo, J.J.; Skeith, S.L.; Mertens, F. Reversible Storage of Hydrogen in Destabilized LiBH
_{4}. J. Phys. Chem. B**2005**, 109, 3719–3722. [Google Scholar] [CrossRef] - Vajo, J.J.; Olson, G.L. Hydrogen storage in destabilized chemical systems. Scr. Mater.
**2007**, 56, 829–834. [Google Scholar] [CrossRef] - Mauron, P.; Buchter, F.; Friedrichs, O.; Remhof, A.; Bielmann, M.; Zwicky, C.N.; Züttel, A. Stability and reversibility of LiBH4. J. Phys. Chem. B
**2008**, 112, 906–910. [Google Scholar] [CrossRef] [PubMed] - Bösenberg, U.; Doppiu, S.; Mosegaard, L.; Barkhordarian, G.; Eigen, N.; Borgschulte, A.; Jensen, T.R.; Cerenius, Y.; Gutfleisch, O.; Klassen, T.; et al. Hydrogen sorption properties of MgH2–LiBH4 composites. Acta Mater.
**2007**, 55, 3951–3958. [Google Scholar] [CrossRef] - Vajo, J.J.; Salguero, T.T.; Gross, A.F.; Skeith, S.L.; Olson, G.L. Thermodynamic destabilization and reaction kinetics in light metal hydride systems. J. Alloys Compd.
**2007**, 446-447, 409–414. [Google Scholar] [CrossRef] - Bösenberg, U.; Ravnsbæk, D.B.; Hagemann, H.; D’Anna, V.; Minella, C.B.; Pistidda, C.; van Beek, W.; Jensen, T.R.; Bormann, R.; Dornheim, M. Pressure and temperature influence on the desorption pathway of the LiBH4−MgH2 composite system. J. Phys. Chem. C
**2010**, 114, 15212–15217. [Google Scholar] [CrossRef] - Shao, H.; Felderhoff, M.; Weidenthaler, C. Kinetics enhancement, reaction pathway change, and mechanism clarification in LiBH4 with Ti-catalyzed nanocrystalline MgH2 composite. J. Phys. Chem. C
**2015**, 119, 2341–2348. [Google Scholar] [CrossRef] - Bösenberg, U.; Kim, J.; Gosslar, D.; Eigen, N.; Jensen, T.R.; Von Colbe, J.B.; Zhou, Y.; Dahms, M.; Kim, D.; Gunther, R.; et al. Role of additives in LiBH4–MgH2 reactive hydride composites for sorption kinetics. Acta Mater.
**2010**, 58, 3381–3389. [Google Scholar] [CrossRef] [Green Version] - Jin, O.; Shang, Y.; Huang, X.; Mu, X.; Szabó, D.V.; Le, T.T.; Wagner, S.; Kübel, C.; Pistidda, C.; Pundt, A. Microstructural Study of MgB2 in the LiBH4-MgH2 Composite by Using TEM. Nanomaterials
**2022**, 12, 1893. [Google Scholar] [CrossRef] - Le, T.-T.; Pistidda, C.; Puszkiel, J.; Riglos, M.V.C.; Karimi, F.; Skibsted, J.; GharibDoust, S.P.; Richter, B.; Emmler, T.; Milanese, C.; et al. Design of a Nanometric AlTi Additive for MgB
_{2}-Based Reactive Hydride Composites with Superior Kinetic Properties. J. Phys. Chem. C**2018**, 122, 7642–7655. [Google Scholar] [CrossRef] [Green Version] - Deprez, E.; Justo, A.; Rojas, T.; López-Cartés, C.; Minella, C.B.; Bösenberg, U.; Dornheim, M.; Bormann, R.; Fernández, A. Microstructural study of the LiBH4–MgH2 reactive hydride composite with and without Ti-isopropoxide additive. Acta Mater.
**2010**, 58, 5683–5694. [Google Scholar] [CrossRef] - Deprez, E.; Muñoz-Márquez, M.A.; Roldán, M.A.; Prestipino, C.; Palomares, F.J.; Minella, C.B.; Bösenberg, U.; Dornheim, M.; Bormann, R.; Fernández, A. Oxidation State and Local Structure of Ti-Based Additives in the Reactive Hydride Composite 2LiBH
_{4}+ MgH_{2}. J. Phys. Chem. C**2010**, 114, 3309–3317. [Google Scholar] [CrossRef] [Green Version] - Herley, P.J.; Jones, W. Transmission Electron Microscopy of Beam-sensitive Metal Hydrides*. Z. Für Phys. Chem.
**1986**, 147, 147–159. [Google Scholar] [CrossRef] - Lee, S. Crystal growth of MgB2. Phys. C: Supercond.
**2003**, 385, 31–41. [Google Scholar] [CrossRef] - Zhang, M.X.; Kelly, P.M. Edge-to-edge matching model for predicting orientation relationships and habit planes—The improvements. Scr. Mater.
**2005**, 52, 963–968. [Google Scholar] [CrossRef] - Zhang, M.-X.; Kelly, P. Edge-to-edge matching and its applications: Part II. Application to Mg–Al, Mg–Y and Mg–Mn alloys. Acta Mater.
**2005**, 53, 1085–1096. [Google Scholar] [CrossRef] - Kelly, P.; Zhang, M.-X. Edge-to-edge matching—The fundamentals. Metall. Mater. Trans. A
**2006**, 37, 833–839. [Google Scholar] [CrossRef] - Parker, G. Encyclopedia of Materials: Science and Technology; Elsevie: Amsterdam, The Netherlands, 2001. [Google Scholar]
- Zhang, J.-M.; Zhang, Y.; Xu, K.-W.; Ji, V. Anisotropic elasticity in hexagonal crystals. Thin Solid Films
**2007**, 515, 7020–7024. [Google Scholar] [CrossRef] - Milman, V.; Warren, M. Elastic properties of TiB2 and MgB2. J. Phys. Condens. Matter
**2001**, 13, 5585. [Google Scholar] [CrossRef] - Cline, C.F.; Dunegan, H.L.; Henderson, G.W. Elastic Constants of Hexagonal BeO, ZnS, and CdSe. J. Appl. Phys.
**1967**, 38, 1944–1948. [Google Scholar] [CrossRef] - Christian, J.W. The Theory of Transformations in Metals and Alloys; Newnes: London, UK, 2002. [Google Scholar]
- Avrami, M. Kinetics of phase change. I General theory. J. Chem. Phys.
**1939**, 7, 1103–1112. [Google Scholar] [CrossRef] - Pang, Y.; Li, Q. A review on kinetic models and corresponding analysis methods for hydrogen storage materials. Int. J. Hydrogen Energy
**2016**, 41, 18072–18087. [Google Scholar] [CrossRef] - Jones, L.; Dollimore, D.; Nicklin, T. Comparison of experimental kinetic decomposition data with master data using a linear plot method. Thermochim. Acta
**1975**, 13, 240–245. [Google Scholar] [CrossRef] - Sharp, J.H.; Brindley, G.W.; Achar, B.N.N. Numerical Data for Some Commonly Used Solid State Reaction Equations. J. Am. Ceram. Soc.
**1966**, 49, 379–382. [Google Scholar] [CrossRef] - Khawam, A.; Flanagan, D.R. Solid-State Kinetic Models: Basics and Mathematical Fundamentals. J. Phys. Chem. B
**2006**, 110, 17315–17328. [Google Scholar] [CrossRef] [PubMed] - Puszkiel, J.A. Tailoring the Kinetic Behavior of Hydride Forming Materials for Hydrogen Storage, in Gold Nanoparticles-Reaching New Heights; IntechOpen: London, UK, 2018. [Google Scholar]
- Gilbert, P. Iterative methods for the three-dimensional reconstruction of an object from projections. J. Theor. Biol.
**1972**, 36, 105–117. [Google Scholar] [CrossRef] - Abdi, H.; Williams, L.J. Principal component analysis. Wiley Interdiscip. Rev. Comput. Stat.
**2010**, 2, 433–459. [Google Scholar] [CrossRef] - Wold, S.; Esbensen, K.; Geladi, P. Principal component analysis. Chemom. Intell. Lab. Syst.
**1987**, 2, 37–52. [Google Scholar] [CrossRef]

**Figure 1.**(

**a**) XRD patterns of as-milled 2LiBH

_{4}–MgH

_{2}with x mol% 3TiCl

_{3}·AlCl

_{3}(x = 0, 1, 2.5, 5 and 10); (

**b**) XRD patterns of desorbed 2LiBH

_{4}–MgH

_{2}with x mol% 3TiCl

_{3}·AlCl

_{3}(x = 0, 1, 2.5, 5 and 10); (

**c**) Measurements of dehydrogenation kinetics for 2LiBH

_{4}–MgH

_{2}with x mol% 3TiCl

_{3}·AlCl

_{3}(x = 0, 1, 2.5, 5 and 10) at 400 °C and under 4 bar H

_{2}, showing the improved dehydrogenation kinetics by the additives.

**Figure 2.**As-milled or desorbed 2LiBH

_{4}–MgH

_{2}without additive: (

**a**) STEM-HAADF image and the corresponding DP of as-milled 2LiBH

_{4}–MgH

_{2}; (

**b**) Summed EDX elemental map that was acquired in the same position as image (

**a**), comprising the elemental distribution of Mg (K lines) and O (K lines); (

**c**) STEM-HAADF image and the corresponding DP of desorbed 2LiBH

_{4}–MgH

_{2}; (

**d**) EELS elemental distribution of Mg (K edge) and B (K edge) with respect to the corresponding STEM-HAADF image of desorbed 2LiBH

_{4}–MgH

_{2}shows the bar-like morphology for MgB

_{2}; (

**e**) Schematic illustration of the crystallographic orientations for a MgB

_{2}rectangular bar growing in the direction $\left[1\overline{2}10\right]$.

**Figure 3.**Desorbed 2LiBH

_{4}–MgH

_{2}with 10 mol% 3TiCl

_{3}·AlCl

_{3}: (

**a**) STEM-HAADF image and the corresponding DP; (

**b**) Summed EDX elemental map of Mg (K lines) and Ti (K lines) acquired in the same position as image a; (

**c**) Tomography images based on the dataset of EDX map of Mg (K lines) acquired in the same region as image a visualized at the angle −90°, 0° and +90°. The MgB

_{2}platelet highlighted in the yellow box is exactly the one highlighted in image (

**a**); (

**d**) 3D visualization from tomographic reconstruction of the selected MgB

_{2}crystal indicated in images (

**a**,

**c**) shows a hexagonal platelet; (

**e**) Schematic illustration of the crystallographic orientations for a MgB

_{2}hexagonal platelet in the zone axis [0002].

**Figure 4.**Desorbed 2LiBH

_{4}–MgH

_{2}with 1 mol% 3TiCl

_{3}•AlCl

_{3}: (

**a**) STEM-HAADF image, and the corresponding DP and EDX elemental map of Mg (K lines), where shows a MgB

_{2}morphology similar to that of Figure 2; (

**b**) Volume rendering from tomographic reconstruction of the parallel MgB

_{2}bars (highlighted in blue) of the following: (

**c**) a STEM-HAADF image and the corresponding EDX map of Mg (K lines) showing the similar morphology of MgB

_{2}as that of Figure 3.

**Figure 5.**Desorbed 2LiBH

_{4}–MgH

_{2}with 2.5 mol% or 5 mol% 3TiCl

_{3}·AlCl

_{3}: (

**a**) STEM-HAADF image and the corresponding DP of desorbed 2LiBH

_{4}–MgH

_{2}with 2.5 mol% 3TiCl

_{3}·AlCl

_{3}; (

**b**) EDX elemental map of Mg (K lines) acquired in the same position as image (a); (

**c**) STEM-HAADF image and the corresponding DP of desorbed 2LiBH

_{4}–MgH

_{2}with 5 mol% 3TiCl

_{3}·AlCl

_{3}; (

**d**) Summed EDX elemental map of Mg (K lines) and Ti (K lines) acquired in the same position as image (

**c**); (

**e**) STEM tomography images acquired in the same region as image (

**c**) visualized at the angle −90°, 0° and +90°. The selected MgB

_{2}platelet highlighted in the yellow box is exactly the one highlighted in image (

**c**).

**Figure 6.**Analysis of the dehydrogenation kinetics with varying contents of additive: (

**a**) Hydrogen release over time relating to the second dehydrogenation step for varying contents of additive; (

**b**) Min–max normalization of the image (

**a**); (

**c**) JMAK plots of $\mathrm{lnln}\left(\frac{1}{1-\mathsf{\alpha}}\right)\mathrm{vs}.\mathrm{ln}\left(\mathrm{t}\right)$ with $\mathsf{\alpha}$ ranging from 15% to 85% based on the image (

**b**); (

**d**) Change in the Avrami exponent n (left blue axis) and the corresponding R-square (right red axis) with the increase of additive content.

**Figure 7.**Comparison of different models for kinetic analysis: (

**a**–

**e**) Plots of (t/t

_{0.5})

_{experimental}vs. (t/t

_{0.5})

_{theoretical}based on the reduced time method for a variety of kinetic models in different scenarios with varying contents of additives (0, 1 mol%, 2.5 mol%, 5 mol% and 10 mol%). The optimal fitting is represented by the straight line for reference; (

**f**) The corresponding slope and intercept for the JMAK model (with different Avrami exponents) according to the plots (

**a**–

**e**) indicates that the JMAK model describes the experimental data the best.

**Table 1.**Orientation relationship between MgB

_{2}and Mg or TiB

_{2}, and their corresponding atomic misfits [19].

$\mathbf{Interatomic}\mathbf{Planes},\mathbf{Misfit}{\mathbf{\delta}}_{\mathbf{h}\mathbf{k}\mathbf{i}\mathbf{l}}^{2}$ | $\mathbf{Interatomic}\mathbf{Directions},\mathbf{Misfit}{\mathbf{\delta}}_{\mathbf{h}\mathbf{k}\mathbf{i}\mathbf{l}}^{2}$ | |
---|---|---|

MgB_{2} on Mg | $\left\{0002\right\}|\left\{1\overline{2}10\right\}$, −9.3% | $\langle 10\overline{1}0\rangle \left|\right|\langle 10\overline{1}0\rangle $, 4.2% |

MgB_{2} on TiB_{2} | $\left\{0002\right\}|\left\{0002\right\}$, −8.9% | $\langle 10\overline{1}0\rangle \left|\right|\langle 10\overline{1}0\rangle $, −1.7% |

$\langle 1\overline{2}10\rangle \left|\right|\langle 1\overline{2}10\rangle $, −1.7% |

**Table 2.**The Young’s modulus and the elastic strain energy densities for MgB

_{2}nucleating in the directions $0002$, $10\overline{1}0$ and $1\overline{2}10$ on the respective nucleation centers Mg and TiB

_{2}.

Lattice Plane | $0002$ | $10\overline{1}0$ | $1\overline{2}10$ |
---|---|---|---|

${Y}_{hkl}$(GPa) | 184.7 | 326.9 | 326.9 |

${\u03f5}_{hkl}$(J/m^{3}) | 7.4 × 10^{8} (on Mg)7.3 × 10 ^{8} (on TiB_{2}) | 2.9 × 10^{8} (on Mg)4.7 × 10 ^{7} (on TiB_{2}) | 4.7 × 10^{7} (on TiB_{2}) |

Model | $\mathbf{k}*\mathbf{t}=$ |
---|---|

Two-dimensional growth of contracting volume (2D CV) | $1-{\left(1-\mathsf{\alpha}\right)}^{1/2}$ |

Three-dimensional growth of contracting volume (3D CV) | $1-{\left(1-\mathsf{\alpha}\right)}^{1/3}$ |

One-dimensional diffusion (1D Diffusion) | ${\mathsf{\alpha}}^{2}$ |

Two-dimensional diffusion (2D Diffusion) | $\left[\left(1-\mathsf{\alpha}\right)\mathrm{ln}\left(1-\mathsf{\alpha}\right)\right]+\mathsf{\alpha}$ |

Three-dimensional diffusion of Ginstling-Braunshtein equation (3D Diffusion of GB) | $1-\frac{2}{3}\mathsf{\alpha}-{\left(1-\mathsf{\alpha}\right)}^{2/3}$ |

Three-dimensional diffusion of Jander equation (3D Diffusion of Jander) | ${\left(1-{\left(1-\mathsf{\alpha}\right)}^{1/3}\right)}^{2}$ |

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**MDPI and ACS Style**

Jin, O.; Shang, Y.; Huang, X.; Szabó, D.V.; Le, T.T.; Wagner, S.; Klassen, T.; Kübel, C.; Pistidda, C.; Pundt, A.
Transformation Kinetics of LiBH_{4}–MgH_{2} for Hydrogen Storage. *Molecules* **2022**, *27*, 7005.
https://doi.org/10.3390/molecules27207005

**AMA Style**

Jin O, Shang Y, Huang X, Szabó DV, Le TT, Wagner S, Klassen T, Kübel C, Pistidda C, Pundt A.
Transformation Kinetics of LiBH_{4}–MgH_{2} for Hydrogen Storage. *Molecules*. 2022; 27(20):7005.
https://doi.org/10.3390/molecules27207005

**Chicago/Turabian Style**

Jin, Ou, Yuanyuan Shang, Xiaohui Huang, Dorothée Vinga Szabó, Thi Thu Le, Stefan Wagner, Thomas Klassen, Christian Kübel, Claudio Pistidda, and Astrid Pundt.
2022. "Transformation Kinetics of LiBH_{4}–MgH_{2} for Hydrogen Storage" *Molecules* 27, no. 20: 7005.
https://doi.org/10.3390/molecules27207005