Transformation Kinetics of LiBH₄–MgH₂ for Hydrogen Storage

Abstract

The reactive hydride composite (RHC) LiBH₄–MgH₂ 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 MgB₂. Nevertheless, the poor kinetics can be improved by additives. This work studied the growth process of MgB₂ with varying contents of 3TiCl₃·AlCl₃ 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 MgB₂ preferentially occurs on TiB₂ nanoparticles. The major reason for this is that the elastic strain energy density can be reduced to ~4.7 × 10⁷ J/m³ by creating an interface between MgB₂ and TiB₂, as opposed to ~2.9 × 10⁸ J/m³ at the original interface between MgB₂ and Mg. The kinetics of the MgB₂ growth was modeled by the Johnson–Mehl–Avrami–Kolmogorov (JMAK) equation, describing the kinetics better than other kinetic models. It is suggested that the MgB₂ growth rate-controlling step is changed from interface- to diffusion-controlled when the nucleation center changes from Mg to TiB₂. This transition is also reflected in the change of the MgB₂ morphology from bar- to platelet-like. Based on our observations, we suggest that an additive content between 2.5 and 5 mol% 3TiCl₃·AlCl₃ results in the best enhancement of the dehydrogenation kinetics.

1. Introduction

In the context of a low-carbon economy and the present global energy crisis, there is a rapidly growing demand for sustainable energy based on renewable energy sources, e.g., solar, wind power, and hydroelectric power [1]. Countless studies have been devoted to storing power from these intermittent sources. In addition to electrical energy storage, another important option is to store energy in the form of hydrogen in various media [2,3,4]. Hydrogen as a zero-carbon fuel can deliver an excellent energy density of approximately 120 MJ/kg. Currently, the most commercially utilized way to store hydrogen is by compressing hydrogen under ultrahigh pressure up to several hundred bars or by liquefying hydrogen below its boiling point down to −253 °C under atmospheric pressure and keeping it in specifically designed vessels [5,6]. However, harsh conditions are still necessary for both approaches, which will inevitably reduce the public acceptance of the extensive application of hydrogen. Therefore, storing hydrogen in solid-state materials is commonly regarded as the promising form of hydrogen storage [7].

LiBH₄–MgH₂ is one of the promising reactive hydride composites for hydrogen storage [8,9,10]. By combining the complex metal hydride LiBH₄ and the metal hydride MgH₂, the standard dehydrogenation enthalpy of the mixture is remarkably lowered by ~25 kJ·mol⁻¹ H₂ [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 LiBH₄–MgH₂ occurs in two steps [14]. First, MgH₂ decomposes into H₂ and Mg. Then, the generated Mg reacts with LiBH₄ to produce MgB₂ and LiH, releasing the remaining H₂ from LiBH₄. 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 MgB₂ [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 MgB₂ by lowering the interfacial strain energy [18]. This hypothesis was later experimentally validated by Jin et al., who additionally distinguished between two different MgB₂ morphologies by transmission electron microscopy (TEM) [19]. They considered the generation of MgB₂ platelets assisted by additives rather than the generation of MgB₂ 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 MgB₂ has not been fully clarified yet. This knowledge would be another essential cornerstone of building up a comprehensive understanding of the transformation kinetics of LiBH₄–MgH₂.

In this work, varying amounts of 3TiCl₃·AlCl₃ additives were added to LiBH₄–MgH₂ to study their impact on the MgB₂ 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

Figure 1a shows the XRD diffractograms of the samples with varying contents of 3TiCl₃·AlCl₃ additive in the as-milled state. Different peaks were detected, marking the reactants LiBH₄ and MgH₂. 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 LiBH₄ and 3TiCl₃·AlCl₃ during the ball milling. With 10 mol% additives, the LiCl peaks are significantly enhanced, whereas the peaks for LiBH₄ are greatly weakened. This happens as LiBH₄ is consumed by the additive [20]. For the desorbed samples, the diffraction peaks of the LiBH₄ and MgH₂ were not observed, see Figure 1b, while the peaks of LiH and MgB₂ appeared. This indicates that the reaction between LiBH₄ and MgH₂ proceeded with the generation of MgB₂.

Another way to verify that the dehydrogenation process of LiBH₄–MgH₂ 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 LiBH₄ is available for the reaction with MgH₂. One anomaly is that the sample without additives only released less than 10 mol% H₂, which is below the expectation of a theoretical value of 11.5 mol% H₂. This can be attributed to the partial oxidation of LiBH₄ or/and MgH₂, 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% 3TiCl₃·AlCl₃. 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 MgB₂ growths during the reaction between LiBH₄ and Mg.

2.2. Observation of MgB₂ Using TEM

Figure 2a exhibits the morphology of the reactants LiBH₄–MgH₂ prior to dehydrogenation. The corresponding diffraction pattern shows the diffraction spots representing MgH₂. The missing crystallographic information for LiBH₄ in the diffraction pattern can presumably be attributed either to oxidation or to electron beam damage, as LiBH₄ 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 MgH₂, since Mg only exists as MgH₂ in this region. What’s interesting is that the MgH₂ grains are embedded in some of the oxygen-containing material. It is thus reasonable to assume that this material corresponds to oxidized LiBH₄ present in the surrounding area.

Figure 2c exhibits the STEM-HAADF image of the material after dehydrogenation of LiBH₄–MgH₂. The diffraction pattern was taken from the corresponding 4D-STEM data stack. Accordingly, the crystals growing in the same direction are MgB₂, 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 MgB₂ with a bar-shaped morphology. Given the crystal structure and the rectangular bar-like morphology of MgB₂, 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].

For a more detailed comparison, we first focused on the extreme case where 10 mol% 3TiCl₃·AlCl₃ was added, and then continued with the results on samples with a lower additive content. Figure 3a exhibits the desorbed LiBH₄–MgH₂ with 10 mol% 3TiCl₃·AlCl₃, with the major crystal also being MgB₂ according to the diffraction pattern. Figure 3b displays the EDX map of Mg and Ti, showing the distribution of MgB₂ and Ti-containing materials. Similar to the previous observations without additives, there are parallel MgB₂ crystals oriented in the same direction, yet with a much smaller size. To determine the MgB₂ 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 MgB₂ in the yellow box marked in both Figure 3a,c was further studied; see Figure 3d. In contrast to the bar-like MgB₂ 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 MgB₂, 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 MgB₂ crystals nucleate on Mg grains, whereas the nucleation of platelet-like MgB₂ occurs on TiB₂ 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. Orientation relationship between MgB₂ and Mg or TiB₂, and their corresponding atomic misfits [19].

	$\mathbf{Interatomic} \mathbf{Planes}, \mathbf{Misfit} {\mathbf{\delta }}_{\mathbf{h}\mathbf{k}\mathbf{i}\mathbf{l}}^2$	$\mathbf{Interatomic} \mathbf{Directions}, \mathbf{Misfit} {\mathbf{\delta }}_{\mathbf{h}\mathbf{k}\mathbf{i}\mathbf{l}}^2$
MgB2 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%
MgB2 on TiB2	$\left\{0002\right\} | \left\{0002\right\}$, −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%

.

With this information, we can calculate the elastic strain energy densities ${ϵ}_{\mathrm{hkil}}$ for any given lattice plane $\mathrm{hkil}$ with the equation ${ϵ}_{\mathrm{hkil}}=\frac{1}{2}{ \mathrm{Y}}_{\mathrm{hkil}}{\mathsf{\delta }}_{\mathrm{hkil}}^2$, where ${\mathrm{Y}}_{\mathrm{hkil}}$ and ${\mathsf{\delta }}_{\mathrm{hkil}}$ represent the Young’s modulus and the atomic misfit in a certain direction, respectively [28]. The corresponding Young’s modulus ${\mathrm{Y}}_{\mathrm{hkil}}$ for MgB₂ 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].

$${\mathrm{Y}}_{\mathrm{hkil}}=\frac{{\left[{\mathrm{h}}^2+\frac{{\left(\mathrm{h}+2\mathrm{k}\right)}^2}{3}+{\left(\frac{\mathrm{a}}{\mathrm{c}}\mathrm{l}\right)}^2\right]}^2}{\left[{\mathrm{S}}_{11}{\left({\mathrm{h}}^2+\frac{{\left(\mathrm{h}+2\mathrm{k}\right)}^2}{3}\right)}^2+{ \mathrm{S}}_{33}{\left(\frac{\mathrm{a}}{\mathrm{c}}\mathrm{l}\right)}^4+\left({\mathrm{S}}_{44}+2{\mathrm{S}}_{13}\right)\left({\mathrm{h}}^2+\frac{{\left(\mathrm{h}+2\mathrm{k}\right)}^2}{3}\right){\left(\frac{\mathrm{a}}{\mathrm{c}}\mathrm{l}\right)}^2\right]}$$

(1)

Combining the calculated Young’s modulus ${\mathrm{Y}}_{\mathrm{hkil}}$ for the selected orientations and the related misfit ${\mathsf{\delta }}_{\mathrm{hkil}}$ from Table 1 gives the elastic strain energy densities ${ϵ}_{\mathrm{hkil}}$ for MgB₂; see

Table 2. The Young’s modulus and the elastic strain energy densities for MgB₂ nucleating in the directions $0002$, $10\overline{1}0$ and $1\overline{2}10$ on the respective nucleation centers Mg and TiB₂.

Lattice Plane	$0002$	$10\overline{1}0$	$1\overline{2}10$
$Y_{hkl}$(GPa)	184.7	326.9	326.9
${ϵ}_{hkl}$(J/m3)	7.4 × 108 (on Mg) 7.3 × 108 (on TiB2)	2.9 × 108 (on Mg) 4.7 × 107 (on TiB2)	4.7 × 107 (on TiB2)

.

According to the experimental observations and the determined elastic strain energy presumably induced during the formation of MgB₂, the large energy density of more than 7 × 10⁸ J/m³ along the $\langle 0002\rangle$ direction explains why both MgB₂ bars (on Mg) and MgB₂ platelets (on TiB₂) appeared to be rather thin in this direction. For Mg, the nucleation and growth of MgB₂ along the $\langle 10\overline{1}0\rangle$ direction on Mg also led to a significant amount of strain energy density of up to 3·10⁸ J/m³. 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 MgB₂ and Mg, leading to the morphology of a rectangular bar. In contrast for TiB₂, the nucleation of MgB₂ along either $\langle 10\overline{1}0\rangle$ or $\langle 1\overline{2}10\rangle$ on TiB₂ is equivalent from an energetic point of view, leading to a significantly smaller strain energy density of only 4.7·10⁷ J/m³. 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 MgB₂ platelets. MgB₂ bars are also distinct from MgB₂ platelets in terms of their aspect ratio, which is much larger than one, indicating that they grow predominantly in one direction.

Another interesting point is the observation of a parallel alignment of the MgB₂ crystals observed in both cases (with or without additives). We can understand where the parallel alignment of the MgB₂ bars has come from, as Mg grains are large enough to provide sufficient surface area for the nucleation of several MgB₂ bars on the same plane; see Figure 2b. Since the nucleation of MgB₂ follows a specific crystallographic orientation with respect to Mg, it is natural for the MgB₂ crystals nucleating on the same Mg plane to grow in the same direction. However, given the distance between two parallel MgB₂ platelets up to several hundred nanometers (Figure 3a), and the size of TiB₂ nanoparticles (Figure 3b), it is not likely for two MgB₂ platelets to nucleate and grow on the same TiB₂ nanoparticle. From this perspective, one assumption is that some TiB₂ 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 MgB₂ is then more likely to first occur on these attached nanoparticles. This is not only because the nucleation of MgB₂ based on TiB₂ requires less strain energy per unit volume, but also because the diffusion distance for Mg atoms is much shorter, as these TiB₂ nanoparticles are directly attached on the surface of Mg grains.

To understand the dependence of the MgB₂ morphology on the additive content, samples added with lower contents of 3TiCl₃·AlCl₃ 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 MgB₂. By comparing this image with the corresponding elemental distribution of Mg, the parallel-oriented crystals of MgB₂ can be recognized in the agglomerate. As indicated in Figure 4a, two parallel MgB₂ crystals were selected for electron tomography measurements. It turns out that both pieces of MgB₂ have a bar-like morphology (Figure 4b). In some other regions, a MgB₂ morphology similar to Figure 3 can also be observed, which indicates the generation of MgB₂ platelets (Figure 4c). These observations indicate that the nucleation of MgB₂ on Mg has occurred. Besides, the nucleation of MgB₂ on TiB₂ was not as dominant as in the case of 10 mol% additives, where no more MgB₂ bars were observed. This also implies that there is a competition between the nucleation on Mg grains and TiB₂ nanoparticles for Mg and B atoms to generate MgB₂ bars or MgB₂ platelets.

When the additive content was raised up to 2.5 mol%, we still observed MgB₂ bars in some areas (Figure 5a,b). After further increasing the additive content to 5 mol%, the majority of the observed MgB₂ crystals were platelet-like, as shown in Figure 5c,d. This can be further verified by the tomography analysis on the piece of MgB₂ highlighted in the yellow box in Figure 5c. These tomography images display a MgB₂ platelet at different angles. Based on these observations, it seems to imply a turning point in the competition between the nucleation on Mg and TiB₂.

2.3. Kinetic Modeling

According to the TEM results, when varying contents of 3TiCl₃·AlCl₃ are added to LiBH₄–MgH₂, the dehydrogenation processes of LiBH₄–MgH₂ differ. This difference is not only reflected in the change in MgB₂ 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 MgB₂ plays an essential role, as shown in Figure 1c. In addition, the subsequent step of MgB₂ growth that accompanies a massive amount of hydrogen release is also crucial to the improvement of the dehydrogenation kinetics of LiBH₄–MgH₂. This aspect is discussed in the following.

Figure 6a is extracted from Figure 1c and shows the hydrogen release over time for the respective samples, during the second step of the reaction, ranging from the start of the massive hydrogen release to the quasi-end of the dehydrogenation, when each curve is nearly flat. The process of counting starts with −3.2 wt% of hydrogen release to ensure the self-decomposition of MgH₂ is completed and all the released hydrogen in this case is coming from the reaction between LiBH₄ and Mg.

Figure 6b exhibits the min–max normalized hydrogen release between zero and one for each sample. Notably, it takes more than twice the time to release about 80% of hydrogen from the sample without additives as it does with additives. This means that both the nucleation and the growth of MgB₂ platelets are faster than those of MgB₂ bars. It is thus intuitive to consider a positive correlation between the hydrogen release rate and the amount of 3TiCl₃·AlCl₃. 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 TiB₂ 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 MgB₂ can be distinguished and clarified.

The Johnson–Mehl–Avrami–Kolmogorov (JMAK) equation generally describes the kinetics of phase transformation for solids. To obtain an in-depth understanding of the dehydrogenation kinetics and determine the rate-controlling step for the MgB₂ growth for the respective samples, this equation was applied to model the process of the MgB₂ growth; see Equation (2) [32,33]:

$$\mathsf{\alpha }=1-\exp \left[-{\left(\mathrm{kt}\right)}^{\mathrm{n}}\right]$$

(2)

where $\mathsf{\alpha }$ denotes the fraction of released hydrogen over time (representing the volume fraction of the directly correlated MgB₂ 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 MgB₂ 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:

$$\ln \left[-\ln \left(1-\mathsf{\alpha }\right)\right]=\mathrm{nln}\left(\mathrm{t}\right)+\mathrm{nln}\left(\mathrm{k}\right)$$

(3)

From the equation, $\mathrm{n}$ can be immediately determined from the slope by plotting $\ln \left[-\ln \left(1-\mathsf{\alpha }\right)\right]$ against $\ln \left(\mathrm{t}\right)$. To keep the analysis consistent, the data with hydrogen release $\mathsf{\alpha }$ ranging from 15% to 85% were selected for the plot of $\ln \left[-\ln \left(1-\mathsf{\alpha }\right)\right]$ vs. $\ln \left(\mathrm{t}\right)$; see Figure 6c. The slope is determined by linear regression with the corresponding R-square value evaluating the quality of the fit for the respective samples, as shown in Figure 6d. All the fitting parameters can be found in Table S1. As can be seen, with the increase in additive content, the Avrami exponent decreases.

Based on TEM observations of bar-like and platelet-like MgB₂ crystals, the MgB₂ 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 MgB₂ 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 MgB₂ and TiB₂ compared with that between MgB₂ and Mg during the formation of MgB₂. For the samples with a lower additive content, where both MgB₂ 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 MgB₂ platelets have been observed in this case.

Based on these results, the best additive content that accelerates the dehydrogenation process the most can be determined. It may lay between 2.5 mol% and 5 mol% additive content. According to the interpretation, this is because the growth rate-controlling step changes from interface-controlled for 2.5 mol% additives to diffusion-controlled for 5 mol% additives (Avrami exponent $\mathrm{n}<1.5$). In this range, the formation of MgB₂ platelets becomes gradually dominant. The transition in the growth rate-controlling step is also consistent with the TEM observations, where much fewer MgB₂ bars were found when the additive content was increased to 5 mol%.

To further validate the results of the JMAK equation, several other frequently utilized models to study the kinetics of hydrogen storage materials were utilized for comparison; see

Table 3. The introduction to the applied kinetic models [32,34,37,38].

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)	$\left[\left(1- \mathsf{\alpha }\right)\ln \left(1- \mathsf{\alpha }\right)\right]+ \mathsf{\alpha }$
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)	${\left(1-{\left(1- \mathsf{\alpha }\right)}^{1/3}\right)}^2$

. The fit quality of these models was evaluated by the reduced time method, by plotting the theoretical reduced time ${\left(\mathrm{t}/{\mathrm{t}}_{0.5}\right)}_{\mathrm{theoretical}}$ against the experimental reduced time ${\left(\mathrm{t}/{\mathrm{t}}_{0.5}\right)}_{\mathrm{experimental}}$, where ${\mathrm{t}}_{0.5}$ denotes the time when 50% of hydrogen has been released [35,36]. Figure 7a–e shows the plots of ${\left(\mathrm{t}/{\mathrm{t}}_{0.5}\right)}_{\mathrm{theoretical}} \mathrm{vs}. {\left(\mathrm{t}/{\mathrm{t}}_{0.5}\right)}_{\mathrm{experimental}}$ of all these kinetic models for each sample using the data with the hydrogen release α ranging from 15% to 85%. The fitting parameters can be found in Tables S2–S6. The optimal fitting has a slope equal to one and an intercept equal to zero, so a straight line of $y=x$ is drawn on each figure for reference. In Figure 7f, the respective intercept and slope values for the JMAK model are summarized. In general, the JMAK model performs best in fitting the data to describe the second reaction step of dehydrogenation process of LiBH₄–MgH₂ over time.

3. Materials and Methods

3.1. Material Preparations

The reactants were purchased in the form of powder: MgH₂ (95% purity, Rockwood Lithium GmbH), LiBH₄ (95% purity, Sigma-Aldrich), and 3TiCl₃·AlCl₃ (about 76–78% TiCl₃ purity, Fischer Scientific). The LiBH₄–MgH₂ composite was mixed with a molar content of x% 3TiCl₃·AlCl₃ (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 2LiBH₄–MgH₂ or 2LiBH₄–MgH₂–3TiCl₃·AlCl₃, 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 (O₂, H₂O < 0.5 ppm).

3.2. Kinetics Measurements

The volumetric measurements of hydrogen release were performed using a custom-built Sievert’s-type apparatus. The milled sample (~170 mg) was charged into the stainless steel sample holder of the measuring apparatus. The samples were annealed from room temperature to 400 °C at a heating rate of 10 °C min⁻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

The ex situ XRD experiments were performed using a Bruker D8 Discover diffractometer equipped with a Cu X-ray source (λ = 1.54184 Å) and a 2D VANTEC detector. The operating voltage and current were 50 kV and 1000 mA, respectively. The diffraction patterns were acquired in the 2θ range from 10° to 90° with a step size of 0.005°, Δ2θ = 10° and the exposure time for each step of 400 s. To prevent oxidation of the materials, the specimens were packed onto a sample holder and sealed with an airtight dome made of poly (methyl methacrylate) (PMMA), which was carried out in an argon-filled glovebox (O₂, H₂O < 0.5 ppm).

3.4. TEM Experiments

TEM experiments were performed using a Themis-Z 60-300 (Thermo Fisher Scientific Inc., Waltham, MA, USA) equipped with a monochromator and double aberration correctors (probe and image Cs correctors) operated at 300 kV. TEM sample preparation was carried out under an argon atmosphere in a glovebox (O₂, H₂O < 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.).

The utilized beam current ranged from 50 to 150 pA for TEM experiments. Selected area electron diffraction (SAED) patterns were collected using an OneView camera (AMETEK Gatan Inc.). Scanning TEM (STEM) images were recorded via a high-angle annular dark-field (HAADF) detector with a convergence angle of 21.5 mrad and a camera length of 93 mm. Energy-dispersive X-ray spectroscopy (EDX) spectrum-imaging (SI) was executed with a Super-X windowless EDX detector (Thermo Fisher Scientific Inc.) using the same parameters for STEM imaging.

Electron tomography was carried out using a Fischione 2020 tomography holder in STEM mode with a convergence angle of 8.58 mrad. Other parameters stayed the same as mentioned above. HAADF-STEM tilt series with image dimensions of 1024 × 1024 pixels were collected using Xplore3D (Thermo Fisher Scientific Inc.) over a tilt range with an increment of 2° from −70° to 70° for the desorbed 2LiBH₄–MgH₂ with 1 mol% 3TiCl₃·AlCl₃, from −74° to 76° for the desorbed 2LiBH₄–MgH₂ with 5 mol% 3TiCl₃·AlCl₃ and from −66° to 72° for the desorbed 2LiBH₄–MgH₂ with 10 mol% 3TiCl₃·AlCl₃. Electron tomography combined with EDX mapping was also carried out on the desorbed 2LiBH₄–MgH₂ with 10 mol% 3TiCl₃·AlCl₃ 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.).

4D-STEM measurements were carried out in µ-probe mode using the OneView camera, with a convergence angle of 0.47 mrad, a camera length of 720 mm, an acquisition time of 13.2 ms for each pixel, and a dose of ~4.7 × 10⁷ 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

The second dehydrogenation step of the reactive hydride composite LiBH₄–MgH₂ is controlled by the nucleation and growth of MgB₂ in respective orientations. The observed different MgB₂ morphologies can be directly correlated to the required elastic strain energy per unit volume. The nucleation of MgB₂ on Mg requires an energy up to 2.9 × 10⁸ J/m³ in the $\langle 10\overline{1}0\rangle$ direction, whereas it needs only 4.7·10⁷ J/m³ for the nucleation of MgB₂ on TiB₂ in the $\langle 10\overline{1}0\rangle$ or $\langle 1\overline{2}10\rangle$ directions. The formation of MgB₂ may occur primarily on those TiB₂ nanoparticles that adhere to Mg grains, which leads to the generation of parallel MgB₂ platelets. According to the JMAK equation parameter interpretation, the growth rate-controlling steps for MgB₂ 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 MgB₂ on TiB₂ and the change in the morphology of MgB₂ when additives were included. Based on the second dehydrogenation growth kinetics, the best additive content that accelerates the dehydrogenation process of LiBH₄–MgH₂ the most is between 2.5 mol% and 5 mol%. However, given the consumption of LiBH₄ by additives, the trade-off between a reduced hydrogen storage capacity and improved kinetics also needs to be carefully considered in practice.