Temperature- and Catalyst-Dependent Transformation from Reaction Rate-Limited to Diffusion Rate-Limited Hydrogenation of Mg with Nb₂O₅ Catalyst

Abstract

The hydrogen consumption behavior during the hydrogenation of magnesium (Mg) with niobium oxide (Nb₂O₅) catalyst was analyzed via the volumetric Sieverts method, and categorized into two types of consumption kinetic processes: increasing consumption rate with temperature at lower temperatures and almost constant consumption rate at higher temperatures. The consumption rates were measured as the hydrogen absorption rates of Mg, and were analyzed based on a first-order reaction for two types of absorption processes, reaction rate-limited and diffusion rate-limited. The apparent activation energies in the hydrogen absorption rate increased with temperature at low temperatures, and were 49.5–53 kJ/mol for Mg with 5, 10, and 20 mass% Nb₂O₅ catalyst, which were lower than the activation energy for pure Mg. The apparent activation energies in the absorption rate were almost constant at higher temperatures, ranging from 0–9.6 kJ/mol. The transformation of the absorption reaction process from a reaction rate-limited to diffusion rate-limited process with an extremely lower apparent activation energy is similar to that observed during the combustion of charcoal.

Fig. 7 Scheme of (a) reaction rate limited (RRL) and (b) diffusion rate limited (DRL).

1. Introduction

Magnesium (Mg) is one of the most attractive hydrogen storage materials due to its high hydrogen storage capacity (7.6 mass%), reversible hydrogen reaction, low cost, and practically inexhaustible abundance on earth.¹⁾ However, magnesium hydride (MgH₂) is thermodynamically stable, and the dehydrogenation of MgH₂ requires temperatures of 300°C or higher under 0.1 MPa hydrogen atmosphere.²⁾ Furthermore, it is also known that the reaction speeds of hydrogen absorption and desorption are slow.³⁾ Several approaches have been attempted to solve these limitations, including grain size and crystal size refinements via mechanical grinding (MG) with a high-energy ball mill^4–6) and the addition of suitable catalysts.^7,8)

MG generally requires a significantly long time to improve the hydrogen absorption or desorption kinetics. Barkhodarian et al. reported that the hydrogen absorption kinetics accelerated with grinding time as the MG process was increased from 2 to 100 h.⁹⁾ We reported that 90% of the maximum hydrogen storage capacity could be desorbed from MgH₂ with 50 mass% Al₂O₃ within 30 min using a high-energy ball mill at 150 G (G = gravity of the earth).^10,11)

The effects of several suitable catalysts on MgH₂ absorption/desorption have recently been investigated. The hydrogen absorption (desorption) behavior of Mg (MgH₂) has been improved by adding transition metals,^12–14) metal oxides,^15,16) metal hydrides,^17,18) metal chloride,¹⁹⁾ or metal fluoride¹⁹⁾ via MG, with niobium oxide (Nb₂O₅) inducing the best catalytic effect.¹⁶⁾

Nb₂O₅ serves as a significant catalyst for both dehydrogenation and hydrogenation. However, there have been limited reports on the kinetic analysis of the hydrogenation of Mg with Nb₂O₅ above room temperature due to the difficulty in minimizing the exothermic heat generation during hydrogenation. Kimura et al. reported that Mg with 1 mol% Nb₂O₅ can absorb hydrogen at −50°C,²⁰⁾ and determined an activation energy of 38 kJ/mol for hydrogen absorption in the −50 to −10°C temperature range and under 0.2 MPa hydrogen atmosphere to minimize the effect of exothermic heat generation during hydrogenation. This activation energy was much lower than the 61 kJ/mol required for hydrogen absorption on Mg in the absence of catalysts, which reveals that even a small amount of Nb₂O₅ serves as an effective catalyst for the hydrogenation of Mg. Hanada et al. reported that Mg with 1 mol% Nb₂O₅ absorbs ∼4.5 mass% hydrogen within 15 s at room temperature and >5 mass% hydrogen within 30 s at 150 and 250°C under 1 MPa hydrogen atmosphere.⁷⁾ Barkhodarian et al. also reported that Mg with 0.5 mol% Nb₂O₅ absorbs ∼6 and ∼7 mass% hydrogen at 250 and 300°C, respectively, within 1 min under 8.4 bar hydrogen atmosphere.²¹⁾ Although they did not analyze the absorption kinetics, their experimental results demonstrated that the hydrogen absorption rates were almost constant above 150°C during the initial absorption stage. It has also been reported that the activation energy for hydrogen absorption was almost zero for Pd with 4 mass% Pt below 100°C.²²⁾

Here we attempted to analyze the hydrogen absorption kinetics of Mg with Nb₂O₅ by measuring the hydrogen consumption behavior in a closed chamber as a function of time and temperature, and evaluate the apparent activation energy for hydrogenation. The hydrogen consumption behaviors were categorized into two types based on their consumption kinetic processes: increasing consumption rate with temperature at lower temperatures and almost constant consumption rate at higher temperatures. The observed hydrogen absorption rates occasionally included both processes. The former was kinetically analyzed based on the dissociation of molecular hydrogen to atomic hydrogen as a reaction rate-limited (RRL) step according to the conventional understanding of hydrogen absorption onto Mg with catalytic Nb₂O₅.²³⁾ The latter possessed an absorption rate that was almost constant and temperature-independent, with a similar reaction behavior based on a diffusion rate-limited (DRL) step in the boundary layer for reactions with extremely high rates, such as the heavily reduced activation energy of only 6.56 kJ/mol at higher temperatures for the combustion of charcoal compared to 172 kJ/mol for the RRL process at lower temperatures.²⁴⁾ The latter absorption kinetics were computationally analyzed based on a first-order reaction for the DRL reaction rate.^25,26) The difference between the RRL- and DRL-based hydrogen absorption reaction mechanisms was also discussed based on the kinetic analysis results.

2. Experimental Procedure

Commercially available MgH₂ powder (hydrogenated from a purity of Mg ingot: 99.9%, average particle size of the hydrogenated MgH₂: 60 µm, Biocoke Lab. Co., Japan) and Nb₂O₅ (purity: 99.99%, average particle size: 1 µm, Kojundo Chemical Lab. Co., Ltd., Japan) were used in this work. Powders containing MgH₂ and Nb₂O₅ were mixed in 95:5, 90:10, and 80:20 weight ratios. The powders were placed in a ZrO₂ vial (170 mL; 66-mm inside diameter; 52 mm high) with ZrO₂ balls (φ4-mm diameter; ball-to-powder mass ratio of 40:1), where six 10-min milling cycles were then performed at 10-min intervals using a gear-driven planetary ball mill (High G BX284EH, Kurimoto, Japan) at 673 rpm (150 G) and a fixed rotation: revolution speed ratio of 1.092:1. Each sample was handled in a glove box filled with purified argon before and after ball milling to minimize sample oxidation. The oxygen and water concentrations in the glove box were controlled using an inert gas recirculating system, with concentrations of 1.0–3.0 ppm and 0.5–3.0 ppm, respectively. These samples are hereafter referred to as MG-MgH₂/5 mass%Nb₂O₅, MG-MgH₂/10 mass%Nb₂O₅, and MG-MgH₂/20 mass%Nb₂O₅.

The phase identification of MG-MgH₂/10 mass%Nb₂O₅ was conducted via X-ray diffraction (XRD) analysis. The diffractometer (RINT2500, Rigaku, Japan) was equipped with a Cu–Kα radiation source, and operated at 100 mA and 40 kV.

The powders were characterized using a scanning transmission electron microscope (STEM) with energy dispersive X-ray spectrometry (EDS: JEM-F200, JEOL Ltd., Japan) and transmission electron microscopy (TEM: JEM-2100, JEOL Ltd., Japan) operated at 200 kV. The powders were dispersed with the mixture of epoxy resin (epoxy resin 20-8130-032, Buehler, USA) and epoxy hardener (epoxy hardener 20-8132-008, Buehler, USA) in mass% of 5:1 immediately after taking out from the glove box highly controlled oxygen and water in extremely low as described above. The mixture for TEM specimen was coated on Si substrate and dried for a day. The specimen coated by carbon as a protected film was placed onto a Cu mesh after slicing by the focused-ion beam lift-out method.

The hydrogen consumption (absorption) behaviors of the three samples were evaluated using a volumetric Sieverts apparatus (Suzuki Shokan Co., Ltd., Japan). The sample powders (0.2 g) were loaded into the sample holding tubes (φ9.5 mm × 25 mm, made of SUS316L), and the top and bottom ends were filled with ceramic wool to seal the openings. The tubes with the sample and spacers (made of SUS316L) were then inserted into the sample cell. The samples underwent dehydrogenation under vacuum for 2 h at 350°C prior to performing the hydrogen consumption measurements. These samples are hereafter referred to as Mg/5 mass%Nb₂O₅, Mg/10 mass%Nb₂O₅, and Mg/20 mass%Nb₂O₅. Hydrogen gas was then introduced into the volumetric Sieverts apparatus, and the valve between the apparatus and sample cell was opened, thereby introducing hydrogen gas into the sample cell (∼5 MPa). The change in hydrogen gas pressure as a function of time was measured, and the hydrogen absorption rate constant was calculated based on a first-order reaction equation with the induction time for hydrogenation in the initial stage of hydrogen absorption removed to minimize the increase in temperature due to the exothermic heat generation during hydrogenation for the slower hydrogenation without the abrupt and the faster increase of hydrogen absorption. On the other hand, above the initial temperature indicating the abrupt increase of hydrogen absorption and the faster increase following the slower absorption in the initial stage, the hydrogen absorption rate constant was also calculated from the initial slope in the abrupt increase based on a first order reaction equation by assuming the diffusion-rate limited (DRL). If the assumption of DRL is suitable for this kinetics, the reaction rate constant become similar value and almost temperature-independent²⁴⁾ even at the much higher temperature than the initially set temperature.

The thermal hydrogenation behavior of the three samples was evaluated using a differential scanning calorimeter (DSC) apparatus (DSC8230HP, Rigaku, Japan). The sample powders (∼3 mg) were loaded into an aluminum pan and placed in the DSC apparatus under helium atmosphere. Prior to the hydrogenation, the samples were heated to 400°C at a scan heating rate of 5°C/min under 0.2 MPa helium atmosphere, and then cooled to room temperature. The thermal hydrogenation behavior of the samples was subsequently measured at a scan heating rate of 20°C/min under 4 MPa hydrogen atmosphere.

3. Results and Discussions

Figure 1 shows the XRD patterns of the (a) MG-MgH₂/10 mass%Nb₂O₅, (b) as-milled MgH₂ (MG-MgH₂), (c) high-pressure B-Nb₂O₅ phase (JCPDS No. 18-0917), (d) as-received (commercial) Nb₂O₅, and (e) as-received (commercial) MgH₂. The β-MgH₂ diffraction peaks in patterns (a) and (b) are broader than the peaks of the as-received MgH₂ in pattern (e). We therefore deduced that ball milling decreased the crystallite size. Furthermore, the XRD patterns of milled samples (a) and (b) show that milling resulted in partial transformation from the tetragonal β-MgH₂ structure to the high-pressure orthorhombic γ-MgH₂ structure. The γ-MgH₂ phase is known to form when the β-phase is subjected to compressive pressure in the 2.5–8 GPa range.^22,23) The H-Nb₂O₅ phase of the as-received Nb₂O₅ is observed in Fig. 1(a). The diffraction peak separation of MG-MgH₂/10 mass%Nb₂O₅ in the 2θ = 23–25° region (magnified area) using the Voigt function allowed us to define two peaks. The H-Nb₂O₅ phase has one diffraction peak in the 2θ = 24–25° region according to JCPDS No. 37-1468. However, another diffraction peak is observed. Zibrov and Filonenko demonstrated that H-Nb₂O₅ transforms to high-pressure phase of B-Nb₂O₅ (2θ = 24.45°, middle dotted peak in dotted magnified area of Fig. 1, (11-1), lattice space = 0.364 nm, identified as ζ–Nb₂O₅ in JCPDS No. 18-0917) at 900°C and 5 GPa.^27,28) Furthermore, first-principles calculations have indicated that the B-Nb₂O₅ phase is thermodynamically stable under 9–13 GPa.²⁹⁾ These previous findings suggest that it is possible for H-Nb₂O₅ transformed to B-Nb₂O₅ during the ball milling process due to the generation of the high-pressure γ-MgH₂ phase. We therefore deduced that MG-MgH₂/10 mass%Nb₂O₅ included the high-pressure B-Nb₂O₅ phase.

Fig. 1

XRD patterns of (a) MG-MgH₂/10 mass%Nb₂O₅, (b) as-milled MgH₂ (MG-MgH₂), (c) high pressure phase B-Nb₂O₅ (JCPDS No. 18-0917), (d) as-received (commercial) Nb₂O₅ and (e) as-received (commercial) MgH₂. Magnified area: XRD patterns of dotted area in the figure and fitted curves of (a).

An EDS mapping image of MG-MgH₂/10 mass%Nb₂O₅ is shown in Fig. 2, where a grain (∼100 nm), which consists of Nb atoms that are surrounded by grains, including Mg atoms, is observed. Figure 3 shows a (a) HR (High Resolution)-TEM of the dotted-square area in Fig. 2, (b) fast Fourier transform (FFT) image, (c) Inverse FFT image of spot 1 in the FFT image, and (d) Inverse FFT images of spots 2–4 in the FFT image with the HR-TEM image. We obtained extremely small grains that were less than 5 nm, which existed in Nb atom area, as shown in Fig. 3(c). The lattice plane distance in Fig. 3(c) and (d) matched that for B-Nb₂O₅ (31-1) (2θ = 29.98°, lattice space = 0.298 nm, identified as ζ–Nb₂O₅ in JCPDS No. 18-0917).²⁷⁾ Therefore, the Nb₂O₅ grain in the MG-MgH₂/10 mass%Nb₂O₅ sample was an agglomeration of the primary particles, which were several nm in size. We obtained a particle size of ∼10 nm and lattice plane distance that matched those for β-MgH₂ (200) (lattice space = 0.226 nm, JCPDS No. 35-1184) and γ-MgH₂ (112) (lattice space = 0.201 nm, JCPDS No. 12-0697) in spots 2, 3 and 4, as shown in Fig. 3(d). Both of high-pressure phases of B-Nb₂O₅ and γ-MgH₂ should generate by the high energy ball milling as shown in Fig. 3.

Fig. 2

EDS mapping images of MG-MgH₂/10 mass% Nb₂O₅.

Fig. 3

(a) HR-TEM image of dotted-square area in Fig. 2, (b) FFT, (c) Inverse FFT of Spot 1 in (b) and (d) Inverse FFT of Spot 2–4 in (b) with HR-TEM image.

The hydrogen consumption behavior in the dehydrogenated sample, Mg/5 mass%Nb₂O₅ at ∼5 MPa hydrogen atmosphere, is shown in Fig. 4. Below 140°C, the hydrogen consumption rate accelerated as the temperature increased. While the rate was temperature-dependent below 140°C in the initial stage, the following consumption rate was almost temperature-independent above 160°C. The rate was particularly temperature-independent for the hydrogen consumption behavior measurements above 200°C. Figure 5 shows the hydrogen consumption behavior in Mg/10 mass%Nb₂O₅ at ∼5 MPa hydrogen atmosphere. Similar behaviors were observed below 60°C and above 80°C. Figure 6 also shows the behavior in Mg/20 mass%Nb₂O₅ at ∼5 MPa hydrogen atmosphere, with similar behaviors observed below 20°C and above 40°C.

Fig. 4

Hydrogen consumption behavior of Mg/5 mass%Nb₂O₅ at 100–240°C.

Fig. 5

Hydrogen consumption behavior of Mg/10 mass%Nb₂O₅ at 23–160°C.

Fig. 6

Hydrogen consumption behavior of Mg/20 mass%Nb₂O₅ at 20–120°C.

In hydrogen absorption of Mg, it is known that the RRL step is an adsorption/dissociation process of molecular hydrogen onto the Mg particle surface during hydrogen absorption,³⁰⁾ as opposed to a diffusion process into the Mg matrix,²³⁾ with the hydrogen adsorption/dissociation reaction proceeding across the entire surface of the Mg particle. We have determined that adding a catalyst allows the hydrogen adsorption/dissociation reaction to proceed at the catalyst surface that is in contact with Mg, such that the reaction can be the rate-limiting step (RRL, see Fig. 7(a)). We presumed that this increase in the hydrogen consumption rate with temperature was due to the RRL step. Conversely, a boundary layer forms, which is derived from the hydrogen molecule concentration gradient for the extreme consumption of hydrogen molecules on the Mg surface when hydrogen adsorption and dissociation are significantly accelerated on the Nb₂O₅ catalyst. The temperature increases due to exothermic heat generation during hydrogenation and the acceleration of hydrogenation simultaneously occur in the agglomerated Mg particles. We presumed that the diffusion of molecular hydrogen in the boundary layer could be rate-limiting step (DRL, see Fig. 7(b)). The reaction rate did not increase much with temperature for the DRL-based reaction since this reaction is controlled by the diffusion of the reactant in the boundary layer.²⁴⁾

Fig. 7

Scheme of (a) reaction rate limited (RRL) and (b) diffusion rate limited (DRL).

The reaction rates were analyzed according to their presumed rate-limiting step (RRL or DRL). The RRL-based case indicates that the reaction proceeds according to a first-order reaction since the adsorption/dissociation of molecular hydrogen takes place on the catalyst.²³⁾ Therefore, the reaction rate constants were calculated via   

\begin{equation} \ln \frac{A_{0}}{A} = k_{R}t, \end{equation} (1)

where A₀ is the initial pressure [MPa], A is the measured pressure [MPa], k_R is the RRL-based reaction rate constant [s⁻¹], and t is the time [s]. The reaction rate constants in the DRL-based case, which are based on the diffusion of molecular hydrogen in the boundary layer, were analyzed using a first-order reaction whose DRL-based reaction rate can be described as^25,26)   

\begin{equation} \ln \frac{A_{0}}{A} = k_{D}t, \end{equation} (2)

where k_D is the DRL-based reaction rate constant [s⁻¹].

The hydrogen consumption behavior of Mg/10 mass%Nb₂O₅ at each temperature, which is based on eqs. (1) and (2), is shown in Fig. 8. Here k_R and k_D correspond to the slopes marked RRL and DRL, respectively. Similar calculations were performed for the Mg/5 mass%Nb₂O₅ and Mg/20 mass%Nb₂O₅ samples.

Fig. 8

Analyzed hydrogen consumption rate of Mg/10 mass%Nb₂O₅ at 23–160°C.

The RRL- and DRL-based activation energies were then calculated as   

\begin{equation} \ln k = - \frac{E_{a}}{RT_{i}} + \ln f, \end{equation} (3)

where E_a is the apparent activation energy for either the adsorption/dissociation reaction or diffusion of molecular hydrogen in the boundary layer, k is the reaction rate constant (k_R or k_D), f is the frequency factor, R is the gas constant, and T_i is the initial temperature at the measurement. Although these kinetic measurements had to be conducted isothermally, the initial temperature set in the apparatus was utilized for the analysis at the much lower reaction fraction during the initial stage of hydrogenation. Arrhenius plots of the reaction rate constant at the set initial temperature are shown in Fig. 9, with the solid and dotted lines indicating the RRL- and DRL-based activation energies, respectively. The calculated apparent activation energies and frequency factors are listed in Table 1.

Fig. 9

Arrhenius plots of the temperature dependence of the rate constant for hydration of Mg/5 mass% Nb₂O₅, Mg/10 mass% Nb₂O₅ and Mg/20 mass% Nb₂O₅. (i: Initial temperature)

Table 1 The calculated apparent activation energy and frequency factor of hydrogenation of Mg/5 mass% Nb₂O₅, Mg/10 mass% Nb₂O₅ and Mg/20 mass% Nb₂O₅.

RRL-based apparent activation energies ranged from 49.5 to 53 kJ/mol, and were lower than the reported activation energy of pure Mg (72.4–96.5 kJ/mol).³¹⁾ These results demonstrate that Nb₂O₅ is an effective catalyst for hydrogenation. We note that the frequency factor increased with the amount of catalyst in the sample. The frequency factor corresponds to the number of active spots for the hydrogen adsorption/dissociation reaction on the catalyst surface that is in contact with Mg. However, the DRL-based apparent activation energies were 0–9.6 kJ/mol, which were extremely lower than the RRL-based values. A similar significant decrease in the apparent activation energy due to the formation of a boundary layer in the combustion reaction of charcoal has been reported,^24,32,33) where the high activation energy of 172 kJ/mol determined for the RRL step at lower temperatures decreased to only 6.56 kJ/mol for the DRL step at higher temperatures.²⁴⁾ The temperatures when the transformation from the RRL to DRL step for hydrogenation occurred were >160, >80, and >40°C for 5, 10, and 20 mass% Nb₂O₅ catalyst, respectively, based on the Arrhenius plots in Fig. 9. There was a much greater acceleration in the hydrogen absorption reaction at lower temperatures when the amount of catalyst was increased. After this transformation from the RRL to DRL step during hydrogenation, the hydrogenated fraction should increase significantly, while the reaction temperature should also increase and not be constrained by the initial temperature set before the measurement. However, the hydrogen absorption rate constant for DRL did not change much, remaining almost constant, which suggests that the DRL-based rate constant is temperature-independent.^24,32)

The hydrogenated DSC curves for the dehydrogenated (heated to 400°C at a heating rate of 5°C/min) sample are shown in Fig. 10. The exothermic peaks were observed at 160, 80, and 40°C for Mg/5 mass%Nb₂O₅, Mg/10 mass%Nb₂O₅, and Mg/20 mass%Nb₂O₅, respectively. The DSC measurements for the hydrogenation of Mg with Nb₂O₅ catalyst under 4.0 MPa hydrogen atmosphere showed that high heat generation simultaneously occurred with hydrogenation over the temperature ranges that yielded the extremely low activation energies for each sample (>160, >80, and >40°C for 5, 10, and 20 mass% Nb₂O₅ catalyst, respectively), as shown in Fig. 9.

Fig. 10

DSC curves of hydrogenation of Mg/5 mass% Nb₂O₅, Mg/10 mass% Nb₂O₅ and Mg/20 mass% Nb₂O₅.

We have concluded that the hydrogen absorption mechanism of the hydrogen consumption rate, which is almost constant and temperature-independent, is as follows (Fig. 11). The adsorption/dissociation reaction of molecular hydrogen initially proceeds on the catalyst surface in contact with Mg. Mg–H bonds are then formed by the reaction of dissociated atomic hydrogen and Mg, resulting in localized heat generation. This local heat generation accelerates the adsorption/dissociation reaction, and a boundary layer, which is derived from the molecular hydrogen concentration gradient, forms due to the extreme consumption of molecular hydrogen on the Mg surface with the catalyst. The rate-limiting step then transforms from a RRL to DRL step in the boundary layer. This results into an almost constant hydrogen consumption rate that is likely temperature-independent compared to the RRL-based rate at lower temperatures and/or in the early absorption stage, even at relatively higher temperatures, provided that the RRL step is succeeded by the DRL step.

Fig. 11

Formation process of boundary layer by accelerated hydrogen absorption on Mg with Nb₂O₅ catalyst.

4. Conclusion

Here Mg with Nb₂O₅ was prepared via the dehydrogenation of MG-MgH₂ with Nb₂O₅. The MG-MgH₂ crystallite sizes were measured as ∼10 nm via TEM. The MG-MgH₂ samples included a high-pressure γ-MgH₂ phase, as shown in the XRD patterns. The Nb₂O₅ milled with MgH₂ also included a high-pressure B-Nb₂O₅ phase, which was characterized using the TEM images and XRD patterns. The crystallite size of agglomerated Nb₂O₅, with a particle size of 100 nm, was less than 5 nm. The Nb₂O₅ grains were strongly bonded onto the surface of the MgH₂ grains.

The hydrogen consumption regimes via absorption onto Mg with Nb₂O₅ catalyst in the initial stage were categorized into two regimes, moderate consumption at lower temperatures and abrupt consumption at higher temperatures, with both regimes occasionally occurring in a step-by-step manner at moderate temperatures. The moderate hydrogen consumption rate, where the absorption rate was calculated based on a first-order reaction for the RRL step, was defined by the adsorption/dissociation reaction of hydrogen molecules on the catalyst. The apparent activation energies were in the 49.5–53 kJ/mol range for Mg with 5, 10, and 20 mass% Nb₂O₅ at lower temperatures. The abrupt hydrogen absorption rate was also calculated based on a similar first-order reaction for the DRL step, and was defined by the diffusion of molecular hydrogen in the boundary layer. The apparent activation energies were in the 0–9.6 kJ/mol range for Mg with 5, 10, and 20 mass% Nb₂O₅ at higher temperatures. The hydrogen absorption kinetics transformed from a RRL to DRL process at moderate temperatures. Although the exothermic heat generation during hydrogenation was detected by the DSC apparatus in the temperature range where abrupt hydrogen absorption occurred, the hydrogen absorption rate was almost constant and likely temperature-independent compared to the RRL process at lower temperatures.

Acknowledgments

The authors would like to acknowledge financial support from the Innovative Materials and Processing Research Center, Ryukoku University.

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