# The catalytic effect of nano-sized TiVCrMo upon the hydrogen storage in Mg.

Lubomir Kral, Tomáš Němec, Jiri Cermak, Pavla Roupcová, Ondrej Zobac, Bedřich Smetana

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Lubomir Kral, Tomáš Němec, Jiri Cermak, Pavla Roupcová, Ondrej Zobac, et al.. The catalytic effect of nano-sized TiVCrMo upon the hydrogen storage in Mg.. 2025. hal-05289760

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# The catalytic nano-sized TiVCrMo effect upon the hydrogen storage in Mg

Lubomir Kral¹,²*, Tomas Nemec³, Jiri Cermak¹, Pavla Roupcova¹,⁴, Ondrej Zobac¹, Bedrich Smetana⁵

¹ Institute of Physics of Materials AS CR, Zizkova 22, CZ-61662 Brno, Czech Republic, EU

² CEITEC-Institute of Physics of Materials, AS CR, Zizkova 22, CZ-61662 Brno, Czech Republic, EU

³ Institute of Thermomechanics, AS CR, Department of Electrical Engineering and Electrophysics, Dolejskova 5,
CZ-182 00 Praha 8, Czech Republic, EU

⁴ CEITEC-Brno University of Technology, Purkynova 123, CZ-612 00 Brno, Czech Republic, EU

⁵ TUO - Technical University of Ostrava, Ostrava, Faculty of Materials Science and Technology, Department of Chemistry and Physico-Chemical Processes, Czech Republic, EU

## Abstract

In the present paper, nano-powdered multiprinciple-elements alloy (MPEA) TiVCrMo was prepared by spark ablation technique from arc-melted-and-quenched pre-prepared pin-like ingots. Hydrogen storage performance of this powder itself as well as the performance of its mixture with Mg particles was investigated in order to reveal catalytic effect of TiVCrMo upon the hydrogen storage kinetics in Mg. The experiments were carried out by Sieverts method in the temperature interval from 270°C to 360°C under hydrogen pressure up to 46 bar. It was found that the pure MPEA can ab/desorb about $c_{max}$ = 3 wt. % H₂ at 360°C. However, the hydrogen sorption kinetics was poor. Much more promising was the catalytic effect of the MPEA nano-powder deposited on the surface of Mg grains upon the hydrogen sorption kinetics in Mg. By mixing Mg and MPEA (10:1 by weight), a significant increase of hydrogen sorption kinetics in Mg was observed.

Keywords: hydrogen storage; multi-principal elements alloys; medium entropy alloys; nano-sizing

*Kral L. - corresponding author; lkral@ipm.cz, permanent address: Institute of Physics of Materials v. v. i., Academy of Sciences of the Czech Republic, Zizkova 22, CZ-61662 Brno, Czech Republic

## Highlights:

* Nano-powder of TiVCrMo alloy (TVCM) was prepared by spark-ablation technique.

* Sorption kinetics of spark-ablated TVCM was poor ($0-c_{max}$ in tens of hours).

* TVCM as a catalyst improved sorption kinetics in Mg ($0-c_{max}$ in several mins).

## 1.Introduction

Hydrogen is considered the energy vector of the future [1,2]. The main reasons are abundance of its sources in the nature and the fact that the energy conversion is clean. The hydrogen energy cycle is closed and reversible. Nonetheless, it should be kept in mind that the eco-friendly manufacturing of hydrogen has not yet been resolved on a large scale. This segment of the hydrogen energy cycle is a source of pollution and still mostly depends on non-renewable sources [3]. Another open issue is hydrogen storage (HS) [4, 5]. Pressurisation and liquefaction
are not sufficiently effective and safe ways of hydrogen storage (HS). As another plausible way of HS is the
hydrogen binding to the surface of solids or HS *inside* the solid phase in a form of chemical compound –
typically as a hydride [6-12]. It should be noted that there is not a sharp distinction between the weak bonding of
hydrogen to the surface (physisorption due to van der Waals force) and strong hydrogen bonding resembling a
regular chemical compound formed at the surface. In this paper, only HS via hydride phase formation is
considered and the term *sorption* stands either for absorption (when hydride is formed) or for desorption (when
hydride phase decomposes). HS density (and consequently energy density) achieved in such a way is higher than
when using pressure vessels or cryogenic tanks. Typical figures on achievable HS density are: 0.063 g/cm³ for
pressurised hydrogen at normal temperature and 700 bars and 0.071 g/cm³ for liquefied hydrogen. On the other
hand, effective hydrogen density stored, for example, as MgH₂, is 0.11 g/cm³. The really comparable numbers
are influenced by the mass of appropriate containments. Anyway, the mass of a tank for HS in solid state is
much less because its walls do not need to be designed neither for high pressure nor for preserving high
temperature gradient. Last but not least, the operational safety risks are also lowered in case of HS in solid state.

There is a number of materials that have been tested as media for HS up to now [6, 8]. One challenge for MgH<sub>2</sub>
is its slow kinetics and high dehydrogenation temperature, typically above 300 °C [8]. Mg-containing storage
materials are the most frequently studied alloy systems [13]. Many studies focus on the size effect on hydrogen
storage in Mg-based systems (e.g., [14-18]), since nanosizing improves hydrogen absorption kinetics [14,18].
However, no storage alloy system meets the desired criteria regarding storage capacity, kinetics, reversibility,
cyclic stability, acceptable operation pressure, temperature and price. The latest advances in prospective
hydrogen storage alloys are surveyed in a recent review [19]. The DOE's strict limits of key hydrogen sorption
characteristics for mobile applications are yet to be met. Therefore, the design of an effective material for HS
remains a challenge for functional materials science.

The literature sources collectively demonstrate that the incorporation of nanocatalysts significantly enhances the
hydrogen storage (HS) properties of magnesium (Mg) and its hydride (MgH₂), primarily by improving reaction
kinetics, reducing operating temperatures, and enhancing cycling stability, although the impact on
thermodynamics varies. Multi-principle-elements alloys (MPEAs) are materials developed some 17 years ago
originally as construction materials [21,22]. During the years of investigation of their behavior, it appeared that
some of them show also interesting functional features, among others also HS ability [23-28]. The most
frequently studied HS phenomenon in MPEAs is reported for so called refractory elements family of MPEAs
[23]. Studies of other types of MPEAs appeared subsequently – devoted, e.g., to light elements MPEAs [23].

These type alloys like higher entropy alloys and their oxides represent an emerging class of nanocatalysts. NiCoFeCuMg alloys nanocatalysts, supported on carbon (NiCoFeCuMg@C), significantly improve hydrogen storage performance, lowering the initial dehydrogenation temperature of MgH₂ to 167.2 °C (compared to 331.0 °C for pure MgH₂) [29]. This enhancement is attributed to a synergistic effect of in-situ generated Mg₂Ni(Cu)/Mg₂Ni(Cu)H₄ acting as a "hydrogen pump" and stable Co₃Fe₇ serving as a "hydrogen gateway," along with carbon material preventing particle agglomeration. Similarly, high entropy oxides like CrMnFeCoNiO with a size of about 10 nm enable MgH₂ to release hydrogen at 200 °C, reducing activation energy to 69.77 ± 3.75 kJ mol⁻¹ and supporting room temperature hydrogen absorption [29]. Beyond specific
catalyst compositions, nanostructuring itself plays a critical role. Ball milling, a common synthesis method, reduces particle and crystallite sizes, disperses additives, and creates highly reactive surfaces with increased defect density [30]. This leads to shortened hydrogen diffusion distances and more grain boundaries providing diffusion channels [31]. The increased surface energy in smaller particles can also partially compensate for the reaction heat of hydrogenation/dehydrogenation, leading to a slight reduction in dehydrogenation enthalpy [32]. Generally, the nano-sizing is very an effective way how to enhance sorption kinetics and also beneficially influences hydrogen sorption dynamics [33-38].

In our previous paper [39], we studied the possible beneficial catalytic effect of two chosen ball-milled MPEAs upon hydrogen sorption in Mg. The aim was to combine storage/catalytic ability of MPEAs with relatively high storage capacity of Mg, whose main drawback – in pure state – is a lazy sorption kinetics. In the present paper, we try to improve the storage performance of a chosen light weight elements MPEA, TiVCrMo (hereafter, referenced to as TVCM) studied before [39], by extremely intensive nano-sizing through spark ablation synthesis. Catalytic effect of nano-sized TVCM upon HS in Mg is also studied.

## 2. Experimental

### 2.1 Material preparation - ingot of MPEA

In the first step, two ingots of TVCM (TVCM-I) were made from pure components purchased from Alfa-Aldrich and Evek GmbH. Ti was in the form of a foil of 0.1 mm in thickness (purity 99.8 wt. %; all purities from metal basis), V in chips (99.9 wt. %), Cr in pieces (99.5 wt. %) and Mo as a rod (commercial purity ~ 99.5 wt. %). The choice of elements followed the intention to prepare a material, which might possess a potential for HS applications [23,28,39].

Ingots were prepared by repeated arc-melting (AM) steps using the Arc-Melting Furnace MAM-1 Edmund Bühler/Johanna Otto GmbH with an adaptor for rapid suction melting. The mass of the batch was about 10 g. Pieces of the batch elements (V, Cr, Mo) were wrapped into Ti foil and were arc re-melted several times in Ar (purity 6N) atmosphere to reach a complete homogeneity of the ingot. During the last AM run, the melt was sucked in a pre-evacuated water-cooled Cu mold to guarantee as high cooling rate as possible. Two pin-like ingots were prepared in this way. Their diameter was 2 mm and length about 30 mm.

### 2.2 Spark ablation

In the second step, we have employed our in-house developed spark ablation setup, which was described in [40]. Using an upgraded pulsed power supply unit, we were able to generate voltage pulses peaking at -9 kV, which allowed us to use a simplified 2-electrode setup (shown in Fig. 1) instead of a 3-electrode setup used in our previous work. The arrangement of the spark ablation experiment in the spark discharge chamber (Fig. 1), featured two axially-aligned, pin-like ingots of TVCM-I, separated by a 1.25 mm spark gap. The tips of the ingots were polished to achieve two parallel planes forming a constant-width spark gap. The carrier gas was introduced through a nozzle with 2 mm outlet orifice located 10 mm above the spark gap. A mixture of nitrogen (95 %) and hydrogen (5 %) (forming gas H5 by Messer Technogas s. r. o.) was used as the carrier gas, in which the presence of hydrogen helped to remove excess heat from the spark gap more efficiently and therefore to
<figure><img src="image_2.png" /><figcaption>Fig. 1. Spark ablation – experimental arrangement of two pieces of pin-like TVCM ingots as electrodes during the ablation procedure.</figcaption></figure>

generate finer nano-structures. A 2 standard-liter-per-minute flowrate of the carrier gas was set during the synthesis.

An electrostatic trap was located below the spark gap in 10 mm distance, consisting of a stainless-steel cylinder held at 7 kV and a central grounded stainless-steel electrode. The carrier gas with the nano-material generated by spark discharge was passing through this arrangement, which acted as an electrostatic filter depositing the nano-material at the inner wall of the stainless-steel cylinder. An average efficiency of the electrostatic filtration process was around 70 wt. %.

The spark frequency during the synthesis was held at 1 kHz. Individual sparks were generated in the unipolar regime. The peak in voltage around -5 kV signals the breakdown of the gas in the spark gap and the initiation of the plasma channel. Afterwards, a peak in the spark current at around 15 A was generated. The spark current was linearly decreasing during the spark event reaching zero after 35 µs. The spark energy in such case was around 20 mJ. The nano-material synthesis was running for 11 hours and the total amount of sample extracted from the electrostatic trap in the form of powder was 17 mg, resulting in a production rate of TVCM material (TVCM-SA) of 1.55 mg/hour.

## 2.3 Samples for HS experiments

Sorption experiments were conducted with the sample in the form of nano-powder TVCM-SA in as-prepared state and with two grades of mixture TVCM-SA and Mg (TVCM-SA/Mg = 1/10 by weight). The first grade was a coarse-grained material (TVCM-CG) and the second one was a fine-grained composition (TVCM-FG). The TVCM-CG was prepared by a short-time ball-milling (200 rpm 5 min) and TVCM-FG by a long-time milling (200 rpm 20 cycles consisting of 5 min milling followed by 50 min cooling). Ball-milling (BM) was carried out in hydrogen (0.8 bar, purity 99.996 %) using a ball planetary milling machine *Pulverisette 7 Premium Line*.
## 2.4 Characterization of the samples

Phase composition was obtained with the help of XRD EMPYREAN device using CoKa radiation and the results were interpreted with the HighScore Plus SW and ICSD databases (Rietveld analysis). The detection accuracy of phase composition was about 1 wt.%.

Morphology of the samples was observed by SEM TESCAN LYRA3 equipped with X-max80 EDS and HRTEM imaging was done using JEOL JM-2100 F.

## 2.5 Sorption measurements

Hydrogen absorption under pressure up to p = 46 bar and desorption into a fixed volume with the hydrogen pressure below the equilibrium pressure $p_{eq}(T)$ was carried out using Sieverts-type gas sorption analyzer PCT-Pro Setaram Instrumentation at temperatures T lying between 270°C and 360°C.

# 3. Results and discussion

## 3.1 Structure of spark ablated TVCM-SA

Chemical analysis of spark ablated powder, done with SEM/EDS, led to the composition Ti: 28.5±0.3, V: 22.9±0.3, Cr: 24.1±0.6 and Mo: 24.5±0.6 (all in at. %), which agree reasonably with the intended equimolar composition and which is close to the composition of TVCM prepared in [36]. The melting charge was enriched slightly with Cr to compensate for the Cr evaporation. This chemical composition meets empirical conditions assuring that the alloy is a medium-entropy and prevailingly single-phase BCC solid solution [23]: Difference in atomic radii $\delta_r = 5.8$, average valence electron concentration VEC = 5.2, enthalpy of mixing $H^{SS} = -4.0$ kJ/mol, mixing entropy SSS = 1.38 R and term $\Omega$ that combines $H^{SS}$ and $S^{SS}$ is $\Omega = 6.57$. For the definition of the parameters – see in [23].

Phase composition was checked by X-ray diffraction. The measured XRD patterns are shown in Fig. 2, where they are compared with the phase composition of ball milled alloy TVCM prepared in previous study [36].
<figure><img src="image_3.png" /><figcaption>Fig. 2. XRD patterns. Upper panel: TVCM-SA sample – Curves I2-pin-like ingot, SA-spark ablated powder, C-hydrogen charged powder, D-desorbed. Lower panel: Ball-milled sample TVCM studied in ref. [36] shown for comparison: I1-arc melted and suction cast.</figcaption></figure>

The upper panel shows that the phase composition of the cast pins (curve I2) is the same as that observed in [39] (lower panel, curve I1): Namely, it was a medium entropy alloy, formed exclusively of BCC phase with lattice parameter *a* = 3.070586 Å (peaks 1 – ICSD Nr. 105514). It is also obvious that whereas the phase composition of ball-milled sample transformed subsequently into another BCC (peaks 2 653294, peak 3 653395, peak 4 625712) and, in hydrogen charged state, into a small amount of hydrides TiH₂ (peak 5 658062) and V₂H (peak 6 61423), the SA technique produced a very fine structure (curve SA) approaching *almost* an amorphous state. A tiny peak only was detected at 2θ = 47.7° and identified with BCC structure rich in Mo (52267). This peak can be ascribed to very small fraction of Mo-rich droplets of submicron size. Generation of these particles can be explained by explosive evaporation or to acoustic ejection [41]. The described structure remained unchanged even after high-temperature charging in the pressurized hydrogen (curve C) and, subsequently, after annealing in vacuum without hydrogen (curve D).

Morphology of the spark ablated nano-powder, observed by SEM, showed very fine particles in the nanometer scale. These smallest, primary particles form in the first step after each spark discharge event. The primary particles then agglomerate into larger structures of roughly 100 nm in size. The final feather-like structures observed by SEM (Fig. 3a) are a result of further aggregation of the nano-material assisted by the electric field of the electrostatic filter. This appearance did not change neither after hydrogen absorption nor desorption. Small spherical Mo-rich droplets can be also sparsely seen in Fig. 3a (small bright spherical particle). They can be identified by the small amount of the Mo-rich BCC phase that is visible in the XRD pattern. This was approved by composition mapping using SEM EDS.
<figure><img src="image_4.png" /><figcaption>Fig. 2a. SEM micrograph of the TVCM-SA sample.</figcaption></figure>

<figure><img src="image_5.png" /><figcaption>Fig. 3b. TEM micrograph of the TVCM-SA sample.</figcaption></figure>
TEM enabled us to visualize the fine structure of aggregates in more detail. It is obvious in Fig. 3b that the branches of feather-like agglomerates are composed of continual set of nano-sized *crystalline* grains. In other words, the branches are *nano-polycrystalline*. This is a more precise finding than XRD results (shown in Fig. 2) that pointed to an *almost* amorphous structure.

## 3.2 Kinetic measurements with spark ablated alloy TVCM-SA

Before using the spark ablated material as a catalyst of HS kinetics in its mixture with Mg, its HS performance was investigated, separately - without Mg. The experiments were carried out at three sorption temperatures 300°C, 330°C and 360°C. For absorption, initial nominal hydrogen pressure in the reservoir was 25 bar. After the reservoir was connected to reaction cell, the value of the pressure decreased down to 23 bar. The results are plotted in Fig. 4 in terms of hydrogen concentration $c_H$ in the sample vs. sorption time $t$. According to common convention, positive values of $c_H$ correspond to absorbed hydrogen and negative ones mean desorbed hydrogen. The higher scatter of $c_H$$_{exp}$ during absorption compared to $c_H$'s during desorption originated in the lower accuracy of the high-pressure transducer. Solid curves show limits of 90 % prediction of the true experimental values. I. e., any new observation will fall within this range with probability of 90 %. Since the amount of synthesized powder was limited (about 17 mg), the number of moles of hydrogen ab/desorbed in the sample was comparable with the number of moles ad/absorbed by walls of the reactor cell itself.

<figure><img src="image_6.png" /><figcaption>Fig. 4. Kinetic curves measured with TVCM-SA at (a)-360°C, (b)-330°C and (c)-300°C. (d) - Kinetic curves (dashed thick lines from Figs. 4a-c) corrected to ad/absorption in walls of reaction cell. Points: TVCM [39].</figcaption></figure>
Therefore, the blind experiment with empty cell ($c_{H0}$) was done before each measurement. The correction procedure is described in [39]. The scattered values (90% prediction limits) of $c_{H0}$ are represented by the shadow bands and the corrected values $c_H = c_H \exp - c_{H0}$ lie between the thick solid curves with average value between them (thick dashed curves). It is obvious that the physical sense of corrected values at small times $t$ is not well defined because of a competition of sorption in the sample and adsorption in the walls at the beginning. This is why the corrected curves (dashed and solid thick lines) do not start exactly at the co-ordinates origin. Time dependence of corrected average values of $c_H$ for all three temperatures $T$ are plotted in Fig. 4d together with our previous results for ball-milled alloy TVCM [39].

<figure><img src="image_7.png" /><figcaption>Fig. 5. Linearized kinetic curves measured in TVCM-SA (a), temperature dependence of the slope $k$ (b).</figcaption></figure>

There are obvious differences in kinetic curves obtained for TVCM and TVCM-SA. Contrary to sorption in ball-milled TVCM studied in our preceding paper [39], a considerable ab/desorption was observed in TVCM-SA. The amount of absorbed hydrogen in TVCM-SA reached several units of wt. %. However, these values were approached after a relatively long sorption time $t$.

Activation energy of hydrogen sorption, $E_a$, was evaluated using the isoconversion method [42] for isothermal analysis of reaction kinetics [43]. It is based on Avrami-Erofeev equation [44]

$$ \alpha = 1 - \exp(-kt^{1/n}) \quad (1) $$

Where $\alpha$ stands for relative hydrogen concentration $\alpha = c_H/c_{max}$, $k$ is temperature dependent rate constant (Eq. 2)

$$ k = \text{const} \cdot \exp - \frac{E_a}{RT} \quad (2) $$

and $n$ represents a coefficient related to specific mechanism of hydride sorption kinetics. The various modifications of the term standing in parentheses in Eq. 1 and various values of $n$ are summarized in ref. [45]. Plotting the kinetic curves in co-ordinates $[-\ln(1-\alpha)]^n$ vs. $t$ (Fig. 5a), the activation energy of sorption $E_a$ can be
evaluated from the temperature dependence of slopes *k* of the straight lines using Eq. 2. Temperature dependence of rate constant *k* is shown in Fig. 5b and all fitting parameters are listed in Table 1.

Linearization of kinetic curves according to [45] and values of *n* obtained for TVCM-SA point to the sorption kinetics controlled by the mechanism *nucleation-and-growth*. Activation energy *E*<sub>a</sub> calculated for absorption equals to that of *E*<sub>a</sub> for desorption and both of them are considerably lower than value for pure Mg (192 ± 13) kJ/mol H<sub>2</sub> [39].

<table><caption>Table 1
Rate constant *k*, exponent *n* and activation energy *E*<sub>a</sub> for sorption in TVCM-SA.</caption><thead><tr><th rowspan="2">Temperature</th><th colspan="2">absorption</th><th colspan="2">desorption</th></tr><tr><th><i>k</i></th><th><i>n</i></th><th><i>k</i></th><th><i>n</i></th></tr></thead><tbody><tr><td>°C</td><td>10<sup>4</sup>/h</td><td></td><td>10<sup>4</sup>/h</td><td></td></tr><tr><td>360</td><td>143</td><td>1.4</td><td>150</td><td>1.5</td></tr><tr><td>330</td><td>77</td><td>1.3</td><td>78</td><td>1.6</td></tr><tr><td>300</td><td>39</td><td>1.4</td><td>39</td><td>1.6</td></tr><tr><td><i>E</i><sub>a</sub> in kJ/mol H<sub>2</sub></td><td>67.7 ± 1.4</td><td></td><td>67.6 ± 1.0</td><td></td></tr></tbody></table>

### 3.3 Kinetic measurements with TVCM-CG and TVCM-FG

To perform the sorption experiments with TVCM-SA combined with Mg, magnesium from *PkChemie* in the form of small splinters was used (average particle size 200 µm, purity min 98.0 %). The mixing was done by a short-time ball-milling of a blend of Mg with spark ablated TVCM-SA in hydrogen (mixing ratio Mg : TVCM-SA = 10 : 1 by weight, 200 rpm, 5 min). The morphology of pristine Mg lumps and morphology of the resulting TVCM-CG composition is shown in Fig. 6a, b.

It can be seen that the Mg lumps were rounded during the short-time milling, but their average size did not change significantly. Element mapping (Fig. 6c) revealed that the fine particles at the surface of Mg grains are partly oxides (mainly MgO) and partly fine fluffs of spark-ablated TVCM-SA. The fine particles were distributed over the surface of the larger Mg grains. Traces of Al, Zn, Cu, Si and Fe in tenths of % were also identified, introduced as impurities of Mo and Mg.

After mixing Mg with TVCM-SA, the powder blend was hydrogen charged at 46 bars (nominal hydrogen pressure in the reservoir before its connection with reaction cell with the sample was 50 bars) up to the total saturation. Then the desorption at the chosen temperature was started. The kinetic study with each alloy was done using the same sample. During the first desorption, a kinetic curve has been obtained, the sample was totally desorbed, then it was charged again and desorption measurement proceeded at the next temperature.

Since the powder blend consisted mainly of Mg (Mg:TVCM-SA=10:1), and the charging of TVCM-SA is very slow (Fig. 4d), MgH<sub>2</sub> was the only hydride phase identified in the hydrogen-charged sample by XRD. This is
<figure><img src="image_8.png" /><figcaption>b)</figcaption></figure>

<figure><img src="image_9.png" /><figcaption>c)</figcaption></figure>

<figure><img src="image_10.png" /></figure>

Fig. 6. SEM micrograph of pristine Mg used for mixing with TVCM-SA (a) and TVCM-CG (b). Surface of an Mg grain after mixing Mg with TVCM-SA (c) (Surface of the Mg grain – dark area, MgO – light particles, TVCM-SA – grey particles).

exemplified at bottom panel in Fig. 7 for TVCM-CG. Phase composition of TVCM-FG was the same, since the

prevailing fraction is Mg in both grades. The phase composition of the desorbed state, which followed, is shown in upper panel in Fig. 7. It is obvious that during the cycling, a certain fraction of Mg (ICSD Nr. 77908) always persisted in charged state and also that a fraction of MgH₂ (ICSD Nr. 638288) remained in following desorbed state. The broad peak observed close to 2θ=50° comes mainly from a thin layer of oxide MgO (ICSD Nr. 52026). Traces of Cr₂O₃ (ICSD Nr. 290240) and (Mg₀.964Ti₀.036)O₄ (ICSD Nr. 80848) were also detected. Kinetic curves for alloy TVCM-CG are plotted in Fig. 8a. The desorption kinetics was further improved by long-time ball-milling, which decreased the mean grain size down to about 1 µm (Fig. 9). In this case, however, the desorption curves were composed of two components. The initial one was rapid and it

<figure><img src="image_11.png" /></figure>

Fig. 7. XRD pattern of TVCM-CG during hydrogen charging.
was followed by a slow tail. The rapid components only are plotted in Fig. 8b.

<figure><img src="image_12.png" /><figcaption>Fig. 8. Kinetic curves measured in desorption regime with TVCM-CG (a) and TVCM-FG (b). Comparison of the present results with the desorption curve obtained in [39] with pure Mg – all at 360°C (c).</figcaption></figure>

Kinetic curves obtained with TVCM-FG and TCVM-CG and results with hydrogen desorption kinetics in pure Mg ([39]) are compared in Fig. 8c, where also the slow desorption component is shown for the sake of comparison, measured with TVCM-FG (dotted line). For illustration, the curves measured at 360°C only are presented that characterize the picture that has been observed also at other temperatures. It was found that

TVCM-CG improves considerably the hydrogen desorption kinetics compared with the Mg and, at the same time that it conserves approximately the hydrogen storage capacity. Differences between the sorption kinetics and sorption capacity of the three compared materials shown in Fig. 8c can be, at least qualitatively, interpreted on the basis of different grain size of Mg and TVCM-SA and using the different population of Mg grains with TVCM-SA in TVCM-CG and in TVCM-FG: Sorption kinetics in pure Mg with coarse grains is lazy, but maximum $|c_H|$ is high – after long sorption time it can approach theoretical value 7.6 wt. % H₂ [4]. In TVCM-CG

with similar grain size, the maximum value of $|c_H|$ is similar, but due to the catalytic effect of TVCM-SA, the

<figure><img src="image_13.png" /><figcaption>Fig. 9. SEM micrograph of TVCM-FG.</figcaption></figure>
kinetics are improved. The kinetics is further improved in TVCM-FG with small Mg grains but in this case, values of maximum $|c_H|$ are lower due to relatively lower population of Mg grains with TVCM-SA fine particles. This fraction of poorly catalyzed Mg grains is most likely responsible for the slow sorption kinetics at great *t*'s observed in TVCM-FG (dotted line tail on kinetic curve in Fig. 8c). Morphology of TVCM-CG and TVCM-FG is schematically illustrated in Fig. 10.

<figure><img src="image_14.png" /><figcaption>Fig. 10. Hydrogen charging of coarse-grained alloy TVCM-CG (a) and fine-grained alloy TVCM-FG (b) decorated with the same fraction of catalyzing particles TVCM-SA – schematically.</figcaption></figure>

Linearized kinetic curves are plotted in Fig. 11a in coordinates [-ln(1-α)]ⁿ vs. time *t* and temperature dependence of their slope *k* is shown in Fig. 11b. Activation energy of desorption kinetics was evaluated using Eq.(2). All numerical parameters are summarized in Table 2.

<figure><img src="image_15.png" /><figcaption>Fig. 11. Linearized kinetic curves measured in desorption regime (a), temperature dependence of the slope *k* (b).</figcaption></figure>
<table><caption>Table 2
Rate constant *k*, exponent *n* and activation energy *E*<sub>a</sub> for desorption in TVCM-CG a TVCM-FG.</caption><thead><tr><th></th><th colspan="2">TVCM-CG</th><th colspan="2">TVCM-FG</th></tr><tr><th>temperature</th><th><i>k</i></th><th><i>n</i></th><th><i>k</i></th><th><i>n</i></th></tr><tr><th>°C</th><th>1/h</th><th></th><th>1/h</th><th></th></tr></thead><tbody><tr><td>360</td><td>3.569</td><td>0.6</td><td>46.516</td><td>0.5</td></tr><tr><td>330</td><td>1.424</td><td>0.8</td><td>13.634</td><td>0.6</td></tr><tr><td>300</td><td>0.457</td><td>0.7</td><td>5.350</td><td>0.4</td></tr><tr><td>270</td><td></td><td></td><td>1.329</td><td>0.5</td></tr><tr><td><i>E</i><sub>a</sub> in kJ/mol H<sub>2</sub></td><td colspan="2">103.4 ± 3.4</td><td colspan="2">109.6 ± 5.5</td></tr></tbody></table>

From the comparison of $E_a$'s from Table 2 with activation energy known for pure Mg (192 ± 13) [39], it comes out clearly that TVCM-SA improves hydrogen sorption kinetics in Mg. Further, value of $E_a$ for the coarse-grained grade TVCM-CG is lower than the value $E_a = (113±2 \text{ kJ/molH}_2)$ reported in [39] for TVCM-BM. This implies that nano-sized powder TVCM-SA is more effective catalyst of sorption kinetics in Mg than mere presence of the components Ti, V, Cr and Mo in TVCM-BM (at the same average chemical composition). Somewhat higher average value of $E_a$ for TVCM-FG compared to TVCM-CG is most likely due to un-even coverage of smaller Mg grains by TVCM-SA – see the discussion above.

### 3.4 PCT measurements with TVCM-CG and TVCM-FG

To examine the formation entropy and enthalpy of the hydride phase, thermodynamic study was carried out with TVCM-CG and TVCM-FG. PCT measurements were conducted with TVCM-CG in absorption mode and with TVCM-FG both in absorption and desorption modes.

The results are shown in Fig. 12a. It can be seen that in TVCM-CG, well-defined and almost perfectly flat plateaus were observed, in TVCM-FG the plateaus were significantly tilted and shorter compared to those in TVCM-CG. Possible explanation of different appearances of PCT isotherms consists, most likely, in structural differences shown schematically in Fig. 10: In TVCM-FG, the surface of fine grains is differently populated with fine particles of TVCM-SA, whereas the surface coverage of all, much greater grains in TVCM-CG, can be considered approximately uniform. This may imply the considerable tilt of PCT plateaus in TVCM-FG compared to those in TVCM-CG. Certain fractions relatively sparsely TVCM-SA-decorated grains in TVCM-FG contribute to a less extent to the totally absorbed amount of hydrogen, which results, most likely in shorter plateaus.

Entropy $\Delta S$ and enthalpy $\Delta H$ of hydride formation were calculated from straight lines in Van't Hoff diagram in Fig. 12b using Arrhenius relation $p/p_0 = \exp(\Delta S/R) \times \exp(-\Delta H/RT)$, where $p_0$, R, and T stand for normal pressure (1 bar), universal gas constant and sorption temperature respectively. Numerical results are listed in Table 3.
<figure><img src="image_16.png" /><figcaption>Fig. 12 PCT curves (a), Van't Hoff diagram (b); $p_0$ – normal pressure (1 bar).</figcaption></figure>

One can see in Table 3 that Arrhenius parameters $\Delta S$ and $\Delta H$ obtained for TVCM-CG and TVCM-FG are equal in frame of experimental errors (mean value of $\Delta H$ for absorption and desorption is about 65±5 kJ/mol $H_2$). Similarly, $\Delta S$ and $\Delta H$ for TVCM-BM agree reasonably with those for pure Mg (mean value of $\Delta H$ for TVCM-BM and Mg in Table 3 is about 76±2 kJ/mol $H_2$). However, there is a small but significant difference between formation entropy and enthalpy $\Delta H$ observed in alloys catalyzed by spark ablated TVCM-SA and in TVCM-BM (for $\Delta H$ makes the difference about 11±6 kJ/mol $H_2$), which means that formation of hydride phase in TVCM-CG and TVCM-FG is somewhat easier than in TVCM-BM. This difference may be possibly caused by a slightly different phase composition. In intensively ball-milled and hydried TVCM-BM also minority phases were detected [39], whose content was close to the XRD detection limits: Ti (HCP; 1.9 %), secondary BCC phases rich in Mo, V, TiV and $Mo_2Ti$ (0.7 – 1.4 %), hydrides $TiH_2$, $V_2H$ (summary content of these hydrides was about 4 %) and about 2 % of WC from the walls of the milling jar. Detailed explanation of the observed difference in $\Delta H$, however, remains open for further study.

It is interesting to compare the present results with literature data. In Table 4, relevant data for partial subsystems Mg-TM (TM = Ti, V, Cr) are shown in cases, where Mg and TM form no intermetallic compound. For subsystem Mg-Mo, no comparable data was found.
<table><caption>Table 3
Entropy and enthalpy of hydride formation. Comparison of present data with average data for Mg and with results reported for ball-milled alloy in [36].</caption><thead><tr><th rowspan="3">Material</th><th colspan="2">Absorption</th><th colspan="2">Desorption</th><th rowspan="3">Ref.</th></tr><tr><th>ΔS<sup>abs</sup></th><th>-ΔH<sup>abs</sup></th><th>ΔS<sup>des</sup></th><th>-ΔH<sup>des</sup></th></tr><tr><th>J/K/mol H<sub>2</sub></th><th>kJ/mol H<sub>2</sub></th><th>J/K/mol H<sub>2</sub></th><th>kJ/mol H<sub>2</sub></th></tr></thead><tbody><tr><td>TVCM-CG</td><td>123 ± 6</td><td>66.4 ± 3.7</td><td></td><td></td><td>this work</td></tr><tr><td>TVCM-FG</td><td>116 ± 6</td><td>61.3 ± 1.8</td><td>120 ± 7</td><td>67.1 ± 4.1</td><td>this work</td></tr><tr><td>TVCM-BM</td><td></td><td></td><td>140 ± 1</td><td>76.8 ± 0.9</td><td>[36]</td></tr><tr><td>Mg</td><td></td><td></td><td>137 ± 2</td><td>75 ± 2</td><td>[36]</td></tr></tbody></table>

As for TM=Ti, catalysis of hydrogen sorption in Mg by stable TiH₂ hydride was also studied [46, 47]. It is obvious that elemental Ti is, on average, more effective in lowering of ΔH than V and Cr. Comparing data in Table 3 and Table 4, it is easy to conclude that our average values of ΔH are lower than relevant literature hydride formation enthalpies in Mg-TM. This points to the synergy effect of components in MPEAs leading to improvement of HS performance of Mg. Similar synergy of V and Ni was reported in [49]. The price for the benefit of lower ΔH in Mg catalyzed by TVCM-SA is somewhat lower sorption capacity (compare maximum values of |c<sub>H</sub>| in Fig. 8 with values SC in Table 4).

Formation entropy in Tables 3, 4 is close to a constant theoretical value (about 140 J/K/mol H₂). This value is mainly given by entropy loss of gaseous hydrogen as it enters the solid phase. Therefore, ΔS is almost independent on the nature of the metallic host and its experimental values offer no substantial information on HS for any specific solid material [6]. This is why the ΔS is even not reported in many studies – see empty fields in Table 4.
<table><caption>Table 4
Hydride formation enthalpy $\Delta H$ (kJ/mol H₂), entropy $\Delta S$ (J/K/mol H₂) and sorption capacity SC (wt.% H₂).</caption><thead><tr><th rowspan="2">Alloy</th><th colspan="2">Absorption</th><th colspan="2">Desorption</th><th rowspan="2">SC</th><th rowspan="2">Remark</th><th rowspan="2">Ref.</th></tr><tr><th>ΔS<sup>abs</sup></th><th>-ΔH<sup>abs</sup></th><th>ΔS<sup>des</sup></th><th>-ΔH<sup>des</sup></th></tr></thead><tbody><tr><td rowspan="5">Mg-Ti</td><td rowspan="5">142±2</td><td>69.5±0.2</td><td rowspan="5">130.6±1.4</td><td rowspan="5">74.1±0.7</td><td>5.5</td><td>10MgH<sub>2</sub>/TiH<sub>2</sub>; high energy BM, high pressure</td><td>[46]</td></tr><tr><td rowspan="4">72.8±0.7</td><td>5.5</td><td>10MgH<sub>2</sub>/TiH<sub>2</sub>; high energy BM, high pressure</td><td>[46]</td></tr><tr><td>4.4 - 5</td><td>Mg-6 at. %Ti</td><td>[50]</td></tr><tr><td>4</td><td>ultra fine Mg-Ti; Mg/Ti = 1/2</td><td>[48]</td></tr><tr><td>4</td><td>Mg H<sub>2</sub>-0.1TiH<sub>2</sub></td><td>[47]</td></tr><tr><td rowspan="4">78.8±1.1</td><td>127</td><td rowspan="4">130.5-136.1</td><td>5.8 - 6.7</td><td>Mg+Ti-based catalysts</td><td>[51]</td></tr><tr><td>77.2</td><td>5.5 - 6</td><td>15Mg@Ti</td><td>[52]</td></tr><tr><td>74.3</td><td>up to 5</td><td>Mg-10.2 at.% V</td><td>[53]</td></tr><tr><td>77.5</td><td>5 - 6</td><td>Mg-V nanocomposite</td><td>[54]</td></tr><tr><td rowspan="5">Mg-V</td><td rowspan="5">139.6</td><td>74.3</td><td rowspan="5">138.5</td><td>77.4</td><td>82.7</td><td>Mg-(V-Ti-Zr-Ni) spark-plasma-sintering</td><td>[55]</td></tr><tr><td>77.5</td><td>71,6</td><td>5 - 6</td><td>Mg-V-Ni; nanocomposite; synergy V + Ni</td><td>[49]</td></tr><tr><td>70,2</td><td>5.71</td><td>Mg-V-Ni;</td><td>[56]</td></tr><tr><td>79.2±3.6</td><td>73.3±0.3</td><td>5 - 6</td><td>Mg/V multilayers</td><td>[57]</td></tr><tr><td>133.4±0.5</td><td>73.6±0.6</td><td>5 - 6</td><td>Mg/Cr multilayers</td><td>[57]</td></tr><tr><td rowspan="3">Mg-Cr</td><td rowspan="3">141.2±6.4</td><td>133.7±1.0</td><td rowspan="3">132.0</td><td>72.1</td><td>0.2 - 2.4</td><td>Mg<sub>x</sub>Cr<sub>(1-x)</sub>; x = 0.2-0.4; deuterium sorption</td><td>[58]</td></tr><tr><td>132.0</td><td>72.1</td><td>0.2 - 2.4</td><td>Mg<sub>x</sub>Cr<sub>(1-x)</sub>; x = 0.2-0.4; deuterium sorption</td><td>[58]</td></tr></tbody></table>

4. Conclusions

1. Hydrogen storage performance of near-equimolar multiprinciple alloy TVCM-SA and its catalytic effect upon the hydrogen sorption in magnesium was studied.

2. It was found that hydrogen sorption capacity of fine-grained spark-ablated TVCM-SA, scaled by maximum of $|c_H|$, was about 3 – 4 wt.% H₂. This limiting hydrogen concentration, however, was reached after several tens of hours. No hydride having definite stoichiometry was identified.

3. A more promising finding is the catalytic effect of TVCM-SA upon the hydrogen sorption in Mg. Two grades of the alloy TVCM-SA@Mg were prepared, each having the weight ratio TVCM-SA / Mg = 1 / 10: coarse-grained grade (TVCM-CG) and fine-grained one (TVCM-FG). It was found that 90% of maximum hydrogen desorption capacity (4.8 wt. % H₂) was reached in TVCM-CG within about 9 min, whereas maximum hydrogen desorption capacity (2.7 wt. % H₂) was approached in TVCM-FG in 1.9 min at 360°C. The observed different
HS behavior of fine-grained and coarse-grained grade was explained qualitatively by the morphology of TVCM-CG and TVCM-FG.

4. Activation energies $E_a$ and the absolute values of formation enthalpy of hydride state $\Delta H$ evaluated for all three alloys, TVCM-SA, TVCM-CG and TVCM-FG, are significantly lower compared to pure Mg. Obtained values of $\Delta H$ are also lower than relevant values reported for Mg-TM binary subsystems of TVCM. This points to an evident synergy effect of components in TVCM upon the HS characteristics of TVCM-FG and TVCM-CG.

**Acknowledgements**

This paper was created as part of the project No. CZ.02.01.01/00/22_008/0004631 Materials and technologies for sustainable development within the Jan Amos Komensky Operational Program financed by the European Union and from the state budget of the Czech Republic and the present paper was supported by the Institute of Physics of Materials AS CR, CZ-61662 Brno, Czech Republic, program Strategy AV21, program Sustainable energy; Project: Hydrogen technologies AV21/27.

**CRediT authorship contribution statement**

Lubomír Kral: Writing – review & editing, Visualization, Validation. Tomas Nemec: Review & editing, nano-materials preparation. Jiri Cermak: Writing – review & editing, Supervision, Formal analysis. Pavla Roupcova: Structure analysis and evaluations. Ondrej Zobac: Editing, microscopy and structure analysis. Bedrich Smetana: Editing, review.

**Competing interests**

Authors declare that they have no competing interests.

**Data availability**

All data supporting this study are provided in the main article. Raw data are available on Zenodo https://doi.org/10.5281/zenodo.17226885.

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