Hydrogen Desorption Kinetics of V₃₀Nb₁₀(Ti_xCr_1–x)₆₀ High-Entropy Alloys

Abstract

In recent years, high-entropy alloys (HEAs) have attracted wide attention for their enormous hydrogen storage potential, fast hydrogen absorption kinetics, and a wide range of composition selectivity, and the fact that alloys with body-centered cubic (BCC) structure are considered to possess large capacity. Herein, three V₃₀Nb₁₀(Ti_xCr_1–x)₆₀ HEAs with different Ti contents (Ti25, Ti30, Ti35) forming BCC structures were designed using the method of CALPHAD. The microstructure characteristics and the hydrogen storage performances, especially the kinetics of hydrogen desorption, were systematically investigated. The results show that after absorbing ~3.7 wt.% hydrogen at 300 K with 100 bar hydrogen pressure, the studied alloys exhibit similar hydrogen release behaviors at different temperatures. Taking the V₃₀Nb₁₀Ti₂₅Cr₃₅ alloy as an example, it was able to release 1.96 wt.%, 2.21 wt.%, and 2.48 wt.% of hydrogen at 353, 373, and 423 K, respectively. The higher the temperature, the faster the hydrogen desorption kinetics and the more hydrogen released. The hydrogen desorption kinetics of the alloys were successfully fitted with the Ginstling–Brounshtein model, and the main rate-controlling step was diffusion. In addition, the diffusion activation energy of hydrogen desorption decreases with the substitution of Cr content. The present study is expected to provide valuable information for the better development of high-entropy-based hydrogen storage alloys.

1. Introduction

Hydrogen energy is playing an increasingly important role in the decarbonization of the global economy. Applications based on hydrogen have penetrated all aspects [1] of traditional energy sources, including transportation, industrial fuels, and electric energy storage. With the rapid development of the hydrogen economy industry, further challenges must be considered, that is, how to store and transport hydrogen in a safe and efficient manner. Among different hydrogen storage techniques such as gas-, liquid- and solid-state storage, the solid-state storage in the form of metal hydrides [2] shows remarkable advantages in terms of security and volumetric hydrogen storage density. Metal hydrides with different thermo-physical properties have actually been explored for many engineering applications. Mg-based materials [3] possess the advantage of high weight capacity, but their unfavorable thermodynamic properties (hydrogen absorption and discharge under high temperatures) discourage their wide application in many scenarios. Although intermetallic compounds (such as TiFe [4] and LaNi₅ [5]) exhibit good thermodynamic features for hydrogen storage at ambient temperature, these materials either require complex thermal activation processes or suffer from low hydrogen storage capacity. Therefore, it is necessary to design and carry out in-depth basic research on new high-performance materials for room-temperature hydrogen storage.

In recent years, high-entropy alloys (HEAs) as hydrogen storage materials [6] have received a lot of attention for their multiple principal elements composition [7] and the thermodynamic miscibility of the constituent elements, providing not only a nearly limitless multi-dimensional compositional space but also specific unpredicted properties. HEAs with Laves-phase structure have embodied some properties that are superior to those of conventional hydrogen storage alloys. For example, TiZrCrMnFeNi HEA exhibits hydrogen absorption kinetics without activation [8] compared to TiFe/TiMn alloys [9]. The high configurational entropy [10] in ZrNbCuCoNi restrains the occurrence of disproportionation reactions common in ZrCo-based alloys [11], resulting in ultra-high cyclic stability. Although the cycle retention/activation kinetics perform well in the Laves-structure HEAs, the hydrogen storage capacity (<2 wt.%) limits its application [12]. Another prominent candidate of HEAs for hydrogen storage is based on body-centered cubic (BCC) solid solutions. Sahlberg et al. demonstrated experimentally that TiVZrNbHf [13] can absorb a much higher amount of hydrogen than conventional BCC alloys and reach a hydrogen-to-metal ratio of 2.5. Although the origin of anomalous hydrogen occupation in BCC-structured HEAs remains controversial [14], it will clearly provide great opportunities for the development of promising materials for hydrogen storage [15].

The hydrogen absorption/desorption kinetics [16] are extremely critical for BCC HEAs in hydrogen storage applications. The Ti-V-Zr-Nb-Hf system (with ternary, quaternary and pentanary components) studied by Gustav et al. shows absorption kinetics with a thermal activation at 613 K for 3 h under dynamic vacuum [17]. Zhang et al. synthesized the TiZrNbTa HEA [18] for hydrogen storage, which required three activations at a temperature of about 1000 K for hydrogen absorption. The difficulty of activation is a common problem for BCC HEAs, and it can be improved by introducing second phases [19] or reducing the specific surface area of alloy particles [20]. BCC HEAs usually exhibit good hydrogen uptake kinetics after activation. The Ti-V-Nb HEA prepared by Silva et al. reached an absorption of 3.1–3.2 wt.% H₂ in less than one minute at room temperature [21]. A similar TiZrNbTa HEA [22] reached its maximum hydrogen storage within one minute after 150 s of incubation time at 293 K. The fitting of kinetic hydrogenation curves indicates that the process follows the Johnson–Mehl–Avrami–Kolmogorov (JMAK) equation and that the hydrogen uptake process of BCC high-entropy hydrogen storage alloys can be described by nucleation and growth mechanisms. While some progress has been made in the study of hydrogen absorption kinetics of HEAs, there is still a shortage of research on their hydrogen desorption kinetics, especially the kinetic fitting models.

This study is dedicated to understanding the desorption kinetics of BCC HEAs. In our previous studies [23], it was found that TiVNbCr HEAs show great potential for hydrogen storage applications. TiVNbCr with a BCC structure allows a wide range of compositions for hydrogen–metal atom ratios of up to 2. Herein, we designed a series of TiVNbCr HEAs (V₃₀Nb₁₀Ti₂₅Cr₃₅, V₃₀Nb₁₀Ti₃₀Cr₃₀ and V₃₀Nb₁₀Ti₃₅Cr₂₅) with a substitution of Cr for Ti element. CALPHAD calculations and heat treatment have been carried out to ensure the formation of a single BCC phase. All alloys showed fast hydrogen absorption kinetics, and the V₃₀Nb₁₀Ti₂₅Cr₃₅, V₃₀Nb₁₀Ti₃₀Cr₃₀, and V₃₀Nb₁₀Ti₃₅Cr₂₅ alloys reached the maximum hydrogen absorption equilibria of 3.60 wt.%, 3.67 wt.%, and 3.72 wt.%, respectively, within 100s at 300 K. The kinetic behavior of hydrogen desorption has been successfully fitted with the Ginstling–Brounshtein model, and it implies that the main rate-controlling step of the hydrogen desorption kinetics is diffusion. In addition, we also calculated the diffusion activation energy and found that the increase in Cr content was favorable to improve the hydrogen release kinetics.

2. Materials and Methods

In this study, TiVNbCr HEA button ingots with different Ti contents were prepared by arc melting in a water-cooled copper furnace (Hefei Kejing Material Technology Co., Ltd., Hefei, Anhui, China) under argon atmosphere, using Ti, V, Nb, and Cr particles with purity greater than 99.0% (Alfa Aesar, part of Thermo Fisher Scientific, Lancashire, United Kingdom) as alloy raw materials, as shown in

Table 1. The designed TiVNbCr HEAs with different Cr.

Alloys	Abbreviations	Ti Content (at.%)	V Content (at.%)	Nb Content (at.%)	Cr Content (at.%)
V30Nb10Ti25Cr35	Ti25	25	30	10	35
V30Nb10Ti30Cr30	Ti30	30	30	10	30
V30Nb10Ti35Cr25	Ti35	35	30	10	25

. After the vacuum degree reached 3 × 10⁻³ Pa, the argon pressure was controlled to be (−0.05) MPa, and the button ingot was repeatedly melted four times to ensure uniform composition. Heat treatments at high temperatures were necessary to ensure that single-phase BCC alloys were obtained. The treatment conditions were determined according to the CALPHAD method with Thermo-calc software using the TCHEA3 database (Thermo-Calc 2019a, Thermo-Calc Software, Stockholm, Sweden), as will be discussed later.

The samples for phase structure and microstructure characterization were taken from the core of the heat-treated samples. For crystal structure examination, X-ray diffractometer (XRD, Rigaku, Japan) with Cu K_α radiation (λ = 0.15406 nm, 45 kV, 40 mA) was used to identify the phase structure of the samples. The XRD data were collected in the 2θ range of 20°–90° with a 0.02° step increment at ambient temperature. Samples measuring 6 mm × 6 mm × 3 mm were cut from the button ingots using the wire-cutting technique, ground, and polished, and then their microstructures were observed. A HI-TACHI S4800 cold field emission scanning electron microscope (Hitachi Ltd., Tokyo, Japan) equipped with a backscattered electron detector was used to observe the microstructure at 15 kV, and an energy spectrometer (EDS, Hitachi Ltd., Tokyo, Japan) was used to analyze the chemical composition of the alloy at 20 kV.

The hydrogen absorption and desorption properties of the alloy were obtained using a Sieverts type PCT tester(Yangzhou University [19], Yangzhou, Jiangsu, China). The prepared alloys were cut into 3 × 3 × 3 mm³ cubes, polished to remove the surface oxide, and then placed in a vacuum at 673 K for 1 h to fulfill the activation.

3. Results and Discussion

3.1. CALPHAD Calculations of TiVNbCr HEAs

The acquisition of a single-phase structure is the first step in the design of HEAs with high performance for hydrogen storage. The calculation of the equilibrium phase diagram by applying the Gibbs–Helmholtz free-energy formulations for every phase is widely used in the design of HEAs [24]. Using CALPHAD modelling, the phase formation of the investigated HEAs (Ti35, Ti30 and Ti25) was predicted through Thermo-Calc software (version 2019a, Thermo-Calc Software, Stockholm, Sweden) and the TCHEA3 database, as shown in Figure 1. As with the previously reported TiVNbCr-based HEAs [23], all of them show a wide temperature range of BCC phase formation domains. The single BCC phase of the Ti25 alloy is predicted to be in the temperature range of 1070 K-1828 K, and then decompose into BCC + C15_Laves phases. Three phases coexist as the temperature drops below 788 K, including BCC, C15_Laves, and HCP_A3 phases. A similar phase diagram can be found for Ti30 and Ti35 alloys, as shown in Figure 1b,c. It would not be surprising to find the coexistence of multiple phases in TiVNbCr alloys at medium temperature in the calculated phase diagram. Herein, a heat-treatment of holding at 1500 K for 3 h was adopted to ensure that the alloys’ single-phase BCC was obtained.

3.2. XRD Phase and Microstructure

The XRD patterns of the three alloys after heat-treatment are shown in Figure 2. The position of the diffraction peak of the alloy is consistent with that of a typical BCC HEA, and no significant diffraction pattern of second phases was found, which is in accordance with our expected results. Although the morphology of XRD is essentially the same, the peaks of diffraction are angularly shifted to different degrees. It is found that the peaks of BCC phase shifted toward higher 2θ with the increase in Cr concentration, which implies that the lattice parameters of the BCC phase become smaller due to the addition of Cr. According to the Bragg equation, the lattice parameters of the strongest diffraction peak along <110> directions are calculated for all alloys (Ti35, Ti30, and Ti25), corresponding to the lattice constant values of 3.125 Å, 3.102 Å, and 3.079 Å, respectively. The variation in the lattice constant are attributed to the substitution of Cr element for Ti, which shows a larger atomic radius. The larger radius implies larger interstitial position for hydrogen storage, but this may also lead to easier trapping of hydrogen in the interstitial sites, which, in turn, affects hydrogen dynamics and kinetics.

As shown in Figure 3, the microstructures of different alloys can be clearly seen from the representative SEM backscattered electron (BSE) images. All three alloys show a compositionally homogeneous morphology, without significant second phases. It should be noted that the contrast in the BSE images was controlled to show the crystallographic orientation information (i.e., the backscattering effect versus the channeling effect) resulting from the electron plane-wave diffraction, in order to show the microstructural features at a grain-level, and no significant atomic number contrast (Z-contrast) was identified, as can also be confirmed by the corresponding EDS analysis in Figure 3d,e. It can be found that the microstructure of the heat-treated alloys presents an approximately equiaxed grain characteristic rather than the dendritic morphology that is commonly found in cast alloys [25]. The grain size of the Ti25, Ti30, and Ti35 alloys are ~200 µm, ~400 µm, and ~500 µm, respectively. This variation in grain size can be attributed to the different interfacial energy in the different compositions [26]. This grain size distinction is no longer retained after hydrogen absorption as the alloy bulk is broken [27] and even pulverized after hydrogen absorption. From the EDS results, the atomic fraction of each element is almost the same as the actual ratio. The surface scans of all three alloys show that the surface distribution of Ti, V, Nb, and Cr is fairly similar between the elements, and no obvious elemental segregation is found, as is also confirmed by the EDS maps in Figure 3. These results are consistent with the presented XRD data, and it can be concluded that the prepared TiVNbCr series of HEAs are composed of solid solution with uniform structure and single phase.

3.3. Hydrogen Absorption/Desorption Kinetics in TiVNbCr HEAs

The construction of numerical models for hydrogen–metal reactions, especially the rate of hydrogen release reaction, is essential for the application of hydride-based hydrogen storage devices [28]. Herein, all three TiVNbCr alloys with different Cr contents underwent an activation process by high temperature evacuation, and were then completely hydrogenated at 300 K under a H₂ atmosphere at 100 bar. The kinetics of hydrogen absorption after activation is shown in Figure 4. After less than 180 s of the hydrogen absorption process, the Ti25, Ti30, and Ti35 alloys reached the maximum hydrogen absorption equilibria of 3.60 wt.%, 3.67 wt.%, and 3.72 wt.%, respectively. It took nearly 60 s to reach 90% hydrogen reaction fraction (ξ = 0.9) for the three alloys, and the fast kinetics may be attributed to the severe lattice distortion in the HEA [29]. Moreover, the hydrogen-to-metal ratio can easily reach 2, as with our previously reported TiVNbCr alloy [23], which, again, demonstrates the wide range of compositional options for HEAs as hydrogen storage materials.

After the completion of hydrogenation, the kinetics of hydrogen desorption from the alloy was investigated at different temperatures. All the hydrogen desorption tests were started with the fully hydrogen-absorbing samples at 300 K temperature and 100 bar H₂. Considering the structural design of the Sieverts PCT device, the sample was dehydrogenated into a large enough cavity that the final stable hydrogen pressure was close to 0.06 MPa. As shown in Figure 5a, the Ti25 alloy was subjected to hydrogen release at temperatures of 353 K, 373 K, and 423 K, respectively. The kinetics of hydrogen release from the Ti25 alloy is not as fast as that of hydrogen absorption. It takes ~600 s for the alloy to reach hydrogen release equilibrium, whereas 1.96 wt.%, 2.21 wt.%, and 2.48 wt.% capacity of hydrogen can be desorbed at 353 K, 373 K, and 423 K, respectively. The temperature increase speeds up the desorption process, and dehydrogenation at 423 K even takes no more than 200 s to complete. Similar operations were carried out for Ti30 and Ti35 alloys. It should be noted that different alloys were tested at different temperatures to ensure better hydrogen release. We also conducted hydrogen release tests on Ti30 and Ti35 alloys at the temperature of 353 K, yet the amount of hydrogen release was essentially negligible. This is understandable because the lower valence electron concentration (VEC) of the alloy makes it difficult to release hydrogen [30]. For the sake of comparability of data and subsequent fitting of kinetic equations, we conducted hydrogen release tests at higher temperatures for Ti30 and Ti35 alloys. The hydrogen release properties of the Ti30 alloy were investigated at 393 K, 423 K, and 443 K, while the same tests were performed at 423 K, 443 K, and 473 K for the Ti35 alloy, as is shown in Figure 5b,c. As in the case of the Ti25 alloy, the increase in temperature favors the improvement of the hydrogen release kinetics of Ti30 and Ti35 alloys. Due to the stronger hydrogen–metal interaction, the Ti30 and Ti35 alloys desorb less hydrogen, and they typically only release up to 2 wt.% of hydrogen capacity, as is listed in

Table 2. The hydrogen desorption of TiVNbCr HEAs at different temperatures.

Alloys	Desorption	353 K	373 K	393 K	423 K	443 K	473 K
Ti25	wt.%	1.96 in 402 s	2.21 in 202 s	/	2.48 in 85 s	/	/
Ti30	wt.%	/	/	1.97 in 282 s	2.10 in 230 s	2.17 in 120 s
Ti35	wt.%	/	/	/	1.31 in 740 s	1.77 in 590 s	2.06 in 400 s

.

3.4. Model Fitting of Hydrogen Desorption in TiVNbCr HEAs

The hydrogen absorption and desorption behavior of alloys can usually be fitted with the rate equation [31]. It has been reported that the kinetics of hydrogen absorption in HEAs follows the JMAK equation, indicating that it is controlled by hydride nucleation and growth [32]. However, there are few reports on the kinetics of hydrogen release from HEAs. Understanding the transformation reaction processes of alloys and their hydrides is the basis for the construction of kinetic equations. As can be seen from the hydrogenation steps of the alloy, the kinetics of hydrogen uptake and release are mainly controlled by the dissociation of hydrogen molecules, chemisorption, hydride nucleation, and diffusion [33]. This suggests that it may be more appropriate to describe the dehydrogenation of HEAs in terms of a nucleation growth mechanism or a diffusion mechanism. Herein, three typical hydride kinetic models (the JMAK equation, Jander diffusion model and Ginstling–Brounshtein model) are applied in the desorption of TiVNbCr alloys.

The (JMAK) equation [34] is a model commonly used to describe the reaction of hydrogen with alloys. Considering the reversibility of the hydrogen absorption reaction and hydrogen release reaction, an attempt is also made to fit the hydrogen release reaction process with this equation, as follows:

$$\mathit{ln}\left[-\mathit{ln}\left(1-\alpha \right)\right]=n\mathit{ln}k+n\mathit{ln}t$$

(1)

where α is the reaction fraction, k is the temperature-dependent rate parameter, and n is the order of reaction. The JMAK model represents the random nucleation and growth mechanism described in detail in reference [34].

The Jander diffusion model [35] is a classical fitted model describing gas–solid reactions, in which the particles of the metal hydride are considered as spherical in shape. The concentration of the reactants in the product layer varies linearly, that is, the two- and three-dimensional diffusion is simply viewed as one-dimensional diffusion. Diffusion is the only rate-controlling step. The rate expression is described as:

$${\left[1-{\left(1-\mathrm{\alpha }\right)}^{1∕3}\right]}^2=kt$$

(2)

where α denotes the reacted fraction at any time t, and k is the rate constant, which depends on temperature and supply pressure.

The Ginstling–Brounshtein equation [36] is also a kinetic model to describe three-dimensional diffusion. On the basis of the Jander model, the Ginstling–Brounshtein model modifies the assumption of constant diffusion cross-sectional area, which means that diffusion is considered as a non-stationary system, as follows:

$$1-\frac{2}{3}\alpha -{\left(1-\alpha \right)}^{2∕3}=kt$$

(3)

where α is the reacted fraction at any time t, and k is the rate constant.

Figure 6, Figure 7 and Figure 8 show the correlations fitted using the three kinetic models in the TiVNbCr alloys. The kinetic model (equation) with the highest correlation coefficient (R²) is considered as the best-fitting model to describe the kinetics of hydrogen desorption. Among the three kinetic models, the Ginstling–Brounshtein model describing three-dimensional diffusion is the best fitted. These results suggest that non-uniform diffusion in three dimensions may be the key rate-controlling step for the hydrogen release behavior of TiVNbCr alloys. Five reaction partial steps are typically required for the overall dehydrogenation reaction: hydride decomposition at the hydride/metal interface, diffusion of hydrogen atoms through the solid solution phase, surface penetration of hydrogen atoms, recombination of chemisorbed hydrogen atoms, and physisorption and desorption to the gas phase. The hydrogenation and dehydrogenation reactions proceed in a dynamic equilibrium, which means that when the hydrogen pressure is withdrawn, the decomposition of the hydride has already started. This determines that the nucleation growth is unlikely to be the rate-controlling step of the overall reaction, which is why the JMAK model commonly used for hydrogenation reactions is not applicable in the dehydrogenation process. Additionally, because of the low activation energies involved in the desorption of physisorbed molecules to the gas phase, the diffusion of hydrogen atoms through the alloy layer becomes the rate-controlling step of the entire dehydrogenation reaction.

The rate constant of any thermally activated process is usually described by an Arrhenius relationship [37]:

$$\mathit{ln}k=\mathit{ln}A-\frac{E_a}{RT}$$

(4)

where k is the rate constant, A is the pre-exponential factor, E_a is the activation energy, T is the temperature, and R is the universal gas constant. As is shown in

Table 3. The Arrhenius activation energies of hydrogen desorption for the Ti25, Ti30, and Ti35 alloys.

Alloys	Temperature (K)	Rate Constant (k)	Activation Energy (kJ/mol)
Ti25	353	9.51 × 10−4	24.28 ± 2.29
	373	1.68 × 10−3
	423	3.84 × 10−3
Ti30	393	1.09 × 10−3	25.96 ± 10.3
	423	1.44 × 10−3
	443	2.82 × 10−3
Ti35	423	3.36 × 10−4	31.90 ± 4.83
	443	5.78 × 10−4
	473	8.89 × 10−4

, the Arrhenius activation energies of hydrogen desorption for the Ti25, Ti30, and Ti35 alloys have been found to be 24.28 ± 2.29 kJ/mol, 25.96 ± 10.3 kJ/mol, and 31.90 ± 4.83 kJ/mol, respectively. Although a standard deviation can be read from the fitting results, it is clearly shown that the hydrogen desorption activation energy is decreasing with the increase in the Cr content, and the hydrogen desorption kinetics improve accordingly. This can also be confirmed by the desorption data of the tested specimens at the same desorption temperature (i.e., 423 K in Table 2).

4. Conclusions

In this study, three TiVNbCr alloys with different Cr contents with single BCC-phase structure were prepared by arc melting in the design of CALPHAD calculations. The microstructure characteristics and the hydrogen storage performances were studied in explicit detail. The obtained conclusions are summarized as follows:

(1)

According to CALPHAD calculations, the TiVNbCr series HEAs with different Cr contents were designed, and a BCC single-phase uniform structure was obtained by arc melting and heat treatment.

(2)

TiVNbCr HEAs with different Cr contents show fast hydrogen absorption kinetics, reaching maximum hydrogen absorption within 100 s at 300 K. Among those alloys, the maximum hydrogen storage capacity of V₃₀Nb₁₀Ti₃₅Cr₂₅ alloy reached 3.72 wt.% with a high hydrogen-to-metal ratio of 2. It takes ~700 s for the alloy to reach hydrogen release equilibrium, where 1.31 wt.%, 1.77 wt.%, and 2.06 wt.% capacity of hydrogen can be desorbed at 423 K, 443 K, and 473 K, respectively. Higher temperatures lead to faster hydrogen release kinetics as well as higher hydrogen desorption, and similar phenomena were found for V₃₀Nb₁₀Ti₃₀Cr₃₀ and V₃₀Nb₁₀Ti₂₅Cr₃₅ alloys.

(3)

The kinetic behavior of hydrogen desorption from TiVNbCr-based HEAs was successfully fitted. The fitted equations are consistent with the Ginsling–-Braunshteinn model of three-dimensional diffusion, and the main rate-controlling step of the hydrogen release kinetics is diffusion. Meanwhile, the diffusion activation energy of hydrogen release decreases with the increase in Cr content, and, thus, hydrogen release becomes easier.