Roles of Ti-Based Catalysts on Magnesium Hydride and Its Hydrogen Storage Properties

Abstract

Magnesium-based hydrides are considered as promising candidates for solid-state hydrogen storage and thermal energy storage, due to their high hydrogen capacity, reversibility, and elemental abundance of Mg. To improve the sluggish kinetics of MgH₂, catalytic doping using Ti-based catalysts is regarded as an effective approach to enhance Mg-based materials. In the past decades, Ti-based additives, as one of the important groups of catalysts, have received intensive endeavors towards the understanding of the fundamental principle of catalysis for the Mg-H₂ reaction. In this review, we start with the introduction of fundamental features of magnesium hydride and then summarize the recent advances of Ti-based additive doped MgH₂ materials. The roles of Ti-based catalysts in various categories of elemental metals, hydrides, oxides, halides, and intermetallic compounds were overviewed. Particularly, the kinetic mechanisms are discussed in detail. Moreover, the remaining challenges and future perspectives of Mg-based hydrides are discussed.

1. Introduction

Depletion of fossil fuels and changes in the global climate urge people to seek green, sustainable energy resources and high-efficiency energy systems. Hydrogen is one of the secondary energy solutions with high gravimetric energy density, high efficiency, and zero carbon emission [1]. However, the hydrogen economy relies on safe and mature technology to store hydrogen, which remains a great challenge [2]. Solid-state hydrogen storage using metal hydrides is considered to be a safe and efficient method in comparison to other storage technologies, such as compressed hydrogen gas or liquid hydrogen.

Among various solid-state hydrogen storage materials, magnesium hydride (MgH₂) is one of the metal hydrides that has been considered to be promising, due to its high storage capacity, abundant resources, and relative safety. MgH₂ was first prepared in 1912 [3], and was proposed that can be used as energy storage media since the 1960s [4]. MgH₂ is known for its high hydrogen storage content, up to 7.76 wt%. More importantly, Mg has a single and flat pressure plateau under desorption/absorption, and is an abundant resource in the crust, which makes it one of the most promising hydrogen storage materials comparing to others. Thus, Mg-based hydride is expected to play important roles in future hydrogen storage techniques. In past decades, research efforts have made significant progress on improving Mg-based hydrides in terms of thermodynamics, kinetics, and reversibility. The utilization of MgH₂ for “energy storage” relates to two aspects, namely, hydrogen storage (HS) [5] and thermal energy storage (TES) [6]. Despite the difference in material-level for HS and TES, both applications require Mg-based hydride with fast hydrogen absorption and desorption rates. This leads to a large demand for studying catalysis in the Mg-H₂ system.

Due to the extensive research activities on Mg-based hydrides, a series of review papers have been published [7,8,9,10,11,12,13,14]. A comprehensive review by Yartys et al. [15] provides a historical overview as well as future perspectives. Recent reviews have covered various directions for Mg-based hydrogen storage, such as downsizing (nanostructuring) [7,10], catalysis and kinetics [7,16,17], and destabilization [18,19]. However, given the large volume of publications as well as many review papers on Mg-based hydride, it still lacks a review regarding a specific group of catalysts and responsible effects. Transition metals (TM)-based additives have been proved to be effective to enhance the hydrogen storage properties of MgH₂. Among different TM-based additives, Ti and its compounds are recognized as a group of promising additives, which have been widely investigated from many different aspects, including catalytic effects, catalysis mechanism, nano- and microstructures, and synthetic methods. In the past decades, much attention and many efforts were directed to this group of additives, with progress being continuously made. With a special emphasis on Ti-based catalysts, we intend to provide overviews of specific fundamental understanding and clear catalysis mechanisms for Mg-based material.

2. Fundamentals of the Mg-H₂ System

2.1. Crystal Structure

MgH₂ is a stoichiometric compound with a H/Mg atomic ratio of 1.99 ± 0.01 [20]. The Mg-H bond is an ionic type that is similar to alkali and alkaline earth metal hydrides [21]. MgH₂ with different types of structures can be synthesized by the reaction of magnesium with hydrogen under different conditions. β-MgH₂, which is stable at ambient pressure (1 bar) and room temperature, has a tetragonal TiO₂-rutile-type structure with space group P4₂/mnm [22]. β-MgH₂ can be formed under moderate conditions during reversible hydrogen cycling. Nevertheless, MgH₂ has at least four high-pressure forms, and the corresponding crystal structure parameters are tabulated in Table 1. At high applied pressures exceeding 0.387GPa or milled under high energy, β-MgH₂ transforms into the orthorhombic γ-MgH₂ form with α-PbO₂-type structure [23]. Additionally, a subsequent phase transition from γ-MgH₂ to a modified-CaF₂-type structure was observed experimentally using in situ synchrotron diffraction when hydrogen pressure is above 3.84 GPa [24]. According to Varin et al., high energy ball-milling of MgH₂ produced γ-MgH₂ coexisted with nanocrystalline β-MgH₂. They suggested that the presence of the γ-MgH₂ phase contributed to reducing the hydrogen desorption temperature of MgH₂ [25].

2.2. Thermodynamics of the Mg-H₂ System

The first experimental evaluation of the thermodynamics of the Mg-H₂ system was reported by Stampfer et al., showing the enthalpy of formation of MgH₂ to be −74.5 kJ/mol·H₂, and the entropy of formation is 136 J/K·mol·H₂ [20]. The thermodynamics parameters of the Mg-H₂ system have been reported, see Table 2. The pressure-composition-isotherm (PCI) method is commonly used to determine the enthalpy (ΔH) and entropy (ΔS) of the Mg-H₂ system. By measuring a series of equilibrium pressures at various temperatures, ΔH and ΔS can be derived by Van’t Hoff relation.

For on-board solid-state hydrogen storage, a thermodynamic window in the range of approximately 25–45 kJ/mol·H₂ is recognized for suitable metal hydride material [27]. Therefore, efforts have been directed to destabilize the MgH₂, or in other words, reducing the ΔH of MgH₂. It is expected that reducing ΔH can lower the working temperature for Mg-based hydride, which is crucial for on-board applications. Three typical approaches were proposed to destabilize MgH₂, namely, alloying, downsizing, and stress effect.

The alloying method refers to alloying other elements with Mg to form a new alloy or hydride compound with lower stability of its hydride. So far, alloying systems have been reported including Mg₂NiH₄ [28], Mg₂FeH₆, Mg₂CoH_5, Mg₂Cu [29], Mg(Al) [30], Mg₅₁Zn₂₀ [31], Mg₂Si [32], Mg(In) [33], Mg(Sn) [21], Mg(AgIn) [34], MgReNi [35], Mg₂M-xM_xH_y (M = Fe, Co, Ni), and so on. The principle is using a less-stable hydriding element A to form an Mg-A alloy. The energy diagram of the alloying method is illustrated in Figure 1. Since Mg-Ti is an immiscible system, Mg and Ti do not form an alloy. However, metastable Mg-Ti-H compounds have been reported. Kohta et al. [36,37,38,39] successfully synthesized Mg_xTi_100−x (35 ≤ x ≤ 80) alloys with hexagonal close-packed (HCP), face-centered cubic (FCC), and body-centered cubic (BCC) structures by ball milling. Vermeulen et al. [40] reported that Mg-Ti-H system has a very low plateau pressure (≈10⁻⁶ bar at room temperature). Additionally, it will have a higher plateau pressure and a reversible hydrogen storage capacity of more than 6 wt%, when forming ternary compositions with Al or Si.

Nano-sizing of Mg-based materials is not only a strategy to enhance kinetics, but also considered as an approach to destabilize MgH₂. It has attracted a great deal of effort in the past decades, despite its effectiveness and feasibility remaining controversial. The influence of nano-sizing on pressure-temperature dependence as well as ΔH is given in Figure 2. Theoretically, nanosizing to hydrides introduces excessive free energy to bulk or coarse particles. The excessive free energy may originate from lattice distortion [42]. Sadhasivam et al. [8] summarized the dimensional effects of nanostructured Mg/MgH₂ materials. They reported that Mg/MgH₂ with a particle size <5 nm has improved hydrogen storage properties. However, a great challenge remains in synthesizing such fine particles as well as maintaining the nano-size after thermal cycling for Mg-based materials. According to [8], the 1-dimensional Mg nanowire shows a promising hydrogen storage property. However, the nanowire structure would collapse into nanoparticles after a few cycles. Additionally, it is reported that reducing magnesium hydride structure to nanosize induces the stress/strain effect, which has been reviewed by Zhang et al. [43] It was pointed out that the stress/strain applied on MgH₂ leads to lattice deformation and volume change, which endows the extra strain energy for MgH₂. The research of Berube et al. [44] supported this claim. They reported that a 15% reduction of the formation enthalpy of nanostructured MgH₂ can be achieved by the introduction of surfaces, grain boundaries, as well as the presence of γ-MgH₂. Recent reviews [8,45,46], have provided thoughtful introduction and discussion into the thermodynamic aspects.

2.3. Kinetics

Kinetics for hydrogen storage materials is generally defined as the dynamic rate where hydrogenation and dehydrogenation take place in time. Kinetics measurements provide critical information on the rates of hydrogen uptake or release from Mg-based materials. It is necessary to be rather explicit when investigating hydrogenation and dehydrogenation kinetics. For pure Mg and MgH₂ in the conventional form of coarse powders, they demonstrate very sluggish kinetics for hydrogen absorption and release, usually requiring over 400 °C for the reverse reactions. The slow hydrogenation rate of Mg, as well as dehydrogenation rate of MgH₂, can be attributed to several intrinsic factors: dissociation of the hydrogen molecule, penetration of hydrogen through the surface, diffusion of hydrogen in the matrix, in addition to possible contamination in the sample environment.

For hydrogenation of Mg, dissociation of the hydrogen molecule on the Mg surface is often considered as a rate-limiting step. Table 3 summarizes the energies for hydrogen molecule dissociation on Mg and modified Mg surfaces. The reported values of hydrogen dissociation energy on the Mg surface are in the range of 0.4–1.15 eV (38.59–110.96 kJ/mol), which is higher than most transition metals, such as Ti, V, Ni, and Fe [48]. This means that a large energy barrier needs to be overcome for dissociation of H₂ on pure Mg (0001) surfaces [49]. Another intrinsic issue is the slow hydrogen diffusion rate in MgH₂. Figure 3 shows the geometry model of the reaction for an Mg/MgH₂ particle. Based on the model, the hydride layer formed on the particle surface becomes the major barrier during hydrogenation, since the hydrogen atom diffusion rate in the hydride phase is much slower than that in the metallic phase. According to Spatz et al., the hydrogen diffusion coefficient (D_H) of MgH₂ is quite low (1.1 × 10⁻²⁰ m²/s at 305 K) [50]. Figure 4 shows that the D_H of MgH₂ is at magnitudes lower than the D_H of the Mg metal phase. It is also evident in this figure from the diffusion coefficient plots that most transition metals and their hydrides have D_H several magnitudes higher than the D_H of MgH₂.

Catalytic doping and nanosizing of Mg-based systems have been considered as important methods to improve their kinetics. In general, the catalyst is defined as an agent which reduces the activation barrier without participating in the chemical reaction, as illustrated in Figure 5. A common consensus is that transition metals (TM) and their compounds are effective catalysts. These catalysts can be doped into Mg/MgH₂ material by different synthetic approaches. Most TM catalysts are effective in both hydrogenation and dehydrogenation reactions. The roles of different Ti-based catalysts and the underlying mechanism will be reviewed in the following section.

Downsizing MgH₂ to nano-scale is also shown to be effective to improve the kinetics. It is believed that nano-sizing can enhance kinetics by the creation of a large amount of fresh surface, shortening hydrogen diffusion, and promoting nucleation of the hydride/metal phase [12]. It is noteworthy that a combination of nanosizing and catalytic doping is usually realized during synthesis. For example, using a high-energy ball milling technique, co-milling MgH₂ with transition metal powder could produce a nanocomposite with nano-size microstructure and homogeneously doped catalyst particles.

3. Catalytic Effects

3.1. Transition Metals Catalysts

Among various additives for improving Mg-based materials, TM catalysts have been intensively investigated. Interestingly, most of the transition metals and their compounds are found to be effective as both hydrogenation and dehydrogenation catalysts. In general, 1–5 at.% addition of TM catalyst leads to dramatic improvement while the hydrogen storage capacity is not sacrificed significantly. Research efforts have been directed to investigate the effectiveness of various TM-based catalysts. Table 4 compiles the reported results from Ti-based additive-enhanced MgH₂ systems as well as corresponding synthetic approaches and kinetic behaviors.

Early work by Liang et al. [53] evaluated the catalytic effects of 3d-TM elements (Ti, V, Mn, Fe, and Ni) on the reaction kinetics of ball-milled catalyzed MgH₂ (see Figure 6). The MgH₂-Ti composite showed superior hydrogen desorption/absorption kinetics, exhibiting the best desorption kinetics at 573 K, followed in order by V, Fe, Ni, and Mn. The activation energies (E_a) of MgH₂-Ti, MgH₂-V, MgH₂-Mn, MgH₂-Fe, and MgH₂-Ni are calculated to be 71.1 kJ/mol, 62.3 kJ/mol, 104.6 kJ/mol, 67.6 kJ/mol, and 88.1 kJ/mol, respectively, which are significantly reduced compared to that of the ball-milled pure MgH₂ (120 kJ/mol). It was indicated that the TM catalysts could drastically improve the kinetic properties of MgH₂, among which Ti-catalyzed MgH₂ shows superior performance. Rizo-Acosta et al. [54] compared hydrogenation properties of MgH₂ with the addition of early transition metals (Sc, Y, Ti, Zr, V, and Nb). As shown in Figure 7a,b, their results indicated that full reactions finished within less than 120 min in all cases and the hydrogen absorption rate increased along the sequence Y < V < Ti < Nb < Sc < Zr. However, an apparent degradation was observed when the cycling number increases. Interestingly, this evolution is less pronounced in the Ti-doped system, as shown in Figure 7c, which was attributed to the lattice mismatch between Mg and TiH₂ hydride that limits Mg grain growth. Among all cases, MgH₂-TiH₂ nanocomposite presented the best cycling properties with a reversible capacity of 4.8 wt% after 20 cycles and the reaction time arbitrarily limited to 15 min.

Zhou et al. [90] prepared 49 additive-doped MgH₂ samples by ultra-high-energy-high-pressure ball milling, in order to conduct a comprehensive survey on a wide range of additives and corresponding dehydrogenation temperatures of the catalyzed MgH₂. The plot of the Thermogravimetric Analysis (TGA) dehydrogenation temperatures is shown in Figure 8, indicating that the additives containing the IV-B and V-B group elements are the most effective catalysts while the VII-B (Mn), VIII-B (Fe, Co, and Ni) groups show moderate catalytic effects. Besides, Ti and its compounds are more effective compared to those catalysts based on heavier elements (Zr, ZrH₂, ZrO₂, and Ta) in the same periodic group.

Cui et al. [91] synthesized micro-sized Mg particles coated with nano-sized TM catalyst, showing that the nano-coating of TM on the Mg/MgH₂ surface is more effective than co-ball-milling of Mg with TMs. The authors also suggested that the catalytic improvement on dehydrogenation kinetics can be ranked as Mg-Ti, Mg-Nb, Mg-Ni, Mg-V, Mg-Co, and Mg-Mo, and the hydrogenation kinetics is in a sequence of Mg-Ni, Mg-Nb, Mg-Ti, Mg-V, Mg-Co, and Mg-Mo.

It has been recognized that early transition metals (ETM) belong to the group of most effective catalysts. Despite some discrepancies in reported data, Ti-based catalysts, involving not only elemental Ti but also Ti hydrides, oxides, halides, and intermetallic compounds have shown great benefits in improving the hydrogen storage properties of MgH₂. In-depth investigations of Ti-based catalysts are also beneficial for understanding the catalysis mechanism for the Mg-H₂ system.

3.2. Catalytic Effects of Ti-Based Compounds

A large number of Ti-based catalysts have been explored for enhancing the hydrogen storage properties of MgH₂. Early attempts using elemental Ti powder to ball-mill with MgH₂ received encouraging results [53]. Soon, researchers found that TiH₂ powder additive is very effective as well. Lu et al. [92] reported exceptional room temperature hydrogenation properties of MgH₂-0.1TiH₂ material prepared by ultra-high-energy-high-pressure (UHEHP) ball milling. Liu et al. [72] studied the effects of two different Ti hydrides (TiH_1.971 and TiH_1.5) on the hydrogenation kinetics of Mg. It pointed out an important fact that elemental Ti can easily react with hydrogen to form various Ti hydrides under certain temperatures and hydrogen pressures. During the reverse hydrogen reaction, the following equations can be summarized:

Mg + Ti + H₂ → Mg + TiH_1.971(1)

Mg + TiH_1.5 + TiH_1.971 + H₂ → MgH₂ + TiH_1.5 + TiH_1.971(2)

MgH₂ + TiH_1.5 + TiH_1.971 → Mg + TiH_1.5 + TiH_1.971 + H₂(3)

According to the Mg-Ti phase diagram, neither Ti nor Ti hydrides are immiscible with Mg or MgH₂ phases. Furthermore, no ternary Mg-Ti hydride exists in the phase diagram. However, under a metastable condition, it is possible for Ti to dissolve into Mg and form a solid solution. Ponthieu et al. [93] reported Ti solubility in β-MgD₂ up to 7 at.%, and Mg solubility in TiD₂ up to 8%, which suggested shortened D-diffusion path due to the introduction of TiD₂. An Nuclear Magnetic Resonance (NMR) study of MgD₂/TiD₂ composite found lattice coherent fluorite (fcc) structured TiD₂ and MgD₂, which is expected to be a fast H-diffusion pathway to accelerate the kinetics [94].

Another focus is discovering a novel metastable Mg-Ti-H hydride with a new structure. Kyoi et al. [95] synthesized Mg₇-Ti-H FCC hydride using a high-pressure anvil cell. Asano and Akiba reported the ball-milling synthesis of a series of Hexagonal Closest Packed (HCP), Face-centered Cubic (FCC), and Body-centered Cubic (BCC) Mg_xTi_100−x alloys, and Mg-Ti-H FCC hydride phases with chemical formulae of Mg₄₀Ti₆₀H₁₁₃ and Mg₂₉Ti₇₁H₅₇. These ternary hydrides had lower stabilities in comparison to MgH₂ and thus show lower desorption temperatures.

TiO₂ was considered an effective catalyst. Wang et al. [75] prepared ball-milled Mg-TiO₂ and showed good hydrogenation and dehydrogenation kinetics. For the past two decades, however, the investigation of oxide catalysts paid more attention to Nb₂O₅, since it seems to be more efficient among transition metal oxides [96]. Actually, doping of TiO₂ would present a similar effect comparing to the Nb₂O₅ catalyst. As suggested by Pukazhselvan et al. [97], TiO₂ can be partially reduced to a lower 3⁺/2⁺ state (TiO and Ti₂O₃). The presence of Mg_xTi_yO_{x + y} oxide was also suspected, but no direct support was seen by X-ray Diffraction (XRD) results. More recently, Zhang et al. [98] showed good catalytic activity of carbon-supported nanocrystalline TiO₂ (TiO₂@C). It was reported that the dehydrogenation temperature of MgH₂-10 wt%TiO₂@C can be lowered to 205 °C and hydrogen uptake took place at room temperature. Berezovets et al. [99] reported that the Mg-5 mol% Ti₄Fe₂O_x was able to absorb hydrogen even at room temperature after hydrogen desorption at 300–350 °C and its cycling stability could be substantially improved by introduction of 3 wt% graphite into the composite.

Ti halides have been reported to offer a positive effect on the kinetics of MgH₂. TM fluorides usually present superior catalytic effects and satisfactory kinetics. Malka et al. [80] reported the catalytic effects of a group of TM fluorides (FeF₂, NiF₂, TiF₃, NbF₅, VF₄, ZrF₄, CrF₂, CuF₂, CeF₃, and YF₃) on the kinetics of MgH₂. The best catalysts for magnesium hydride decomposition were selected to be ZrF₄, TaF₅, NbF₅, VCl_3, and TiCl₃. In another investigation by Jin et al. [100], it was suggested that TiF₃ and NbF₅ showed better effects over other TM fluorides. It was found that the hydride, for example, TiH₂, formed after co-milling MgH₂ with the fluorides, with an in situ reaction described as follows:

3MgH₂ + 2TiF₃ → 3MgF₂ + 2TiH₂ + H₂(4)

Moreover, Wang et al. [101] conducted a comparison study on the elemental Ti, TiO₂, TiN, and TiF₃ catalyzed MgH₂ materials, showing that TiF₃ had the strongest catalytic effect among them.

Ti-based intermetallics as catalysts have been receiving active attention in recent years. Early researchers used TiFe [102], (Fe_0.8Mn_0.2)Ti [103], Ti₂Ni [104], and TiMn_1.5 [105] additives to improve hydrogen storage properties of MgH₂, showing that all these intermetallics were effective catalysts. Interestingly, some Ti-based intermetallics themselves, including TiFe and TiMn_1.5, are known as hydrogen storage alloys. Zhou et al. [58] conducted a systematic investigation focusing on a series of Ti-based intermetallic catalysts (i.e., TiAl, Ti3Al, TiNi, TiFe, TiNb, TiMn₂, and TiVMn). The results found that TiMn₂-doped Mg demonstrated extraordinary hydrogen absorption capability at room temperature and 1-bar hydrogen pressure while its apparent activation energy is 20.59 kJ/mol·H₂. The strong catalytic effect of TiMn₂ is also confirmed by another experimental work by El-Eskandarany et al. [106,107] and first principles calculation by Dai et al. [108].

4. Synthetic Approaches

The synthesis methods of Mg-based hydrides have a great impact on their hydrogen storage properties. With expanding research scope of hydrogen storage materials, there are emerging preparation methods in recent years. Many hydrogen storage alloys can be prepared by physical methods, including ball milling [109], induction melting [110], arc melting [111], et cetera. Complex hydrides are usually prepared by chemical methods, such as organic synthesis, hydrothermal method, and solvothermal method [112]. However, conventional high-temperature preparations such as sintering or melting have been largely restricted due to the low melting temperature and high vapor pressure of magnesium [15]. Widely-used methods for Mg-based hydride preparation include ball milling, thin film deposition, and chemical methods.

4.1. Ball Milling

Ball milling is a mechanical method that grinds metal or alloy powder into extremely fine powders [113]. During ball milling, the collision between powder particles and grinding balls will generate localized high pressure and cold welding of powder particles repeatedly, which leads to interdiffusion and alloying between different elements to produce hydrides with nano-size structure [114,115,116]. By technical categorizing, there are mainly four kinds of high-energy ball-milling techniques to prepare Mg-based hydride: agitator [117], shaker/vibration type mills [118], planetary mill [119], and uni-ball mill [120]. The ball milling technique is quite effective to improve the hydrogen storage properties of magnesium-based alloys due to the following reasons. First, the native oxide layer can be broken during ball milling, and thus a large number of fresh surfaces is created [121,122]. Second, defects and grain boundaries can be produced during the ball milling process, which provides channels for bulk hydrogen diffusion [123]. Third, reduced grain size accelerates the diffusion of hydrogen atoms inside grains [124,125]. Fourth, ball milling of magnesium in hydrogen gas resulted in the formation of a mixture of β-MgH₂ and γ-MgH₂, which can destabilize the MgH₂ system, reduces H₂ desorption temperature, and improves the desorption kinetics [126,127]. Last, the defects and strain generated during ball-milling usually disappear after cycling the hydride, which may raise a concern about the kinetic degradation. However, several cycling studies observed that the high-temperature kinetics (~300 °C) maintained good stability, yet the low-temperature hydrogenation kinetics suffered a severe degradation after hydrogen cycles [128,129,130].

4.2. Thin Film Deposition

The thin-film deposition method can prepare doped Mg-based material with one dimension in the range of a few atoms to micrometers. It can be divided into two categories, physical vapor deposition (PVD) and chemical vapor deposition (CVD) coating systems. PVD is an atomistic deposition processes in which materials are vaporized from a solid or liquid source and then condensed onto the substrate [131]. Using PVD processes, Ti and other elements can be added into Mg to form the Mg-Ti-H system which can reduce the stability of MgH₂. Gremaud et al. [132] prepared Mg-Ni-Ti ternary alloy films, showing that the enthalpy of absorption/dehydrogenation of Mg_0.69Ni_0.26Ti_0.05 film reduced to 40 kJ/mol·H₂, as shown in Figure 9.

CVD is a coating process using a thermally induced vapor phase chemical reaction to deposit matter on a substrate surface, which provides great versatility for synthesizing both simple and complex compounds with relative ease at generally low temperatures [133]. This method is favorable for large-scale production because of its simple equipment, easily controlled reaction conditions, high purity, and narrow particle size distribution of products. Different shapes of crystals with different compositions were prepared by CVD at different temperatures and pressures, as shown in Figure 10, which might support the mass production of nano- and micro-sized MgH₂/Mg using hydrogen. Another approach to improve the hydrogen storage properties of Mg is by forming an alloy with other elements. For example, 1.5 μm thick Mg-Al-Ti, Mg-Fe-Ti, and Mg-Cr-V ternary alloy films showed remarkable kinetics at 200 °C [81,134].

4.3. Chemical Methods

MgH₂ and doped Mg-based hydrides can also be synthesized by a chemical reaction from organic compounds. Chemical reduction to prepare Mg-based material nanoparticles is one of the bottom-up approaches with several advantages, including morphology control, easy separation, facile post-synthesis modifications, stable nanoparticles, and ease of scaling up [136]. In the last two decades, molecular magnesium hydride chemistry has received a major boost from organometallic chemists with a series of structurally well-characterized examples [137]. Norberg et al. [138] reported that the density of defect sites of Mg nanocrystals is increased through the low-temperature reduction, which provides a simple route to enhance H₂ sorption kinetics dramatically. Mg nanoparticles synthesized by chemical reduction in solution usually have an irregular shape, with particle lengths/widths ranging from 7 to 60 nm. For a typical synthesis routine, Ti-catalyzed MgH₂ nanocrystalline was obtained from the reaction using Mg powder, anthracene, anhydrous tetrahydrofuran (THF) solution, and ethyl bromide, according to Equations (5)–(7) [139]. The nanocrystalline material consists of 89 wt% for the dominant β-MgH₂ phase and 11 wt% for γ-MgH₂, which surprisingly obtains γ-MgH₂ under relatively mild conditions (hydrogenation reaction at room temperature and under 8 MPa hydrogen pressure) [122].

(5)

(6)

(7)

5. Mechanisms of Catalysis

Understanding the catalysis is critical to improving hydrogen absorption and desorption kinetics for Mg-based systems. Based on the understanding of the hydrogen reaction in the metal-hydrogen system [140], the hydrogenation of metal should go through the following five steps: (1) Physisorption of the H₂ molecule, (2) dissociation of the H₂ molecule, (3) surface penetration of H atoms, (4) diffusion of H atoms in the host lattice, and (5) hydride formation at metal/hydride interface, as shown in Figure 11. For the dehydrogenation reaction, a hydride particle could go through the following steps: (1) Hydride decomposition, (2) diffusion of hydrogen atom, (3) surface penetration, (4) recombination to hydrogen molecule, and (5) desorption to the gas phase. Either hydrogen absorption or desorption should be controlled by a rate-limiting step while other steps are likely in equilibrium.

However, the rate-controlling mechanisms in hydrogenation and dehydrogenation may not necessarily be the same. The physisorption of a H₂ molecule on a metal surface needs a very low activation energy, so it is generally not considered a limiting step. The rest of the steps can be rate-limiting which is worthy of discussion. For dehydrogenation, steps 1, 2, and 3 (illustrated in Figure 11) can be considered as possible rate-limiting steps. Note that the hydrogen atoms should diffuse across the metal phase, in which the diffusion coefficient is much higher compared to that in the hydride phase. Moreover, the dehydrogenation has a H₂ recombination step instead of dissociation. The recombination of H atoms into a molecule does not have an energy barrier to overcome [141]. From these aspects, it seems reasonable that the kinetic barrier of dehydrogenation could be lower than that of hydrogenation. However, dehydrogenation is an endothermic reaction whereas hydrogenation is exothermic, which means the hydrogenation of Mg is favored in respect of thermodynamics. These fundamental differences may change the activation barrier and lead to different reaction behaviors.

5.1. Hydrogen Dissociation

Both theoretical calculation and experimental work have suggested that a large energy barrier needs to be overcome when hydrogen dissociates on a pure Mg surface. A density functional theory (DFT) study by Du et al. [142] shows that the hydrogen dissociation activation barrier will decrease from 1.051 eV for a pure Mg(0001) surface to 0.103 eV and 0.305 eV for Ti-doped and Pd-doped Mg(0001) surfaces, respectively. Another DFT work conducted by Yao et al. [143] reported the energy barrier for molecular hydrogen dissociation on the Mg surface to be 1.15 eV. The calculated activation energies for hydrogen dissociation on V and Ti atoms are 0.201 eV and 0.103 eV, respectively. Pozzo et al. [48] calculated that the energy for hydrogen dissociation on pure Mg(0001) is as high as 0.87 eV and Mg-Ti, Mg-V, Mg-Zr, and Mg-Ru have nearly zero dissociation barrier. In addition, nanosized metal surfaces may provide additional promotion for hydrogen dissociation, due to the increases of metal surface area and a number of steps, kinks, and corner atoms [12].

Once the hydrogen molecules dissociate into atoms on the surface, the obstacle may still exist to prevent transferring hydrogen atoms from catalytic sites into bulk. The so-called “hydrogen spillover” mechanism may play the role in Mg-TM catalyzed systems [83]. Hydrogen spillover refers to the surface migration of activated hydrogen atoms from a catalytic particle onto the matrix. This phenomenon has been intensively studied in catalysis science. However, hydrogen spillover in a catalyzed Mg-based system and migration is challenging to observe so it still lacks direct evidence.

According to Sabatier’s principle, the catalyst for dehydrogenation/hydrogenation reactions should not bond with hydrogen too strongly or too weakly. This leads to a volcano plot [144] for elements in the hydrogen evolution reaction, see Figure 12a. Interestingly, when screening more effective catalytic species for the Mg-H₂ system, the experimental result does not always follow this prediction. Pozzo et al. [48,49] proposed an inverse volcano plot (see Figure 12b) combining the effects of hydrogen dissociation and hydrogen diffusion, suggesting that doping of Ni and Pd could provide the top catalytic activities. However, Ti and V have been experimentally demonstrated as strong catalysts, at least equivalent to Ni and Pd. In fact, the IV and V group elemental catalysts (such as Ti or V) in the hydrogen atmosphere may transform into hydride phases (TiH_x or VH_x) instead of their metallic phases. Therefore, a more comprehensive model and understanding of the catalytic behavior is still required to design an optimized catalyst.

5.2. Surface Penetration

To improve dehydrogenation and hydrogenation kinetics, surface modification is necessary due to the presence of a surface oxide layer, which hinders the penetration of hydrogen atoms into the bulk. The continuous passive MgO/Mg(OH)₂ layer would easily cover the Mg/MgH₂ surface, even under inert gas with a trace amount of O₂/H₂O [145]. Recent work on the effect of air exposure on TiMn₂ catalyzed MgH₂, [146] showed that the direct air exposure leads to reduction of hydrogen storage capacity, but only moderate deterioration in kinetics. Further surface characterizations found that the surface of MgH₂ forms a layer with Mg(OH)₂ and MgO. However, the layer may crack during hydrogen cycling while the nanocomposite can be re-activated with the presence of catalyst. The doped catalyst particles on hydride surfaces can serve as paths to transfer hydrogen from surface to bulk, or from MgH₂ to the outside. This mechanism is often referred as the “hydrogen gateway” effect, as having been claimed in MgH₂-Nb [147] and MgH₂-Pt [148] catalyzed systems. In several in situ characterizations, intermediate phases (NbH_0.7 or TiH) were observed during dehydrogenation, supporting the assumption that the surface activated catalyst can create a hydrogen penetration path over the MgO layer.

5.3. Accelerating Hydrogen Diffusion

The addition of catalyst may play an important role in accelerating the hydrogen diffusion rate in the matrix. Due to the slow diffusion rate in MgH₂, it is thus believed that the reaction is likely to shift to diffusion-control when the forming hydride covers the particles during hydrogenation. For both hydrogenation and dehydrogenation processes, nano-doped catalytic species have been believed to help to accelerate hydrogen diffusion. This mechanism was often referred as the “hydrogen pathway” effect.

The “pathway effect” was first suggested by Friedrichs et al. [149] in the study of the MgH₂-Nb₂O₅ system. They suggested the hydrogen sorption improvement through a pathway effect of lower-oxidation-state Nb₂O_5-x, which was believed to help hydrogen transport into the particle. Ponthieu et al. [93] studied the structure and reversible deuterium uptake of MgD₂-TiD₂ nano-composites by X-ray and neutron diffractions, suggesting that TiD₂ addition limits the grain growth of Mg and MgD₂ phases and thus reduce the D-diffusion path. The study also found coherent coupling between TiD₂ and Mg/MgD₂ and the presence of sub-stoichiometric MgD_2-η and TiD_2-η phases, which are indications that the TiD₂ phase can favor the H-mobility. Note that the diffusion pathway may contribute to the grain boundaries between catalyst and matrix because the boundary and interface play the role of tunnels for fast hydrogen diffusion. Needless to say, nano-sized Mg/MgH₂ grains doped with catalysts lead to a significant number of boundaries, interfaces, and dislocations. This mechanism is supported by many experimental works where a refined catalyzed Mg/MgH₂ composite is favored for the kinetics [150,151].

5.4. Nucleation and Growth

Nucleation and growth of the MgH₂ phase can be considered as the final step for the hydrogenation of Mg. The nucleation and growth of a hydride phase will lead to considerable interfacial energy changes due to the crystal structure difference between Mg metal and its forming hydride. Although, whether the rate-limiting step is controlled by nucleation and growth or hydrogen diffusion is still under debate; many investigations have successfully applied the Johnson–Mehl–Avrami–Kolmogorov (JMAK) model—a nucleation and growth model—to various catalyzed MgH₂ systems [152,153]. Some other results showed that the kinetics can be fitted by diffusion models, such as the Jander diffusion model [154,155]. In early works, Schimmel et al. [156] assumed that saturated catalyst particles in close contact with a Mg particle act as nucleation centers. A recent hydrogenography study of Mooij and Dam [157] showed evidence of nucleation and growth mechanism in the hydrogenation of the 1-dimensional nanoconfined Mg/TiH₂. They also suggested that the desorption mechanism is not simply the reverse of the absorption mechanism, and the energy barrier for nucleation of Mg is smaller than the nucleation of MgH₂. Danaie and Mitlin [158] established the metal hydride orientation relationship (OR) for the ball-milled MgH₂-TiF₃ system during hydrogen absorption and it was determined to be (110)MgH₂ || (−110−1)Mg and (111)MgH₂ || (01−11)Mg. The authors observed that during desorption the TiF₃ catalyst substantially increases the number of the newly formed Mg crystallites, which displays a strong texture correlation to the parent MgH₂ phase. Mulder et al. [159] made an assumption that MgF₂ may act as seeding crystals for MgH₂ because MgF₂ and MgH₂ have the same crystallographic structure and good lattice matching.

6. Kinetic Modeling

Kinetics study focuses on the quantitative interpretation of the reaction rates and of the factors upon which they depend. Early studies of the kinetics of the pure Mg-H₂ system attempted first-order reaction, second-order reaction, 2D contraction area, 3D diffusion, and Jander diffusion model. Due to the sluggish diffusion of hydrogen in the MgH₂ phase, it is believed that the hydrogenation of Mg is best described by the 3D diffusion-controlled contracting volume model [121]. As more doped systems have been examined, alternate kinetic models have been proposed to analyze the kinetic behavior of Mg-based hydrides [160]. Despite the debate and deviation, kinetic analysis has been recognized as a useful tool for Mg-based systems [161]. This section will summarize and discuss the kinetic models and analytic methods that are commonly applied for analyzing kinetics.

Basically, the reaction progress of a solid-gas system is defined as the fraction of the transformation, ξ (0 ≤ ξ ≤ 1), which is a function of reaction time t, and rate constant k, as shown in Equation (8):

(8)$\xi =f\left(k, t\right)$

The rate constant k is defined as a specific rate and the rate coefficient and is a function of temperature. This rate constant k varies with temperature T following the Arrhenius Equation (9):

(9)$lnk=-\frac{E_a}{RT}+\ln A$

In this relationship, activation energy can be calculated by the Arrhenius plot, which is lnk against the reciprocal of the absolute temperature 1/T. As mentioned above, activation energy ($E_a$) for a catalyzed Mg/MgH₂ can be considered as a useful scale to evaluate the effectiveness of a catalyst. More importantly, the kinetic analysis could not only calculate ($E_a$) and rate constant $k$, but also provide an understanding of reaction mechanisms. As can be seen in Table 5, the kinetic models can be divided into two categories: isothermal models, which are based on analysis of isothermal hydrogen absorption or desorption $\left(\xi -t\right)$ curves; and non-isothermal models, which are based on $\left(\xi -t\right)$ curves usually obtained under linearly increasing temperature (by utilizing TGA or Differential Scanning Calorimeters (DSC) techniques).

6.1. Isothermal Models

Several isothermal models, such as Johnson–Mehl–Avrami–Kolomogorov (JMAK) model [162], Jander model [163], Ginsling–Braunshtein (GB) model [164], contraction volume (CV) model [165], Valensi–Carter (V–C) model [166], and Chou model [163], have been applied to Mg-based systems. These models represent different rate-controlling processes, in other words, the JMAK model is established based on nucleation-growth-impingement mode; the Jander and GB models are derived from Fick’s diffusion law and thus for a diffusion-controlled reaction; the CV model assumes that the hydrogen absorption/desorption is controlled by the interface (hydride/metal) movement. Generally, by examination of best-fitting using the above-mentioned and other models, rate-limiting step(s) and kinetic parameters (such as rate constant k, dimensionality d, Avrami exponent n), as well as corresponding physical interpretation, can be determined to investigate the hydrogenation/dehydrogenation behaviors. In addition, in some scenarios, the isothermal condition is difficult to maintain during hydrogenation, due to the highly exothermic reaction of Mg with H₂. Particular cautions are needed to minimize the thermal effect when dealing with catalyzed MgH₂ with fast hydrogenation rate and poor heat conductivity, which leads to heat accumulation of the material [71].

The classic JMAK model is widely accepted for studying the kinetics of various Mg-based materials [167]. The JMAK model assumes a solid-state phase transformation containing three overlapping procedures: nucleation, growth, and impingement. Theoretically, for the nucleation, it may be either saturation or linear continuous mode, and the former mode is usually described in heterogeneous catalysis. As for growth, both the interface-controlled growth and diffusion-controlled growth modes are taken into account within the JMAK model. Therefore, Avrami exponent n indicates different modes regarding the nucleation modes, dimensionality, and rate-controlling steps.

Li et al. [168] applied various kinetic models for ball-milled pure MgH₂, TiH₂-, TiMn₂- and VTiCr-catalyzed MgH₂ under different temperatures and pressures, showing the best-fitting model for hydrogenation of the various materials is the JMAK model. However, problems with the JMAK model still exist. It was pointed out that the obtained values of Avrami exponent n are in a very wide range (n = 0.11–1.64), which is difficult to interpret using the classic JMAK theory. Small values of n have also been reported in the hydrogenation of Mg-Ti [168] and Mg-V-Nb [130] thin films. Overall, the kinetic parameters and corresponding discussions obtained from isothermal modeling are usually difficult to be conclusive. As pointed out in the review by Pang and Li [161], it is difficult to elucidate the assumption and derivation steps of the kinetics models, and it is also difficult to select proper methods to analyze the experimental data.

6.2. Non-Isothermal Method

The dehydrogenation kinetics method is based on Kissinger’s theory. It allows deriving activation energy by measuring the weight change via TGA, or heat flow via DSC under a constant heating rate.

(10)$\ln \left(\frac{\beta }{T_{max}^2}\right)=-\frac{E_a}{R}\left(\frac{1}{T_{max}}\right)+F_{KAS}\left(\xi \right)$

In Equation (10), T_max is the temperature when the reaction rate reaches the maximum, β is the heating rate, E_a is the activation energy, R is the gas constant, and F_KAS(ξ) is the function of the fraction of transformation ξ. The Kissinger method has been widely employed for the calculation of dehydrogenation E_a of catalyzed MgH₂ materials. This method has the advantages of efficiency and convenience to evaluate dehydrogenation activation energy. However, the estimation for kinetics cannot be conducted under different hydrogen pressures, since most of the TGA/DSC tests are performed under the flow of inert gas. Consequently, it is difficult to identify the actual process that is controlling the reaction rates, which leads to inconsistent interpretations that cannot be reliability validated.

6.3. Activation Energies

The activation energies (summarized in Table 4) for various Ti-additive doped MgH₂ systems are plotted in Figure 13. For the reactions of pure MgH₂, the activation energies are reported to be 160 kJ/mol for dehydrogenation and 100 kJ/mol for hydrogenation [138]. Doping with different Ti-based catalysts reduced the MgH₂ dehydrogenation E_a to as low as approximately 70 kJ/mol. The majority of dehydrogenation E_a values were derived using TGA/DSC and the Kissinger method. It is interesting to find that many catalyzed systems reported dehydrogenation E_a in the range of 70–75 kJ/mol, which corresponds with the ΔH of MgH₂ (74.5 kJ/mol·H₂) although there are some outliers in the reported values. Note that in general the calculated dehydrogenation E_a should be no less than the ΔH (see Figure 5). The low values of E_a imply that in these systems the energy barriers of dehydrogenation have been largely overcome. Additionally, some abnormally low E_a should be carefully examined in terms of the systematic deviations or apparatus errors during the experiments. For hydrogenation, many published hydrogenation E_a are below 30 kJ/mol, which is significantly lower than that of pure MgH₂ [70,71]. From the survey of published E_a data, it is shown that the kinetics can be significantly enhanced by Ti-based addition. Ti and Ti hydrides, halides, and intermetallic compounds present excellent catalytic effects.

7. Summary and Perspectives

Mg-based hydrides have shown great prospects as high-energy-density media for hydrogen storage and thermal energy storage. The high hydrogen capacity, abundant resources, reversibility, and low toxicity make Mg-based materials promising candidates. It has been well recognized that doping Ti-based additive is an effective method to enhance the hydrogen storage properties of MgH₂. The catalytic doping combined with ball-milling techniques is widely used for synthesizing nano-structured MgH₂-additive composite. Additionally, other synthetic methods such as thin film deposition and chemical methods have been employed. Recent research showed that Mg-based material can be modified into various nano-structures, while the kinetics are dramatically improved by catalytic doping. Various types of Ti-based catalysts including hydrides, oxides, halides, and intermetallics showed positive effects in improving dehydrogenation and hydrogenation kinetics. However, it is still difficult to assess the effectiveness of different catalysts.

The survey of reported activation energies shows that the energy barrier can be largely overcome by the use of Ti-based additives. The mechanism of catalysis can be resolved into several steps, for example, for hydrogenation: hydrogen dissociation, surface penetration, diffusion, hydride nucleation, and growth. Although a comprehensive understanding of the role of Ti-based catalysts still remains unclear, there has been evidenced that catalysts do play important roles in promoting some of the steps. It was believed that the doped catalyst species can reduce the dissociation energy barrier of the hydrogen molecule, and can also facilitate the hydrogen diffusion in the Mg/MgH₂ matrix. Kinetic modeling could become a more useful tool for interpreting the controlling steps of the reactions. Future mechanism works should be directed to observe catalytic activities and microstructure evolution during highly controlled reaction conditions to provide closer comparisons with boundary conditions for the alternative models used for interpretations.

Author Contributions

C.Z. conceived and designed the concept. C.Z. and J.Z. collected the references and contributed to the writing of the original draft. R.C.B.J. design some of the main ideas for the construction of the paper. C.Z. contribute to the supervision and funding acquisition. C.Z., R.C.B.J. and Z.Z.F. contribute to the review and editing of the review. All authors have read and agreed to the published version of the manuscript.

Funding

National Natural Science Funds for Young Scientists of China (Grant No. 51704336); Innovation-Driven Project of Central South University (Grant No. 2020CX025).

Acknowledgments

C.Z. acknowledges the National Natural Science Funds for Young Scientists of China (Grant No.51704336) and the Innovation-Driven Project of Central South University (Grant No. 2020CX025). J.Z. thanks the China Scholarship Council (CSC) for financial support.

Conflicts of Interest

The authors declare no conflict of interest.

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Figures and Tables

Figure 1. Schematic of destabilization process of a hydride MH using third element A. (Reproduced with permission from ref. [41]. Copyright 2016 Elsevier).

Figure 2. (a)Temperature dependence of the dissociation pressure of MgH2 and associated evolution of such a dissociation pressure for various approaches investigated, and (b) evolution of ΔH and ΔS as a function of the particle size of Mg. (Reproduced with permission from ref. [47]. Copyright 2018 Elsevier).

Figure 3. Schematic of the hydrogen absorption/desorption process in the MgH2/Mg. (Reproduced with permission from ref. [47]. Copyright 2018 Elsevier).

Figure 4. Hydrogen diffusion coefficients in different metals and hydrides. (Reprinted from ref. [51]. Copyright 2015 Chengshang Zhou).

Figure 5. Representation of the kinetic barrier of the reaction and lowering the activation energy (Ea) using a catalyst. (Reprinted from ref. [52]. Copyright 2018 MDPI).

Figure 6. Hydrogen desorption curves ((a), desorption pressure of 0.015 MPa, 573 K) and absorption curves ((b), absorption pressure is 1.0 MPa, 302 K) of Mg–Tm composites. (Reproduced with permission from ref. [53]. Copyright 1999 Elsevier).

Figure 7. (a) Hydrogen uptake curves of 95Mg-5ETM powder mixtures during reactive ball milling synthesis; (b) the corresponding absorption rates (derivative curves of a); and (c) hydrogen sorption curves at 573 K of MgH2-ETMHx NCs for different sorption sweeps. (Reproduced from ref. [54]. Copyright 2019 RSC).

Figure 8. Effect of various additives on dehydrogenation temperatures of MgH2. (Reprinted with permission from ref. [90]. Copyright 2015 Elsevier).

Figure 9. Diagram of enthalpy change of Mg0.69Ni0.26Ti0.05 film and MgyNizTi1–y–z gradient film. (Reproduced with permission from ref. [132]. Copyright 2007 John Wiley and Sons).

Figure 10. Simplified morphology and composition distributions of the deposited products at different deposition temperatures and H2 pressures plotted in the P-T diagram of MgH2 [135]. Copyright 2010 ACS Publications.

Figure 11. Reaction partial steps for the absorption (left) and desorption (right) of hydrogen by a spherical metal/hydride powder particle. (Reproduced with permission from ref. [140]. Copyright 1996 Elsevier).

Figure 12. (a) Volcano plot for the hydrogen evolution reaction as function of the metal hydrogen bond enthalpy. (Reproduced with permission from ref. [144]. Copyright 1972 Elsevier). (b) Activation energy barrier for hydrogen dissociation (blue) and diffusion (red) of hydrogen on pure Mg and metal-doped Mg surfaces as a function of the d-band center positions. (Reproduced with permission from ref. [48]. Copyright 2009 Elsevier).

Figure 13. Apparent activation energies derived from experiments of kinetic rates for the hydrogenation and dehydrogenation in MgH2 with the addition of various Ti-based catalysts.

Table 1

Optimized structural parameters, bulk modulus (B₀), and pressure derivative of bulk modulus (B^’₀) for MgH₂ in ambient and high-pressure phases. (Reprinted with permission from ref. [22]. Copyright 2006 American Physical Society).

Modification	Unit Cell (Å)			Positional Parameters	B0 (GPa)	B′0
Structure Type	a	b	c
β-MgH2, TiO2-rutile (P42/mnm)	4.5176	4.5176	3.0206	Mg (2a): 0, 0, 0	45.00 ± 2	3.35 ± 0.3
$\mathsf{\gamma }-{\mathrm{MgH}}_2, \mathrm{Modified} {\mathrm{CaF}}_2 (\mathrm{Pa}\overline{3}$)	4.6655	4.6655	4.6655	Mg (4a): 0, 0, 0	47.41 ± 4	3.49 ± 0.4
α-MgH2, α-PbO2 (Pbcn)	4.5246	5.4442	4.9285	Mg (4c): 0, 0.3313d, 1/4d	44.03 ± 2	3.17 ± 0.4
δ’-MgH2, AuSn2 (Pbca)	8.8069	4.6838	4.3699	Mg (8c): (0.8823, 0.0271, 0.2790)	49.83 ± 5	3.49 ± 0.6

Table 2

Thermodynamic parameters and energy storage properties of MgH₂ [26].

Thermodynamic Parameters	Values
Formation enthalpy, kJ/(mol·H2)	−74.5
Formation entropy, J/(mol·H2·K)	−135
Hydrogen Storage Capacity (Theoretical)
Gravimetric capacity, wt%	7.6
Volumetric capacity, g/(L·H2)	110
Thermal Energy Storage Capacity (Theoretical)
Gravimetric capacity, kJ/kg	2204
Volumetric capacity, kJ/dm3	1763

Table 3

Dissociation energy of hydrogen molecule on the surface of Mg. (Reproduced with permission from ref. [49]. Copyright 2008 AIP Publishing).

Metal	Dissociation Energy (eV)
Pure Mg	0.87, 0.40, 0.50, 1.15, 1.05, 0.95, 1.00
Ti-doped Mg	Null, negligible
Ni-doped Mg	0.06
V-doped Mg	Null
Cu-doped Mg	0.56
Pd-doped Mg	0.39
Fe-doped Mg	0.03
Ag-doped Mg	1.18

Table 4

Hydrogen storage properties of Mg with various types of Ti-based catalysts.

Materials	Synthetic Methods	Hydrogen Storage Properties				Reference
		Desorption Kinetics	Eades (kJ/mol)	Absorption Kinetics	Eaabs (kJ/mol)
Titanium/Titanium Hydrides
Mg-2%Ti	Inert gas condensation	Des: 4.50%/320 °C/0.2 bar/25 min		Abs: 4.80%/320 °C/8 bar/21 min		[55]
MgH2 + 2 at% Ti	Ball milling (argon)	Des: 6.32 wt%/623 K/35 kPa/0.5 h		Abs: 6.32 wt%/623 K/2000 kPa/4 min		[56]
	Cold rolling (5 times, air)	Des: 6.00 wt%/623 K/35 kPa/0.5 h		Abs: 5.70 wt%/623 K/2000 kPa/4 min
MgH2-4 mol% Ti	Ball milling	Des: 1.10%/573 K/2 MPa/5 min		Abs: 6.40%/573 K/2 MPa/5 min		[57]
MgH2-5 at% Ti	Ball milling	Des Temperature: 235.6 °C	70.11			[58]
MgH2-5 at% Ti	Ball milling	Des: 5.50%/523 K/0.015 MPa/20 min	71.1	Abs: 4.20%/373 K/1.0 MPa/15 min		[53]
MgH2-5 at% Ti	Ball milling	Des: 5.20%/573 K/0.03 MPa/15 min		Abs: 6.70%/ 573 K/0.8 MPa/15 min		[54]
Mg-5% Ti	Chemical vapor synthesis		104			[59]
Mg-14 at% Ti	Gas phase condensation		35		52	[60]
Mg-22 at% Ti			31		47
MgH2-15% Ti	Ball milling	Des: 0.12%/573 K/1 bar/60 min		Abs: 3.48%/573 K/12 bar/60 min		[61]
Mg0.9Ti0.1	Ball milling		76	Abs: 6.62% (after milling)		[62]
Mg0.75Ti0.25	Ball milling		88	Abs: 6.18% (after milling)
Mg0.5Ti0.5	Ball milling		91	Abs: 5.21% (after milling)
MgH2-20% Ti	Ball milling		72 ± 3			[63]
MgH2-coated Ti	Ball milling	Des: 5.00%/250 °C/15 min (TPD) Des Temperature: 175 °C				[64]
Mg83.5Ti16.5	Inert gas condensation	Des: 2.50%/300 °C/0.15 bar/2 min		Abs: 2.20%/300 °C/9 bar/1 min		[65]
15Mg-Ti	Chemical method				72.2	[66]
MgH2-4 mol% TiH2	Ball milling	Des: 0.70%/573 K/2 MPa/5 min		Abs: 6.10%/573 K/2 MPa/5 min		[57]
MgH2-5 at% TiH2	Ball milling	Des: 5.80%/270 °C/0.12 bar/10 min Des Temperature: 235.5 °C	67.24	Abs: 2.70%/25 °C/1 bar/250 min		[58]
10MgH2-TiH2	Ball milling		73			[67]
7MgH2-TiH2	Ball milling		71			[68]
4MgH2-TiH2	Ball milling		68			[68]
MgH2-10 mol% TiH2	Ball milling			Abs: 5.70%/240 °C/2 MPa/200 s	16.4	[69]
MgH2-10% TiH2	Ball milling				24.2	[70]
MgH2-10% TiH2	Ball milling				17.9	[71]
Mg-9.2% TiH1.971-3.7% TiH1.5	Ball milling	Des: 4.10%/573 K/100 Pa/20 min	46.2	Abs: 4.30%/298 K/4 MPa/10 min	12.5	[72]
Mg0.65Ti0.35D1.2	Ball milling		17			[73]
Titanium Oxides
MgH2-10% TiO2	Ball milling	Des: 6.00%/300 °C/vacuum/20 min		Abs: 6.00%/300 °C/0.84 MPa/5 min		[74]
Mg-20% TiO2	Reactive ball milling	Des: 4.40%/350 °C/1 bar/8.5 min		Abs: 3.80%/350 °C/20 bar/2 min		[75]
MgH2-6% TiO2	Ball milling		145.8 ± 14.2			[76]
MgH2 + 10% TiO2	Ball milling	Des Temperature: 200 °C	75.50			[77]
Titanium Halides
MgH2-10% TiF4	Ball milling	Des Temperature: 216.7 °C	71	(Des: 6.6%)		[78]
MgH2-10% TiF4	Ball milling (2 h, argon)	Des Temperature: 154 °C	70			[79]
MgH2 + 10% TiF4	Ball milling	Des Temperature: 150 °C	70			[77]
MgH2-4 mol% TiF3	Ball milling	Des: 4.50%/573 K/2 MPa/5 min		Abs: 5.10%/573 K/2 MPa/5 min		[57]
MgH2-4 mol% TiCl3	Ball milling	Des: 3.70%/573 K/2 MPa/5 min		Abs: 5.30%/573 K/2 MPa/5 min		[57]
MgH2-7% TiCl3	Ball milling	Des temperature: 274 °C	85			[80]
Titanium Alloys
MgH2-5a% TiAl	Ball milling	Des: 4.90%/270 °C/0.12 bar/10 min Des Temperature: 219.6 °C	65.08	Abs: 2.50%/25 °C/1 bar/250 min		[58]
MgH2-5 a% Ti3Al	Ball milling	Des Temperature: 232.3 °C	70.61			[58]
Mg85Al7.5Ti7.5	DC-magnetron co-sputtering	Des: 5.30%/200 °C/vacuum/20 min		Abs: 5.60%/200 °C/3 bar/0.5 min		[81]
Mg0.63Ti0.27Si0.10D1.1	Ball milling		27			[73]
MgH2-5 at%TiNi	Ball milling	Des Temperature: 242.4 °C	73.09			[58]
15Mg-Ti-0.75Ni	Chemical method				63.7	[66]
Mg0.63Ti0.27Ni0.10D1.3	Ball milling		21			[73]
MgH2-5at%TiNb	Ball milling	Des: 5.90%/27 °C/0.12 bar/10 min Des Temperature: 231.3 °C	71.72	Abs: 2.80%/25 °C/1 bar/250 min		[58]
MgH2-5at% Cr-5a% Ti	Film	Des: 6.00%/200 °C/5 mbar/25 min		Abs: 6.20%/200 °C/3 bar/10 min		[82]
MgH2-7 at% Cr-13 at% Ti	Film	Des: 5.00%/200 °C/5 mbar/25 min		Abs: 5.60%/200 °C/3 bar/10 min
MgH2-5 at% TiFe	Ball milling	Des: 5.20%/270 °C/0.12 bar/10 min Des Temperature: 237.7 °C	72.63	Abs: 3.00%/25 °C/1 bar/250 min		[58]
MgH2-5% FeTi	Ball milling			Abs: 2.30%/150 °C/2 MPa/5 min	21	[83]
MgH2-5 at% TiMn2	Ball milling	Des: 4.80%/270 °C/0.12 bar/10 min Des Temperature: 219.7 °C	74.22	Abs: 3.20%/25 °C/1 bar/250 min		[58]
MgH2-10% TiMn2	Ball milling				22.6	[70]
MgH2-5% VTi	Ball milling			Abs: 3.30%/150 °C/2 MPa/5 min	10.4	[83]
Mg87.5Ti9.6V2.9	Hydrogen plasma metal reaction	Des: 4.00%/300 °C/1 mbar/5 min	73.8	Abs: 4.80%/200 °C/40 bar/5 min	29.2	[84]
MgH2-5 at% TiVMn	Ball milling	Des: 5.70%/270 °C/0.12 bar/10 min Des Temperature: 216.7 °C	85.20	Abs: 3.00%/25 °C/1 bar/250 min		[58]
Multiple Catalysts
Mg-10% Ti-10% Pd	Ball milling		114 ± 4			[85]
Mg-TiH1.971-TiH1.5-ZrH1.66	Arc melting		36.6		21.2	[86]
Mg0.9Ti0.1 + 5% C	Ball milling		88	Abs: 6.43% (after milling)		[62]
MgH2-6% NiTiO3	Ball milling		74 ± 4			[87]
MgH2-6% CoTiO3	Ball milling		100 ± 2
MgH2-10 mol% TiH2-6 mol% TiO2	Ball milling		118			[88]
MgH2-5% VTi-CNTs	Ball milling			Abs: 5.10%/150 °C/2 MPa/5 min	10.2	[83]
MgH2-5% FeTi-CNTs	Ball milling			Abs: 0.60%/150 °C/2 MPa/5 min	65.5	[83]
MgH2-10% Ni-TiO2	Ball milling	Des: 6.50%/265 °C/0.02 bar/7 min	43.7 ± 1.5	Abs: 5.00%/100 °C/60 bar/7 min		[76]
MgH2-4% Ni-6% TiO2	Ball milling		91.6 ± 8.5			[76]
MgH2-10% Co-TiO2	Ball milling	Des: 6.20%/250 °C/0.02 bar/15 min	77	Abs: 4.24%/100 °C/60 bar/10 min		[89]

Table 5

Kinetic models applied for hydrogenation. (Reproduced with permission from ref. [71]. Copyright 2014 Elsevier).

Model	Kinetic Equation
Johnson-Mehl-Avrami (JMA)	$\ln \left(-\ln \left(1-\mathsf{\xi }\right)\right)=\ln \left(\mathrm{k}\right)+\mathrm{nln}\left(\mathrm{t}\right)$
Jander diffusion model (JMD)	${(1-{\left(1-\mathsf{\xi }\right)}^{1/3})}^2=\mathrm{kt}$
1-D diffusion	${\mathsf{\xi }}^2=\mathrm{kt}$
2-D diffusion (Bidimensional partical shape)	$\left(1-\mathsf{\xi }\right)\ln \left(1-\mathsf{\xi }\right)+\mathsf{\xi }=\mathrm{kt}$
3-D diffusion (Ginsling-Braunshteinn model)	$\left(1-2\mathsf{\xi }/3\right)-{\left(1-\mathsf{\xi }\right)}^{2/3}=\mathrm{kt}$
2-D contracting area	$1-{\left(1-\mathsf{\xi }\right)}^{1/2}=\mathrm{kt}$
3-D contracting volume	$1-{\left(1-\mathsf{\xi }\right)}^{1/3}=\mathrm{kt}$