It is instructive to start considerations of metal–hydrogen (M–H) interaction using concepts simple enough to afford a clear physical picture, but at the same time accurate enough to provide results of significant interest. Such a starting point could be the Effective Medium Theory (EMT) [74]. The basic idea of EMT is to replace, in the first approximation, the energy change of an atom (molecule, cluster) interacting with an inhomogenous host, with the energy change ΔE_hom valid if it is embedded in a homogenous electron gas of density ρ_o equal to the density of the host ρ_h at the embedding position. Then, if necessary, corrections accounting for the specific features of the ρ_h, embedding system characteristics, and their interaction should be introduced. This approach offers numerous advantages:

However, most important of all, the approach offers a clear insight into various physical processes taking place during the host-embedding system (in our case M–H) interaction at the electronic level. This particular insight is not always obvious from the results of extensive first-principle calculations. To illustrate this point, we will mention here the most interesting general results that model has provided for the M–H interaction, as well as some specific results for the particular aspect of this interaction, which will be elaborated in more detail in the chapters that follow.

The ΔE_hom(ρ) dependence also predicts that H will prefer the most open structures inside the metals, e.g., octahedral interstices in fcc and hcp, and tetrahedral interstices in bcc structures, and that higher diffusion barriers could be more relevant in fcc or hcp than in bcc metals, due to the larger ρ at the saddle point in the denser structures [78]. For the same reasons, H will be instable in the high electron density bulk of Al, and be of about the same stability in the Mg bulk as on its surface, and much more stable in the bulk than on the surface of Na, explaining the low solubility of H in Al, and the quite different behavior of H in Mg and Na.

Obviously, the EMT offers a quite general and transparent picture of processes during the M–H interaction, predicting the H (and H₂) behavior close to, and on the particular metallic surface, as well as in the bulk. In the following sections we will consider these processes in more detail using also the results of more accurate calculations and experiment.

One large success of EMT, was the explanation of H₂ adsorption and dissociation on the hcp Mg (0001) surface [77]. To illustrate this, charge distribution on the Mg (0001) surface calculated by the pseudopotentials method as implemented in the Abinit package [79] is presented in Figure 2. The results of EMT can be briefly presented as follows:

It has been established [77] that dissociation of H₂ depends on the filling of its antibonding resonant state, and this filling depends on the nature and amount of the surface electron density, and its extension above the surface, explaining quite simply the above mentioned positioning of H₂ (and H) and their behavior on the Mg (0001), and generally, any other surface.

The results of more accurate calculations [67,79,80] and experiments [81,82] support the presented picture, even though some values are a bit different. For instance, distance of H₂ dissociation (also at (B) position) from the Mg (0001) surface was obtained in [67] to be d_dis = 1.02 Å, and the dissociation barrier E_dis = 1.05 eV, is in good agreement with experiment [81]. The analyses of the results have shown that a major discrepancy arises from the LDA approximation of the exchange-correlation potential used in EMT, and some control calculations in [67]. The calculations also confirm the C_fcc positions as the final state for the H adsorption on the Mg (0001) surface.

After dissociation of H₂ and accommodation of H at the most convenient surface positions, H diffuses into the bulk of Mg metal. The EMT predicts that H is going to search for the positions inside the hcp structure of Mg with the most appropriate ρ value, which are the octahedral interstices.

As the H concentration increases during hydrogenation, it is very important to establish positions of its further incorporation into the Mg crystal lattice. This pattern of H-accommodation into the Mg lattice, which influences the kinetics of H absorption and probability for various hydride phases formation was the subject of several investigations [37,50,65,66]. Ab initio calculations of Schimmel et al. [50] suggest that hydrogen diffuses through the Mg metal phase, jumping between octahedral and/or tetrahedral interstitials, and that for large Mg particles and low temperatures, hydrogen diffusion is not expected to be the limiting factor of H kinetics. According to our investigations [65], the H incorporation into the Mg crystal lattice proceeds as follows:

After H has populated the first sub-surface row of octahedral interstices, it diffuses toward, not the first, but the next neighbouring row of octahedral interstices in an attempt to form an ordered Mg₂H structure of the CdI₂ structure type (Figure 4a), which is, although thermodynamically slightly unstable, with enthalpy of formation of about ΔH≈ 22 kJ/mol H₂, the most stable structure in the composition range (Mg:H = 2:1).

Among several possible ordered structures in the concentration range (Mg:H = 1:1), the most stable (although thermodynamically slightly unstable, with enthalpy of formation also about ΔH ≈ 22 kJ/molH₂) is the rutile structure containing two H-vacancies, indicating that the structural phase transition between the hcp lattice of Mg-metal and the bcc Mg sublattice of the rutile structure of MgH₂ takes place in this concentration range, or just below it. Indication of structural changes in this concentration range, manifested through the abrupt change of the Mg-H bond lengths were also noticed by the Mg-H clusters calculations [83]. By analyzing the structure of the competing phases DOS’s in this concentration range (Figure 4), one can see that the metastable Wurtzite structure is much more similar to the final rutile MgH₂ structure. This suggests that the transformation path of hcp-Mg to rutile MgH₂, upon hydrogenation, is not predisposed solely by thermodynamic conditions, and that some particular steps of the process could be controlled by appropriate (perhaps symmetry induced) transformation of electronic structure. The substoichiometric Mg-H rutile structures becomes thermodynamically stable at the concentration range of about Mg:H = 3:2, with enthalpy of formation of Mg₃H₂ of ΔH≈ −14 kJ/molH₂.

The presented results provide quite a detailed picture of the most important stages of the Mg structure transformation during hydrogenation. If true, they imply some serious consequences on H absorption kinetics. For instance, the finding that H prefers accommodation in particular (almost) ordered structures, that some of them are not the most convenient thermodynamically, and that they cannot be reached using stohastic diffusion paths (as proposed in [37,50]), imposes strong limitations on H absorption kinetics. Also, the same discards all kinetic models of H absorption which consider the movement of the Mg/MgH₂ interface as the limiting step, because this interface does not form until at least (if ever) the Mg:H = 1:1 concentration range. Of course, the mentioned calculations have been performed at T = 0 K, they do not include the zero point, anharmonicity, and perhaps the quantum tunneling effects, which all could be important for hydrogen behavior.

The processes connecting the particular steps considered above also have not been explicitly accounted for, and some more knowledge about them could be obtained from the reverse process of MgH₂ dehydrogenation that is addressed in the next chapter.

We shall start the analysis of the MgH₂ dehydrogenation process by investigation of H (H₂) desorption from the most stable MgH₂ (110) and MgH₂ (001) surfaces. The structure and charge density distribution of the MgH₂ (110) surface system is presented in Figure 5

The activation barrier for H desorption was calculated [84] to be about 1.78 eV for the MgH₂ (110), and about 2.8 eV for the (001) surface Similar activation energies for H desorption from both considered surfaces were found also in [85].

These energies are higher than those obtained for various H vacancies formations, ranging from 1.3 to 1.6 eV [86], diffusion on the MgH₂ (110) surface (ranging from 0.15 to 0.80 eV), and from the surface into the bulk (ranging from 0.45 to 0.70 eV). Despite somewhat larger values obtained for defects formation and diffusion in [87], it is H desorption from the MgH₂ surfaces that is usually considered [88,89] as the rate-limiting step for dehydrogenation process of MgH₂. The common, and to a great extent, correct explanation for this is a strong ionic interaction between Mg and H. But, as can be seen in Figure 6a, besides the bonding between Mg (red spheres) and H (blue spheres), H–H bonding interaction also exists in the system (see also Figure 3b in [84]). It is also clearly visible in Figure 6b, in the (110) crystallographic plane. The bonding H–H interaction is a rare appearance in metal hydrides, which certainly considerably hampers the H desorption kinetics from MgH₂.

It should be also remembered that conditions on the MgH₂ desorption surface changes substantially during the process, both due to depletion of the surface, and, in a more severe way, due to the structural phase transitions which should be expected for concentrations around Mg:H = 1:1 and below. One attempt in this direction is presented in Figure 7a,b, illustrating the H-desorption from the MgH₂ (110) surface, and the energy changes of the (fully relaxed) surface during the particular stages of the process.

Although all mentioned [80,82,85,86,87,88,89,91,92] and other numerous investigations deal with only some particular aspects of the process (e.g., distinct points on the MgH₂ dehydrogenation curve), they are accurate enough to justify the expectation that the entire process (as well as the process of Mg hydrogenation) will be resolved “from the first principles” in the near future. Also, the investigations have “located’’ the main obstacles that should be resolved in the further attempts to improve the performances of the Mg-H system. Some possibilities for that are discussed in the following chapter.

As we mentioned previously, practical applications of metal hydrides for H storage require strict conditions to be fulfilled [1,2,5,9,10,11,12,13,14]: H absorption/desorption at moderate temperatures and pressures, reversibility of cycling, material stability under operating conditions, large H-uptake, low weight, reasonable price, and so on. Obviously, it is difficult to find the material that can satisfy all these requirements at the same time, and for that reason a huge amount of various systems have been investigated.

The most improvements have come from the catalytic approaches, in which the size of the MgH₂ particles have been reduced down to the nanometer dimensions (increasing the surface/volume ratio), their surface made more active and (or) the bulk less ordered by introduction of defects of various kinds, and by adding various elements to the system, molecules and compounds [3,4,6,7,8,41,44,53,54,55,56,57,58,59,60,61,62,63,64,93,94]. All above mentioned approaches could be understood and its particular relation to H-behavior resolved and established from the electronic structure point of view. The influence of more open, or more dense, metal surfaces and bulk structures on H accommodation has been briefly mentioned in previous chapters, and the importance of surface defects has been also recognized [77]. Simply speaking, any dilution of the metal structure (for instance with defects) would in principle lead to a charge density structure which is more convenient for H accommodation, and its trapping [78]. If the diffusion barrier between different defects or between defects and interstices is lower than between the interstices themselves, defects could facilitate H mobility in the system, but the opposite scenario is also possible.

Although it is generally true for all defects, the effects of impurity atoms on H-behavior in the system depend essentially on their electronic structure. Here we will briefly outline the influence of transition metal (TM) impurities on the Mg/MgH₂ system properties. Extensive experimental [3,4,6,7,8,44,55,56,57,58,59,60,61,62,8,44,55] and theoretical (computational) [21,44,67,68,69,70,71,72,91,93,94,95,96,97,98,72,91,93] investigations have been devoted to the subject, and the importance of the TM(d)–H(s) interaction for the TM catalytic properties [67,71,72,93,95,96] established. To illustrate this, the difference between the center of the TM 3d-band and H(s) level, and its position relative to the 3d-band [99], are presented in Figure 8. The figure shows how the H(s) level taken as a zero energy level, enters and leaves the 3d band while moving along the series.

The consequence of such behavior is an increase of electron density around TM impurity, and therefore an increase of strength of TM–H bonding (reflected in the shortening of the TM–H bond). The trend is visible while moving from Ti to Fe, and eventually could be violated if magnetic interaction in the system becomes important [70,91]. Further filling of the d-band going from Co to Ni and on (Cu, Zn) leads to gradual movement of Fermi level (E_F) away from the center of the d-band, and the ongoing population of the H(s*) anti-bonding level. This leads to weakening of the TM–H interaction and to expansion of the TM–H bond length [70]. The existence of such a clear trend implies that single TM impurity could not satisfy all requirements (adsorption, dissociation, diffusion into and from the bulk and desorption) necessary to improve the H-sorption kinetics of the Mg/MgH₂ system. Indeed, both experimental (for instance [4] and [59]), and calculation results are often inconsistent. For instance, in ref. [4] it has been found that among the TM of the 3d-series Ti and V improve the most, and Ni the least, both absorption and desorption properties of Mg/MgH₂ among the TM of the 3d-series, and [59] claims that Ni is a much better catalyst than Fe and Co. A recent computational study [93] predicts that all 3d TM when absorbed at the Mg (0001) surface induce dissociation of H₂, but that Ti and V provide much slower H-absorption kinetics, than for instance Mn, Fe and Co.

The reason for these discrepancies could be major differences in performed experimental conditions (milling time and energy, particle size, formation of stable TM–Hydrides and other “parasitic” phases, etc.), measuring techniques and conditions and the used computational methods.

However, the fact that all details of the catalytic mechanism of TM in Mg/MgH₂ are still not adequately explained also deserves consideration. For instance, it has been found [71] that catalytic properties of TM in Mg–H clusters strongly depend on its environment (edge, surface, or bulk) in different ways for different TM impurities. It has been also shown [70,72] that TM impurities exhibit a different behavior in different crystal structures of the Mg–H system

An interesting insight in influence of Ti and Co impurity (10 wt.%) on the MgH₂ rutile structure is presented in [72,91]. In Figure 9, the valence charge distributions around Ti and Co impurity in (110) plane are presented.

The charge distributions around Ti and Co atoms are quite different, both being of predominantly t_2g character. Around Ti it is however directed between the neighboring H atoms, and around Co it is more spherical, with significant contribution of charge directed toward the H atoms. Both Ti and Co interact with four neighboring H atoms in (110) plane, but also in (−1−10) plane where the interaction is extended from the two nearest neighbor H toward the two H in the third coordination of TM. In Table 1, one can see that Co–H bond length is shorter than Ti–H one, but that Co destabilize the MgH₂ structure more than Ti. It has been also found that magnetic interaction in the MgH₂:Co system affords an important contribution to the ground state energy of the system.

One possible explanation why Co destabilizes MgH₂ more than Ti could be that strong local TM–H interaction weakens the rest of the bonds in the compound due to the strong localization of the valence charge in the first coordination of TM more around Co than around Ti. If this hypothesis is correct, it should be reflected in the H-desorption kinetics from these systems which, after the initial acceleration, could slow down for the H-poor phases.

It should be mentioned here that a consistent explanation of TM hydrides formation and stability is challenging in itself [21,91,96], and this is particularly true for hydrides of complex intermetallic compounds [100,101,102,103].

The established fact that some local structures inside the very same unit cell of the complex compounds of the Ti₂Ni structure type are much more susceptible to H absorption than others [104,105], should be due to remarkably different charge topology observed at different lattice positions in some of these systems [106].

Although the large specific weight prevent their practical applications as H-storage materials, the fact that their electronic properties, and consequently the environment for H-uptake could be altered considerably inside the same structure by changing the constitutive elements of the compound [107,108], provides a valuable example of how to adjust the local electronic charge distribution inside a complicated system, which could be of importance for understanding another type of complex hydrides presented in the next chapter.

After the first encouraging results with alanates [27,28,29], a large variety of complex metal hydrides [25,30,31,32,107,108,109,110,111,112,32,107] have been considered as potential candidates for hydrogen storage. These are usually materials with complicated crystal structures in which H is accommodated in specific clusters or molecules. In these materials the process of H absorption/desorption is often accompanied and promoted by structural phase transitions, improving the kinetics, and enabling the processes to take place under favorable thermodynamic conditions. Together with the small specific weight and large hydrogen uptake, this makes these materials (various alanates, amides-imides, borohydrides etc.) promising candidates for practical applications. As a representative of kind, we will shortly consider the reversible LiNH₂ (Li-amide) to Li₂NH (Li-imide) transformation, which recently attracted considerable interest in the scientific community [30,31,32,109,113].

In Figure 10a the LiNH₂ crystal structure (space group I-4), in Figure 10b the charge distribution in the LiNH₂ (110) plane and in Figure 10c, one of the several possible Li₂NH crystal structures (space group Im2m) is presented.

It has been found [32] that LiNH₂ crystal structure induces considerable elongation of the Li-N bond in LiNH₂ molecule, which increase energy of the molecule, and soften some of the molecular vibrational modes. This makes detachment of H fast at temperatures around 250 °C [30] (which are likely to be lower by addition of suitable impurities, like Mg [31]), and structure changes to Li₂NH. The ground state structure of Li₂NH was a subject of considerable debate, and it seems [26] that quantum effects enable the H-diffusion among available crystal positions stabilizing the Fd-3m structure at low temperatures, which changes into anti-fluorite Fm-3m phase at about 360 K [114]. Perhaps the same effect is responsible for the existence of numerous metastable phases [113] with very close ground state energies, which could also play a role in the Li-amide/imide transformation process, opening numerous channels for hydrogen desorption. Similar mechanisms were found also in some other “modern” complex hydrides, encouraging investigation of structures and structural transformations, which could manage H sorption, and not just follow it.