The physical properties of rare earth hydrides with manganese RMn₂H_x largely coincide with the properties of metal hydrides (MH_x). Also, alloys of RMn₂ compounds absorb hydrogen very easily. At close to atmospheric hydrogen pressure and temperatures above 100 °C, it is possible to achieve a hydrogen concentration of ~4.5 H/f.u. [48]. As noted in metal hydrides, hydrogen occupies the interatomic sites of the elements that comprise the RMn₂ unit cell. There are three types of tetrahedral sites in RMn₂ compounds: A2B2, AB3 and B4, where A and B represent atoms of R and Mn, respectively, surrounding the site (Figure 4). The largest and at the same time most willingly filled by hydrogen site (below x ≈ 3.5 H/f.u.) is the A2B2 type. For x ≳ 3.5 H/f.u., there is also a tendency to fill smaller sites, such as AB3 sites [49,50,51,52]. However, no B4 site filling was observed. The same types of sites occur in both C14 and C15 types of Laves phases. When filling the sites, hydrogen occupies crystallographic positions (Table 1).

Although the number of sites is significant, every site cannot be occupied by hydrogen. Two criteria are useful: (i) the Switendick criterion [53] states that the distance d_H-H must be larger than ~2.1 Å and (ii) the Westlake criterion indicates that the radius of the sphere available for hydrogen cannot be less than ~0.37 Å. [54]. As an effect, criteria preclude occupancy of A2B2 tetrahedrons that have a common wall, and the B4 site is not available for hydrogen due to size restrictions. The Switendick criterion, confirmed in neutron measurements [55,56], largely determines the maximum content of absorbed hydrogen. The theoretically determined maximum hydrogen concentration in RT₂H_x (R: rare earth, T: transition metal = Y, Mn) compounds is therefore 6.0 H/f.u. [57]. Only the use of ultra-high hydrogen pressures of the order of 10³ MPa led to the formation of RMn₂H₆ hydrides; the first being YMn₂H₆ [58,59]. Highly hydrogenated (x ≳ 4.5 H/f.u.) compounds show different physical properties compared to low-hydrogen compounds (x ≲ 4.5 H/f.u.) [60,61] and will not be discussed in this study.

In the discussed hydrides, the sample preparation was similar and usually involved the following scenario.

The host materials (RMn₂) were prepared from high purity elements using the standard induction melting technique under argon atmosphere. Next, materials were usually annealed to obtain a single-phase compound. The RMn₂ samples were saturated with hydrogen using a standard volumetric method (Sievert) to obtain RMn₂H_x hydrides in the typical range of x: 0 < x < 4.3–4.5 [7,8,9,55,62,63,64,65,66,67]. The first test after hydrogen saturation was XRD measurements at 300 K. As a representative example, the HoMn₂H_x_C15 diffractogram is presented in Figure 5a. The most visible effect of hydrogen absorption by the sample is the shift of the diffraction lines towards smaller angles (in 2 theta), which means an increase in the distance between atoms in the cell, and consequently an increase in the unit volume of the cell with x.

Even at room temperature, the RMn₂H_x hydrides do not persist in the crystallographic structure of the host compound. For the HoMn₂H_x_C15 hydride, a combination of the cubic (α) and rhombohedral distortion (β) is observed (Figure 5a). The obtained results are in agreement with [68]. To compare lattice parameters of hydrides with different crystallographic structures, their parameters were converted into parameters of the pseudo-cubic cell considering abundance phases, if the system is not a single-phase system. For example, the lattice parameters of the rhombohedral phase were converted into lattice parameters 𝑎*𝛿 of the pseudo-cubic phase according to the relationship reported below: where a_δ and c_δ are lattice parameters of the rhombohedral phase (space group: 𝑅3, nr166, setting: 1) [66].

The relative volume change in unit cell versus hydrogen content in HoMn₂H_x_C15 is depicted in Figure 5b. The first ‘model’ that attempted to describe the relation between ΔV/V₀ and x was just a linear relationship. The next one, the Hirata model, only correctly reproduces the lowest range of x (0 < x < 3.0) (Figure 5b, dashed line) [69], and its development was proposed by Figiel et al. [51]. In the last one (farther: Hirata–Figiel model), the authors assume a two-stage approach to occupying interstitial sites (Figure 5b red line). Initially, with a characteristic parameter X_c < 3.0–3.5 H/f.u. (see below), the A2B2 type sites are filled (this part is identical with Hirata model). Next, above X_c > 3.0–3.5 H/f.u., the AB3 type sites are also occupied. It is represented by a characteristic break in the red curve (x~3.2 H/f.u., Figure 5). The Hirata-Figiel model is described according to the relationship described below [51]. where ΔV/V₀ is the relative increase in unit cell volume; B₀ is a parameter of the lattice contraction, a quantity analogous to the bulk modulus at starting concentration related to the intrinsic pressure; b is the first derivative with respect to concentration x: (B_x = B₀ + b_x); and P is the probability of filling the AB3 sites by hydrogen atoms for concentrations greater than X_c (P = 0 for x ≤ X_c) [34,51]. Fitted parameters for the RMn₂H_x (R: Y, Dy, Gd, Tb, Ho) hydrides are presented in Table 2. For all compounds, the characteristic X_c belongs to the region of ~3.0–3.5 and probabilities of entering the AB3 interstitial sites P~0.6–0.9. This type of filling sites was also postulated in [50,51].

The relative volume increase (ΔV/V₀) of unit cells of hydrides determined at room temperature and depending on the hydrogen content in the sample is non-linear and can be described by the same function, indicating that this effect is determined only by the presence of hydrogen. The fits of the Hirata–Figiel model to the change in (ΔV/V₀) depending on the hydrogen concentration for the various studied hydrides RMn₂H_x are shown in Figure 6.

For x < 3.0 H/f.u., the curves, except for those corresponding to (Gd and Nd)Mn₂H_x, are almost identical. At values greater than x ≈ 3.0 H/f.u., distinct behavior becomes visible with increasing x, especially for concentrations close to the maximum, where the relative increase in volume increases with the atomic number of the rare earth element.

With a temperature change, the RMn₂H_x hydrides undergo complex phase transformations in many cases, which, combined with the often occurring multi-phase states, makes the interpretation of their X-ray diffraction magnetic transformation results extremely difficult. Some authors have even argued that it will never be possible [39]. One of the first hydride families to be studied over a wide range of x and temperature changes was YMn₂H_x, showing a very wide range of structural transformations as a function of temperature. In contrast, TbMn₂H_x hydride families show a very ‘modest’ spectrum of structural transformations. Very interesting are the structural and magnetic properties of HoMn₂H_x hydrides, in which the base compound can crystallize in a C14 or C15 Laves phase structure, depending on the sample preparation [10].