Hydrogen mobility in the lightest reversible metal hydride, LiBeH3

Lithium-beryllium metal hydrides, which are structurally related to their parent compound, BeH2, offer the highest hydrogen storage capacity by weight among the metal hydrides (15.93 wt. % of hydrogen for LiBeH3). Challenging synthesis protocols have precluded conclusive determination of their crystallographic structure to date, but here we analyze directly the hydrogen hopping mechanisms in BeH2 and LiBeH3 using quasielastic neutron scattering, which is especially sensitive to single-particle dynamics of hydrogen. We find that, unlike its parent compound BeH2, lithium-beryllium hydride LiBeH3 exhibits a sharp increase in hydrogen mobility above 265 K, so dramatic that it can be viewed as melting of hydrogen sublattice. We perform comparative analysis of hydrogen jump mechanisms observed in BeH2 and LiBeH3 over a broad temperature range. As microscopic diffusivity of hydrogen is directly related to its macroscopic kinetics, a transition in LiBeH3 so close to ambient temperature may offer a straightforward and effective mechanism to influence hydrogen uptake and release in this very lightweight hydrogen storage compound.


Results and Discussion
The temperature dependence of the elastic (within the resolution of the spectrometer) neutron intensity is presented in Fig. 1. The data normalized to the lowest measured temperature overlap up to ca. 265 K, when LiBeH 3 exhibits a dramatic drop in the elastic intensity. The elastic intensity does not drop to a near-zero value, as would be the case for a complete melting of the sample. Nevertheless, a sudden change in the state of the hydrogen sublattice, which dominates the scattering signal, is evident. The sharpness of the elastic intensity drop is remarkable; it surpasses, e.g., the already rather sharp elastic intensity drop due to the onset of rapid oxygen diffusivity in bismuth oxide above ca. 740 °C underlined by a phase transition to δ-Bi 2 O 3 structure 29 , while most order-disorder transitions observed in ion conductors are much more gradual. The abrupt transition in the hydrogen sublattice in LiBeH 3 is reminiscent of partial melting. To this end, it is of interest to investigate the mechanism of hydrogen hopping in BeH 2 and LiBeH 3 at various temperatures. Unlike the data presented in Fig. 1, which are completely model-independent, such analysis of microscopic hydrogen diffusivity has to rely on fitting QENS data with a suitable model scattering function. In the simplest case, the model scattering function in QENS is a superposition of Lorentzian terms, where each Lorentzian term in the energy transfer space is a Fourier transformation of the corresponding term in the time space describing exponential decay with time of self-correlation for diffusing particles. For a comprehensive overview of QENS technique and data analysis, see 30 .
The QENS data, I(Q, E), collected as a function of energy and momentum transfer, E and Q, are fitted with the following model scattering function: The fits of the scattering intensity, I(Q, E), are performed separately at each Q value, and include a superposition of elastic line (delta-function) with a spectral weight x(Q) and a quasielastic model scattering function term, S(Q, E), with the complementary spectral weight 1−x(Q), convolved with the resolution function, R(Q, E), and a linear background term, (C 1 (Q)E + C 2 (Q)). The model scattering functions used in the current study included either one, or two Lorentzian terms, as follows: The drastic difference of the scattering signal from LiBeH 3 observed above the transition is illustrated by Fig. 2. A simple one-Lorentzian fits adequately described the data for BeH 2 and LiBeH 3 below the transition; the resulting Q-dependence of the Lorentzian half-width at half-maximum, HWHM(Q), is presented in Fig. 3. The data for BeH 2 exhibit stronger Q-dependence compared to those for LiBeH 3 . In particular, they show an increase at low Q followed by a weak maximum in the mid-Q range, which suggests that the hydrogen hopping in BeH 2 can be described by Chudley-Elliott jump diffusion model 30 (Fig. 3a): where ℏ is reduced Planck constant, D is the diffusion coefficient and L is the diffusion jump length. Chudley-Elliott jump diffusion model assumes that, for some characteristic time between jumps, τ, a particle engages only in vibrational motions near an equilibrium position, and then relatively quickly (compared to the time between jumps) performs a diffusion jump into a new equilibrium position. The jump length and diffusion coefficient are related to the characteristic time between jumps, τ, as D = L 2 /6τ; they are listed in Table 1.
The HWHM(Q) values for LiBeH 3 below the transition are relatively Q-independent, indicative of localized, rather than long-range translational, hydrogen jumps. They can be described by the values averaged over the measured Q-range, <HWHM(Q)> (Fig. 3b), which can be converted to the characteristic time between jumps as τ = ℏ/<HWHM(Q)>. On the other hand, a two-Lorentzian fit was needed to adequately describe the data for LiBeH 3 above the transition. The resulting HWHM(Q) of the narrower Lorentzian can still be fitted with Figure 1. Temperature dependence of the elastically scattered (within the resolution limit of the spectrometer) neutron intensity averaged over the entire investigated momentum transfer range and normalized to unity at the baseline temperature of 20 K. The spectra, dominated by the incoherent scattering from the hydrogen in the hydrides, show a sharp melting-type transition for LiBeH 3 at ca. 265 K.
Chudley-Elliott jump diffusion model, but the HWHM(Q) of the broader Lorentzian is different in character; while increasing with Q, it lacks a maximum in the mid-Q range (Fig. 4). Thus, it has to be described by a liquid-diffusion model 30 :   Hydrogen hopping mechanism in LiBeH 3 above the transition is highly unusual in that it exhibits characteristic traits of both solid state and liquid diffusion processes. Resemblance to the solid-state diffusion is evident from the fact that the HWHM(Q) for the narrower Lorentzian, which is typically associated with the long-range translational diffusivity, is described by a solid-state Chudley-Elliott jump diffusion model with a well-defined jump length, not a liquid-diffusion model with a distribution of jump lengths. However, resemblance to the liquid diffusion is evidenced by the strongly Q-dependent spectral weight of the narrow Lorentzian (parameter    Fig. 4 inset. Such Q-dependence of the p(Q) indicates that the two observed Lorentzian components originate from the same diffusing entity 31-33 , and not two separate diffusing species; in the latter case, a Q-independent Lorentzian spectral weight would be expected. In liquids, the narrow Lorentzian is associated with the long-range translational diffusivity, whereas the broad Lorentzian is due to the localized center-of-mass motions in the transient cage made by the neighboring liquid particles [31][32][33] . These localized motions give rise to a broad Q-dependent component, which should, however, plateau at low Q. No leveling off is observed for the broad component presented in Fig. 4, which may indicate that the characteristic volume associated with the localized diffusivity of hydrogen in LiBeH 3 above the transition could be too large to be detected within the Q range of our experiment. The diffusion jump lengths for hydrogen in BeH 2 and LiBeH 3 above the transition (slow component) presented in Table 1 exhibit rather strong and systematic temperature dependence, consistent with long-range hydrogen diffusivity. On the other hand, the diffusion jump length associated with the localized motions of hydrogen in LiBeH 3 above the transition (fast component) does not exhibit a pronounced temperature dependence, as expected for localized motions in the liquid state. Figure 5 shows Arrhenius plots of the characteristic times between jumps and the long-range diffusion coefficients. The long-range diffusion is not measurable for the localized hydrogen hopping in LiBeH 3 below the transition. Furthermore, here we chose not to display the diffusivity values listed in Table 1 for the fast component measured in LiBeH 3 above the transition, because of their likely association with localized rather than long-range diffusivity. The activation energy for the long-range translational diffusivity (solid lines in Fig. 5b) is (2.8 ± 0.3) kJ/mol and (13.3 ± 1.1) kJ/mol for BeH 2 and LiBeH 3 , respectively. Likewise, even below the transition, where hydrogen in LiBeH 3 engages only in localized hopping, its associated activation energy of the residence times appears much larger compared to that of the residence times for hydrogen in BeH 2 , as evidenced by much steeper temperature dependence seen at low temperatures in Fig. 5a.
It is unclear as to whether the unusual character of hydrogen hopping in LiBeH 3 above the transition is related to the amorphous structure of this hydride. On the one hand, it is tempting to attribute the unusual resemblance of hydrogen mobility in this hydride to both liquid-and solid-state diffusion to the fact that the LiBeH 3 structure is amorphous, characterized by the local order and long-range disorder, which can introduce a variety of jump distances. On the other hand, BeH 2 , which is also amorphous, does not exhibit any sudden transition in the hydrogen mobility. If the amorphous structure of a hydride is indeed essential for the unusual hydrogen hopping mechanism as reported here, there is a possibility that other amorphous compounds derived from BeH 2 may exhibit similar mechanism of hydrogen diffusivity, including the transition, if they happen to remain thermodynamically stable to the sufficiently high temperature.
In summary, a sharp increase in the hydrogen mobility observed in LiBeH 3 above 265 K is associated with the abrupt transition of the hydrogen sublattice to a peculiar state that exhibits characteristic traits of both solid-like and liquid-like diffusivity. Because this transition is so close to ambient temperature, it can be used as a mechanism to regulate hydrogen diffusivity in LiBeH 3 . Ultimately, it may help control hydrogen uptake and release in this very lightweight hydrogen storage compound, even though we should note that our QENS measurements were performed in the temperature range of the sample stability, and thus were not directly associated with hydrogen uptake and release.

Materials and Methods
Materials. BeH 2 and LiBeH 3 materials investigated in the current study were the same samples as described in earlier work 28 , which refers to the materials synthesis procedures. In general, solid BeH 2 had primarily been synthesized from decomposition of organometallic precursors [34][35][36] . This synthesis method typically produces amorphous products, which can be transformed to crystalline phases at elevated pressure and temperature. Pressure is required to keep the solid amorphous BeH 2 from decomposing into its elemental constituents. Both BeH 2 crystalline phases and the amorphous solid material have been shown to consist of network of corner-sharing BeH 4 tetrahedral units 17 .

QENS Data Collection and Reduction.
Quasielastic neutron scattering (QENS) experiment was carried out using high energy resolution backscattering spectrometer BASIS 37 at the Spallation Neutron Source (SNS) at Oak Ridge National Laboratory. The energy resolution was 3.4 μeV (full width at half-maximum) for the Q-averaged resolution value, and the energy transfer window suitable for the data analysis was ±100 μeV. The minimum and maximum momentum transfer, Q, value suitable for data analysis was 0.3 Å −1 and 1.5 Å −1 , respectively. The powder samples contained in aluminum foil were placed in annular aluminum sample holders. Initially, each sample was cooled down to the baseline temperature of 20 K to measure the spectra (for several hours each) used for the sample-specific resolution function under the conditions when the measurable hydrogen hopping had ceased. Then the temperature was ramped up at a rate of 1 K/min while the data almost continuously collected for about 5 hours were integrated over ±3.4 μeV energy transfer range to obtain the temperature dependence of the elastically scattered neutron intensity (averaged over all Q values). Then longer dynamic measurements (several hours each) were performed at a few temperatures chosen to remain below the known limits of thermal decomposition 38 . A vanadium standard was used for data normalization. Data Availability. The datasets analyzed during the current study are available from the corresponding author on reasonable request.