Structural and reorientational dynamics of tetrahydroborate (BH₄⁻) and tetrahydrofuran (THF) in a Mg(BH₄)₂·3THF adduct: neutron-scattering characterization

Abstract

Metal borohydrides are considered promising materials for hydrogen storage applications due to their high volumetric and gravimetric hydrogen density. Recently, different Lewis bases have been complexed with Mg(BH₄)₂ in efforts to improve hydrogenation/dehydrogenation properties. Notably, Mg(BH₄)₂·xTHF adducts involving tetrahydrofuran (THF; C₄H₈O) have proven to be especially interesting. This work focuses on exploring the physicochemical properties of the THF-rich Mg(BH₄)₂·3THF adduct using neutron-scattering methods and molecular DFT calculations. Structural analysis, based on neutron diffraction measurements of Mg(¹¹BH₄)₂·3TDF (D – deuterium), has confirmed a lowering of the symmetry upon cooling, from monoclinic C2/c to P1̄ via a triclinic distortion. Vibrational properties are strongly influenced by the THF environment, showing a splitting in spectral features as a result of changes in the bond lengths, force constants, and lowering of the overall symmetry. Interestingly, the orientational mobilities of the BH₄⁻ anions obtained from quasielastic neutron scattering (QENS) are not particularly sensitive to the presence of THF and compare well with the mobilities of BH₄⁻ anions in unsolvated Mg(BH₄)₂. The QENS data point to uniaxial 180° jump reorientations of the BH₄⁻ anions around a preferred C₂ anion symmetry axis. The THF rings are also found to be orientationally mobile, undergoing 180° reorientational jumps around their C₂ molecular symmetry axis with jump frequencies about an order of magnitude lower than those for the BH₄⁻ anions. In contrast, no dynamical behavior of the THF rings is observed with QENS for a more THF-deficient 2Mg(BH₄)₂·THF adduct. This lack of comparable THF mobility may reflect a stronger Mg²⁺–THF bonding interaction for lower THF/Mg(BH₄)₂ stoichiometric ratios, which is consistent with DFT calculations showing a decrease in the binding energy with each additional THF ring in the adduct. Based on the combined experimental and computational results, we propose that combining THF and Mg(BH₄)₂ is beneficial to (i) preventing weakly bound THF from coming free from the Mg²⁺ cation and reducing the concentration of any unwanted impurity in the hydrogen and (ii) disrupting the stability of the crystalline phase, leading to a lower melting point and enhanced kinetics for any potential hydrogen storage applications.

---

Introduction

Using hydrogen as an energy carrier provides an opportunity to achieve zero-emission propulsion, which will help to reduce the consumption of fossil fuels and limit the extent of anthropogenic contributions to climate change.¹ Storing hydrogen in chemical bonds, i.e., hydrogen storage materials, is one approach to storing and transporting hydrogen that provides greater volumetric and gravimetric hydrogen densities compared to compressed hydrogen gas. Hydrogen storage materials must fulfill a wide range of requirements to be industrially applicable. Among these, a high hydrogen content, fast kinetics of hydrogen desorption and absorption at low operating temperature and pressure, and a high purity of the released hydrogen are the most important. Promising alternatives for hydrogen storage include carbon nanostructures,^2,3 liquid organic hydrogen carriers,⁴ metal organic frameworks⁵ and complex borohydrides.⁶

Metal borohydrides [M(BH₄)_n] are considered as attractive materials for hydrogen storage applications due to their high volumetric and gravimetric hydrogen densities. M(BH₄)_n are largely ionic compounds composed of tetrahedral hydrogen-rich molecular BH₄⁻ anions counterbalanced by metal cations, Mⁿ⁺. Among the alkali- and alkaline-earth-based borohydrides, magnesium borohydride [Mg(BH₄)₂] displays very interesting properties both from fundamental and application points of view. Mg(BH₄)₂ has a more favorable thermodynamic stability in comparison to, e.g., LiBH₄, while still maintaining attractive hydrogen storage capacities of 14.9 mass%.^7,8 However, the reaction kinetics of Mg(BH₄)₂, which is still not fully understood, along with its decomposition pathways occurring in a multi-step process only at 600 K,^9,10 and its limited reversibility,¹¹ make Mg(BH₄)₂ still unsuitable for practical applications.

Recently, different additives have been used in order to enhance the kinetics of hydrogen release from Mg(BH₄)₂.^12–15 These studies have found that the onset temperature of hydrogen release could be reduced upon addition of metal fluorides^13–15 or by mechanically milling Mg(BH₄)₂ with TiO₂.¹⁵ Additionally, accelerated thermal dehydrogenation of Mg(BH₄)₂ was observed in mixtures with LiBH₄.^16–18

Several studies have also suggested that adducts of Mg(BH₄)₂ complexed with solvent molecules might lead to beneficial enhancements in hydrogen kinetics.^19–23 Among these, adducts with tetrahydrofuran (THF = C₄H₈O) have proven to be especially interesting, as it was found that THF binds to the Mg²⁺ and appears to modify its chemistry, increasing both selectivity and kinetics for H₂ release (and reversible uptake).²³ However, the specific role of THF in the hydrogenation and dehydrogenation process is still ambiguous, and as such, in-depth foundational studies of the THF interactions with BH₄⁻ and Mg²⁺ may provide further insight.

Investigating physicochemical properties of Mg(BH₄)₂·xTHF adducts constitutes a challenge from an experimental point of view, as selectivity to different components, e.g., BH₄⁻ and THF, is required. Neutron scattering techniques are invaluable in this case, as they offer selectivity to a given component through isotopic (H/D) labeling. In the case of incoherent neutron scattering techniques (neutron vibrational spectroscopy (NVS) and quasielastic neutron scattering (QENS)) related to hydrogen self-motions, deuteration can significantly reduce the scattered intensity, thereby masking the deuterated component to neutrons. Additionally, QENS also provides space/time resolution at a molecular level through the momentum transfer dependence of the magnitudes measured. On the other hand, structural information, which is crucial for the understanding of vibrational and dynamical results, can be provided from neutron powder diffraction (NPD) measurements.

This work focuses on exploring the structural, vibrational, and dynamical properties of the THF-rich Mg(BH₄)₂·3THF adduct through neutron-scattering methods and molecular DFT calculations. Some additional limited experimental and theoretical comparisons with Mg(BH₄)₂ and the relatively THF-poorer 2Mg(BH₄)₂·THF adduct provide further insights concerning the dependences of BH₄⁻ and THF dynamics on adduct stoichiometry. In some experiments, selective masking of the THF molecules within the Mg(BH₄)₂·xTHF adducts via their deuteration allowed us to isolate and characterize more effectively the individual behaviors of the BH₄⁻ anions and THF molecules.

Experimental details

Materials

To facilitate neutron scattering measurements, all samples were prepared using ¹¹B-enriched Mg(¹¹BH₄)₂ from Katchem²⁴ as a starting material; this leads to a significant reduction of the neutron absorption otherwise due to the ¹⁰B isotope in natural boron. Moreover, for some neutron scattering measurements, where appropriate, synthesized adducts with fully deuterated THF (i.e., TDF) were used.

Sample preparation and storage were conducted either in a nitrogen glovebox or on a Schlenk line. The solvents were dried over molecular sieves and verified by NMR for purity before use.

Two Mg(BH₄)₂·xTHF adduct stoichiometries were prepared with THF/Mg(BH₄)₂ stoichiometric ratios x = 3 and 0.5, as previously described in ref. 23. Briefly, diethyl ether was added to a round-bottom flask containing 400 mg of α-phase Mg(BH₄)₂ until the borohydride was dissolved. In a subsequent step, a stoichiometric quantity, 0.5 or 3 equivalents of THF or TDF per Mg(BH₄)₂, was added by a micropipette to the ether solution at room temperature and stirred for 30 min. The excess ether was then removed in vacuo at room temperature for 12 hours to yield the THF adducts of Mg(BH₄)₂. This vacuum treatment did not remove THF, since prolonged exposure of Mg(BH₄)₂·3THF under vacuum did not change its stoichiometry or crystallinity.

Room-temperature XRD data for Mg(BH₄)₂·3THF confirmed the formation of the known monoclinic structure. The indexing of comparable XRD data for the more THF-deficient 2Mg(BH₄)₂·THF (i.e., x = 0.5) also suggested primarily a single phase with monoclinic symmetry but of as-of-yet unknown structure and exact stoichiometry.

Methods

All neutron scattering measurements were performed at the National Institute of Standards and Technology Center for Neutron Research using 0.5 g of each powdered sample mounted in a thin-walled annular geometry (5 cm height × 1.2 cm annulus diameter) inside a He-filled, indium o-ring-sealed, cylindrical Al sample cell.

Neutron powder diffraction (NPD) measurements were performed between 5 K and 300 K using the BT-1 High-Resolution Neutron Powder Diffractometer²⁵ with the Cu(311) monochromator at λ = 1.5397(2) Å and an in-pile collimation of 60 min of arc. Neutron vibrational spectroscopy (NVS) measurements were performed at 4 K using the Filter-Analyzer Neutron Spectrometer (FANS)²⁶ with both the Cu(220) and pyrolytic graphite PG(002) monochromators and pre- and post-collimations of 20′ of arc, yielding a full-width-at-half-maximum (fwhm) energy resolution of about 3% of the neutron energy transfer. QENS measurements were performed up to 315 K using two complementary instruments: the Disc Chopper Spectrometer (DCS)²⁷ between 4 K and 315 K using an incident neutron wavelength (λ) of 4.5 Å, 10 Å and 12 Å with respective fwhm resolutions of 67 μeV, 17 μeV and 10.9 μeV and respective maximum attainable elastic scattering vector (Q) values of around 2.62 Å⁻¹, 1.18 Å⁻¹ and 0.98 Å⁻¹; and the High Flux Backscattering Spectrometer (HFBS)²⁸ between 4 K and 315 K [plus up to 350 K during an elastic-scattering fixed-window scan (FWS)] using an incident neutron wavelength of 6.27 Å (2.08 meV) with a fwhm resolution of 0.8 μeV and a maximum attainable Q value of 1.75 Å⁻¹. Instrumental resolution functions were determined from QENS spectra at lower temperatures free of quasielastic scattering, i.e., at 4 K. QENS data were analyzed using the DAVE software package.²⁹

Solid-state density-functional theory (DFT) calculations were performed using the Quantum-Espresso package.³⁰ A cutoff energy of 544 eV and a 2 × 2 × 1 k-point mesh (generated using the Monkhorst–Pack scheme) were used and found to be enough for the total energy to converge within 0.01 meV per atom. Crystal structures were first fully optimized, based on the experimental structures, and are presented in the ESI.† For comparison with the NVS measurements, simulated phonon densities of states (PDOSs) were generated from the DFT-optimized structures using the supercell method (2 × 2 × 1 cell size) with finite displacements (0.02 Å) and were appropriately weighted to take into account the total neutron scattering cross sections of the different elements. Gas phase DFT calculations were done using the B3LYP functional^31–34 and the Gaussian 6-31+G* basis set^35,36 to calculate the binding energies of the 1st, 2nd and 3rd THF molecules to Mg(BH₄)₂. The optimized geometries were verified by the absence of imaginary frequencies from the frequency analysis in the harmonic oscillator/rigid-rotor approximation. The frequencies were also used to calculate the enthalpic and entropic contributions to the free energy for binding. All calculations were done using the NWChem software.³⁷

Structural depictions were made using the VESTA (Visualization for Electronic and Structural Analysis) software.³⁸ For all figures, standard uncertainties are commensurate with the observed scatter in the data, if not explicitly designated by vertical error bars.

Results and discussion

Structural behavior and vibrational dynamics of Mg(BH₄)₂·3THF

Neutron powder diffraction measurements of the partially deuterated sample, Mg(BH₄)₂·3TDF, upon heating from 5 K to 298 K indicate a phase transition in the temperature range between 175 and 225 K, as shown in Fig. 1. Prior low-temperature (100 K) and room-temperature (298 K) XRD measurements of Mg(BH₄)₂·3THF suggested two crystalline forms of this material with triclinic (space group P1̄)³⁹ and monoclinic (space group C2/c)⁴⁰ structures, respectively. To confirm these structures, Rietveld refinements of the NPD patterns (at 298 K and 225 K) above and (at 5 K) below this phase transition were performed. The analysis corroborated a lowering of the symmetry upon decreasing the temperature, from monoclinic C2/c to P1̄ via a triclinic distortion from respective α, β, and γ values of 90°, 144.992(4)°, and 90° at 298 K to 102.596(3)°, 103.984(4)°, and 92.239(3)° at 5 K. Fig. S1 in the ESI† presents the model refinements of the NPD data at 298 K, 225 K, and 5 K. Table S1 and supplemental CIF files, also in the ESI,† summarize the structural analysis details. It should be noted that the lattice parameters from ref. 40 were associated with a different unit cell convention than that used in this paper. Converting these parameters to the present convention yield values of a = 12.120 Å, b = 12.646 Å, c = 20.216 Å, and β = 144.96°, which are in good agreement with our values. We note that the slightly smaller lattice constants associated with the present results are consistent with the incorporation of TDF, instead of THF, in our NPD samples. Molecular vibrational amplitudes associated with deuterated molecules are somewhat smaller than their hydrogenated analogues, leading to slightly less space required to accommodate the former molecules compared to that for the latter.

Fig. 1 Progression of NPD patterns [λ = 1.5397 Å] of Mg(BH₄)₂·3TDF with temperature, upon heating from 5 K to 298 K, showing the structural transformation from triclinic P1̄ symmetry to monoclinic C2/c symmetry. The inset shows patterns at 5 K, 225 K, and 298 K for clarity to distinguish from the intervening patterns measured at other temperatures. Asterisks mark the reflections obtained from the Al container.

Fig. 2 shows the molecular and crystal structures of the low- and room-temperature Mg(BH₄)₂·3TDF phases. It is apparent that the packing of molecules in both crystalline forms takes place in a layered lattice, with interchangeable layers of BH₄⁻ anions and TDF rings. The three TDF molecules and two BH₄⁻ anions are located around the central Mg²⁺ cation in a trigonal bipyramidal motif. The BH₄⁻ anions are bonded to the Mg²⁺ cation via double hydrogen bridges. The coordination polyhedron of Mg²⁺ can be described by a distorted pentagonal-bipyramidal geometry, where the axial vertices are occupied by the O atoms of the two apical TDF rings, while the four bridging H atoms from the BH₄⁻ anions and the O atom from the third TDF ring lie mostly in the equatorial plane. The detachment of the apical TDF rings from the BH₄⁻ anions is observed from the O–Mg–O angles of 172.1° and 163.6° in the respective P1̄ and C2/c structures, as well as from the slightly longer Mg–O distances to the apical TDF molecules. However, the arrangement of the Mg, O, and two B atoms in the equatorial plane is perfectly coplanar, with low deviations from the ideal angle of 120° in a trigonal bipyramidal coordination geometry. Higher values of the B–Mg–B angle in comparison to both B–Mg–O angles are observed due to a more repulsive force between the negatively charged BH₄⁻ anions than between the coordinated TDF ring and BH₄⁻ anion. No significant distortion of the TDF rings or BH₄⁻ anions has been observed in either crystalline form, with bond lengths and bond angles not being different from the expected values.⁴¹ However, the interatomic Mg and B separations of 2.49 Å in P1̄ and 2.46 Å in C2/c are slightly greater than 2.41 Å reported for pristine α-Mg(BH₄)₂.⁴¹

Fig. 2 Molecular and crystal structures of the low-temperature (P1̄ symmetry) and room-temperature (C2/c symmetry) Mg(BH₄)₂·3TDF phases.

The neutron vibrational spectra for Mg(BH₄)₂·3THF and Mg(BH₄)₂·3TDF at 4 K based on FANS measurements are shown in Fig. 3 and compared with the simulated phonon density of states (PDOS) from the DFT-optimized triclinic structure, indicating overall good agreement between experiment and theory. Further information about the character, symmetry, and energies of the different phonon modes contributing to the simulated PDOSs can be found in the ESI.†

Fig. 3 Neutron vibrational spectra for Mg(BH₄)₂·3THF (red) and Mg(BH₄)₂·3TDF (orange) at 4 K compared with the simulated 0 K 1-phonon- (light gray) and 1+2-phonon-density-of-states spectra (dark red and brown) after DFT energy optimization of the triclinic P1̄-symmetric structure derived from the 5 K NPD data. Neutron vibrational spectra of pristine α-Mg(BH₄)₂ (black), THF (blue), and TDF (dark blue), as well as the simulated 0 K 1-phonon- (light gray) and 1+2-phonon-density-of-states spectrum (light blue) of THF are shown for reference and comparison. The Cu(220) and pyrolytic graphite (002) monochromators were used above and below 40 meV, respectively. Vertical error bars denote ±1σ.

Upon comparison of the Mg(BH₄)₂·3THF NVS spectrum with that of pristine α-Mg(BH₄)₂, obvious peak splitting in the lower frequency region (<80 meV) is observed. This is mostly due to the coordination of THF rings, which affects the bonding between the Mg atoms and BH₄⁻ anions. Based on the structural data, the presence of THF rings causes extension of the interatomic distance between the Mg and B atoms and reduction in the B–Mg–B angle in comparison to the pristine α-Mg(BH₄)₂.

Direct comparison between NVS spectra of Mg(BH₄)₂·3THF and Mg(BH₄)₂·3TDF, as well as the mode identification obtained from the DFT PDOS calculations, can help distinguish the modes dominated by the vibrational displacements of the BH₄⁻ anions and those of the THF molecules. This is due to the fact that, while the TDF spectrum by itself is measurable, as can be seen in Fig. 3, its overall contribution to the Mg(BH₄)₂·3TDF spectrum is very small, thus accentuating the BH₄⁻ contributions. Additionally, it should be mentioned that the noticeable shift in peak positions between the crystalline THF and TDF compounds is due to the mass difference between H and D atoms, where heavier D atoms cause peak-shifting to lower energy transfer.

By analyzing the spectra in this way, it can be seen that most peaks observed in the low-energy region from 20 to 65 meV (1 meV ≈ 8.066 cm⁻¹) for Mg(BH₄)₂·3THF in Fig. 3 correspond to the BH₄⁻ librational (torsional) modes.⁴² Moving to higher energy-transfer values, two sharp features are observed at around 70 and 84 meV, and are attributed to vibrations related to THF ring deformations and CH₂ wagging.⁴³ Furthermore, a number of sharp peaks are noticeable in the 100–190 meV spectral region of Mg(BH₄)₂·3THF, of which eight peaks centered at around 107, 114, 120, 128, 144, 154, 167 and 182 meV are particularly intense. According to group-theory calculations,^44,45 BH₄⁻ anions have a high tetrahedral (T_d) symmetry for which the irreducible representation in the Mulliken notation can be written as Γ = A₁ ⊕ E ⊕ 2F₂, while THF rings have two-fold rotational (C₂) symmetry with the irreducible representation given as Γ = 17A ⊕ 16B. Here, the A and B modes are non-degenerate, while the E modes are doubly degenerate, and the F modes are triply degenerate. Having in mind this notation and comparing the results with the DFT simulations and the experimental spectra of pristine α-Mg(BH₄)₂, THF, and TDF, the very intense peaks observed in the 100–190 meV region could be resolved as follows: the peaks observed at 144 and 154 meV mostly correspond to the asymmetric bending vibrations of BH₄⁻ (F₂ symmetry mode), while the peaks at 167 and 183 meV are attributed to the symmetric bending vibrations of BH₄⁻ (E symmetry mode). The lower energy peaks at 107, 114, 120, 128, 144 meV are related to the A and B modes of THF, corresponding mostly to stretching vibrations.

Reorientational dynamics of Mg(BH₄)₂·3THF

The neutron-elastic-scattering fixed-window scan (FWS) presents a plot of the temperature dependence of the neutron scattering intensity at zero energy transfer. As such, a direct comparison of the FWSs measured from the different compounds provided some insights into the reorientational dynamics of the THF and BH₄⁻ groups in these materials. Fig. 4 shows the FWS for Mg(BH₄)₂·3THF and Mg(BH₄)₂·3TDF measured on HFBS at Q = 0.87 Å⁻¹ between 4 K and 315 K [limited by the decomposition temperature of Mg(BH₄)₂·3THF]. The FWS for pristine α-Mg(BH₄)₂ was measured as a reference in a similar temperature region, from 4 K to 350 K. Again, due to the much lower incoherent neutron scattering cross section of D in comparison to H, the contribution of TDF molecules to the FWS could be neglected (to first order), allowing for all FWSs to be scaled according to their number of H atoms. The FWS of Mg(BH₄)₂·3THF, with a total of 32 H atoms, was normalized to 1 at the lowest temperature, while FWS plots of Mg(BH₄)₂·3TDF and α-Mg(BH₄)₂, with a total of 8 H atoms each, were scaled to 1/4 of the value of Mg(BH₄)₂·3THF at the lowest measured temperature of 4 K. Assuming that the FWS for Mg(BH₄)₂·3TDF reflects only the dynamical contributions of the BH₄⁻ anions allows the estimation of the dynamical contributions solely from the three THF molecules in Mg(BH₄)₂·3THF (labeled in Fig. 4 as “Calculated 3THF”) by subtracting the FWS of Mg(BH₄)₂·3TDF from that of Mg(BH₄)₂·3THF.

Fig. 4 Scaled neutron-elastic-scattering fixed-window scans (FWSs) (upon heating at 0.5 K min⁻¹) for Mg(BH₄)₂·3THF and Mg(BH₄)₂·3TDF measured between 4 K and 315 K, at Q = 0.87 Å⁻¹ with 0.8 μeV fwhm instrumental resolution on HFBS. FWS of pristine β-Mg(BH₄)₂ was measured as a reference in a similar temperature region, from 4 K to 350 K under the same conditions. The scan labeled “Calculated 3THF” was obtained by subtracting the FWS of Mg(BH₄)₂·3TDF from that of Mg(BH₄)₂·3THF using the procedure explained in the text. Inset shows zoomed comparison of the FWSs from Mg(BH₄)₂·3TDF and α-Mg(BH₄)₂.

Upon heating from 4 K, a fall-off in intensity with increasing temperature occurs for all scans depicted in Fig. 4, reflecting the composite Debye–Waller-type hydrogen vibrational displacements associated with the THF and BH₄⁻ groups. Above certain threshold temperatures (at around 230 K for THF and 160 K for BH₄⁻ in the adducts) the fall-offs accelerate, signaling that THF and BH₄⁻ reorientational jumps are coming into the HFBS resolution window with frequencies beginning to exceed 10⁷–10⁸ s⁻¹. As temperatures further increase, the fall-off in intensity begins to slow again, signaling that the reorientational jump frequencies are now approaching the order of 10¹⁰ s⁻¹ and moving out of the HFBS dynamic range window. For Mg(BH₄)₂·3THF, this seems to occur above around 300 K for THF and 190 K for BH₄⁻.

Comparison of the FWSs from Mg(BH₄)₂·3TDF and pristine α-Mg(BH₄)₂, presented in the inset in Fig. 4, shows differences in the slopes of the two curves in the lower-temperature region, up to 200 K, leading to the conclusion that the BH₄⁻ anions in Mg(BH₄)₂·3TDF have lower reorientational mobilities compared to the BH₄⁻ anions in Mg(BH₄)₂ at the same temperature in this region. However, above 200 K, BH₄⁻ anions in both compounds behave the same, based on the overlap of the FWS plots. The drastic change of the reorientational mobilities of the BH₄⁻ anions in the 200 K temperature region coincides with the triclinic to monoclinic structural phase transition for Mg(BH₄)₂·3TDF, as explained previously by the NPD experiments. Additionally, the noticeable change in slope above about 175 K for the FWS component intensity for THF in Mg(BH₄)₂·3THF likely marks a change in the Debye–Waller factor for THF due to this same phase transition.

Complementary QENS measurements on the DCS and HFBS instruments were undertaken to gain further insights concerning the reorientational behavior of both THF and BH₄⁻ groups. Fig. 5 presents two exemplary QENS spectra for Mg(BH₄)₂·3TDF measured at (a) 280 K and (c) 200 K, and two spectra for Mg(BH₄)₂·3THF measured at (b) 267 K and (d) 290 K, on two instruments at different resolutions [(a) and (b) on HFBS with 0.8 μeV resolution; and (c) and (d) on DCS with 16.9 μeV resolution]. All QENS spectra were adequately fit with a delta function and a single Lorentzian component, both convoluted with the resolution function, above a flat background. For all temperatures, the width of the Lorentzian function, Γ, associated with each component group was found to be Q-independent over the measured Q-range (Fig. S2 in the ESI†), consistent with simple localized hydrogen jump motions⁴⁶ for both THF and BH₄⁻ groups, as opposed to long-range diffusive motions.

Fig. 5 QENS spectra measured on HFBS at Q = 1.16 Å⁻¹, 0.8 μeV resolution, for (a) Mg(BH₄)₂·3TDF at 200 K, and (b) Mg(BH₄)₂·3THF at 290 K. QENS spectra measured on DCS at Q = 0.6 Å⁻¹, 16.9 μeV resolution, for (c) Mg(BH₄)₂·3TDF at 280 K, and (d) Mg(BH₄)₂·3THF at 267 K.

Fig. 6 conveys the Arrhenius-like dependencies between 160 K and 320 K of the fundamental jump correlation frequency τ₁⁻¹ = Γ/(2ℏ) vs. T⁻¹ for Mg(BH₄)₂·3TDF, Mg(BH₄)₂·3THF, and pristine α-Mg(BH₄)₂.

Fig. 6 Jump correlation frequency τ_i1⁻¹vs. inverse temperature for Mg(BH₄)₂·3TDF, Mg(BH₄)₂·3THF, and pristine Mg(BH₄)₂. Different symbols denote the different instruments used. Different colors denote the different samples. Dashed lines represent linear fits to the QENS data.

Similarities in the BH₄⁻ reorientational jumps for Mg(BH₄)₂·3TDF, Mg(BH₄)₂·3THF and unsolvated Mg(BH₄)₂ lead to the conclusion that the mobilities of the BH₄⁻ anions are not noticeably affected by the presence of THF rings in the higher-temperature region from 200 K to 320 K, displaying jump correlation frequencies of the order of 10¹⁰ to 10¹¹ s⁻¹, in agreement with those previously reported in Mg(BH₄)₂.⁴⁷ Further lowering the temperature, from 200 K to 160 K, leads to a sudden 75% drop in the BH₄⁻ jump frequencies, compared to the trending values above 200 K. This decrease is explained by the phase transition of Mg(BH₄)₂·3TDF from the monoclinic to the triclinic structure with a smaller unit cell size, presumably leading to enhanced steric effects and thus smaller jump frequencies. This is further portrayed by the calculated activation energies for reorientations, E_a, (derived from the slope (−E_a/k_B) of the linear fit to ln(τ_i1⁻¹) vs. T⁻¹), where a higher barrier is observed in the triclinic structure, i.e., E_a = 137(3) meV for T ≤ 200 K, compared to the monoclinic structure with E_a = 113(3) meV for T > 200 K.

The nature of the reorientational mechanism of the BH₄⁻ anions in Mg(BH₄)₂·3TDF and Mg(BH₄)₂·3THF was determined by the calculated Elastic Incoherent Structure Factor (EISF) over the large Q-range accessible with DCS and using 4.5 Å incident wavelength neutrons. Fig. 7 shows the experimentally derived EISF data at 315 K due solely to the BH₄⁻ anions in Mg(BH₄)₂·3TDF. Based on the invariant Lorentzian widths with Q, two possible localized hydrogen motions are expected in this system, rotations around any one of the three two-fold (C₂) or four three-fold (C₃) molecular symmetry axes of the BH₄⁻ units. For BH₄⁻ rotations around a C₂-axis, the tetrahedral anions have two equal equilibrium orientations, while for BH₄⁻ rotations around a C₃-axis, the tetrahedral anions have three equal equilibrium orientations, while one hydrogen atom remains immobile. In both cases, the final expression for the EISF is identical and given by:⁴⁶

where j₀(x) is a zeroth-order Bessel function equal to sin(x)/(x), and d ≈ 2.0 Å is the jump distance between two BH₄⁻ hydrogen atom positions. Excellent agreement is seen between the plotted C₂/C₃ model and the experimental data at 315 K. (It should be noted that the minor deviations seen at lower Q-values are a signature of minor multiple-scattering effects due to a sample that is somewhat thicker than desired.) As the EISF by itself cannot distinguish between a C₂- or C₃-type jump mechanism for the BH₄⁻ anions, it is also necessary to consider the jump frequencies and the activation energies corresponding to this process. In principle, different jump frequencies and activation energies are expected for different types of reorientations of the same BH₄⁻ anion. The coordination of the BH₄⁻ anions in Mg(BH₄)₂·3TDF with respect to the Mg²⁺ cations is similar to that in unsolvated Mg(BH₄)₂ compounds, namely, the BH₄⁻ anions are oriented toward the Mg²⁺ cations roughly along a molecular two-fold symmetry axis so that the Mg²⁺ cations are straddled by two of the four BH₄⁻ hydrogen atoms. Although the Mg²⁺–BH₄⁻ bond distances are also similar among the solvated and unsolvated compounds, the structures differ somewhat in that each BH₄⁻ anion in unsolvated Mg(BH₄)₂ is in nearly linear coordination with two near-neighbor Mg²⁺ cations, whereas each BH₄⁻ anion in Mg(BH₄)₂·3TDF coordinates to only one Mg²⁺ cation (see Fig. 7). This coordinative arrangement suggests that the rotation around the particular two-fold symmetry axis that is roughly parallel with that connecting B and Mg atoms (horizontal C₂-axis in Fig. 7) does not break any Mg–H bonds. Thus, this type of motion is expected to have a lower activation energy than the rotation around the two other two-fold symmetry axes of the BH₄⁻ anion, which breaks all Mg–H bonds, or, the rotation around any of the three-fold symmetry axes (one of which is shown as C₃ in Fig. 7), which breaks half of the Mg–H bonds. The activation energy and the jump frequencies measured for Mg(BH₄)₂·3TDF and Mg(BH₄)₂ in this case compare well with the values obtained by the recent NMR measurements for Mg(BH₄)₂ (E_a = 116(6) meV and τ₁⁻¹ = 1.5 × 10⁸ s⁻¹ at 170 K),⁴⁸ which correspond to the rotation around the two-fold axis connecting B and Mg atoms. Therefore, the most likely mechanism in the present case for the BH₄⁻ anions in Mg(BH₄)₂·3TDF involves two-fold jumps around the symmetry axis nearly parallel to that connecting B and Mg atoms (C₂ model). Additionally, based on the EISF dependence with temperature for Mg(BH₄)₂·3TDF, no differences in the reorientational mechanisms are observed upon the phase transition from a monoclinic to triclinic structure.

Fig. 7 The EISF for the BH₄⁻ anions in Mg(BH₄)₂·3TDF determined from 315 K DCS data (using 4.5 Å and 10 Å incident wavelength neutrons) compared with the model curve corresponding to uniaxial reorientations involving either two-fold or three-fold jumps of BH₄⁻ anions (C₂/C₃(BH₄⁻) model).

Another type of dynamics could be identified from Fig. 6, observed from the HFBS measurements of Mg(BH₄)₂·3THF. Order-of-magnitude-slower jump correlation frequencies, in the range of 10⁹ s⁻¹ to 10¹⁰ s⁻¹, when compared to BH₄⁻ anions at the same temperature, could be attributed to the localized hydrogen motion associated with the THF rings. This is further confirmed by investigating possible reorientational mechanisms of the THF molecules in Mg(BH₄)₂·3THF and comparing with the experimentally obtained EISF.

Due to the C₂ symmetry of the THF ring and the Q-independent Lorentzian widths obtained from the QENS fitting of Mg(BH₄)₂·3THF measured on the HFBS instrument, the only possible localized motion of H atoms involves two-fold jumps around the anchored C₂-axis, which passes through the O atom and the middle of the opposite C–C bond within the THF ring [C₂(THF) model]. Such THF reorientations involve much larger moments of inertia than for BH₄⁻ reorientations, since the former also require the jump displacements of the C atoms. In this case, the EISF is given as:

where d₁ = 2.89 Å, d₂ = 2.57 Å, d₃ = 3.70 Å and d₄ = 3.89 Å are distances between the exchanging H atoms, as shown in Fig. S3 in the ESI.†

Considering that the BH₄⁻ anions have an active dynamical behavior in the measured temperature range, the EISF associated with the BH₄⁻ anions should also be included in the calculation of the total EISF for Mg(BH₄)₂·3THF. The total EISF is calculated by including the weighting factors based on the number of H atoms in front of the EISF of each chemical group. Considering that there are a total of 32 H atoms, with 24 present in the three THF rings, and 8 present in the two BH₄⁻ anions, the total EISF is given as:

In the HFBS data measured, the elastic peak contribution is actually the sum of the elastic peak intensities due to both THF and BH₄⁻ reorientations, whereas the fitted quasielastic contribution is due only to the slower THF reorientations. The much faster BH₄⁻ reorientations yield quasielastic scattering that is an order of magnitude too broad to be observed by HFBS and resides as broad background scattering buried under the flat baseline. In order to extract the EISF solely due to the THF molecules, it is necessary to determine the amount of THF elastic scattering intensity by calculating and subtracting the BH₄⁻ elastic scattering intensity from the total elastic scattering measured. This can be done with the aid of eqn (3) and the fact that the EISF behavior for the BH₄⁻ anions is known. The mathematical details are outlined in the ESI.† The resulting experimental EISF for THF reorientations in Mg(BH₄)₂·3THF at 315 K is shown in Fig. 8 and is in good agreement with the theoretically predicted EISF from eqn (2) for two-fold THF jumps. The very different Q-dependent behavior of the comparative EISF plot for BH₄⁻ reorientations in Fig. 8 provides further corroboration that we are indeed observing two-fold THF reorientations in the HFBS data.

Fig. 8 The derived EISF for the THF molecules in Mg(BH₄)₂·3THF determined from 315 K HFBS data matched with the model curve (red) corresponding to uniaxial two-fold jumps [C₂(THF)]. The EISF (black) corresponding to uniaxial two- or three-fold jumps of BH₄⁻ anions [C₂/C₃(BH₄⁻)] is shown for comparison.

Effect of THF concentration on Mg(BH₄)₂·xTHF properties

The structural results show that THF is bound to the Mg²⁺ cation and there is little direct interaction between THF and the BH₄⁻ anion at the investigated temperatures. With three THF molecules bound to each Mg²⁺ cation, it is tempting to predict that the interactions between the Mg²⁺ cation and the BH₄⁻ anion will be weaker in THF-containing compounds. It is therefore surprising that no measurable change was observed in the rotational dynamics of the BH₄⁻ anion between the unsolvated α-Mg(BH₄)₂ and the solvated Mg(BH₄)₂·3THF adduct.

One possible explanation for this is the asymmetry in the Mg²⁺–BH₄⁻ alignment that arises in the THF adducts. In unsolvated α-Mg(BH₄)₂, the BH₄⁻ anions sit approximately equidistant between two Mg²⁺ cations, with distances of around 2.41 Å and are oriented such that one of their C₂ anion symmetry axes is effectively aligned with the Mg–B–Mg bond direction. In Mg(BH₄)₂·3THF, the Mg–B distance is slightly larger, 2.46–2.49 Å, but each BH₄⁻ anion only interacts with one Mg²⁺ cation. The next-nearest Mg²⁺ is more than 6 Å away. One would expect that this decreased Mg²⁺–BH₄⁻ interaction, arising from the competing Mg⁺–THF coordination and evidenced by a larger Mg–B distance would lead to an enhanced BH₄⁻ orientational mobility compared to that in Mg(BH₄)₂. Yet, in the Mg(BH₄)₂·3THF crystal structure, the Mg–B bond direction is not as well aligned with the corresponding BH₄⁻C₂ symmetry axis (see Fig. 7) as in the unsolvated compound. Because of this misalignment, one can expect more steric interference with the adjacent Mg²⁺ cation while performing the BH₄⁻ two-fold reorientation. The counterpositioning of these two opposing effects on BH₄⁻ mobility may indeed result in similar BH₄⁻ reorientational dynamics for Mg(BH₄)₂ and Mg(BH₄)₂·3THF as observed. This is also corroborated by the fact that the BH₄⁻ librational energy around this easy C₂-axis in Mg(BH₄)₂·3THF is located between 25 meV and 28 meV by the DFT PDOS calculations and NVS experiments, which is very similar to the calculated and observed BH₄⁻ librational energy around the Mg–B–Mg axes in unsolvated Mg(BH₄)₂ phases.⁴² Hence, it is not unreasonable to expect the corresponding rotational potential wells and dynamics to also be similar.

In addition to the observed BH₄⁻ mobility, one can speculate that a relatively weak Mg²⁺–THF interaction in Mg(BH₄)₂·3THF is one key factor for enabling the THF rings to be orientationally mobile, undergoing 180° reorientational jumps around their C₂ molecular symmetry axis. In order to explore this proposition further, molecular DFT calculations and additional QENS and NVS experiments were conducted for samples with a lower amount of THF present in the adduct. DFT calculations for Mg(BH₄)₂·THF, Mg(BH₄)₂·2THF and Mg(BH₄)₂·3THF isolated clusters showed a slight lengthening of the Mg–O distance with each additional THF molecule that coordinates to the Mg²⁺ cation. The calculated Mg–O distance for the Mg(BH₄)₂·THF adduct is 2.06 Å, whereas addition of a second THF results in a symmetric structure with two Mg–O distances of 2.11 Å. Adding the third THF molecule results in further distancing of the THF molecules from Mg²⁺ and bond distances of 2.15–2.17 Å. Fig. 9 presents the zero-point corrected electronic energies calculated based on the gas-phase reference models for all compounds, which correspond more closely to low-temperature conditions. The calculated energies show that the first THF molecule binds most strongly with −85.7 kJ mol⁻¹, the second one binds with −60.7 kJ mol⁻¹, and the third one binds with −23.0 kJ mol⁻¹ (Table S2 in the ESI†). Absolute energies and geometries of the structures are provided in Tables S3 and S4 in the ESI.† We expect that the simplicity of the molecular model and its treatment in the gas phase introduce entropic inaccuracies, and as such, result in positive binding free energies. However, because the DFT treatment is consistent for each addition reaction, we can reliably estimate the relative weakening in the binding energy for each subsequent THF molecule. This observation suggests that the reorientational dynamics of the THF rings may be more hindered in a material with a lower amount of solvent present. Indeed, comparative QENS measurements on the samples with the substoichiometric compositional ratio 2Mg(BH₄)₂·THF and 2Mg(BH₄)₂·TDF have shown no observable reorientational dynamics of the THF rings within the resolution window of the spectrometer (Fig. S4 in the ESI†), which is in line with a stronger binding energy of the THF rings to the Mg²⁺ cations. Additionally, no noticeable changes in the H dynamics of the BH₄⁻ anions are observed in this case either (Fig. S5 in the ESI†), leading to the conclusion that the THF solvent does not seem to appreciably affect the BH₄⁻ dynamical behavior in Mg(BH₄)₂·xTHF adducts. (Comparative NVS spectra of these substoichiometric compounds are provided in Fig. S6 in the ESI.†)

Fig. 9 THF binding energies for Mg(BH₄)₂·THF, Mg(BH₄)₂·2THF and Mg(BH₄)₂·3THF obtained from the molecular DFT calculations. Red, green, pink, dark gray, and light gray spheres denote the respective O, Mg, B, C and H atoms.

The presence of a much stronger interaction between the THF and the Mg²⁺ cation for lower THF/Mg(BH₄)₂ stoichiometric ratios implies that using a more THF-deficient Mg(BH₄)₂·xTHF adduct will reduce the amount of THF that might be released from the adduct during the concomitant thermal release of hydrogen. Indeed, thermal desorption measurements showed that such adducts with lower THF/Mg(BH₄)₂ ratios required higher temperatures to liberate THF. Hence, with respect to potential hydrogen-storage applications, the beneficial properties of the THF solvent can be retained over a greater temperature range while reducing the concentration of any unwanted impurity in the released hydrogen.

Conclusions

Various neutron scattering experiments, including NPD, NVS, FWS, and QENS, as well as molecular DFT calculations, were employed to gain deeper insights into the structural, vibrational, and dynamical properties of Mg(BH₄)₂·3THF. Structural analysis has confirmed a lowering of the symmetry upon cooling, from monoclinic C2/c to P1̄ via a triclinic distortion, with the phase transition occurring around 200 K. Vibrational properties are strongly influenced by the THF environment. In particular, splitting in spectral features is observed and explained by the lowering of the overall symmetry. Interestingly, for the monoclinic structure, the orientational mobilities of the BH₄⁻ anions obtained from QENS are not particularly sensitive to the presence of THF and compare well with the mobilities of BH₄⁻ anions in unsolvated Mg(BH₄)₂. In contrast, a decrease in the BH₄⁻ jump frequencies is observed in the triclinic low-temperature structure and correlated with the enhanced steric effects presumably due to the smaller unit cell volume. Uniaxial jump reorientations of the BH₄⁻ anions around a two-fold (C₂, 180° jumps) axis are observed over the whole temperature range. The THF rings are also shown to be dynamically active, with orientational mobilities about an order of magnitude slower than for the BH₄⁻ anions, and with a reorientational mechanism also corresponding to uniaxial two-fold 180° jumps around the THF C₂ symmetry axis. In contrast, no noticeable reorientations of the THF rings are observed in the case of a more THF-deficient 2Mg(BH₄)₂·THF adduct. This may be, at least in part, a consequence of a relatively stronger Mg²⁺–THF bonding interaction, as the Mg²⁺ cation likely coordinates with only one THF molecule in this adduct. This is unlike THF-rich Mg(BH₄)₂·3THF, where each Mg²⁺ cation coordinates with three THF molecules. Indeed, DFT calculations show a decrease in the binding energy with each additional THF coordinated to the Mg²⁺ cation.

Although the physicochemical behavior of this THF-solvated Mg(BH₄)₂ adduct determined from this combined experimental and computational study is of general fundamental interest, the observed and calculated interplay between Mg²⁺ cations, BH₄⁻ anions, and THF adduct molecules also has likely technological relevance toward understanding better the role of THF for improving the hydrogen desorption/absorption cycling properties of Mg(BH₄)₂. The dynamical results for different THF/Mg(BH₄)₂ stoichiometric ratios suggest little direct interaction, in general, between the THF molecules and the BH₄⁻ anions, whereas the THF–Mg²⁺ interaction is strongly ratio-dependent, with stronger interactions occurring for the lower THF/Mg(BH₄)₂ ratios. Hence, we would propose that using lower THF/Mg(BH₄)₂ ratios is beneficial to (i) preventing weakly bound THF from coming free from the Mg²⁺ cation and (ii) disrupting the stability of the crystalline phase leading to a lower melting point and enhanced kinetics.

Authors’ contributions

M. D., T. A. and T. J. U. conceived and planned the experiments. M. D. and T. J. U. carried out the experiments. W. Z., I. N. and B. G. planned and carried out the DFT calculations. M. C. contributed to sample preparation. M. D., M. B., H. W., T. A., B. G., T. G., C. J. and T. J. U. contributed to the interpretation of the results. M. D. took the lead in writing the manuscript. All authors provided critical feedback and helped shape the research, analysis and manuscript.

Legal disclamer

The views and opinions of the authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof. Neither the United States Government nor any agency thereof, nor any of their employees, makes any warranty, expressed or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights.

Conflicts of interest

The authors declare no competing financial interest.

Acknowledgements

M. D. gratefully acknowledges support from the US DOE Office of Energy Efficiency and Renewable Energy, Fuel Cell Technologies Office, under Contract No. DE-AC36-08GO28308. The authors gratefully acknowledge support from the Hydrogen Materials – Advanced Research Consortium (HyMARC), established as part of the Energy Materials Network under the U.S. Department of Energy, Office of Energy Efficiency and Renewable Energy, Fuel Cell Technologies Office. Pacific Northwest National Laboratory is a multi-program national laboratory operated by Battelle for the U.S. Department of Energy under Contract DE-AC05-76RL01830.

References

1. C. Liu, F. Li, L.-P. Ma and H.-M. Cheng, Adv. Mater., 2010, 22, E28–62.
2. N. P. Stadie, J. J. Vajo, R. W. Cumberland, A. A. Wilson, C. C. Ahn and B. Fultz, Langmuir, 2012, 28, 10057–10063.
3. A. F. Gross, J. J. Vajo, S. L. Van Atta and G. L. Olson, J. Phys. Chem. C, 2008, 112, 5651–5657.
4. D. Teichmann, W. Arlt, P. Wasserscheid and R. Freymann, Energy Environ. Sci., 2011, 4, 2767–2773.
5. N. L. Rosi, J. Eckert, M. Eddaoudi, D. T. Vodak, J. Kim, M. O’Keeffe and O. M. Yaghi, Science, 2003, 300, 1127–1129.
6. S. Orimo, Y. Nakamori, J. R. Eliseo, A. Züttel and C. M. Jensen, Chem. Rev., 2007, 107, 4111–4132.
7. K. Chłopek, C. Frommen, A. Léon, O. Zabara and M. Fichtner, J. Mater. Chem., 2007, 17, 3496–3503.
8. Y. Nakamori, K. Miwa, A. Ninomiya, H. Li, N. Ohba, S. Towata, A. Züttel and S. Orimo, Phys. Rev. B: Condens. Matter Mater. Phys., 2006, 74, 045126.
9. N. Hanada, K. Chłopek, C. Frommen, W. Lohstroh and M. Fichtner, J. Mater. Chem., 2008, 18, 2611–2614.
10. G. L. Soloveichik, Y. Gao, J. Rijssenbeek, M. Andrus, S. Kniajanski, R. C. Bowman, S.-J. Hwang and J.-C. Zhao, Int. J. Hydrogen Energy, 2009, 34, 916–928.
11. G. Severa, E. Rönnebro and C. M. Jensen, Chem. Commun., 2010, 46, 421–423.
12. H.-W. Li, K. Kikuchi, Y. Nakamori, K. Miwa, S. Towata and S. Orimo, Scr. Mater., 2007, 57, 679–682.
13. E. G. Bardají, N. Hanada, O. Zabara and M. Fichtner, Int. J. Hydrogen Energy, 2011, 36, 12313–12318.
14. R. J. Newhouse, V. Stavila, S.-J. Hwang, L. E. Klebanoff and J. Z. Zhang, J. Phys. Chem. C, 2010, 114, 5224–5232.
15. I. Saldan, C. Frommen, I. Llamas-Jansa, G. N. Kalantzopoulos, S. Hino, B. Arstad, R. H. Heyn, O. Zavorotynska, S. Deledda, M. H. Sørby, H. Fjellvåg and B. C. Hauback, Int. J. Hydrog, Energy, 2015, 40, 12286–12293.
16. H. Hagemann, V. D’Anna, J.-P. Rapin, R. Černý, Y. Filinchuk, K. C. Kim, D. S. Sholl and S. F. Parker, J. Alloys Compd., 2011, 509(Suppl. 2), S688–S690.
17. E. G. Bardají, Z. Zhao-Karger, N. Boucharat, A. Nale, M. J. van Setten, W. Lohstroh, E. Röhm, M. Catti and M. Fichtner, J. Phys. Chem. C, 2011, 115, 6095–6101.
18. A. Nale, M. Catti, E. G. Bardají and M. Fichtner, Int. J. Hydrogen Energy, 2011, 36, 13676–13682.
19. J. Chen, Y. S. Chua, H. Wu, Z. Xiong, T. He, W. Zhou, X. Ju, M. Yang, G. Wu and P. Chen, Int. J. Hydrogen Energy, 2015, 40, 412–419.
20. Y. Yang, Y. Liu, Y. Zhang, Y. Li, M. Gao and H. Pan, J. Alloys Compd., 2014, 585, 674–680.
21. S. Zhao, B. Xu, N. Sun, Z. Sun, Y. Zeng and L. Meng, Int. J. Hydrogen Energy, 2015, 40, 8721–8731.
22. G. Soloveichik, J.-H. Her, P. W. Stephens, Y. Gao, J. Rijssenbeek, M. Andrus and J.-C. Zhao, Inorg. Chem., 2008, 47, 4290–4298.
23. M. Chong, T. Autrey, C. Jensen, M. Chong, T. Autrey and C. M. Jensen, Inorganics, 2017, 5, 89.
24. The Mention of All Commercial Suppliers in This Paper Is for Clarity. This Does Not Imply the Recommendation or Endorsement of These Suppliers by NIST.
25. J. K. Stalick; E. Prince; A. Santoro; I. G. Schroder and J. J. Rush, Materials Science Applications of the New National Institute of Standards and Technology Powder Diffractometer, in Neutron Scattering in Materials Science II, ed. D. A. Neumann, T. P. Russell, B. J. Wuensch, Materials Research Society, Pittsburgh, 1995, vol. 376, pp. 101–106.
26. T. J. Udovic, C. M. Brown, J. B. Leão, P. C. Brand, R. D. Jiggetts, R. Zeitoun, T. A. Pierce, I. Peral, J. R. D. Copley, Q. Huang, D. A. Neumann and R. J. Fields, The Design of a Bismuth-Based Auxiliary Filter for the Removal of Spurious Background Scattering Associated with Filter-Analyzer Neutron Spectrometers, Nucl. Instrum. Methods Phys. Res., Sect. A, 2008, 588, 406–413.
27. J. R. D. Copley and J. C. Cook, The Disk Chopper Spectrometer at NIST: A New Instrument for Quasielastic Neutron Scattering Studies, Chem. Phys., 2003, 292, 477–485.
28. A. Meyer, R. M. Dimeo, P. M. Gehring and D. A. Neumann, The High Flux Backscattering Spectrometer at the NIST Center for Neutron Research, Rev. Sci. Instrum., 2003, 74, 2759–2777.
29. R. T. Azuah, L. R. Kneller, Y. Qiu, P. L. W. Tregenna-Piggott, C. M. Brown, J. R. D. Copley and R. M. Dimeo, J. Res. Natl. Inst. Stand. Technol., 2009, 114, 341–358.
30. P. Giannozzi, S. Baroni, N. Bonini, M. Calandra, R. Car, C. Cavazzoni, D. Ceresoli, G. L. Chiarotti, M. Cococcioni, I. Dabo, A. D. Corso, S. de Gironcoli, S. Fabris, G. Fratesi, R. Gebauer, U. Gerstmann, C. Gougoussis, A. Kokalj, M. Lazzeri, L. Martin-Samos, N. Marzari, F. Mauri, R. Mazzarello, S. Paolini, A. Pasquarello, L. Paulatto, C. Sbraccia, S. Scandolo, G. Sclauzero, A. P. Seitsonen, A. Smogunov, P. Umari and R. M. Wentzcovitch, J. Phys.: Condens. Matter, 2009, 21, 395502.
31. A. D. Becke, J. Chem. Phys., 1993, 98, 5648–5652.
32. C. Lee, W. Yang and R. G. Parr, Phys. Rev. B: Condens. Matter Mater. Phys., 1988, 37, 785–789.
33. S. H. Vosko, L. Wilk and M. Nusair, Can. J. Phys., 1980, 58, 1200–1211.
34. P. J. Stephens, F. J. Devlin, C. F. Chabalowski and M. J. Frisch, J. Phys. Chem., 1994, 98, 11623–11627.
35. G. A. Petersson, A. Bennett, T. G. Tensfeldt, M. A. Al-Laham, W. A. Shirley and J. Mantzaris, J. Chem. Phys., 1988, 89, 2193–2218.
36. G. A. Petersson and M. A. Al-Laham, J. Chem. Phys., 1991, 94, 6081–6090.
37. M. Valiev, E. J. Bylaska, N. Govind, K. Kowalski, T. P. Straatsma, H. J. J. Van Dam, D. Wang, J. Nieplocha, E. Apra, T. L. Windus and W. A. de Jong, Comput. Phys. Commun., 2010, 181, 1477–1489.
38. K. Momma and F. Izumi, J. Appl. Crystallogr., 2011, 44, 1272–1276.
39. M. Visseaux, M. Terrier, A. Mortreux and P. Roussel, Eur. J. Inorg. Chem., 2010, 2867–2876.
40. E. B. Lobkovskii, L. V. Titov, S. B. Psikha, M. Y. Antipin and Y. T. Struchkov, J. Struct. Chem., 1983, 23, 644–646.
41. Y. Filinchuk, R. Černý and H. Hagemann, Chem. Mater., 2009, 21, 925–933.
42. M. Dimitrievska, J. L. White, W. Zhou, V. Stavila, L. E. Klebanoff and T. J. Udovic, Phys. Chem. Chem. Phys., 2016, 18, 25546–25552.
43. B. Cadioli, E. Gallinella, C. Coulombeau, H. Jobic and G. Berthier, J. Phys. Chem., 1993, 97, 7844–7856.
44. M. I. Aroyo, J. M. Perez-Mato, C. Capillas, E. Kroumova, S. Ivantchev, G. Madariaga, A. Kirov and H. Wondratschek, Z. Kristallogr. – Cryst. Mater., 2009, 221, 15–27.
45. M. I. Aroyo, A. Kirov, C. Capillas, J. M. Perez-Mato and H. Wondratschek, Acta Crystallogr., Sect. A: Found. Crystallogr., 2006, 62, 115–128.
46. M. Bee, Quasielastic Neutron Scattering, Principles and Applications in Solid State Chemistry, Biology and Materials Science, CRC Press, Bristol, England, Philadelphia, 1988.
47. D. Blanchard, J. B. Maronsson, M. D. Riktor, J. Kheres, D. Sveinbjörnsson, E. Gil Bardají, A. Léon, F. Juranyi, J. Wuttke, K. Lefmann, B. C. Hauback, M. Fichtner and T. Vegge, J. Phys. Chem. C, 2012, 116, 2013–2023.
48. A. V. Skripov, A. V. Soloninin, O. A. Babanova, H. Hagemann and Y. Filinchuk, J. Phys. Chem. C, 2010, 114, 12370–12374.

---

Footnote

† Electronic supplementary information (ESI) available. CCDC 1963436 and 1963437. For ESI and crystallographic data in CIF or other electronic format see DOI: 10.1039/c9cp03311d

---