3.1. Y(BH4)3·3NH3
The behavior of the proton spin-lattice relaxation rate measured at two resonance frequencies ω/2π (14 and 28 MHz) in Y(BH4)3·3NH3 over the temperature range of 8–298 K is shown in Fig. 1. As can be seen from this figure, the temperature dependence of the relaxation rate is dominated by two overlapping frequency-dependent peaks near 118 K and 96 K. Such peaks are typical of the relaxation mechanism due to motionally-modulated dipole-dipole interactions between nuclear spins [36]; they are expected to occur at the temperatures at which the proton jump rate becomes nearly equal to the resonance frequency ω (in our case, ω ~ 108 s-1). In addition to the two strong peaks, there is another small-amplitude frequency-dependent peak at very low temperature (~ 20 K).
For borohydrides, the relaxation rate peaks are usually associated with BH4 reorientations strongly modulating the dipole-dipole 1H – 1H and 1H – 11B interactions [27, 32]. However, since in Y(BH4)3·3NH3, both BH4 and NH3 groups contain H atoms, additional experiments are required for the peak assignment. For this purpose, we may use the 11B spin-lattice relaxation rate measurements. Indeed, since B atoms are close to H atoms in BH4 groups, but rather far from H atoms in NH3 groups, we can expect that the measured 11B spin-lattice relaxation rate should be governed by the motion of BH4 groups. The behavior of the 11B spin-lattice relaxation rate in Y(BH4)3·3NH3 at 28 MHz is presented in Fig. 2. Comparison of Figs. 1 and 2 shows that in the region of 50–290 K, the temperature dependence of the 11B relaxation rate resembles that of ; in particular, it also exhibits two peaks at nearly the same temperatures as the 1H relaxation rate peaks. Thus, we can conclude that the peaks near 118 K and 96 K originate from BH4 reorientations. As typical of many borohydrides [27, 32, 39, 40], the presence of two peaks may be related to a coexistence of two types of reorientational motion with different characteristic jump rates. In the low-temperature region, we have not found any signs of the peak (see Fig. 2). This means that the low-temperature feature cannot be attributed to BH4 motion; most probably, it may be ascribed to NH3 reorientations.
It should be noted that the atomic motions revealed in Y(BH4)3·3NH3 by our spin-lattice relaxation measurements are very fast. In fact, the position of the peak may serve as an indicator of the H mobility in different systems. Since at the temperature of the peak the hydrogen jump rate (governed by the Arrhenius-type relation) is expected to reach ω ~ 108 s-1, in the systems with higher H jump rates, the peaks should occur at lower temperatures. For most of the studied borohydrides, the peaks due to BH4 reorientations are observed at temperatures considerably exceeding 120 K [41]; in particular, in the pristine Y(BH4)3, the maximum of the proton spin-lattice relaxation rate has been found near 365 K [37]. Thus, the inclusion of NH3 molecules in the structure of Y(BH4)3·3NH3 strongly enhances the reorientational mobility of BH4 groups. This conclusion is consistent with the results QENS experiments [38]. The additional low-temperature peak observed near 20 K and attributed to NH3 motion is reminiscent of the case of rotational tunneling [42, 43]. However, an unambiguous evidence for the low-temperature rotational tunneling of NH3 groups can be obtained only from inelastic neutron scattering experiments with very high energy resolution. The characteristic tunneling peaks at the energies of ~ 30 µeV and ~ 90 µeV have been observed recently in the low-temperature QENS experiments for Y(BH4)3·3NH3 [38].
The evolution of the proton NMR spectra for Y(BH4)3·3NH3 (shown in Fig. S1 of the Supplementary Information) is also consistent with high H mobility down to low temperatures. The “rigid lattice” second moment of the 1H NMR line calculated on the basis of the structural data for Y(BH4)3·3NH3 [25] is 3.59×1010 s-2. This value corresponds to the line width Δν (at half-maximum) of 71.1 kHz, if we assume a Gaussian shape of the low-temperature NMR line. The experimental value of Δν at T = 6 K (52.7 kHz) is considerably smaller than the estimated “rigid lattice” one. This means that even at the lowest temperature of our measurements, the dipole-dipole interactions are partially averaged by H motion. As the temperature increases, it can be seen from Fig. S1 that the line narrowing starts already in the low-temperature region (T < 16 K).
The standard model of the nuclear spin-lattice relaxation due to motionally-modulated dipole-dipole interaction [36] predicts that in the limit of slow motion (ωτ » 1), is proportional to ω-2τ -1, while in the limit of fast motion (ωτ « 1), is proportional to τ, being frequency-independent. If the temperature dependence of the H jump rate is governed by the Arrhenius law,
τ -1 = τ0-1exp(− Ea/kBT), (1)
where Ea is the activation energy and kB is the Boltzmann constant, a plot of vs. T -1 is expected to be linear in the limits of both slow and fast motion with the slopes of − Ea/kB and Ea/kB, respectively. Figure 3 shows such a plot at T > 50 K (i. e., in the region where the relaxation data should be dominated by BH4 reorientations). Although this plot bears some resemblance to the predictions of the standard model, it is evident that the behavior of the experimental data deviates from the model predictions. In particular, the high-temperature slope of the experimental vs. T -1 plot appears to be steeper than the low-temperature one, and the frequency dependence of at the low-temperature slope is considerably weaker than the predicted ω-2 dependence. These features suggest the presence of a certain distribution of H jump rates [44].
For parametrization of the proton spin-lattice relaxation data related to BH4 reorientations, we have used the two-peak model analogous to that described in Ref. [40]. We have not tried to fit the relaxation rate peak near 20 K (attributed to the motion of NH3 groups), since this peak has a rather small amplitude. The two-peak model is based on a coexistence of two different reorientational processes characterized by the jump rates τi-1 (i = 1, 2). For the faster of these processes (i = 1), we assume the jump rate distribution, which is modeled by a Gaussian distribution of the activation energies. The details of the two-peak model are presented in the Supporting Information. The model parameters are the average activation energy and the dispersion of the activation energy distribution for the faster process, the activation energy Ea2 for the slower process, the corresponding pre-exponential factors τ01 and τ02 of the Arrhenius law, and the amplitude factors ΔM1 and ΔM2 characterizing the strength of dipole-dipole interactions modulated by the ith process. These parameters have been varied to give the best fit of the model to the experimental data at two resonance frequencies simultaneously. The results of such a simultaneous fit are shown by solid curves in Fig. 3; the dashed curves in this figure show the individual contributions of the two reorientational processes. The model parameters resulting from the fit are = 69(4) meV, = 10(1) meV, τ01 = 1.1(1)×10–12 s, and ΔM1 = 3.65(2)×109 s-2 for the faster process, and Ea2 = 126(1) meV, τ02 = 7.5(1)×10–14 s, and ΔM2 = 1.74(1)×109 s-2 for the slower process. Note that the small values of the activation energies found for both motional processes in Y(BH4)3·3NH3 are typical of those borohydride-based systems that retain high reorientational mobility down to low temperatures [27, 32].
Even smaller activation energy values (~ 35 meV and ~ 45 meV) were found from the analysis of QENS data for Y(BH4)3·3NH3 [38]. It should be noted, however, that a comparison of the activation energies derived from QENS data with those obtained from proton spin-lattice relaxation measurements requires a certain caution. Because of the limited energy resolution of the available neutron spectrometers, it is usually quite problematic to trace the changes in the quasielastic line width over the dynamic ranges exceeding 1–2 orders of magnitude. On the other hand, due to non-monotonic dependence of on , the proton spin-lattice relaxation measurements generally probe wider dynamic ranges of H jump rates (4 orders of magnitude or even more [35]). Additional problems may occur in the case when a certain distribution of H jump rates is present [46]. While for spin-lattice relaxation measurements over wide ranges of temperature and the resonance frequency, the effects of this distribution could be easily modeled [44], it is difficult to detect the presence of a jump rate distribution from the shape of QENS spectra. If a broad distribution exists, the standard analysis of QENS spectra tends to underestimate the changes in the quasielastic line width with temperature [46]. Indeed, the faster part of the distribution may be outside the energy “window” of a neutron spectrometer (contributing only to the flat background of QENS spectra), and the slower part of the distribution may be below the spectrometer resolution. As the temperature changes, different parts of the H jump distribution may appear within the energy “window” of a neutron spectrometer.
In order to discuss possible types of BH4 reorientations, we have to consider the local environment of the BH4 tetrahedra in Y(BH4)3·3NH3. Note that all [BH4]− anions in Y(BH4)3·3NH3 experience a similar local environment [25]. This environment is schematically shown in Fig. 4 on the basis of the structural results [25].
As can be seen from this figure, the BH4 tetrahedron is coordinated to a single Y3+ ion via the triangular face, and to a number NH3 groups via the edges or vertices. Generally, a BH4 tetrahedron can rotate around different 3-fold and 2-fold symmetry axes. It should be noted that the coordination of a BH4 tetrahedron to a single metal ion via a triangular face is very favorable for the occurrence of fast reorientational motion, since the rotation around the 3-fold symmetry axis along the Y – B line does not break any of the three Y···H bonds. Similar coordination environments have been found to facilitate fast BH4 reorientations with low activation energies in the hexagonal phase of LiBH4 [45] and in LiLa(BH4)3Cl [31]. Therefore, it is reasonable to attribute the faster process of BH4 reorientations in Y(BH4)3·3NH3 to the rotation around the 3-fold symmetry axis along the Y – B line (vertical axis in Fig. 4). This is also consistent with the behavior of the elastic incoherent structure factor (EISF) found in the recent QENS experiments [38].
3.2. Y(BH4)3·7NH3
For this system, the reorientational motion of BH4 groups is found to be even faster than for Y(BH4)3·3NH3. The behavior of the proton spin-lattice relaxation rates at two resonance frequencies in Y(BH4)3·7NH3 is shown in Fig. 5. The peaks are observed near 98 K and 73 K, and in addition, there is also a well-pronounced peak near 33 K.
The results of the 11B spin-lattice relaxation rate measurements at 28 MHz and 14 MHz (in the region of the low-temperature peak) for Y(BH4)3·7NH3 are shown in Fig. 6. It can be seen that the peaks are observed at nearly the same temperatures as the corresponding peaks. In particular, in contrast to the case of Y(BH4)3·3NH3, the low-temperature 1H peak in Y(BH4)3·7NH3 is accompanied by the strong 11B relaxation rate peak. These results suggest that all the observed 1H relaxation rate peaks are dominated by BH4 reorientations. However, this assignment does not exclude the possibility that NH3 groups also participate in ultrafast low-temperature motion, since the peak due to NH3 motion is expected to have a small amplitude, so that it may be hidden within the relaxation rate peak due to BH4 reorientations. It should be noted that the tunneling peaks at ~ 1 µeV and ~ 2.5 µeV attributed to NH3 groups have been found in the low-temperature QENS spectra of Y(BH4)3·7NH3 [38].
The extremely high reorientational mobility of BH4− anions in Y(BH4)3·7NH3 may be related to the coordination environment of BH4 groups in this compound. Although the structure of Y(BH4)3·7NH3 includes three crystallographically inequivalent BH4 groups [23], the local environment of all these groups has similar features. In particular, in contrast to the case of Y(BH4)3·3NH3, there are no Y3+ ions in the nearest-neighbor environment of BH4−. As an example, Fig. 7 shows the coordination environment of one of the BH4 groups in Y(BH4)3·7NH3. It can be seen that the BH4− anion is surrounded by a number of NH3 molecules, being coordinated via relatively weak dihydrogen bonds. Such a loose coordination suggests low energy barriers for BH4 reorientations.
As in the case of Y(BH4)3·3NH3, the low-temperature proton NMR line width in Y(BH4)3·7NH3 appears to be considerably smaller than that estimated for the “rigid lattice”. The evolution of the 1H NMR spectra for Y(BH4)3·7NH3 is shown in Fig. S2 of the Supplementary Information. The “rigid lattice” second moment of the 1H NMR line calculated on the basis of the structural data for Y(BH4)3·7NH3 [23] is 3.68×1010 s-2. This value corresponds to the line width Δν (at half-maximum) of 72.1 kHz, if we assume a Gaussian shape of the low-temperature NMR line. The experimental value of Δν at T = 18 K (42.8 kHz) is considerably smaller than the estimated “rigid lattice” one; this suggests a partial averaging of the dipole-dipole interactions by H motion.
For parametrization of the proton spin-lattice relaxation results for Y(BH4)3·7NH3, we have used the model similar to that presented above. However, since the experimental data exhibit three peaks and the well-pronounced “shoulder” near 140 K (Fig. 5), at least 4 types of reorientational motion are required to describe the data. As previously, for the two faster motional processes, we assume a certain distribution of the jump rates (modeled by a Gaussian distribution of the activation energies); this is necessary to account for the frequency dependence of at low temperatures. Thus, the parameters of the model are , (i = 1, 2), Eai (i = 3, 4), τ0i (i = 1, 2, 3, 4), and the amplitude factors ΔMi (i = 1, 2, 3, 4). These parameters have been varied to give the best fit of the model to the experimental data at two resonance frequencies simultaneously. The results of such a simultaneous fit over the temperature range of 18–268 K are shown as solid red curves in Fig. 5; the dashed curves in this figure represent the individual contributions of the four motional processes. The corresponding fit parameters are = 18(2) meV, ΔEa1 = 4(1) meV, τ01 = 2.0(2)×10–11 s, and ΔM1 = 1.9(2)×109 s-2 for the fastest motional process; for the other processes they are = 78(7) meV, ΔEa2 = 12(1) meV, τ02 = 2.6(2)× 10–14 s, and ΔM2 = 2.6(2)×109 s-2; Ea3 = 108(10) meV, τ03 = 6.4(6)×10–14 s, and ΔM3 = 9.1(8)×108 s-2; Ea4 = 115(10) meV, τ04 = 3.5(3)× 10–13 s, and ΔM2 = 5.6(5)×108 s-2. It is interesting to note that the average activation energy for the fastest reorientational process is rather close to that found from the QENS experiments in Y(BH4)3·7NH3 (23.8 ± 4.5 meV [38]). However, as discussed above, such a comparison should be treated with caution. In any case, we can conclude that BH4− anions in Y(BH4)3·7NH3 retain extremely high reorientational mobility down to low temperatures, and the corresponding activation energies for reorientations are very small.