LiBH4 in Aerogel: Ionic Motions by NMR - The Journal of Physical

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LiBH in Aerogel: Ionic Motions by NMR Hongyang Zou, Anton Gradišek, Samuel B Emery, John J. Vajo, and Mark S. Conradi J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.7b04520 • Publication Date (Web): 05 Jul 2017 Downloaded from http://pubs.acs.org on July 10, 2017

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The Journal of Physical Chemistry

LiBH4 in Aerogel: Ionic Motions by NMR Hongyang Zou1, Anton Gradišek2, Samuel B. Emery1, John J. Vajo3, and Mark S. Conradi1,4,* 1234-

Washington University, Dept. of Physics-1105, Saint Louis, MO 63130, USA Jozef Stefan Institute, Jamova 39, SI-1000 Ljubljana, Slovenia HRL Laboratories LLC, 3011 Malibu Canyon Road, Malibu, CA 90265, USA ABQMR, 2301 Yale Blvd. SE, Suite C2, Albuquerque, NM 87106, USA

Submitted to the Journal of Physical Chemistry, May 10th, 2017. * author for correspondence

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Abstract LiBH4 in nm-size pores of carbon aerogel displays a motionally-narrowed fraction of its hydrogen NMR spectrum. The fraction of mobile spins grows with decreasing pore size, indicating that the mobile spins are those nearest the aerogel walls. Here, we report selective inversion experiments to measure the rate of exchange between the mobile and immobile BH groups. We find the exchange time constant to be nearly temperature independent at ~5 ms. This unexpected result is explained by a broad distribution of motion rates, all thermally activated. The net effect is to place the border between the spins contributing to the broad and narrow resonance peaks always at the same rate of motion, leading to nearly the same rate of exchange. In addition, exchange within the mobile fraction prevents the development of an extremely sharp resonance component from the fastest moving BH. We also report measurement of hydrogen T1 at 298 K as a function of hydrogen frequency, obtained by fast field-cycling relaxometry. The variation is nearly ∝ , demonstrating a broad distribution of Li+ hopping rates, reflecting the disordered environment in the nm-pores.

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Email addresses: Hongyang Zou [email protected] Anton Gradisek [email protected] Samuel B. Emery [email protected] J.J. Vajo [email protected] Mark S. Conradi [email protected]

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INTRODUCTION LiBH4 is a candidate for solid-state hydrogen storage. While its mass-fraction of reversibly stored H is large (13.6 wt %), the kinetics of hydriding and dehydriding are slow. Thus, the behavior of LiBH4 in the nm-size pores1 of a carbon aerogel has been studied.2,3 The hydrogen NMR line displays a motionally narrowed component (~1 kHz wide) in addition to the broad component (~25 kHz wide) characteristic of pure LiBH4.4

The observed narrow-component reflects translational hopping of the BH groups. At 298 K, the rate of BH reorientation is of order 1011 s-1 in pure LiBH4, ensuring that reorientations remain more than sufficiently rapid to average intramolecular interactions at and above 120 K5,6,7,8.

For LiBH4 in aerogel, the fraction of spins in the motionally narrowed peak increases with temperature and increases with smaller pore size (larger surface/volume ratio)4. This suggests that at any temperature, there is a broad distribution of BH hopping rates; the smallest rates are too slow to narrow the spin resonance while the fastest rates (faster than 105 s-1) are effective at line narrowing9,10.

The existence of a narrowed NMR component in small particles, supported by a scaffold or not, is not unique to LiBH4. Our group has presented11,12 narrowed components in the ball-milled hydrides NaMgH3 and MgH2. Heitjans and co-workers have reported13,14 narrowed components that grow with temperature, for Li+ in nanocrystalline Li2O-Al2O3 and for F- in nanocrystalline CaF2 and BaF2: CaF2. We focus on LiBH4 in aerogel because it displays such a large narrowed-fraction in the vicinity of room temperature. But we believe the underlying physics is the same for most or all of these systems.

Our model is one of layers of BH groups, with the layers closest to the aerogel wall (i.e., the surface of the LiBH4 particle) moving fastest and the inner layers (where disruption of the crystal structure is least) moving slowest. Because the various layers contact each other, there must be 4


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exchange between the layers. We describe selective inversion NMR experiments to measure the exchange of spins between the mobile and immobile pools of spins. The surprising result is that the exchange rate is nearly independent of temperature. This result and the result of field-cycling relaxometry ( varies nearly as ) are both in accord with the existence of a broad distribution of hopping rates of the BH and Li ions, due to the disorder imposed by the nearby scaffold wall.

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EXPERIMENTAL Sample preparation: LiBH4 from Sigma-Aldrich was used without further purification. Carbon aerogel with 9 nm average pore size was obtained from HRL, Malibu CA. The pore size distribution is peaked at 9 nm; 75% of the volume is contained within the pores of sizes between 4 and 12 nm. Carbon aerogel cubes were first dried under dynamic vacuum at 370 0C for 3 hours. Then LiBH4 was melt infused over a 5 minute interval into a single monolith of aerogel at 270--300 0C. The proportion of LiBH4 to aerogel was chosen to yield ~90% filling of the pores, based on pore volume data (0.648 mL/g for 9 nm aerogel) from HRL. Any LiBH4 outside of the carbon aerogel cube was removed by scraping with a razor blade; typically this removed 10% of the total LiBH4. Thus the filling of the volume of the pores by LiBH4 is close to 80%. All handling and infiltration were performed under N2 atmosphere. The LiBH4-in-aerogel samples were sealed in glass tubes with 1 atm of Ar gas for NMR studies.

NMR: Hydrogen NMR at 85.03 MHz (2.0 T) was performed in an iron-core electromagnet (Varian) with

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F field-frequency stabilization. A homebuilt NMR spectrometer was used with a low-Q

probe for fast (2 μs) recovery. Phase cycling of rf pulses and data accumulation were performed with locally-developed FIDo software.

Temperature was controlled by a thermally-regulated (Omega controller) stream of air for work above 298 K. For lower temperatures, liquid N2 was boiled and the resulting gas heated to the desired temperature. All temperatures were measured by a type-T thermocouple within 2 cm of the sample, in the flowing gas stream.

To investigate exchange between the mobile and immobile pools of BH, selective inversion of the narrowed resonance was used. In principle, selective inversion uses a long pulse of 1800 nutation; the pulse bandwidth Δf is approximately the reciprocal of the pulse duration Δt. Because the pulse is long, the amplitude B1 must be small to satisfy the nutation equation, (1)

∆ = . 6


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We found it simple to use a Dante inversion pulse, as presented in Figure 1. Here the long 1800 nutation is split into 18 pulses of 100 each (1.1 μs). The spacing between the pulses (here, 7 μs) is adjusted to make the overall Dante length Δt have the correct value. The time-average B1 is reduced by the spaces between the pulses. Here Δt for 18 pulses and 17 spaces is 139 μs, giving a bandwidth of the order of 7 kHz. This is wide enough to fully invert the narrowed resonance and is narrow compared to the broad resonance. Following the selective inversion, exchange and relaxation occur during the recovery interval of duration t. Finally, a hard 900 pulse (9 μs) excites an FID which is recorded.

Field-cycling relaxation measurement: T1 of the LiBH4-in-aerogel sample was measured at 298 K as a function of magnetic field B (corresponding to proton Larmor frequency, = /2, where is the proton gyromagnetic ratio), using a fast field-cycling relaxometer SPINMASTER FFC-2000 (Stelar, s.l.r.). This method allows us to measure spin-lattice relaxation rates over several orders of magnitude of magnetic field, which is made possible by the fast switching time of the Stelar electromagnet (~1 ms). There are two types of sequences used for the measurements. For higher fields (from 20 to 6 MHz), a non-polarized sequence is used. Here, magnetization is first left to relax to zero at zero field. Next, a magnetic field at a chosen strength is switched on for time τ, after which the magnetization build-up M is measured by a single 90° pulse at the acquisition field, in our case 9.25 MHz. The τ-dependence of M is used to determine T1. For lower field strengths, a pre-polarized sequence is used. Spins are first polarized at high field (20 MHz) and then left to relax at a chosen low field. The acquisition again takes place at 9.25 MHz. Provided the times for the field to rise and fall are constant, with only the time τ spent at the adjustable (relaxation) field varying, the analysis is straightforward with M obeying = / + ,

(2)

with A and C being constants. The measurements reported here by field-cycling span 50 kHz (1.2 mT) to 20 MHz (0.47 T); they are augmented by static field work at 85.03 MHz and 299.67 MHz (in a 7.04 T superconducting magnet). In principle, the measurements with the field-cycling method are possible down to 5 kHz; however, in our sample, T1 becomes too short to measure below 50 kHz.

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RESULTS AND DISCUSSION Hydrogen NMR spectra of LiBH4 melt-infused into 9 nm pore-size carbon aerogel reveal a superposition of clearly distinct broad and narrow components. The fraction of spectral intensity (area) in the narrow component is presented in Figure 2, together with the previously published data4 from 13 and 25 nm aerogels. This is also the fraction of translationally mobile BH groups on the NMR time-scale of approximately 10" s. From 223 K to 423 K, the broad component's linewidth changes from 25 kHz to 15 kHz, while the narrow component’s linewidth changes from 5 kHz to 0.8 kHz. For all three materials, the mobile fraction increases with increasing temperature and with increasing surface/volume ratio (decreasing pore size). This supports the model of the mobile BH groups residing closest to the aerogel walls; this leaves the immobile fraction in the particle’s core, farthest from the walls where disruption of the crystalline order is smallest.

To investigate exchange between the mobile and immobile pools of BH, selective inversion of the narrowed resonance was used. Typical spectra for several values of recovery interval t are displayed in Figure 3 for 298 and 403 K. The long-t spectra are fully recovered (t >> T1) and show the superposition of narrow and broad components. It is evident that the Dante pulse nicely inverts the narrow component, but it is also clear that the broad component is nearly saturated (area driven to zero) by the Dante pulse. However, the important aspect here is that the two components are treated very differently by the pulse – the narrow component’s spin temperature10 is inverted while the broad component’s spin temperature becomes nearly infinite after the Dante pulse. In Figure 3, the narrow peak disappears on a short time scale by broad-narrow exchange; subsequently the overall resonance returns to equilibrium on a longer time scale by T1 relaxation.

We were surprised by the similar time-evolution of the spectra in Figure 3 and of spectra at other temperatures. Specifically, the time for appreciable broad-narrow exchange to occur is not a strong function of temperature. We were initially surprised because all of the fundamental motions here are certainly thermally activated, so their rates should be strongly increasing 8


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functions of temperature. We note that spin diffusion, the transport of spin magnetization by dipolar spin flip-flops, is not expected to play a role in broad-narrow magnetization exchange. The spins in the narrow line are motionally narrowed; their dipole interactions (including interactions with the broad spins) are time-averaged to zero. Of course, spin diffusion is effective at transporting magnetization within the broad component.

This is quantified at 298 K in Figure 4, where the recovery time t is on a logarithmic axis. The intensity (spectral area) of the narrow component (filled circles, right axis) shows a two-step time evolution, with exchange dominating at short time and T1 relaxation at long time. The data are well-described by the solid curve fit to a sum of two exponentials, with a short time constant (exchange) of 4.6 ms and a long time constant (T1) of 315 ms. This interpretation is confirmed by the recovery time t dependence of the total intensity (the sum of broad and narrow parts, represented by open triangles, left axis); the total area is insensitive to exchange of spin magnetization between the two components. Indeed, the dashed-line fit to a single exponential is a good description of the data. The time constant T1 of 343 ms is very close to the longer time constant of the fit to the narrow component intensity, as expected for a system with much faster exchange than relaxation.

The exchange of BH groups between the narrow and broad components brings the spin temperatures of these components towards equality. In all that follows, we use the reciprocal spin temperature β (= 1/T) because the spin energy in the high-temperature limit is proportional to β and not to T. Also, the spin magnetization is linear10 in terms of the reciprocal temperature β.

The resonance intensity (or spectral area, A) is proportional to β; this proportionality serves to define β from experimental spectra. At thermal equilibrium (so the spin temperatures equal the physical lattice temperature 1/βL), the spectral area Aeq is proportional to βL. Thus, a measured area AN of the narrow (N) component is described by reciprocal spin temperature βN, #$ = #

%& '(

%&

.

(3)

Similarly, for the broad (B) component, 9



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#) = #

%* '(

%*

(4)

Equations (3) and (4) allow interpretation of the experimental spectra in terms of the reciprocal spin temperatures βN and βB and allow the evolution of the reciprocal temperatures towards equality to be followed.

Figure 5 presents the difference in reciprocal spin temperatures βN and βB as a function of recovery time t from data such as in Figure 3, for three different temperatures with a time axis that is logarithmic. The difference βN - βB decays to zero at times t that are short compared to T1 (e.g., see data in Figure 4), confirming that exchange is completed before appreciable relaxation has occurred. The decays are not single exponentials, particularly at the lower temperatures, as implied by the poor fit of the 298 K data by the solid curve. This indicates that a broad distribution of exchange rates15 is present. This distribution is more evident in Figure 5 than in Figure 4, probably because the second, slower decay (time T1) in Figure 4 complicates the presentation.

Figure 5 makes clear that the characteristic exchange time (say for βN - βB to fall by 1/e) is not a strong function of temperature, a result suggested qualitatively from Figure 3.

The exchange time constant τex and relaxation time T1 are plotted in Figure 6 for LiBH4 in 9 nm carbon aerogel as functions of temperature. The relaxation times are from data as shown in Figure 4, displaying separately the narrow component and total intensities (broad plus narrow). The exchange times are from the faster recovery piece of the narrowed intensity (solid triangles) and from the best single exponential fit to the decay of βN - βB, as in Figure 5 (open triangles in Figure 6). There is no exchange time constant data at or below 200 K because it is difficult to separate the narrow and broad components at low temperatures and difficult to separate the two relaxation contributions. The T1 values from the two sources agree very well. The exchange time values agree only reasonably, with the exchange time exhibiting a plateau of ~5 ms. The difference between the two measurements of the exchange time constant becomes larger at low temperatures, where the separation of the exchange and T1 time scales is smaller. We believe the 10


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difference in our two measurements is due to the non-exponential nature of the exchange process, especially at lower temperatures, as evidenced in Figure 5. The difference of the two measurements is large enough that the weak apparent temperature dependence of the exchange time constant in Figure 6 cannot be taken as significant.

Our model of translational hopping motion of BH groups in this system is that there is a wide and continuous distribution of rates ωH, with the fastest rates nearest the wall of the aerogel pore and the slowest rates in the particle interior, far from the wall. At any fixed location, the hopping rate ωH is thermally activated. From standard line narrowing theory, ωH must be greater than ~105 s-1 to narrow the intermolecular-dipole broadened line9,10. Thus, the divide between the narrowed region and the broad region will be wherever the motion rate is of order 105 s-1. This divide moves deeper into the particle, away from the wall, with increasing temperature.

The rate of broad-narrow magnetization exchange is essentially given by the rate of BH ions crossing the divide. Thus, the near temperature-independence is a natural result of our model, since ωH at the divide has a rate independent of temperature. Evidently, an approximately constant fraction of the hopping events at the divide results in exchange across this divide. In a model of a spherical pore, the exchange area becomes slightly smaller (but we ignore this small change) as T grows and the boundary moves inward toward smaller radius. The fact that 5 ms is so much longer than 10-5 s indicates that only a small fraction of hops (on the mobile side of the divide) manage to cross the divide and become exchange events.

Beyond our two-pool (narrow and broad) model, exchange between more mobile and less mobile parts within the narrowed region is important too. That is, at any given temperature, the narrowed region has BH moving at a variety of rates. We recall that the narrowed linewidth + obeys + = + /, where M2 is the mean-squared dipole interaction10,16. If there were no exchange amongst the narrowed spins at any given temperature, the fastest moving ions (the ones that narrowed at the lowest temperature) would yield a very sharp peak. The narrowed line would be composed of Lorentzians with widths ranging from “just barely narrowed” to extremely 11



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narrow, particularly at high temperatures. We note this is not evident in the spectra of Figure 3 nor in the previously published spectra4. The exchange of BH ions between the layers with different ωH means that a spin that moves very fast now will later be moving more slowly and will eventually be moving too slowly for line narrowing. This exchange prevents the development of a very sharp part of the narrowed peak (or equivalently, a very long time tail on the free induction decay). As evident in Figure 3, the narrowed component has a somewhat reduced width at elevated temperature; this reflects the exchange-averaging of rates of motion. That is, at higher temperature, the distribution of ωH values extends to higher values, but still extends down to ~105 s-1, so the narrowed peak is only somewhat narrower. We note that all of the observed linewidths of the narrow component have negligible contributions from the external field inhomogeneity of the 2.0 T electromagnet.

The disorder in LiBH4-in-aerogel is also evident in the hydrogen spin-lattice relaxation time T1. In pure LiBH4, in the ordered phase below 112 0C (385 K), T1 is controlled entirely by BH reorientations5,7,8. At all temperatures above 200 K, the reorientations are much faster than the angular resonance frequency ω0, so T1 should be independent of frequency. For LiBH4 in aerogel, T1 at 85 and 90 MHz follows T1 of pure LiBH44,5,7,8 from 200 K to 270 K, but by 295 K the in-aerogel T1 is noticeably smaller than the T1 of pure LiBH4. This indicates an additional relaxation mechanism has appeared, due to Li+ ion hopping17.

In the ordered phase of pure LiBH4, the lithium ions are not mobile on the relevant time scale (10- − 10/0). But in the disordered phase of pure LiBH4 above 385 K, the motion of Li+ ions controls the hydrogen T1 through Li-H dipole-dipole interaction5,8,18. This is confirmed by lithium-7 T1 measurements.18 With the disorder present in LiBH4 in aerogel, lithium ion motion is present and is evident in the hydrogen T1 at 85 MHz even at room temperature. Its effect on the hydrogen T1 is even larger at low frequencies. In bulk solid solutions lithium iodide - lithium borohydride, a similar effect on the hydrogen T1 from Li+ ion motion has been reported19,20,21, together with suppression of the order-disorder transition.

Field-cycling T1 data at 298 K for LiBH4 in 9 nm carbon aerogels are presented in Figure 7. Over 12


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./6 the range from 50 kHz to 20 MHz, follows a 1234 frequency dependence (here frlx is the

frequency where relaxation occurs). The same behavior is found at 371 K (not shown). Clearly, this is not due to BH reorientations, as these are very fast (in pure LiBH4, ~1011 s-1). We believe the BH translational hopping in the aerogel does not extend to sufficiently high frequencies (from Figure 2, these are only fast enough to narrow the resonance for a fraction of BH), leaving Li+ motion as the source of this relaxation. The disorder from the aerogel walls allows Li+ motions, even at temperatures below the order-disorder transition of pure LiBH4. We note that in many disordered systems22-26, the spectrum of motions follows approximately 1/f, so the result here is not unexpected. At the highest frequencies, 85 and 300 MHz, the hydrogen T1 of LiBH4 in aerogel becomes less frequency dependent; here the relaxation contribution from the Li ion motion is weaker and is weaker than the frequency independent contribution from the BH reorientations.

The relaxation rates of the two processes, from BH reorientations and from Li ion hopping, should add as rates. Thus we expect

%

= .- 7 + 8.

(5)

9:;

Here 0.8 s was chosen to best fit the 85 and 300 MHz data points. And parameter A represents the strength of the relaxation due to Li+ ion motion. The prediction of this equation appears in Figure 7 as a red dashed curve and describes the data well.

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CONCLUSIONS A fraction of BH ions in LiBH4 in carbon aerogel are mobile on the NMR time scale of 10-5 s above 223 K, as evident by a narrowed resonance component. The mobile fraction increases with temperature, as expected for a thermally activated process with a broad and continuous distribution of motion rates. The fraction also increases with decreasing pore size (increasing surface/volume ratio), demonstrating the important role of the aerogel walls. Our model has the fastest moving BH nearest the walls, with the slowest moving ions in the particle core.

Exchange of BH between the narrow and broad resonance lines has been measured with selective inversion of the narrow peak with a Dante pulse sequence. The exchange occurs on a short timescale, ~5 ms, much shorter than T1. The exchange time constant is approximately independent of temperature, which is unexpected for an activated process. However, the divide between the BH ions yielding the narrow and broad resonances moves into the particle’s interior with increasing temperature. The result is that the rates of motion ωH of BH straddling the divide (where broad-narrow exchange takes place) are nearly the same at all temperatures. Thus, the repositioning of the divide leads to narrow-broad exchange that is nearly temperature independent.

Furthermore, exchange of the hopping rate ωH within the mobile fraction, between the fastest and slowest mobile ions, prevents the development of a very sharp part of the narrowed peak. Exchange limits the T2 of any mobile spin, by having it spend some of its time moving at slower rates ωH. This explains why the NMR line does not develop an extremely narrow component at high temperatures.

The disorder due to the aerogel walls also results in a distribution of lithium ion motion rates. We note that disorder from anion mixing in lithium iodide - lithium borohydride is known to lead to greater Li ion mobility, similar to what is seen in the bulk high-temperature (disordered) phase of LiBH4. Here this distribution is proved by field-cycling (relaxometry) hydrogen T1 data, which ./6 follow ∝ 1234 over the wide range from 50 kHz to 20 MHz.

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ACKNOWLEDGMENTS The authors acknowledge support from the U.S. Department of Energy, Office of Science, through grant DE-FG02-ER 46256. AG was a Fulbright scholar while at Washington University and also acknowledges the grant of the Slovenian National Research Agency BI-US/16-17-025.

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(13) Heitjans, P.; Indris, S. Fast Diffusion in Nanocrystalline Ceramics Prepared by Ball Milling. J. Mater. Sci. 2004, 39, 5091-5096. (14) Ruprecht, B.; Wilkening, M.; Steuernagel, S.; Heitjans, P. Anion Diffusivity in Highly Conductive Nanocrystalline BaF2:CaF2 Composites Prepared by High-Energy Ball Milling. J. Mater. Chem. 2008, 18, 5412-5416. (15) Kaplan, J. I.; Garroway, A. N. Homogeneous and Inhomogeneous Distributions of Correlation Times. Lineshapes for Chemical Exchange. J. Magn. Reson. 1982, 49, 464-475. (16) Anderson, P. W.; Weiss, P. R. Exchange Narrowing in Paramagnetic Resonance. Rev. Mod. Phys. 1953, 25, 269-276. (17) Matsuo, M.; Nakamori, Y.; Orimo, S. I.; Maekawa, H.; Takamura, H. Lithium Superionic Conduction in Lithium Borohydride Accompanied by Structural Transition. Appl. Phys. Lett. 2007, 91, 224103. (18) Soloninin, A. V.; Skripov, A. V.; Buzlukov, A. L.; Stepanov, A. P. Nuclear Magnetic Resonance Study of Li and H Diffusion in the High-Temperature Solid Phase of LiBH4. J. Solid State Chem. 2009, 182, 2357-2361. (19) Miyazaki, R.; Karahashi, T.; Kumatani, N.; Noda, Y.; Ando, M.; Takamura, H.; Matsuo, M.; Orimo, S. I.; Maekawa, H. Room Temperature Lithium Fast-Ion Conduction and Phase Relationship of LiI Stabilized LiBH4. Solid State Ionics 2011, 192, 143-147. (20) Skripov, A. V.; Soloninin, A. V.; Rude, L. H.; Jensen, T. R.; Filinchuk, Y. Nuclear Magnetic Resonance Studies of Reorientational Motion and Li Diffusion in LiBH4–LiI Solid Solutions. J. Phys. Chem. C 2012, 116, 26177-26184. (21) Maekawa, H.; Matsuo, M.; Takamura, H.; Ando, M.; Noda, Y.; Karahashi, T.; Orimo, S. I. Halide-Stabilized LiBH4, A Room-Temperature Lithium Fast-Ion Conductor. J. Am. Chem. Soc. 2009, 131, 894-895. (22) Walstedt, R. E.; Dupree, R.; Remeika, J. P.; Rodriguez, A. 23Na Nuclear Relaxation in Na β-Alumina: Barrier-Height Distributions and the Diffusion Process. Phys. Rev. B 1977, 15, 3442-3454. (23) Borsa, F.; Torgeson, D. R.; Martin, S. W.; Patel, H. K. Relaxation and Fluctuations in Glassy Fast-Ion Conductors: Wide-Frequency-Range NMR and Conductivity Measurements. Phys. Rev. B 1992, 46, 795-800. 17



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(24) Markert, J. T.; Cotts, E. J.; Cotts, R. M. Hydrogen Diffusion in the Metallic Glass a-Zr3RhH3.5. Phys. Rev. B 1988, 37, 6446-6452. (25) Kuhns, P.L.; Conradi, M.S. NMR Study of Molecular Motions in Cyclohexanol, A Glass-Forming Rotor Crystal. J. Chem. Phys. 1984, 80, 5851-5858. (26) Sholl, C. A. A BPP (Bloembergen-Purcell-Pound) Model For Nuclear Spin Relaxation Due to Diffusion in Disordered Systems: Combined Barrier-and Site-Energy Disorder. J. Phys.: Condens. Matter 2000, 12, 4285-4292.

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Figure 1: Dante pulse sequence for selective inversion of narrow, on-resonance component and for recording subsequent exchange and relaxation. The Dante is 18 pulses of 100 nutation angle each (1.1 μs pulse width). The overall Dante duration Δt of 139 μs determines the frequency bandwidth for inversion. A free induction decay (FID) follows the 90 degree inspection pulse.

19



60

9 nm 13 nm 25 nm

50

narrow %

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40 30 20 10 0 -150

-100

-50

0

50

100

150

200

250

o

T ( C) Figure 2: Fraction of BH groups in the motionally narrowed component, for three pore sizes of aerogel. The 9 nm data are from this work and the large pore size data are from ref 4. The fraction of mobile BH groups increases with higher temperature and larger surface/volume ratio (smaller pores), the latter demonstrating that the mobile spins are nearest the aerogel walls.

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t:

298 K

403 K

100 µs 1 ms 10 ms 100 ms 10 s 0

-20

-10

0

20 -20

10

Freq. (kHz)

-10

0

Freq. (kHz)

Figure 3: Typical spectra after selective inversion, revealing subsequent exchange and relaxation. From pulse sequence of Figure 1; the narrow and broad components are evident.

21


10

20


30

60

298 K 50 40

M, total

20

total: T1 = 343 ms

10

30

narrow: τfast = 4.6 ms

20

0

τslow = 315 ms

10 0

M, narrow peak

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0.1

1

10

100

1000

-10 10000

t (ms)

Figure 4: Spectral intensities M as functions of recovery time t in sequence of Figure 1 at 298 K. The total (broad+narrow) intensity is shown (△) and is well-fit by a single exponential recovery (dashed curve, left-hand scale). The narrow component intensity is also displayed (●) and is fit to a sum of two exponentials (solid curve, right-hand scale). The shorter time constant describes exchange between the narrow and broad spin pools, while the larger time constant is the overall T1. The time constants of the fits are shown.

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3.0 2.5

-3

-1

βN - βB (10 K )

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243 K 298 K 383 K exponential fit for 298 K

2.0 1.5 1.0 0.5 0.0 -0.5 0.1

1

10

100

1000

10000

t (ms)

Figure 5: Difference of reciprocal spin temperatures β for narrow (N) and broad (B) spectral components, as function of time t (in pulse sequence of Figure 1). The spin temperatures become equal at long time, but with t still less than T1, demonstrating the effects of exchange are completed before substantial relaxation has occurred. The solid curve is a single exponential decay with time constant 6.6 ms, for comparison.

23



600 T1 - all

400 200

T1, τex (ms)

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T1 - narrow exchange constant (from narrow component) exchange constant (from spin T difference)

8 4 0 150

200

250

300

350

400

450

T (K)

Figure 6: Upper data are T1 as function of temperature: T1 from total intensity (○) and from slower exponential of two-exponential fit to recovery of narrowed component (●), as in Figure 4. Lower data are exchange time constant τex from faster component of two-exponential fit to narrowed component (▲) and from decay of difference in reciprocal spin temperatures (△) as in Figure 5. Note that τex has only weak temperature variation. Note break in vertical scale.

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1.000 T1 Power fit for low frequency T1 Power fit for T1

0.100

T1 (s)

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0.010

298 K 0.001 0.1

1

10

100

frlx (MHz) Figure 7: Field-cycling hydrogen T1 as function of the relaxation frequency frlx, with 1234 =

?)9:; +@

.

./6 The variation fits = ∗ 1234 , as shown by the straight line fit to the data. The red dash

%

fitting curve follows = .- 7 + 8 function and it has been slightly displaced to avoid overlap

9:;

with the black line. The points at 85.03 MHz and 299.67 MHz are from constant-field work and deviate from the power-law fit. At high field, the dominant relaxation is field-independent, from very fast (~10-11 s) BH reorientations. At low fields, Li ion hopping with a wide range of rates is the dominant source of relaxation.

25



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TOC Graphic: 3.25 in. × 1.75 in.

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LiBH4 in Aerogel: Ionic Motions by NMR - The Journal of Physical

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