Comparison of Anion Reorientational Dynamics in ... - ACS Publications

Subscriber access provided by UB + Fachbibliothek Chemie | (FU-Bibliothekssystem)

Article 9

10

2

10

10

Comparison of Anion Reorientational Dynamics in MCBH and MB H (M= Li, Na) via Nuclear Magnetic Resonance and Quasielastic Neutron Scattering Studies Alexei V. Soloninin, Mirjana Dimitrievska, Roman V. Skoryunov, Olga A. Babanova, Alexander V. Skripov, Wan Si Tang, Vitalie Stavila, Shin-Ichi Orimo, and Terrence J. Udovic J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.6b09113 • Publication Date (Web): 13 Dec 2016 Downloaded from http://pubs.acs.org on December 17, 2016

Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a free service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are accessible to all readers and citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.

The Journal of Physical Chemistry C is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.

Page 1 of 58

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

The Journal of Physical Chemistry

Comparison of Anion Reorientational Dynamics in MCB9H10 and M2B10H10 (M= Li, Na) via Nuclear Magnetic Resonance and Quasielastic Neutron Scattering Studies Alexei V. Soloninin,† Mirjana Dimitrievska,*,‡,∇ Roman V. Skoryunov,† Olga A. Babanova,† Alexander V. Skripov,*,† Wan Si Tang,‡,§ Vitalie Stavila,┴ Shin-ichi Orimo,║,Ⱶ and Terrence J. Udovic*,‡

†

Institute of Metal Physics, Ural Division of the Russian Academy of Sciences, Ekaterinburg 620990, Russia

‡

NIST Center for Neutron Research, National Institute of Standards and Technology, Gaithersburg, MD 20899-6102, United States ∇

National Renewable Energy Laboratory, Golden, CO 80401, United States

§

Department of Materials Science and Engineering, University of Maryland, College Park, MD 20742-2115, United States ┴

Energy Nanomaterials, Sandia National Laboratories, Livermore, CA 94551, United States

║

Institute for Materials Research, Tohoku University, Sendai 980-8577, Japan

Ⱶ

WPI-Advanced Institute for Materials Research, Tohoku University, Sendai 980-8577, Japan

1 ACS Paragon Plus Environment


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

ABSTRACT The disordered phases of the 1-carba-closo-decaborates LiCB9H10 and NaCB9H10 exhibit the best solid-state ionic conductivities to date amongst all known polycrystalline competitors, likely facilitated in part by the highly orientationally mobile CB9H10– anions. We have undertaken both NMR and quasielastic neutron scattering (QENS) measurements to help characterize the monovalent anion reorientational mobilities and mechanisms associated with these two compounds and to compare their anion reorientational behaviors with those for the divalent B10H102- anions in the related Li2B10H10 and Na2B10H10 compounds. NMR data show that the transition from the low-T ordered to the high-T disordered phase for both LiCB9H10 and NaCB9H10 is accompanied by a nearly two-orders-of-magnitude increase in the reorientational jump rate of CB9H10– anions.

QENS measurements of the various disordered compounds

indicate anion jump correlation frequencies on the order of 1010 - 1011 s-1 and confirm that NaCB9H10 displays jump frequencies about 60 % to 120 % higher than those for LiCB9H10 and Na2B10H10 at comparable temperatures. The Q-dependent quasielastic scattering suggests similar small-angular-jump reorientational mechanisms for the different disordered anions, changing from more uniaxial in character at lower temperatures to more multidimensional at higher temperatures, although still falling short of full three-dimensional rotational diffusion below 500 K within the nanosecond neutron window.


Page 2 of 58

Page 3 of 58

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


INTRODUCTION Closo-borate-based salts of Li and Na have been shown to exhibit impressive superionic conductivities in their higher-temperature, entropy-driven, disordered phases. 1 , 2 , 3 , 4 Although these solid-state phases retain a translationally rigid face-centered-cubic (fcc), body-centeredcubic (bcc) or hexagonal stacking of large polyhedral anions (such as B12H122-, CB11H12-, B10H102-, and CB9H10-; see Figure 1 for a depiction of the latter two),2,3,4,5,6 the individual anions are orientationally extremely mobile, with typical reorientational jump frequencies in the range of 1010 – 1011 s-1 above the compound disordering temperatures.3,4,5,7,8,9 Moreover, Li+ and Na+ cations travel with liquid-like mobilities (typically >108 jumps s-1)1,2,4,7,10 throughout the partially vacant interstitial space afforded by these anions. For example, neutron powder diffraction has located Na+ cations in a variety of sites in the disordered fcc Na2B10H10 structure, such as tetrahedral and octahedral interstices, as well intermediate positions between tetrahedral interstices.2,6 It is assumed that the reorienting anions facilitate, to some extent, the cation transport by acting as cooperative “molecular lubricants,” i.e., lowering the effective steric diffusion barriers through the interstitial bottlenecks via their ability to actively participate in the cation transport. Besides purely steric effects, one cannot discount additional favorable effects such as possible attractive or repulsive (bonding and/or coulombic) interactions between anions and cations that might enable the rapidly reorienting anions to help “drag” or “push” the cations to neighboring vacant sites.

A just-published first-principles molecular-dynamics study of

Na2B10H10 (ref. 11) suggests that anion reorientations in the disordered fcc phase indeed provide favorable structural arrangements for Na+ cations to more easily hop between tetrahedral and octahedral interstices, thus forming a more effective network for Na transport. In addition, this study suggests that concerted events involving cation translations concomitant with anion 3 ACS Paragon Plus Environment


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

reorientations are energetically favored over individual sequential events. Further insights into the nature and importance of such dynamical effects will require even more comprehensive theoretical investigations. Of course, these extra dynamical effects are not operational in the more traditional solid ionic conductors such as α-AgI,12 which possesses a monoatomic anion, or cubic Na3PS4 (ref. 13) or Li4SiO4−Li3PO4 solid solutions,14 where the PS43-, SiO44-, and PO43anions exhibit no orientational disorder and likely possess much less orientational mobility. In these cases, anion dynamical effects can be ignored, and cation conduction depends predominantly on the physics of diffusive translations through an orientationally static array of anions. Although the order-disorder transition to superionic behavior is often above room temperature for the closo-borate-based salts (see Table S1 in the supporting information (SI) for a list of transition temperatures of Li and Na closo-borate salts), these disordered phases can be stabilized at and below room temperature by proper chemical or morphological modifications.4,15,16

Figure 1. The similar bicapped-square-antiprismatic geometries of the CB9H10- and B10H102anions. Brown, green, and white spheres denote the respective C, B, and H atoms.


Page 4 of 58

Page 5 of 58

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Obtaining any detailed fundamental understanding of the reorientational dynamics of these hydrogenous complex anions requires appropriate experimental probes, two prime candidates being nuclear magnetic resonance (NMR) and incoherent quasielastic neutron scattering (QENS). Indeed, NMR and QENS are well-known for providing complementary microscopic information on hydrogen jump motion in materials.17 Standard NMR measurements of the spectra and spin relaxation can probe the atomic jump rates over the dynamic range of ~104 – 1011 s-1. Incoherent QENS measurements can probe the H jump rates over the dynamic range of ~108 – 1012 s-1; the lower limit of this range is determined by the energy resolution of the available neutron spectrometers. Thus, the atomic jump ranges probed by NMR and QENS are overlapping. NMR has evident advantages in terms of the width of the dynamic range, being sensitive to much slower motion than QENS. However, standard NMR measurements usually cannot give direct information on the spatial aspects of atomic motion. In contrast, due to its ability to probe the momentum transfer (Q) dependence of the neutron scattering spectra, QENS is crucial for studies of the mechanisms of reorientational motion of these complex anions. Both NMR and QENS measurements have already been performed to probe the anion reorientational dynamics in Na2B12H12, Li2B12H12, NaCB11H12, and LiCB11H12,

1,3,5,7,8,10,15

whereas only exploratory QENS measurements have been made of these dynamics in NaCB9H10, LiCB9H10, Na2B10H10, and Li2B10H10.2,4,9,16 As anion dynamical information is critical for gaining any further insights concerning the relation between anion mobility and ionic conductivity, it makes sense to probe anion dynamical behavior in more detail, especially for the as-of-yet best performing Li and Na salts of the 1-carba-closo-decaborates (MCB9H10). For example, disordered LiCB9H10 and NaCB9H10, with their weakly coordinating monovalent anions, exhibit remarkable ionic conductivities of 0.03 S cm-1 at 354 K and 297 K, respectively.4



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

This is about an order of magnitude better behavior than seen for the related superionic Na2B10H10 salt,2 which contains divalent anions, requiring twice as many cations per anion for charge neutrality (and thus a less vacant, disordered cation sublattice) compared to its MCB9H10 cousins. In this paper, we use both NMR and QENS to characterize and compare the monovalent CB9H10- and divalent B10H102- anion dynamics in MCB9H10 and M2B10H10 (M=Li, Na), hoping to shed some light on the relative importance of anion charge and cation concentration on anion reorientational mobilities and ultimately on the ionic conductivity.

EXPERIMENTAL METHODS Lithium and sodium 1-carba-closo-decaborates (LiCB9H10·xH2O and NaCB9H10) were obtained from Katchem18 and fully dehydrated under vacuum overnight at ≈473 K. These Li and Na compounds contained minor respective CB11H12- anion molar impurities of 6 % and 3 %. Various natural-isotope-abundant and isotope-enriched lithium and sodium closo-decaborates (Li2B10H10, 7Li211B10H10, Na2B10H10, and Na211B10H10) were synthesized and fully dehydrated according to the procedures in refs. 6 and 9. Compound purities were corroborated by X-ray diffraction using a Rigaku Ultima III X-ray diffractometer with a Cu-Kα source (λ=1.5418 Å). NMR measurements of NaCB9H10, LiCB9H10, Na2B10H10, and Li2B10H10 were performed on a pulse spectrometer with quadrature phase detection at the frequencies ω/2π = 14, 28, and 90 MHz for 1H, and 28 MHz for 11B. The samples were flame-sealed in glass tubes under vacuum. NMR measurements were performed in the following temperature ranges: 108 – 384 K


Page 6 of 58

Page 7 of 58

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(NaCB9H10), 139 – 418 K (LiCB9H10), 88 – 435 K (Na2B10H10), and 279 – 560 K (Li2B10H10). The magnetic field was provided by a 2.1 T iron-core Bruker magnet. A home-built multinuclear continuous-wave NMR magnetometer working in the range 0.32 – 2.15 T was used for field stabilization. For rf pulse generation, we used a home-built computer-controlled pulse programmer, the PTS frequency synthesizer (Programmed Test Sources, Inc.), and a 1 kW Kalmus wideband pulse amplifier. Typical values of the π/2 pulse length were 2 – 3 µs for all nuclei studied. For the measurements at T ≤ 460 K, a probehead with the sample was placed into an Oxford Instruments CF1200 continuous-flow cryostat using nitrogen as a cooling agent. The sample temperature, monitored by a chromel-(Au-Fe) thermocouple, was stable to ±0.1 K. Above 460 K, the measurements were performed using a furnace probehead. For this setup, the sample temperature, monitored by a copper – constantan thermocouple, was stable to ± 0.5 K. Except for the cases specifically discussed in the text, NMR measurements were performed with increasing temperature. After reaching the desired temperature, we employed 10 min waiting time necessary to ensure thermal equilibrium before the start of the measurements. The nuclear spin-lattice relaxation rates were measured using the saturation – recovery method. NMR spectra were recorded by Fourier transforming the solid echo signals (pulse sequence π/2x – t – π/2y). Quasielastic neutron scattering (QENS) measurements of LiCB9H10, NaCB9H10, Li211B10H10, and Na211B10H10 were performed at the National Institute of Standards and Technology Center for Neutron Research on the Disc Chopper Spectrometer (DCS),19 utilizing incident neutron wavelengths of 4.08 Å (4.91 meV), 4.8 Å (3.55 meV), and 8 Å (1.28 meV) with respective resolutions of 79 µeV, 118 µeV, and 30 µeV full width at half maximum (fwhm) and respective maximum attainable Q values of around 2.89 Å-1, 2.46 Å-1, and 1.48 Å-1. Temperature ranges explored were 100 K – 450 K (LiCB9H10), 100 K – 410 K (NaCB9H10), 300



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 8 of 58

K – 680 K (7Li211B10H10), and 250 K – 500 K (Na211B10H10). Due to the presence of natural boron (which contains 20 mol % of highly neutron-absorbing 10B) for the two MCB9H10 samples, their spectra were collected using a flat-plate geometry in reflection, with ~0.4 g of each sample distributed over a 12 cm2 area. In contrast, the two 11B-enriched samples (0.38 g for Na211B10H10 and 0.17 g for 7Li211B10H10) were measured using thin-walled annular geometries (5 cm height × 1.3 mm annulus diameter) in transmission. In all cases, these sample masses and configurations precluded any significant multiple scattering effects. All instrument resolution functions were determined from QENS spectra at low temperatures free of quasielastic scattering, typically between 100 K and 300 K. QENS data were analyzed using the Mslice and PAN programs from the DAVE software package. 20 Typically, all Bragg peaks were masked in Mslice before constructing the constant-Q cuts for spectral analyses with PAN.

Because of the

overwhelmingly large incoherent neutron scattering cross section for H compared to Li, Na, B, and C atoms, all analyzed spectra were assumed to reflect only scattering from H. For the natural-boron samples, where overall sample scattering was appreciably reduced, scattering contributions from the empty Al sample can were determined to contribute on the order of 1-2 % to the overall signal, and this effect was ignored in subsequent analyses. It should be noted that standard uncertainties in all figures in the text and SI, if not explicitly indicated, are commensurate with the observed scatter in the data.

RESULTS AND DISCUSSION Proton NMR Measurements for NaCB9H10 and LiCB9H10 The proton spin-lattice relaxation rates ܴଵH measured at the resonance frequencies ω/2π = 14 and 28 MHz for NaCB9H10 as functions of the inverse temperature are shown in Figure 2. 8 ACS Paragon Plus Environment

Page 9 of 58

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Comparison of these ܴଵH (ܶ) data with the previous results for a number of B12H122- and CB11H12--based compounds5,7,10 suggests that the observed proton spin-lattice relaxation rate in NaCB9H10 is governed by the nuclear dipole-dipole interaction modulated by reorientational motion of complex anions. At T < 278 K, the measured relaxation rate increases with increasing temperature and exhibits pronounced frequency dependence. Such a behavior indicates that in this temperature range, the rate τ-1 of the anion reorientations is below ω ~ 108 s-1. According to the standard theory of nuclear spin-lattice relaxation due to atomic motion,21 ܴଵH (ܶ) is expected to pass through a maximum at the temperature at which the jump rate τ-1(T) becomes nearly equal to ω; in the limit of slow motion (ωτ >> 1), the relaxation rate ܴଵH should be proportional to ω-2τ-1, and in the limit of fast motion (ωτ 330 K, the line width reaches a plateau, which is typical of localized H motion.27 The plateau value of ∆H is determined by the fraction of dipole-dipole interactions which is not averaged out by the fast reorientational motion. Therefore, in principle, this value should depend on the mechanism of reorientations. However, for such complex anions as CB9H10–, rigorous calculations of this value for different reorientational models in the high-T phase are practically impossible. More direct information on the mechanism of reorientations can be obtained from QENS data. The behavior of ∆H(T) for LiCB9H10 (Figure 4) resembles that for NaCB9H10. In particular, it exhibits a significant drop above 200 K and a smaller ‘step’ in the phase transition region.


Page 15 of 58

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Figure 4. Temperature dependences of the fwhm widths of the 1H NMR lines measured at 28 MHz for NaCB9H10 and LiCB9H10. Vertical bars mark the vicinities of the phase transitions.



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

1

Page 16 of 58

H and 11B NMR measurements for Na2B10H10 and Li2B10H10. The temperature dependence of the 1H NMR line width ∆H for Na2B10H10 is shown in

Figure 5. General features of this temperature dependence resemble those for NaCB9H10 (Figure 4). The ‘rigid lattice’ second moment of the 1H NMR line calculated on the basis of the structural data for Na2B10H10 (ref. 6) is 2.06×1010 s-2. Assuming that the line shape is Gaussian, this value of the second moment corresponds to ∆H = 53.9 kHz, which is close to the experimental low-temperature value of the line width (~ 58 kHz). A significant line narrowing for Na2B10H10 occurs near 220 K, i.e., at a somewhat higher temperature than that for NaCB9H10. This indicates that in the low-T phase, the reorientational motion in Na2B10H10 is slower than in NaCB9H10. The evolution of the 1H NMR spectrum with temperature for Na2B10H10 is shown in Figure S1 of the SI. The very small ‘step’ of ∆H(T) near 370 K (the phase transition temperature for Na2B10H10) can be related to the averaging of the weak 1H –

23

Na dipole-dipole interaction

due to the onset of fast translational diffusion of Na+ cations.2 It should also be noted that the high-T plateau value of ∆H for Na2B10H10 (~10 kHz) is considerably larger than that for NaCB9H10 (~6 kHz).


Page 17 of 58

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Figure 5. Temperature dependence of the width (full width at half-maximum) of the 1H NMR line measured at 28 MHz for Na2B10H10. The vertical bar marks the vicinity of the phase transition.

The recovery of 1H nuclear spin magnetization in Na2B10H10 below 370 K is found to deviate from a single-exponential behavior. However, above 370 K, the observed spin-lattice relaxation becomes nearly exponential. Thus, we can exclude a presence of H-containing impurity phases as an origin of the non-exponential relaxation in the low-T phase. A possible reason for the deviations from exponential behavior may be related to a presence of spatially separated H atoms with different motional parameters, as in the case of LiZn2(BH4)5. 28 For B10H102− anions, such dynamically inequivalent protons may be expected, e.g., in the case of uniaxial rotations or two different reorientational motions. The recovery of the 1H nuclear magnetization in the low-T phase of Na2B10H10 can be described by a sum of two exponential components. Both components exhibit qualitatively similar temperature dependences. Figure 6 17 ACS Paragon Plus Environment


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 18 of 58

shows the behavior of the slower components of the 1H spin-lattice relaxation rates (in the low-T phase) measured at three resonance frequencies. Note that the slower component is the dominant one in the temperature region just below the transition. A scatter of the data points for T < 370 K can be attributed to a certain instability of the two-exponential description of the relaxation. As can be seen from Figure 6, at T < 370 K, the relaxation rates increase with increasing temperature and exhibit a distinct frequency dependence. At T > 370 K, the relaxation rate decreases with increasing temperature, being frequency-independent. As in the case of CB9H10based compounds, these general features are consistent with the ‘folding’ of the relaxation rate peak due to a phase transition accompanied by an abrupt increase in the reorientational jump rate τ-1. Since for Na2B10H10 we observe both the ‘folding’ of the relaxation rate peak and the deviations from a single-exponential relaxation in the low-T phase, it is difficult to determine the absolute values of τ-1 from the present data. However, it is possible to estimate the activation energy for anion reorientations in the high-T phase from the slope of the lnܴଵH vs. T-1 plot. The Ea value based on the proton spin-lattice relaxation data in the high-T phase is 180(30) meV. Note that this value is close to the activation energy for anion reorientations in the high-T phase of NaCB9H10 (205 meV; see above.)


Page 19 of 58

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Figure 6. The slower components of the 1H spin-lattice relaxation rates measured for Na2B10H10 at three resonance frequencies as functions of the inverse temperature. The vertical bar marks the vicinity of the phase transition. In the high-T phase, the relaxation rates are derived on the basis of a single-exponential approximation. The

11

B spin-lattice relaxation in Na2B10H10 is also found to deviate from a single-

exponential behavior below 370 K, being nearly exponential above 370 K. It should be noted that for

11

B nuclei, deviations from the single-exponential relaxation are more common, since

these nuclei have non-zero electric quadrupole moments. In the region of the non-exponential relaxation, the recovery of the 11B nuclear magnetization can be reasonably described by a sum of two exponential components. Figure 7 shows the behavior of the slower component of the 11B spin-lattice relaxation rate in the low-T phase of Na2B10H10; in the high-T phase, the

11

B

relaxation rates based on a single-exponential approximation are shown. These data also 19 ACS Paragon Plus Environment


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 20 of 58

represent an example of ‘folding’ of the relaxation rate peak, which is consistent with the abrupt increase in τ-1 at the phase transition. The estimate of the activation energy for the reorientational motion in the high-T phase of Na2B10H10 based on the 11B relaxation data gives 224 meV. This estimate should be considered as more reliable than that based on the 1H relaxation data, since the corresponding temperature range for the

11

B data in the high-T phase is broader and the

overall quality of the high-T 11B data is better.

Figure 7. The slow component of the 11B spin-lattice relaxation rate measured for Na2B10H10 at 28 MHz as a function of the inverse temperature. The vertical bar marks the vicinity of the phase transition. In the high-T phase, the 11B relaxation rate is derived on the basis of a singleexponential approximation.

For Li2B10H10, we have not been able to obtain a fully reproducible set of 1H NMR 20 ACS Paragon Plus Environment

Page 21 of 58

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


parameters because this sample shows signs of slow irreversible decomposition after remaining at temperatures above 550 K. The evolution of the 1H NMR spectrum after heating Li2B10H10 to 560 K is illustrated in Figure S2 of the SI. It is possible to measure the proton spin-lattice relaxation rate in the ‘fresh’ sample of this compound in a single heating run; the phase transition accompanied by an abrupt acceleration of the reorientational motion is observed near 597 K (see Figure S3 of the SI). However, because of the slow decomposition, these results cannot be reproduced in subsequent runs.



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 22 of 58

QENS Measurements for NaCB9H10, LiCB9H10, Na211B10H10, and 7Li11B10H10

Figure 8. Exemplary QENS spectra for Na211B10H10 at 500 K using 8 Å wavelength neutrons (with 30 µeV fwhm resolution) at two different Q values of (a) 0.6 Å-1 and (b) 1.2 Å-1. N.B., the very broad fitted Lorentzian L2(Q,E) component is believed to be associated with low-frequency inelastic scattering from overdamped anion vibrational modes. 22 ACS Paragon Plus Environment

Page 23 of 58

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Figure 8 displays T-dependent QENS spectra typical of all the compounds under study, for the exemplary case of Na211B10H10 at Q values of 0.6 Å-1 and 1.2 A-1. Representative QENS spectra for NaCB9H10, LiCB9H10, and 7Li211B10H10 are shown in Figure S5 of the SI. In the disordered phase at any particular Q, a reasonable spectral fit required two Lorentzian components with order-of-magnitude-different widths in addition to an elastic peak component, as was shown previously for NaCB9H10 and LiCB9H10.4 (The broader scattering component is more obvious at higher Q values and plotted over a broader energy range as shown in Figure S4 of the SI.) Besides the narrow quasielastic component, the second overly broad component, originally thought to reflect a much faster H reorientational jump process in these compounds,4 is now believed to be associated with low-frequency inelastic scattering from overdamped anion vibrational modes, which we will discuss in more detail later. Figure 9 indicates the characteristic increase in the width of the narrower (quasielastic) component for Na211B10H10 at 500 K. Such Q-dependent line width behavior is typical of all these compounds in their disordered phases (see Figure S6 of the SI) and consistent with a smallangle reorientational jump mechanism.8 As can be seen in Figure 9, consistent values for the line widths are obtained in the case of measurements with different instrumental resolutions obtained from 4.8 and 8 Å incident neutron wavelengths. A Q value of 0.6 Å-1 was typically used when comparing the anion dynamics of the various compounds, since the QENS spectra at this Q are dominated by the fundamental quasielastic component of the prevailing reorientational jump mechanism, largely free of higher-order Lorentzian components.



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 24 of 58

Figure 9. Q-dependence of the Lorentzian (quasielastic) fwhm line width for Na211B10H10 at 500 K measured with 4.8 Å (full symbols) and 8 Å (open symbols) wavelength neutrons with respective fwhm resolutions of 79 µeV and 30 µeV. Q = 0.6 Å-1 marks the momentum transfer value routinely used to determine the jump correlation frequencies τ1-1. Figure 10 compares the T-dependent Arrhenius behavior of the fundamental jump correlation frequency τ1-1 (which is related to the Lorentzian fwhm line widths w by τ1-1 = w/(2ħ)) based on the fitted narrower Lorentzian component for the disordered NaCB9H10, LiCB9H10, Na211B10H10, and 7Li11B10H10 phases (measured with 30 µeV fwhm resolution). Where we can make a comparison with the NMR data (i.e., for MCB9H10), the corresponding NMR H jump rates of 4.6×109 s-1 (for NaCB9H10 at 287 K) and 8.8×109 s-1 (for LiCB9H10 at 349 K) are in line with the apparent H dynamical motion manifested by this narrower Lorentzian component of the QENS data, being roughly only a factor of two lower than the corresponding QENS jump 24 ACS Paragon Plus Environment

Page 25 of 58

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


correlation frequencies determined from the linear fits to the data in Figure 10. Taking into account the assumptions made in the course of analysis of the NMR data for the disordered MCB9H10 phases (see above) and the fact that the correlation time τ1 may differ from the mean residence time (see ref. 8 for discussion), the agreement can be considered as reasonable. We now turn to a discussion of the much broader quasielastic-like component exemplified in Figure 8. The present NMR data do not show any signs of a coexistence of two types of H jump motion with strongly differing H jump rates. If there were two such types of motion, one would expect to observe two spin-lattice relaxation rate peaks at lower temperatures (at which the jump rate of each of the processes becomes close to 108 jumps s-1). For MCB9H10 and M2B10H10, the disordered phases transform to the ordered phases (upon cooling) before these conditions could be met. However, our recent 1H spin-lattice relaxation measurements of mixed M2(CB9H10)(CB11H12) solid-solution compounds,16 which remain in their high-T-like disordered phases down to very low (cryogenic) temperatures, also failed to observe such two-peak behavior of the relaxation rate. For these solid solutions, we found certain signs of a jump-rate distribution, but this distribution seemed to be centered at a single jump rate. It should be noted that in cases with two types of H jump motion (such as BH4- anion reorientations in the hexagonal LiBH4-LiI solid solutions),29,30 two relaxation rate peaks were indeed observed in the low-T region.



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 26 of 58

Figure 10. Anion jump correlation frequencies τ1-1 vs. inverse temperature for the disordered phases of NaCB9H10, LiCB9H10, Na211B10H10, and 7Li11B10H10. Solid lines represent linear fits to the data. Dashed line denotes comparative τ1-1 behavior for Na211B12H12 from refs. 8 and 15. The order-of-magnitude broader neutron scattering linewidth for this extra component is too large to be a higher-order Lorentzian component of a small-angular jump mechanism associated with the narrower Lorentzian component (Figure S6 of the SI). Thus, it would have to be a second type of more rapid reorientational motion for the same anion. As discussed later, hybrid reorientation mechanisms are possible that consist of different types of reorientational motions. Yet, as for NMR measurements of mixed M2(CB9H10)(CB11H12) solid-solution


Page 27 of 58

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


compounds,16 a potentially faster type of reorientational motion could not be independently observed in these compounds by high-resolution (

Comparison of Anion Reorientational Dynamics in ... - ACS Publications

Recommend Documents