8691
2007, 111, 8691-8694 Published on Web 07/11/2007
Microscopic Access to Long-Range Diffusion Parameters of the Fast Lithium Ion Conductor Li7BiO6 by Solid State 7Li Stimulated Echo NMR Martin Wilkening,*,† Claus Mu1 hle,‡ Martin Jansen,‡ and Paul Heitjans† Institute of Physical Chemistry and Electrochemistry, and Center for Solid State Chemistry and New Materials, Leibniz UniVersity HannoVer, Callinstr. 3a, 30167 HannoVer, Germany, and Max Planck Institute for Solid State Research, Heisenbergstr. 1, 70569 Stuttgart, Germany ReceiVed: May 8, 2007; In Final Form: June 18, 2007
Li self-diffusion in rhombohedral Li7BiO6, being a promising basic material for cathodes of rechargeable ion batteries, is studied by means of 7Li stimulated echo NMR. Using the pulse sequence introduced by Jeener and Broekaert, a spin-alignment echo is created whose amplitude decay is recorded as a function of mixing time. The so-obtained two-time correlation functions follow stretched exponential behavior and lead to decay rates which can be identified directly with microscopic Li motional correlation rates (τ-1). Using a jump distance of about 0.2 nm, this results in a diffusion coefficient (D) of about 0.5 × 10-16 m2 s-1 at 294 K. The activation energy turned out to be 0.53(3) eV which is in very good agreement with recently obtained results by means of dc-conductivity measurements probing long-range diffusion parameters. This shows that stimulated echo NMR, due to its inherent time scale, gives microscopic access to long-range transport. The prefactor τ0-1 of the corresponding Arrhenius law lies in the typical range of phonon frequencies, τ0-1 ) 3 × 1012 s-1.
Lithium ion conducting materials have gained enormous significance as potential electrodes in Li ion batteries, which nowadays are indispensable in everyday life due to their high energy density and high voltage.1,2 This interest is accompanied by the effort in developing a fundamental understanding of ionic transport in solids. In this Letter, the reader’s attention is drawn to 7Li stimulated echo NMR, which has newly been established for the direct measurement of Li jump rates, as well as to the interesting family of hexaoxometalates, LinMO6 (n ) 6, 7, 8).3,4 The members of the Li7MO6 group (M ) Nb, Ta, Sb, and Bi) may build a structural basis of promising compounds being useful when fast Li conductors are needed.3,4 The oxygen anions are hexagonal close-packed, and the Li ions partially occupy tetrahedral and octahedral voids. LinMO6 is built of triple slabs of composition [Li2MO6] with Li+ occupying the octahedral voids of two close-packed oxygen layers.3,4 These slabs are stacked in a way that an approximate hexagonal close packing of oxygen atoms results.4 Within the gap between adjacent [Li2MO6] slaps, lithium is located in tetrahedral voids. All lithium positions, tetrahedral as well as octahedral, are partially occupied. Due to the defective character of the lithium partial structure, fast ion transport was found3,5-7 and intercalation and deintercalation experiments seem to be possible. The highest Li conductivity (σ) was found for the rhombohedral phase of Li7BiO6 (space group R3h) stable at above 283 K,3,5 its crystal structure is displayed in Figure 1. The Li conductivity of rhombohedral Li7BiO6 (1.3 × 10-4 S cm-1 at 400 K) is smaller * Corresponding author. Phone: +49-511-762-3273. Fax: +49-511-76219121. E-mail:
[email protected]. † Leibniz University Hannover. ‡ Max Planck Institute for Solid State Research.
10.1021/jp0734979 CCC: $37.00
than that for the very fast intralayer but comparable to that of the interlayer transport in Li3N (≈4 × 10-4 S cm-1 at 400 K).8-10 Macroscopic Li transport properties, on the one hand, are obtainable by dc-conductivity or field-gradient NMR measurements.11 The well-known radiotracer method is not applicable due to the lack of a suitable radioactive Li isotope. Mass spectrometry combined with a sputtering technique can, however, be applied.12,13 Access to microscopic Li diffusion parameters, on the other hand, is only possible via several NMR techniques or quasi-elastic neutron scattering (QENS).11 For a brief overview of the microscopic and macroscopic techniques, see ref 14. While QENS probes diffusion on the nano- and picosecond time scale only, with the combination of the various 7Li NMR methods, a dynamic range from the sub-Hz to the GHz is accessible.15 Stimulated echo NMR, which has been applied to the 7Li nucleus for a few years only,15-21 has several advantages over standard relaxation NMR experiments. In particular, microscopic Li jump rates can be directly read out from the corresponding two-time echo decay curve.15,21 This is possible otherwise only by means of magic angle spinning (MAS) 2D exchange NMR,7,22-25 giving access to site-specific jump rates, which are in this sense not obtainable by stimulated echo NMR. However, stimulated echo NMR is much less timeconsuming and more easily performed as well as applicable to a broader class of materials than 2D NMR. It is highly suitable for the precise study of Li dynamics in crystalline materials and even applicable to amorphous ones20 where exchange NMR often fails because the necessary resolution cannot be achieved. Moreover, in some cases, stimulated echo NMR allows one to study also Li diffusion pathways by evolution time-dependent measurements. A first example is given in ref 20. © 2007 American Chemical Society
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Figure 1. Crystal structure of rhombohedral Li7BiO6, view along [001] (top), and along [100] (bottom). Mobile Li+ ions are represented in the ball-and-stick mode. The jump lengths between adjacent lithium positions are as follows: T-T ) 0.23 nm, O-T ) 0.20 nm (within the layer of tetrahedrally coordinated lithium); O-O ) 0.25 nm, O-T ) 0.25 nm (between octahedral and tetrahedral layer); O-O ) 0.24 nm (within octahedral layer).
Polycrystalline Li7BiO6 was prepared by solid state reaction of mixtures of Bi2O3 (Merck, 99.9%) and LiOH‚H2O (Fluka, 99+%) in a stream of dry oxygen (5% surplus was required for pure products). The mixture was heated in a nickel boat at 973 K for 1 day. The sample was characterized by X-ray powder diffraction, infrared and Raman spectroscopy, as well as differential scanning calorimetry (DSC); see ref 4 for details. At room temperature, the hexagonal metric is retained. The phase transition from rhombohedral to triclinic symmetry is observed at about 280 K by DSC. A slightly anisotropic thermal expansion occurs at about 423 K, as seen by some reflections in the high-temperature X-ray powder patterns as well as by a small endothermic peak in the DSC measurements. For further details of sample preparation and structural characterization, we refer to refs 3 and 4. We have used a Bruker MSL 400 spectrometer connected to a shimmed Oxford cryomagnet at a fixed magnetic field of B0 ) 9.4 T which corresponds to a resonance frequency of 155.55 MHz for 7Li. Up to 128 scans were accumulated for each spin-alignment echo. The recycle delay was at least 5T1. Spin-lattice relaxation times (T1) were recorded independently via the well-known saturation recovery technique. Moreover, a Bruker MSL 100 spectrometer with a field-variable Oxford cryomagnet was employed in order to check the B0 independence of the stimulated echo decay at 4.7 and 2.35 T, respectively. The NMR measurements presented here were performed between 273 and 333 K. Microscopic Li jump rates in Li7BiO6 were measured by recording two-time 7Li NMR spin-alignment echoes (SAEs)15,26,27 according to the three-pulse sequence introduced by Jeener and Broekaert,28 90° - tp - 45° - tm - 45°, at a sufficiently short preparation time,27 tp ) 10 µs, and for various mixing times (tm) ranging from 10-6 µs to 10 s. Echoes were always read out at t ) tp, where t is the acquisition time. Usually up to
Letters
Figure 2. (a) 7Li spin-alignment echoes recorded at 155.55 MHz and 313 K. They were acquired for fixed evolution time (tp) but variable mixing times (tm) (from 60 µs (largest echo) to 10 ms (smallest echo)). The inset shows an echo obtained at tp ) 10 µs and tm ) 150 µs to clarify the correction procedure (see text). (b) 7Li spin-alignment spectra obtained after FT of the corresponding echoes starting from the echo top at t ) tp measured at 313 K (part a) and 294 K.
128 signals were accumulated for each stimulated echo. Thus, a two-time correlation function was obtained within a few hours, depending on the spin-lattice relaxation time (T1) which in turn depends on temperature. This measuring time is much smaller than that for the corresponding 2D exchange NMR experiments. Extensive phase cycling was used in order to pick out the correct coherence pathway.18,26 A short preparation time (tp) should ensure that preferentially spin-alignment order is created after the first 45° pulse. The 90° pulse length was about 4.5 µs and guaranteed a nonselective excitation of the entire 7Li spinalignment spectrum. Figure 2a shows a set of spin-alignment echoes recorded at 313 K for fixed tp ) 10 µs and various mixing times ranging from 60 µs to 10 ms. They are clearly composed of two components: a fast and a slowly decaying component. The first one leads to the broad quadrupole part of the corresponding spin-alignment spectrum after subsequent Fourier transformation (FT) starting from t ) tp; see Figure 2a. The second one is responsible for the “central” component of the SAE spectrum (Figure 2b). Its presence is presumably due to homonuclear coupling of 7Li spins, as was recently found by simple modeling.18 It should not be confused with the central transition of the corresponding 7Li spectrum which is obtained after FT of the free induction decay following excitation with a single 90° pulse. In the investigated temperature range, the latter one shows a width (full width at halfheight) which is about 70% smaller than that of the corresponding SAE-NMR spectrum recorded at tp ) 10 µs. In order to take the spin-alignment information into account only, the slowly decaying part was subtracted from the total echo (inset of Figure 2a) to obtain S2(tm). The pure spin-alignment echo decay is generally due to two processes: (i) individual jumps of the spins between electrically inequivalent crystallographic sites in Li7BiO6 and (ii) quadrupolar spin-lattice relaxation. In the present case, both processes can be simultaneously measured
Letters
Figure 3. Decay of 7Li NMR stimulated echo amplitudes (S2) of Li7BiO6 at tp ) 10 µs and tm varying over nearly seven decades (10-6 s < tm e 10 s). Data were collected at a resonance frequency of 155.55 MHz and at 288 and 303 K (as indicated). The solid lines are stretched exponentials. The corresponding stretching factors (γ) are 0.53 and 0.4, respectively. The inset shows the decay curve at 303 K in a double logarithmic representation in order to demonstrate its two-step behavior. The solid line represents a fit according to the sum of two stretched exponentials (see text).
and well separated from each other. This is due to the fact that they proceed on largely different time scales. The first process is due to Li jumps between sites with different electric field gradients (EFGs) produced by the electric charge distribution of the neighboring anions. The interaction between the quadrupole moment of the 7Li nucleus (spin-quantum number I ) 3/ ) and the EFG alters the Zeeman levels and leads to a site2 specific angular quadrupole frequency (ωq) experienced by the 7Li spin. Thus, the presence of slow Li diffusion leads to a t m dependence of ωq which can be directly used to monitor the jump rate (1/τ). In the ideal case, the echo amplitude, S2(tp ) const., tm, t ) tp), is directly proportional to a single-particle correlation function, S2 ∝ 〈sin(ωq(t)0)tp) sin(ωq(t)tm)tp)〉, where 〈...〉 denotes the powder average. The upper limit of detectable jump rates by SAE-NMR is about 104 s-1, whereas the lower limit is determined by the quadrupolar spin-lattice relaxation rate (1/T1q) which is of the order of a few hundreds of ms at room temperature, here (see below). A typical decay of SAE amplitudes (S2) of Li7BiO6 is shown in Figure 3. The curve can be well parametrized with a combination of two exponentials. The first decay step is characterized by a stretched exponential, S2 ∝ exp(-(tm/τ)γ), with γ ) 0.4 at, e.g., T ) 303 K. Stretched exponentials may be due to a distribution of jump rates present in Li7BiO6 (see below and cf., e.g., ref 19). Within the temperature range 283-323 K, the stretching factor (γ) decreases from about 0.55 to about 0.3. τ equals the Li residence time between two successful jumps in the rhombohedral phase of Li7BiO6. At about tm ) 10-2 s, a small plateau value, S2,∞, is reached (see inset of Figure 3) before S2 finally decays to zero. In general, S2,∞ depends on the evolution time (tp). Here, we have used tp ) 10 µs to record S2(tp, tm); see above. At sufficiently long tp, the plateau value is related to the inverse number of electrically inequivalent Li sites which participate in the transport process. Recently recorded 6Li MAS NMR have suggested that in Li7BiO6 a large number of Li sites with slightly different chemical shifts exist.4 However, with a spinning speed of 14 kHz, it was not possible to achieve a sufficiently high resolution for 2D exchange NMR experiments. The number of Li sites is not only due to the different crystallographic but, quite generally, to inequivalent Li sites,
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Figure 4. Li jump rates of Li7BiO6 obtained from the two-time correlation functions recorded by 7Li SAE-NMR measurements at 155.55 MHz. The solid line corresponds to an Arrhenius law with EA ) 0.53(3) eV and τ0-1 ) 3 × 1012 s-1.
cf. ref 4. This fact may also support the above assumed explanation concerning the stretching of the correlation functions. The plateau value (S2,∞) found here depends on temperature. At 289 K, we obtained S2,∞ ) 0.03(1), whereas S2,∞ increased to about 0.05(1) at 318 K. This can be explained by the averaging of residual homonuclear dipolar couplings of the 7Li spins, as found recently for, e.g., Li SiO ; see ref 21, where 4 4 it was shown that the more spins that are dipolarly coupled, the smaller S2,∞. The second decay step leads from the plateau value to S2 ) 0. It is simply induced by quadrupolar spinlattice relaxation, as mentioned above.21 The corresponding decay constant (1/T1q) is about one-third of the longitudinal spin-lattice relaxation rate (1/T1). This is in nice agreement with theoretical predictions and recently obtained results for other Li conductors.18,21,29-31 It is noted that also the second step in Figure 3 indicates a deviation from single-exponential behavior. In this case, it may be two-exponential due to the quadrupolar relaxation (see, e.g., ref 32 and references therein). In Figure 4, Li jump rates from the first S2-decay step are shown versus inverse temperature (280-320 K). They obey Arrhenius behavior according to 1/τ ) 1/τ0 exp(-(EA/(kBT))). kB is Boltzmann’s constant. The activation energy for Li hopping is EA ) 0.53(3) eV. It is in very good agreement with results from recent impedance spectroscopy measurements (on a sample from the same batch) by Mu¨hle et al.,3 where the activation energy in the low-frequency limit (dc conductivity) turned out to be 0.58 eV between 323 and 473 K. Such a consistency was recently found also for the diffusion process in polycrystalline Li4Ti5O12 probed by 7Li SAE-NMR and impedance spectroscopy.33 It is noted that, on the contrary, activation energies determined via NMR spin-lattice relaxation from the lowtemperature side of the 1/T1(T) peak, which reflects the shorttime limit of the diffusion process,34 often are much smaller (typically by about a factor of 2) than EA from dc-conductivity measurements; see, e.g., ref 35. This is due to the different inherent time, and consequent length, scales the microscopic and macroscopic methods for studying diffusion are sensing.14 Thus, the present example shows that SAE-NMR probes longrange diffusion. At 294 K, a Li jump rate of 4.5(1) × 103 s-1 was measured, revealing rapid Li+ exchange between the accessible Li sites in rhombohedral Li7BiO6. This rate corresponds to a Li diffusion coefficient of about 0.5 × 10-16 m2 s-1 if a mean Li jump distance of 0.20 nm is assumed (which would correspond to the O-T distance within the layer of tetrahedrally coordinated Li; see Figure 1). At 294 K, the width of the 7Li NMR central
8694 J. Phys. Chem. B, Vol. 111, No. 30, 2007 line of Li7BiO6, obtained with a simple 90° pulse, has already started to narrow. This indicates roughly that the motional correlation time is less than 1 ms which is in good agreement with the measured jump rate at this temperature. Furthermore, careful inspection of the spin-alignment spectra shown in Figure 2b reveals that the width of the broad spin-alignment component is already affected by Li motion in this temperature range. The width (fwhh) decreased from 66.5(1) kHz at 294 K to 56.4(1) kHz at 313 K, indicating a jump rate larger than 104 s-1 above 313 K. At this temperature, we have measured a jump rate (1/τ) of about 1.5 × 104 s-1. As expected, 1/τ is independent of the resonance frequency used to measure the SAE decay. Within the experimental error of 10%, the same result is obtained for 77.72 and 39.80 MHz, respectively. The corresponding prefactor of the Arrhenius relation (τ0-1) is 3 × 1012 s-1, which is in good agreement with typical values for phonon frequencies. Moreover, the Li self-diffusion coefficients from SAE-NMR are consistent with those calculated from the dcconductivity values of ref 3 via the Nernst-Einstein equation. For this purpose, the conductivity data, measured between 323 and 473 K, were extrapolated to lower temperatures. The soobtained diffusion coefficients differ by a factor of only 2.5. For instance, at 318 K, the corresponding values are 2.5 × 10-16 m2 s-1 (SAE-NMR) and ≈6.3 × 10-16 m2 s-1 (dc conductivity) when the above-mentioned jump distance is adopted for the estimation assuming in-layer diffusion. These latter results corroborate once more that the SAE decay rates are equal to Li jump rates here and demonstrate that Li SAE-NMR is on its way to becoming a powerful NMR method for the precise and model-independent investigation of microscopic Li diffusion parameters. In particular, the method is useful to study Li dynamics in a time saving way and at relatively low temperatures. Both are important for a lot of Li conductors being promising electrodes for secondary ion batteries. The very good agreement of the activation energies and diffusion coefficients derived from SAE-NMR and dc-conductivity measurements points out that via stimulated echo NMR measurements long-range diffusion parameters are obtainable with a technique which probes transport properties from a microscopic point of view. Acknowledgment. We thank Alexander Kuhn for his help in some of the SAE-NMR measurements. We acknowledge financial support by the German Science Foundation (Deutsche Forschungsgemeinschaft, DFG).
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