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2009, 113, 4741–4744 Published on Web 02/06/2009
Diffusion in Confined Dimensions: Li+ Transport in Mixed Conducting TiO2-B Nanowires Martin Wilkening,*,† Christopher Lyness,‡ A. Robert Armstrong,‡ and Peter G. Bruce‡,§ Institute of Physical Chemistry and Electrochemistry, and Center for Solid State Chemistry and New Materials, Leibniz UniVersity HannoVer, Callinstreet 3a, 30167 HannoVer, Germany, and EastChem, School of Chemistry, North Haugh, UniVersity of St. Andrews, St. Andrews, FiVe KY16 9ST, Scotland, U.K. ReceiVed: December 08, 2008; ReVised Manuscript ReceiVed: January 14, 2009
The precise determination of diffusion parameters plays a key role in Li battery research and is a rather complex problem when electrode materials, i.e., mixed conductors, have to be investigated. In the present contribution, we show how stimulated echo nuclear magnetic resonance (NMR) can be used to go beyond the limits of standard NMR methods for the characterization of dynamic properties of one of the most promising new electrode materials viz. Li intercalated TiO2-B nanowires. It turned out that Li self-diffusion is very slow with an activation energy of 0.48(1) eV. Obviously, the shorter diffusion length compensates for this low mobility so that, nonetheless, facile incorporation and removal of Li is possible when the nanowires are used in an ion battery. The renaissance of interest in battery research is driven by the ambitious goal of developing powerful secondary Li batteries for new sustainable energy storage systems. For instance, such systems will be used in future hybrid electric vehicles, a key method of transportation in the 21st Century. Battery research is to a high degree dominated by the search for new materials that will enhance energy and power density while improving safety and reducing cost. Recently, nanostructured materials have attracted increasing interest from the battery research community.1,2 They deliver beneficial features for applications such as electrolytes and electrodes in lithium-ion batteries. For instance, nanomaterials significantly shorten the Li+ and e- diffusion lengths within the electrode materials and hence increase the rate (power) capability of the battery. The discovery and development of new nontoxic materials is accompanied by a formidable challenge for researchers: how to quantify the physical parameters determining the ionic transport properties in nanostructured Li conductors? Yet such quantification is essential if we are to understand and optimize battery materials. Unfortunately, the lack of suitable isotopes for Li+ precludes the use of the well-known tracer method. The problem of determining Li+ transport is rendered significantly more complex for electrode materials compared with electrolytes because the former are mixed conductors exhibiting significant electronic and ionic conductivity. These have to be separated out to determine the fundamental transport processes. This may be done by 4-probe or AC impedance methods but such techniques can be fraught with experimental difficulties, e.g., fabricating 4-electrode cells, finding suitable electrodes, grain boundary * To whom correspondence should be addressed. E-mail:
[email protected]. Phone: +49-511-762-3273. Fax: +49-511762-19121. Web: http://www.wilkening.pci.uni-hannover.de. † Leibniz University Hannover. ‡ University of St. Andrews. § See also for correspondence. E-mail:
[email protected]. Web: http:// chemistry.st-and.ac.uk/staff/pgb
10.1021/jp8107792 CCC: $40.75
resistances, separating out self-diffusion from chemical diffusion, etc. The selective measurement of the diffusion parameters of ions in mixed conductors is far from trivial. One method of interest is nuclear magnetic resonance (NMR); however, NMR techniques too reach their limits when mixed conductors have to be studied. The coupling of the spins with conduction electrons and/or the presence of paramagnetic ions, e.g., the existence of mixed valence states Ti3+/Ti4+ in Li intercalated TiO2, usually lead to very short and temperature independent spin-lattice relaxation times T1 which drastically narrow the time window for the study of Li diffusion parameters by means of conventional NMR techniques. However, a way out is given by the use of NMR stimulated echoes. In the present case we will show how Li diffusivity in mixed conductors such as nanowires of LixTiO2 can be easily measured by state-of-theart quadrupolar spin-alignment echo (SAE) NMR spectroscopy using the 7Li isotope with a natural abundance of 92.5%. The technique was recently established for the direct detection of Li+ jump rates with values on the ms time scale. It was adapted from previously developed deuteron NMR3 and applied successfully to a number of pure ionic conductors, i.e., to electronic insulators.4-11 For this purpose we have recorded mixing time dependent amplitudes of 7Li stimulated echoes (Figure 1, panels a and b), leading to two-time hopping correlation functions from which Li diffusion parameters can be obtained in a straightforward way, i.e., without invoking a suitable diffusion model.11 In contrast to conventional NMR relaxation measurements,12 which have been used for several decades to probe Li transport parameters, 7Li as well as 6Li SAE NMR13,14 provides access to hopping correlation functions and is similar to that of 2D 6,7 Li exchange magic angle spinning (MAS) NMR.15-18 Let us note that SAE NMR is a time-saving alternative to exchange experiments and applicable to a much broader range of materials including also amorphous solids. By the use of SAE NMR, we were able to study selectively Li+ hopping in mixed conducting LixTiO2-B nanowires over 2009 American Chemical Society
4742 J. Phys. Chem. C, Vol. 113, No. 12, 2009
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Figure 2. Arrhenius plot of the stimulated echo decay rates 1/τ (O) and 1/τSAE (b) obtained from (i) the S2 curves of Figure 1b and (ii) the background-corrected F2 single-particle two-time correlation functions of Figure 3, which were recorded at a resonance frequency of ω0/2π ) 155 MHz. The rates 1/τSAE exclusively hallmark diffusion of Li+ in the nanowires of the nominal composition Li0.3TiO2. In contrast to SAE NMR, conventional spin-lattice relaxation techniques (the rates 1/T1 and 1/T1F were recorded at ω0/2π )155 MHz and a locking frequency of ω1/2π ) 14(2) kHz, respectively) do not provide a straightforward access to diffusion parameters, e.g., of the activation energy, in this T range (see text for further details). Figure 1. (a) Typical 7Li spin-alignment echo of Li0.3TiO2-B nanowires recorded at 343 K and a resonance frequency of 155 MHz. (b) Corresponding SAE NMR two-time correlation functions (tp ) 10 µs). The echo amplitude S2 is plotted vs mixing time tm. Lines represent fits using stretched exponentials.
a dynamic range of about 3 orders of magnitude. It was shown recently, that Li intercalated nanowires of TiO2-B, the fifth polymorph of TiO2 (space group C2/m), performed well as electrodes in lithium-ion batteries, delivering a specific capacity of 300 mAhg-1 at 1.6 V vs Li+/Li 1,2,19-22 The crystal structure of TiO2-B is composed of ribbons of edge sharing TiO6 octahedra that corner share to form sheets in the ab plane, these sheets being connected in the c direction by further corner sharing. The b direction lies along the axial direction of the wires with c orientated radially. Both b and c directions exhibit wide tunnels, some with Perovskite-like windows that suggest these may be the preferred directions for facile Li intercalation. This and the small diameter of the wires (typically 40 nm) enable fast Li insertion and removal radially.22 Samples with different Li contents (x ) 0.1, 0.3, and 0.6) were used for the present study. Here, we will focus on a sample with x ) 0.3, which was electrochemically intercalated with Li. Stimulated echoes (spin-alignment echoes) were recorded by using the three-pulse NMR sequence introduced by Jeener and Broekaert:5,23 90°-tp-45°-tm-45°-tp-echo. By SAE NMR the ions are labeled microscopically via their locally different quadrupole (resonance) frequencies ωQ/2π arising from the interaction between the quadrupole moment of the nucleus and a nonvanishing electric field gradient produced by the electric charge distribution in the neighborhood of the nucleus.11 Jumping of the Li+ ions renders ωQ/2π time dependent. As a consequence the echo amplitude S2 (recorded for fixed evolution time tp) decays with increasing mixing time tm. In the ideal case S2(tp, tm) directly gives access to the Li jump rate. In Figure 1a a
typical 7Li stimulated echo is shown, which was recorded at tp ) 10 µs and a resonance frequency of ω0/2π ) 155 MHz. By choosing a short tp, the unwanted dipolar contributions to the echo may be better suppressed.4,5 In the present case, the relevant spin-alignment echo appears exactly at t ) tp. Although tp is already rather short, the echo is superimposed on a second one arising from homonuclear dipole-dipole interactions. The latter, which decays much slower than the spin-alignment echo, can be roughly parametrized by a Gaussian function (solid line in Figure 1a). It was subtracted from the total echo (for each mixing time) in order to obtain the pure spin-alignment signal. The normalized amplitude S2 is plotted in Figure 1b as a function of observation time tm and for various temperatures T. The decay curves can be parametrized by stretched exponentials, S2 ∝ exp(-(tm/τ)γ) with 0.6 > γ > 0.3. The faster the echo damping, the larger the influence of Li+ hopping on the decay curve. The corresponding rates 1/τ are shown in Figure 2 in an Arrhenius plot. Only at high T is the echo exclusively damped by Li diffusion. At very low temperatures, i.e., below 240 K, the S2 decay is primarily induced by other effects of nondiffusive nature such as ordinary spin-lattice relaxation or spin-diffusion. The latter are easily identifiable by the temperature independence of 1/τ. Furthermore, within the low-T regime the rate 1/τlow-T roughly follows a tp2 dependence which indicates the influence of a small step diffusion process in frequency space comparable to spindiffusion effects24 (not shown here for brevity). Below 240 K, we obtain τlow-T ) 114(5) ms from the corresponding S2 fit. To a certain degree, this contribution also affects echo damping at higher T; therefore, we have corrected the normalized S2 fits of Figure 1b for this effect by dividing S2 with the factor exp(-(tm/ 114(5) ms)0.6). The resulting single-particle two-time hopping correlation functions F2 are displayed in Figure 3. The decay of F2 is solely due to successful jumps of the ions which is corroborated by the fact that the shape of F2(tp,tm,t) turns out to
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Figure 3. Pure 7Li SAE two-time hopping correlation functions F2 of Li0.3TiO2 nanowires corrected for temperature independent nondiffusive background effects. The shape of F2 is independent of T indicating that the same diffusion process is probed between 320 and 410 K. Inset: Comparison of S2 and F2 recorded at T ) 343 K, before and after the correction procedure (see text for further details).
be independent of temperature. A mean stretching factor of γ ) 0.35(2) is obtained. Such a small γ value either reflects highly heterogeneous Li diffusion in the nanowires or is due to the presence of a spatially confined diffusion process. The latter would mean that the strong deviation from monoexponential time behavior is an intrinsic rather than an extrinsic feature of Li+ diffusion in Li0.3TiO2. Nonexponential correlation functions are expected for low-dimensional diffusion processes. Here, Li diffusion is anticipated to be primarily confined to two dimensions in the TiO2-B structure. The temperature dependence of the SAE decay rates 1/τSAE of the two-time correlation functions F2 of Figure 3 is also shown in Figure 2. 1/τSAE reveals Arrhenius behavior according to 1/τSAE ∝ exp(-EA/kBT) with Boltzmann’s constant kB. The activation energy EA turned out to be 0.48(1) eV. As illustrated in Figure 2, neither conventional SLR NMR measurements in the laboratory frame (T1) nor analogous measurements in the rotating frame of reference (T1F)12 are helpful in determining reliable hopping activation energies in the present case. Even when probed in the rotating frame at a much smaller (locking) frequency ω1/2π ) 14(2) kHz, the corresponding rates 1/T1F reveal a much weaker temperature dependence than observed for 1/τSAE. This reflects the fact that the spin-lattice rates, 1/T1F and 1/T1, are greatly influenced by, e.g., local hopping processes and even unsuccessful Li jumps leading to much smaller activation energies than expected for long-range Li transport. Additionally other nondiffusive and frequency dependent background effects (see above) affect the SLR rates. Thus, diffusion induced contributions are largely masked over the whole temperature range covered here. This clearly shows that for samples comparable to the present one the 7Li SAE NMR technique turns out to be a practicable as well as nondestructive alternative applicable to the characterization of Li hopping processes in mixed conducting materials. In contrast to relaxation NMR techniques, SAE NMR, however, is primarily sensitive to successful displacements of the charge carriers and thus probes macroscopic transport parameters taking advantage of the locally different electric environments of the nuclei.25 This means the activation energy EA ) 0.48(1) eV, characterizing long-range Li diffusion, is measured using an atomic-scale NMR method. EA should be comparable to the activation energy which might be probed by tracer diffusion experiments or electrical measurements of the ionic conductivity.
J. Phys. Chem. C, Vol. 113, No. 12, 2009 4743 Interestingly, interpreting the decay rates as Li jump rates, one clearly recognizes that Li self-diffusion within the nanowires is not very fast in comparison with other nanocrystalline and even coarse grained Li conductors, see, e.g., refs 11 and 26. This observation is confirmed by static 7Li NMR line shape measurements from which the order of magnitude of the Li jump rate can be roughly estimated. According to these measurements (not shown here for brevity) at about 400 K, the jump rate in the Li0.3TiO2-B nanowires is estimated to lie between 103 and 104 s-1 which is in fair agreement with the highly precise SAE data of Figure 2. This means that the observed fast insertion/ removal of Li is not due to an exceptionally fast self-diffusion process. Obviously, the nanosize effect, especially the shorter diffusion length compared with bulk material, is sufficient to compensate for the relatively slow Li self-diffusivity so that an overall fast incorporation and removal of a large number of Li+ ions per unit volume occurs. In the present study, we have shown how useful the measurement of 7Li stimulated echoes is when diffusion properties of mixed conductors have to be studied at moderate temperatures. In particular, this becomes important when other methods are not available or NMR techniques fail, which might be the case for a large range of materials being actually considered as promising candidates for rechargeable lithiumion batteries. Experimental Details 7 Li stimulated echoes, we refer to ref 11 for details of the technique, were recorded on a commercial Bruker MSL 400 spectrometer in connection to a 9.4 T Oxford cryomagnet. We have used a Bruker broadband probe operating between 123 K and 433 K. The 90° pulse length was about 4.5 µs at a resonance frequency of about 155 MHz. The temperature was controlled via an Oxford ITC in combination with a NiCr-Ni thermocouple placed near the sample which was sealed in a quartz tube under vacuum. The three-pulse sequence of Jeener and Broekaert was employed to record the echoes. Spin-lattice relaxation rates (1/T1 and 1/T1F) were recorded using standard pulses sequences such as the well-known recovery saturation experiment or the spin-lock technique.27 For the latter measurements we used a locking frequency of 14(2) kHz. TiO2-B nanowires were synthesized by a simple hydrothermal reaction between NaOH and TiO2 (anatase). Details of the sample preparation as well as the subsequent insertion of Li, which was carried out electrochemically, are described in detail elsewhere.21 Li intercalation was carried out on electrodes prepared using mixtures comprising 75% active material, 18% Super-S carbon and 7 wt % PTFE, pressed into pellets.21,22 The cells consisted of this electrode, a lithium metal counterelectrode and the electrolyte, a 1 M solution of LiPF6 in ethylene carbonate/dimethyl carbonate (1:1 v/v; Merck). The cells were constructed and handled in an Ar-filled MBraun glovebox.
Acknowledgment. The help of J. Heine with some of the NMR measurements is greatly acknowledged. We thank P. Heitjans for allowing us to use his NMR equipment in Hannover. References and Notes (1) Arico, A. S.; Bruce, P. G.; Scrosati, B.; Tarascon, J. M.; Van Schalkwijk, W. Nat. Mat. 2005, 4, 366. (2) Bruce, P. G.; Scrosati, B.; Tarascon, J. M. Angew. Chem.-Int. Ed. 2008, 47, 2930. (3) Spiess, H. W. J. Chem. Phys. 1980, 72, 6755.
4744 J. Phys. Chem. C, Vol. 113, No. 12, 2009 (4) Qi, F.; Jo¨rg, T.; Bo¨hmer, R. Solid State Nucl. Magn. Reson. 2002, 22, 484. (5) Qi, F.; Diezemann, G.; Bo¨hm, H.; Lambert, J.; Bo¨hmer, R. J. Magn. Reson. 2004, 169, 225. (6) Qi, F.; Rier, C.; Bo¨hmer, R.; Franke, W.; Heitjans, P. Phys. ReV. B 2005, 72, 104301. (7) Wilkening, M.; Heitjans, P. Defect Diffus. Forum 2005, 237-240, 1182. (8) Wilkening, M.; Ku¨chler, W.; Heitjans, P. Phys. ReV. Lett. 2006, 96, 065901. (9) Wilkening, M.; Heitjans, P. Solid State Ion. 2006, 177, 3031. (10) Wilkening, M.; Heitjans, P. J. Phys.: Condens. Matter 2006, 18, 9849. (11) Wilkening, M.; Heitjans, P. Phys. ReV. B 2008, 77, 024311. (12) Heitjans, P.; Schirmer, A.; Indris, S. In Diffusion in Condensed Matter - Methods, Materials, Models, 2nd ed.; Heitjans, P., Ka¨rger, J., Eds.; Springer: Berlin, 2005; p 367. (13) Wilkening, M.; Gebauer, D.; Heitjans, P. J. Phys.: Condens. Matter 2008, 20, 022201. (14) Faske, S.; Eckert, H.; Vogel, M. Phys. ReV. B 2008, 77, 10. (15) Xu, Z.; Stebbins, J. F. Science 1995, 270, 1332. (16) Verhoeven, V. W. J.; de Schepper, I. M.; Nachtegaal, G.; Kentgens, A. P. M.; Kelder, E. M.; Schoonman, J.; Mulder, F. M. Phys. ReV. Lett. 2001, 86, 4314.
Letters (17) Cabana, J.; Dupre´, N.; Rousse, G.; Grey, C. P.; Palacı´n, M. R. Solid State Ion. 2005, 176, 2205. (18) Cahill, L. S.; Chapman, R. P.; Britten, J. F.; Goward, G. R. J. Phys. Chem. B 2006, 110, 7171. (19) Armstrong, G.; Armstrong, A. R.; Bruce, P. G.; Reale, P.; Scrosati, B. AdV. Mater. 2006, 18, 2597. (20) Bruce, P. G. Solid State Sci. 2005, 7, 1456. (21) Armstrong, A. R.; Armstrong, G.; Canales, J.; Bruce, P. G. Angew. Chem.-Int. Ed. 2004, 43, 2286. (22) Armstrong, A. R.; Armstrong, G.; Canales, J.; Garcia, R.; Bruce, P. G. AdV. Mater. 2005, 17, 862. (23) Jeener, J.; Broekaert, P. Phys. ReV. B 1967, 157, 232. (24) Geil, B.; Diezemann, G.; Bo¨hmer, R. J. Chem. Phys. 2008, 128, 12. (25) Wilkening, M.; Amade, R.; Iwaniak, W.; Heitjans, P. Phys. Chem. Chem. Phys. 2007, 9, 1239. (26) Wilkening, M.; Epp, V.; Feldhoff, A.; Heitjans, P. J. Phys. Chem. C 2008, 112, 9291. (27) Fukushima, E.; Roeder, S. B. W. Experimental Pulse NMR; Addison-Wesley: Reading, PA, 1981.
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