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J. Phys. Chem. B 2009, 113, 224–230
Li-Ion Diffusion in the Equilibrium Nanomorphology of Spinel Li4+xTi5O12 Marnix Wagemaker,*,† Ernst R. H. van Eck,‡ Arno P. M. Kentgens,‡ and Fokko M. Mulder*,† Department of Radiation, Radionuclides and Reactors, Faculty of Applied Sciences, Mekelweg 15, 2629 JB Delft, The Netherlands, Department of Physical Chemistry - Solid State NMR, Radboud UniVersity Nijmegen, ToernooiVeld 1, 6525 ED Nijmegen, The Netherlands ReceiVed: August 18, 2008; ReVised Manuscript ReceiVed: October 28, 2008
Li4Ti5O12 spinel as Li-ion electrode material combines good capacity, excellent cycleability with a high rate capability. Although the potential of about 1.56 V vs Li is relatively high, these features make it the anode of choice for state of the art high power Li-ion batteries. Although the flat voltage profile reflects a two-phase reaction during lithiation, the small change in lattice parameters upon lithiation (“zero-strain” property) leads to a solid solution in equilibrium, as recently demonstrated with diffraction. In this study, the morphology and Li-ion mobility is studied by NMR spectroscopy leading to a more detailed picture, showing that the solid solution in Li4+xTi5O12 spinel should actually be described as domains with sizes less than 9 nm having either tetrahedral (8a) Li occupation or octahedral (16c) Li occupation. The abundant domain boundaries and the associated disorder appear to be responsible for the facile diffusion through the lattice, and hence these nm-sized domains are most likely the origin of the relative high rate capability of this material as electrode for Li-ion batteries. The small domain size, smaller than typical Debye lengths, makes that the material electrochemically behaves as a solid solution. As such, the results give insight in the fundamental properties of the “zero-strain” Li4Ti5O12 spinel material explaining the favorable Li-ion battery electrode properties on an atomic level. Introduction Li4Ti5O12 spinel is a state-of-the-art Li-ion battery electrode material, described by Deschanvres et al.1 and Johnston et al.2 and electrochemically characterized by Colbow et al.,3 Ferg et al.,4 and Ohzuku et al.5 Operating at 1.56 V versus Li metal it is suitable as anode versus high voltage materials in Li-ion batteries, but also in supercapacitors due to its excellent cycleability and high rate capability6 of almost the theoretical capacity (175 mAhg-1) in the nanostructured form of the material.7 Li4Ti5O12 can be lithiated up to the composition Li7Ti5O12 with both end members having the spinel structure, as shown in Figure 1, with the cubic space group Fd3m and lattice parameter 8.35951 and 8.3538 Å,8 respectively. Li occupies the tetrahedral 8a sites in Li4Ti5O12 and the octahedral 16c sites in Li7Ti5O12, and a fraction (1/6) of the Ti on the 16d site is replaced by Li.9 The edge sharing [Li1/6Ti5/6]O6 octahedra form a three-dimensional network that connects the 8a sites via the 16c sites reflecting the most likely diffusion pathway for the Li-ions in spinel compounds [see e.g., Verhoeven et al.10]. The advantage of Li4Ti5O12 over its pure family member LiTi2O4 spinel is that the 1/6 replacement of Ti by Li leads to almost zero difference in lattice parameters between the end members Li4Ti5O12/Li7Ti5O12, (hence referred to as “zero strain” property). The zero strain property is of key technological importance since lattice strains upon cycling are among the main causes of capacity decays in lithium battery electrodes. For both Li4Ti5O12 and the pure spinel, it is well established that at room temperature the (dis-)charging proceeds through a two-phase equilibrium,3,8,11 which leads to a very constant potential over * To whom correspondence should be addressed. E-mail: (M.W.)
[email protected]; (F.M.M.)
[email protected]. † Faculty of Applied Sciences. ‡ Radboud University Nijmegen.
Figure 1. Perspective view of the Li4Ti5O12 structure, where the polyhedron indicate [Li1/6Ti5/6]O6 units. Dark spheres, oxygen; light spheres, lithium. Left: Li4Ti5O12 with Li occupying the tetrahedral 8a sites. Right: Li7Ti5O12 with Li occupying the octahedral 16c sites.
a large range of overall Li concentrations Li4+xTi5O12 with 0.09 < x < 2.91. However, recently it has been demonstrated that in Li4+xTi5O12 this two-phase separation is unstable above 80 K and most likely kinetically induced by the Li-insertion during (dis)charge.12 This means that in equilibrium the material forms a solid solution at room temperature with associated small changes in the open circuit potential.12 The unique behavior of the material upon Li insertion can be rationalized by the zerostrain property that implies that the interface energy between the two phases is very low, thereby facilitating mixing of the two phases and in this case leading to a solid solution at relative low temperatures. A solid solution implies intimate mixing of 8a and 16c site occupation in contrast to the phase separated system where domains of 8a and 16c occupation are separated on a micrometer length scale. The disorder resulting from the mixed 8a/16c occupation is most likely beneficial for the Li mobility as compared to the ordered coexistence of 8a and 16c domains. The solid solution behavior demonstrates that it is energetically favorable for the material to form defect structures where Li
10.1021/jp8073706 CCC: $40.75 2009 American Chemical Society Published on Web 12/09/2008
Equilibrium Nanomorphology of Spinel Li4+xTi5O12
J. Phys. Chem. B, Vol. 113, No. 1, 2009 225
resides in partly filled 8a and 16c sites. We expect that the abundance of such defects is responsible for the relatively high rate capabilities in Li4+xTi5O12. The aim of this study is to probe the Li-ion dynamics locally by magic angle spinning nuclear magnetic resonance in order to reveal the role of the morphology (phase separation versus solid solution) in relation to the Li-ion mobility and thus in the rate capability (power density). Further, the NMR provides a local probe for the Li environment, which should give additional insight in the morphology, and in the electronic properties of the lithiated material. Methods Synthesis. Microcrystalline Li4Ti5O12 (99%) was obtained from Hohsen. Li4+xTi5O12 samples were prepared by chemical intercalation of the Li4Ti5O12 powder with n-butyllithium (1.6 M Aldrich).13 The Li4Ti5O12 powder was mixed with hexane (anhydrous 95+%, Aldrich), and the n-butyllithium was added slowly while stirring the mixture. Five samples were obtained with different amounts of n-butyllithium to form Li4+xTi5O12 with the overall compositions of x ) 0, 0.3, 1, 2, and 3.0. All the lithium is intercalated in the spinel since n-butyllithium (with a potential of 1 V against lithium) reacts efficiently with LTO, as is illustrated by the rapid change of color of the powder (white to blue). After 3 days with occasional stirring, the samples were filtered, washed with hexane, and dried. All sample preparations were carried out in an argon atmosphere glovebox to prevent reactions of Li with air. After preparation the samples were subjected to wet-chemical inductively coupled plasma (ICP) spectroscopy analysis to check the overall composition (ratio Li/Ti). These results confirmed that during preparation all the lithium reacts with the LTO, thus yielding the overall compositions as mentioned. Nuclear Magnetic Resonance (NMR). 7Li magic angle spinning (MAS) and static NMR spectra were recorded on a Chemagnetics 600 Infinity (B0 ) 14.1 T) operating at 233.2 MHz. The MAS probe head with 3.2 mm airtight zirconia rotors achieved spinning speeds up to 19.2 kHz in a dry nitrogen atmosphere. Chemical shifts were referenced to a 0.1 M LiCl aqueous solution. The spectra were recorded after a 30° (at 2ν1, with ν1 ) 89 kHz) radio frequency pulse. The T1 relaxation time was determined to be well below 5 s for all temperatures using a saturation recovery experiment, hence all experiments were recorded with a recycle delay of 20 s, thus ensuring quantitative measurement conditions. To explore the Li mobility two types of experiments were performed, (1) T2 relaxation was measured under static, that is, nonspinning, conditions using a Hahn echo sequence (π/2-τπ-τ-acq) for a range of temperatures (148-473 K) and (2) twodimensional exchange NMR spectra were recorded using the whole-echo acquisition technique14 and employing a hardware rotor synchronization of the exchange time (also called mixing time). Results and Discussion In Figure 2a,b the starting material Li4Ti5O12 shows only one resonance in the MAS spectrum. As can be observed in the static spectrum in Figure 3a the resonance is actually composed of two resonances, a broad resonance due to Li on 16d (replacing Ti) and a more narrow resonance due to Li on 8a, consistent with previous reports.15,16 As Dalton et al. indicated, the cubic local environment of the 8a position suggests that the broadening of this resonance is mainly due to dipolar interactions and not due to quadrupole and chemical shift anisotropy,16 which is in
Figure 2. (a) 7Li MAS NMR (spinning speed, 18 kHz; field, 600 MHz) spectrum of Lix+4Ti5O12 for increasing Li content at room temperature showing the center bands. (b) 7Li MAS NMR (spinning speed, ∼ 18 kHz; field, 600 MHz) side bands of x ) 0, 1, and 3 Lix+4Ti5O12.
Figure 3. 7Li static NMR spectrum of (a) Li4Ti5O12, (b) Li6Ti5O12, and (c) Li7Ti5O12 in 9.4 T (400 MHz) (black) and 14.1 T (600 MHz) (gray).
line with the field independence observed in Figure 3a. Because of the trigonal distortion of the octahedral 16d environment, in addition to dipolar broadening, these sites give rise to quadrupolar and chemical shift anisotropy interactions.16 The field independence in Figure 3a indicates that dipolar and first order quadrupolar interactions dominate the 7Li resonance due to 16d site occupation. Progressive lithiation of the starting composition Li4Ti5O12 leads to the appearance of a broad additional signal at about -10 ppm in Figure 2b. Since it is well established that upon lithiation octahedral 16c sites are occupied9 this resonance should be assigned to Li occupying 16c sites. At the final composition, Li7Ti5O12, almost all the electrochemical active
226 J. Phys. Chem. B, Vol. 113, No. 1, 2009 Li occupies the 16c sites. Li-ions on the 16d sites can be considered part of the host structure, although they appear to be mobile at a very slow rate.17 Lithiation toward the composition Li7Ti5O12 leads to broadening of the static spectra in Figure 3c. The broadening interaction is independent of the field indicating that dipolar and/or first order quadrupolar interactions are the dominating broadening mechanisms for the Li 16c resonance. To get a more quantitative picture of the interactions in the static spectra of Li4+xTi5O12, we consider both the dipolar and first order quadrupolar in more detail. On the basis of the van Vleck equation,18 the second moment of 7Li in in polycrystalline Li4+xTi5O12 can be calculated. Given the nuclear spins of Ti (49Ti: -1.1039 µN, 5.5% natural abundance (na); 47Ti: -0.7883 µN, 7.5% na), 16O (0.0 µN, 99.8% na) and Li (7Li, 3.256 µN, 92.5% na; 6Li, 0.822 µN, 7.5% na), the dipolar coupling will be dominated by the Li-Li interactions, predominantly by the shortest possible Li-Li distances. The lattice sum of all the dipolar interactions on the 8a sublattice representing Li4Ti5O12 leads to a static (or rigid lattice) powder line width of ∼2.3 and ∼4.9 kHz, the latter also taking Li occupation on 16d into account and assuming full nearest neighbor occupation for calculational simplicity. Full 16d occupation will overestimate the dipolar interaction since in reality only 1/6 of the 16d sites are randomly occupied by Liions. Fitting the spectrum in Figure 3a under the restriction of the known 1:3 16d/8a ratio in the peak integral leads to a width (fwhm) of 4.3 kHz for Li on 8a and 17.5 kHz for Li on 16d. Therefore the width of the 8a resonance can be attributed to dipolar interactions; however, the broadening of the 16d resonance cannot be explained by dipolar interactions and given the field independence of the broadening (in Hz) first order quadrupolar interactions are most likely the dominating 16d broadening mechanism. The static Li7Ti5O12 spectrum in Figure 3c was fitted under the restriction of the known 1:6 16d:16c ratio in the peak integral, leading to a peak width (fwhm) of 15.1 kHz for Li on 16d and 43.6 kHz for Li on 16c. The lattice sum of all the dipolar interactions on a 16c sublattice representing Li7Ti5O12 leads to a static (or rigid lattice) powder line width of ∼4.2 and ∼ 8.5 kHz also taking Li occupation on 16d into account, assuming full occupation for computational simplicity. Again, full 16d occupation will overestimate the dipolar interaction since only 1/6 of the 16d sites is randomly occupied by Li. Clearly, the experimental width of the 16c resonance cannot be explained by only dipolar interactions, and as for the 16d resonance first order quadrupolar interactions need to be considered. Using a simple model based on the positions of the ions surrounding Li and assuming point charges (i.e., an ionic charge model), an estimate for the quadrupole interaction constant, CQ, and the asymmetry parameter, η, can be obtained.19 A complicating factor in the Li4+xTi5O12 structure is the random occupation of Li and Ti on the 16d positions (which is also demanding when more advanced DFT calculations are considered). Various configurations were calculated, however, only a few essential results will be mentioned that reflect the general trend. Two values for each environment are reported, taking into account all neighbors within a 7 Å sphere, by first assuming no Li on the 16d sites (pure spinel LiTi2O4 configuration) and second assuming one out of six Ti replaced by a Li-ion. For the 8a position in Li4Ti5O12, this leads to CQ values of 149 and 154 kHz, respectively (if only the first oxygen coordination is taken into account this leads to CQ ) 0 kHz as should be expected for the cubic tetrahedral environment), and
Wagemaker et al.
Figure 4. 7Li MAS NMR (spinning speed, 18 kHz; field, 600 MHz) center band of Li6Ti5O12 and linear combination of 1/3 Li4Ti5O12 and 2/3 Li7Ti5O12 (leading to overall composition Li6Ti5O12).
for the 16d position in Li4Ti5O12 this leads to CQ values of 409 kHz and 342 kHz, respectively. This indicates that the larger line-width of the 16d resonance compared to the 8a resonance, observed in Figure 3a, is mostly due to first order quadrupole interaction, which is consistent with the field independence. Apparently the simple ionic model overestimates the broadening as only two sidebands originating from the first order quadrupolar interaction are detected in the MAS spectra (Figure 2b) indicating a quadrupolar broadening of the order of 72 kHz. This may be no surprise because the model assumes pointlike charges, whereas the charges in these semiconducting materials are rather delocalized significantly reducing the quadrupole coupling constant. For the 16c position in Li7Ti5O12, the calculation of the quadrupole interaction constant, CQ, leads to of 432 kHz assuming no Li on 16d sites and 331 kHz assuming one out of six Ti on 16d replaced by a Li-ion. Again, the simple point model overestimates the broadening. Nevertheless, we may conclude that the quadrupole interaction of the 16c site is stronger, consistent with the more prominent sidebands (Figure 2b) and the broader static spectrum in Figure 3c. For the 16d environment in Li7Ti5O12 the calculation leads to CQ values of 308 kHz assuming no Li on 16d sites and 257 kHz assuming one out of six Ti on 16d replaced by a Li-ion. From these calculations, it also appears that the quadrupole interaction of the 16d sites reduces upon lithiation from composition Li4Ti5O12 to Li7Ti5O12. This explains the weaker 16d resonance contribution in the sideband manifold shown in Figure 2b. On the basis of these values for CQ the second order quadrupolar broadening and the quadrupole induced shift can be calculated to be negligible in the presented measurements. On the basis of these straightforward considerations, we conclude that the dominant interactions in Li4+xTi5O12 are dipolar and first order quadrupolar interactions. Solid Solution versus Two-Phase Equilibrium. Recent diffraction results showed that Li4+xTi5O12 in equilibrium at room temperature is a solid solution,12 rather than the two-phase system that may be expected from electrochemistry.8 Apparently, the two-phase separation, stable only below 80 K, is kinetically imposed during electrochemical (dis)charging, but given time will relax back to a solid solution. Assuming a two-phase segregation on a length scale that is significantly longer (e.g., 10-6 m) than the Li diffusion path length on the time scale of the NMR experiment (10-4 s), would imply that the NMR spectra of intermediate compositions should be represented by a linear combination of Li4Ti5O12 and Li7Ti5O12. Figure 4 demonstrates that this is not the case, consistent with the diffraction results.12 The fact that both resonances of the intermediate composition are broadened can only mean that the majority of Li on 8a “feel” Li on 16c (and vice versa). As discussed above, the dominant interactions are dipolar and first order quadrupolar, both dominated by local interactions. There-
Equilibrium Nanomorphology of Spinel Li4+xTi5O12
Figure 5. (a-c) 7Li MAS 2D-NMR (field, 600 MHz) center band in Li6Ti5O12 for different exchange times (tmix) at T ) 373 K, f1 and f2 represent the chemical shift before and after tmix, respectively. For increasing tmix, cross signal intensity becomes visible in the marked region (and symmetrical around the diagonal), indicating Li-ion diffusion between the 8a and 16c sites. The starlike shape of the 8a resonance is due to the 2D Fourier transformation of the Lorentz-shaped peak. (d) Cross signal intensity between 8a and 16c versus exchange time, including a fit assuming hopping between 8a and 16c (see text) resulting in a correlation time of 2.3 ms.
fore, the broadening in Figure 4 indicates that the majority of the Li occupying 8a must be located only few Angstroms or less away from Li on 16c and vice versa. Whereas the 8a site is characteristic of the Li4Ti5O12 composition and the 16c site for the Li7Ti5O12 composition, the additional broadening is consistent with the absence of true phase segregation, which should extend over much larger length scales (micrometers), and therefore the present NMR result appears to be confirm our previous diffraction results.12 Li-ion Mobility, 2D Exchange NMR. On the basis of the difference in chemical shift, the exchange between crystallographic distinct sites, such as 8a and 16c, can be probed with 2D exchange NMR.20 This method has proven to be very powerful in revealing the Li-ion dynamics in various materials.10,21,22 In Figure 5a the 2D exchange spectrum of Li4+2Ti5O12 is shown for a short mixing time of 55 µs. All three sites are observed in the 2D spectrum but display very different characteristics. The diagonal peak for the 8a site is cross-shaped, typical for a homogeneously broadened resonance, in good agreement with the second moment calculations which pointed out that the main broadening mechanism is dipolar interaction. The 16c diagonal peak on the other hand is typical for an inhomogeneously broadened line undergoing fast exchange with itself, in good agreement with the quadrupolar interaction being the dominant broadening mechanism for that site. Finally, the 16d resonance can be observed as a ridge along the diagonal: an inhomogeneously broadened line without exchange. In Figure 5a no exchange is observed between the different sites at this short mixing time. In Figure 5b,c, the exchange can be observed as cross intensity between 8a and 16c, and the evolution of the cross peak intensity as a function of time (also called mixing time) provides direct information on the rate of the exchange process between 8a and 16c sites in the intermediate composition Li6Ti5O12. Assuming a hopping model, the exchanged intensity should evolve as 1/2[1 - exp(-2tmix/τC)],10 which results in a 8a-16c (and vice versa) hopping correlation time, τC, of 2.3 ms in Li6Ti5O12 at 373 K. The most likely
J. Phys. Chem. B, Vol. 113, No. 1, 2009 227 diffusion path from 8a to a next 8a site is via the intermediately located 16c site. From the correlation time, the microscopic selfdiffusion can be calculated using D ) d2/(nτC), where d is the hopping distance and n the number of possible jump directions. Assuming the 8a-16c diffusion path, the hopping distance is 1.81 Å, and the average number of jump directions is 2.67 (2 for 16c and 4 for 8a) the diffusion coefficient at 373 K amounts 5.3 × 10-14 cm2/s. This value is 2 orders of magnitude smaller than macroscopic diffusion coefficients for Li4+xTi5O12 at room temperature.23 To understand why this approach leads to an under estimation of the diffusion coefficient, we need to consider the dynamic site occupation on 8a and 16c from an energetic point of view and the manner in which the 2D NMR technique samples the chemical shift information. Each 8a site has four nearest 8a neighbors at 3.62 Å and four nearest 16c neighbors at about 1.81 Å, which is exactly halfway the connecting line between two 8a sites. Lithiation of Li4Ti5O12, where all 8a sites are occupied, leads to occupation of 16c sites. This creates nearest neighbor pairs (8a-16c) which will be energetically unfavorable due to Coulomb repulsion on the short 8a-16c distance (1.81 Å). As a result, Li-ions at 8a sites neighboring occupied 16c sites will also move toward 16c sites, which actually initiates the first-order two-phase transition reaction as was determined in the very similar LiTi2O4 spinel material.24 Therefore, in a domain dominated by 8a occupation, occupation of a 16c site, located between two neighboring 8a sites, will be energetically unfavorable, and hence Li-ions hopping from 8a to 8a will have negligible occupation time at the 16c position. The 2D NMR technique is insensitive to the intermediate, short-term, occupation of a 16c position when before and after the mixing time the Li is on an 8a position. The same argumentation holds for 8a occupation in a domain where 16c occupation is dominant. Hence, the correlation time detected with the 2D NMR represents the average time that it will take a Li-ion to diffuse spontaneously from an 8a domain toward a 16c domain, or vice versa. Clearly, this will depend on the average size of the domains. Unless the material is a solid solution (complete mixture of 8a and 16c occupation, no domains of 8a (or 16c) occupancy), the average distance from a 16c (or 8a) domain to a 8a (respectively 16c) domain will be larger than the smallest 8a-16c distance (1.81 Å). Therefore, it is concluded that the underestimation of the diffusion coefficient by 2 orders of magnitude as determined from 2D NMR indicates the presence of 8a and 16c domains. In order to give a correct estimate of the microscopic selfdiffusion coefficient, the domain size is required. Recent diffraction pointed out that the equilibrium domain size is a function of temperature. Below 80 K, the phase separation in domains of 8a and 16c occupation is stable and appears to occur at a micrometer scale.12 It was suggested that increasing the temperature progressively reduces the domain size until around room temperature; then the domains become too small to be detected by diffraction and a single phase with mixed 8a and 16c occupation (solid solution) is observed.12 The presence of such small 8a and 16c nanodomains will in principle give rise to diffuse scattering in addition to the Bragg reflections depending on the size and the contrast of the domains. Given the difference in Li concentration between 8a and 16c occupation, we calculated the diffuse scattering for a regular matrix of nanosized domains. The intensity of the resulting diffuse neutron scattering (there is even less contrast for X-rays) is less than 0.1% of the Bragg intensity and would disappear in the statistical noise of the neutron spectra.12 The consequence is
228 J. Phys. Chem. B, Vol. 113, No. 1, 2009
Figure 6. (a) 7Li static NMR (field, 600 MHz) spectra of Li6Ti5O12 obtained with a Hahn Echo pulse sequence for a number of temperatures illustrating the effect of Li diffusion on the line-width (motional narrowing). The spectra are normalized on the peak height for display purposes. (b) Plot of the 7Li transversal relaxation time T2 of Li residing on the 8a sites for the various compositions, and Li on 16c for composition Li7Ti5O12; error bars are of the size of the symbols. The data were acquired under nonspinning conditions. The fit is assuming an Arrhenius law for the Li-ion hopping rates as a function of temperature, leading directly to a correlation time and activation barrier of the Li motion. The uncorrected 8a Li6Ti5O12 data set represents the T2 relaxation without the correction of the 8a-16c exchange (see text).
that diffraction does not allow detection of the suggested nanodomains of Li 8a and 16c domains. Therefore, the size and existence of such nanodomains of 8a and 16c occupation cannot be detected by direct observation through diffraction. Alternatively, the spontaneous self-diffusion can be determined by probing the local Li-ion mobility with 7Li NMR T2 relaxation measurements. Li-Ion Mobility, T2 Relaxation. With the onset of Li-ion motion there will be an increase of the 7Li NMR T2 relaxation time with increasing mobility, an effect known as motional narrowing (it causes the actual resonance in the frequency domain to become more narrow, as illustrated in Figure 6a. Motional narrowing occurs when the lithium hopping frequency between sites exceeds a relevant NMR interaction (expressed in hertz). In view of the dominant interactions of the static spectra discussed above, Figure 6b indicates the averaging of the nuclear dipolar interactions of Li on the 8a sublattice, evidencing temperature dependent Li mobility. It should be noted here that the dipolar interactions can only be averaged significantly when the positions of Li nuclei relative to all other nuclei sample many different positions with sufficiently fast rates. Some more local Li motion, for example, enclosed inside the octahedral sites, does not change the average position relative to the other nuclei significantly, and as a result the T2 relaxation does not change. The absence of a shift of the Li resonances as a function of temperature rules out the possibility of relaxation through a hyperfine type of interaction with the electron spins. We conclude that the motional narrowing observed in Figure 6 is due to Li-ion mobility, and knowledge of T2 versus temperature allows quantifying of the barrier and the time-scale for Li hopping through the Li4+xTi5O12 host lattice which can
Wagemaker et al. be used to estimate the self-diffusion coefficient and its activation energy.25,26 Because the T2 relaxation time of 16d, 16c and 8a sites differs, as demonstrated by the difference in homogeneous line width in Figure 5a, the three components can be discriminated. In all cases, Li on the 16d sites appeared not mobile on the time scale of this experiment, that is, these species did not give rise to motional narrowing. The static T2 for Li on the 16d site (10 µs) indicates that if Li-ions hop from or toward the Li 16d sites, the correlation time between the hops should be significantly less than ∼10 µs at 423 K, consistent with the slow hopping observed by Wilkening et al.17 The short T2 relaxation time of Li on the 16c lattice prevents significant motional narrowing and only the onset of mobility was observed (not shown) for the compositions with a mixture of 8a and 16c occupation (x ) 0.3, 1, 2 in Li4+xTi5O12). As a consequence the diffusion on the 16c sublattice could not be determined as accurate as for the 8a sublattice. The absence of motional narrowing in Li4Ti5O12 (only 8a occupancy) in Figure 6b shows that no Li-ion mobility on the 8a sublattice is detected on a time scale related to the static line width (∼80 µs) up to 413 K (maximum temperature achieved). However, lithiation toward Li4.3Ti5O12 leads to considerable motional narrowing for Li-ions on the 8a site (Figure 6b) and the onset of motional narrowing on the 16c sites. The spontaneous mobility of Li-ions becomes detectable around 300 K. Assuming an Arrhenius law for the Li-ion hopping rates as a function of temperature, the correlation time and activation barrier of the Li motion can be obtained. Before doing so, it should be realized that the exchange between the 8a and 16c sites may influence the T2 relaxation. The difference in chemical shift between Li at 8a and 16c is approximately 8 ppm, as can be observed from Figure 2. This implies that exchange between these resonances approaching a time scale in the order of milliseconds will lead to broadening of both resonances, hence to a decrease in T2, eventually leading to merging of both resonances into a single resonance. The exchange correlation time of 2.3 ms at T ) 373 K, resulting from the exchange in Figure 5, indicates that at the high temperature end in Figure 6b the onset of exchange leads to a smaller increase in T2 as may be expected in the absence of exchange. For compositions with mixed 8a and 16c occupancy this implies that during the Hahn Echo experiment the transverse magnetization Mxy of the 7Li spins does not simply decay as a sum of solutions of the Bloch equations -τ/T2 -τ/T2 Mxy(τ) ) M8a + M16c xy (0)e xy (0)e 8a
16c
(1)
Where Mxy(0) is the macroscopic starting magnetization, τ is the echo time of the Hahn echo experiment, and T2 the transversal relaxation time. The exchange of Li-ions from 8a toward 16c and vice versa can simply be accounted for by introducing the exchange rate 1/tmix in the Bloch equations. This leads to the following solution for the transverse magnetization decay:27 8a 16c (0)e-τλ1 + Mxy (0)e-τλ2 Mxy(τ) ) Mxy
λ1,2 ) -
[
1 1 1 2 + 8a + 2 T8a tmix T 2 2
(
1 1 4 + 8a - 16c 2 tmix T2 T2
)] 2
(2)
For composition Li6Ti5O12, Figure 6b shows the uncorrected and the corrected data, indicating a growing correction of the measured T2 at high temperatures. At low temperatures the mixing rate 1/tmix is small compared to the transverse relaxation rate 1/T2, hence the exchange does not affect the measured
Equilibrium Nanomorphology of Spinel Li4+xTi5O12 relaxation rate (in the limit of 1/tmix f 0 eq 2 equals eq 1). However, at higher temperatures the decreasing relaxation rates 1/T2 approach the exchange time scale and eq 2 is required to extract the true relaxation times T2 for both species 8a and 16c. For all compositions investigated, x ) 0.3, 1, 2 (x ) 1 not shown in Figure 6b), we find for the 8a and 16c sublattice correlation times (the average time between two successful hops) at room temperature around ∼75 and ∼30 µs, respectively, and activation barriers of 0.31 ( 0.01 and 0.3 ( 0.1 eV, respectively, resulting in self-diffusion coefficients close to 4.0 × 10-12 cm2/s (see previous publication for details concerning the fitting26). Comparison of the chemical and the self-diffusion coefficient is rather complicated, in particular for nondilute systems as studied at present; however, here we merely report that the present values for the chemical diffusion coefficient fall within the range of values, 10-13-10-9 cm2/s reported for microsized materials by the systematic study of Kavan et al. using electrochemical methods that probe the (chemical) diffusion coefficient.23 Interestingly, similar to the starting composition Li4Ti5O12, no motional narrowing is observed on the 16c sublattice in the end composition Li7Ti5O12, indicating that there is no spontaneous Li-ion mobility on a time scale related to the static line width (∼20 µs) up to 413 K (maximum temperature achieved during the experiments). In the structural end members, Li4Ti5O12 and Li7Ti5O12, respectively 8a and 16c sites, are (close to) fully occupied, hence there is (almost) no mixed 8a/16c occupation. For intermediate compositions at room temperature, the system can be characterized as a solid solution consisting of mixed 8a/16c occupation.12 Hence the presence of significant Li-ion mobility setting in around room temperature appears to be correlated to the presence of abundantly mixed 8a/16c occupation (solid solution). Wilkening et al.17 recently reported on the Li-ion mobility in spinel Li4+xTi5O12 probed with 7Li T1F (spin-lattice) relaxation in the rotating reference frame. In the present T2 (spin-spin) relaxation data, Li-ions residing on the 8a positions in Li4Ti5O12 appear to be frozen indicating poor mobility. Being sensitive to slower diffusion, T1F relaxation allowed quantification of the activation barrier Li-ion mobility leading to EA ) 0.76 eV,17 confirming the poor mobility of Li-ions for the single phase Li4Ti5O12 material. For composition x ) 1.7, Wilkening et al.17 found an activation energy for Li-ion diffusion of ∼0.41 eV, which is significantly different from the value ∼0.31 eV that is found for compositions x ) 0.3, 1, 2 in the present study. Also, Wilkening et al.17 appear to find a single T1F relaxation rate, whereas T2 relaxation indicates 2 motional narrowed components for Li-ions occupying 8a and 16c sites, reflecting observed difference in homogeneous line width (see Figure 5a). A possible explanation for the higher activation energy for Li-diffusion observed by Wilkening et al.17 may be due to a temperature dependent activation barrier. The motional narrowing probed at present extends over a relatively small temperature range, roughly from 300 up to 410 K in Figure 6b. In the larger temperature range data probed by the T1F relaxation presented by Wilkening et al.,17 one can observe that the slope, representing the activation barrier for diffusion, is relatively small in the range 300-410 K. Therefore, in this limited temperature range the activation barrier may be less than the fitted 0.41 eV,17 consistent with the present observation. An temperature depended activation barrier may not be unlikely given the fact that the domain structure varies with temperature, starting with microdomains of 8a and 16c occupation at 80 K up to a solid solution above room temperature.12
J. Phys. Chem. B, Vol. 113, No. 1, 2009 229 Domain Size. In the previous sections, the T2 relaxation measurements and the 2D line shapes showed the presence of spontaneous Li-ion hopping between 8a (16c) sites on a time scale of approximately ∼5 µs (∼2 µs) at 373 K. Because of the size of the domain, hopping from 8a to 16c becomes visible in the 2D NMR spectra on longer timescales, approximately 2.3 ms at 373 K, when Li in an 8a (16c) domain crosses the domain boundary to a 16c (8a) domain. Interestingly, when understanding this mechanism, the time scale of 8a-16c hops observed in the 2D NMR is a rather direct measure of the average distance between the 8a and 16c occupied domains. However, this interpretation introduces a controversy as it assumes the existence of 8a and 16c domains which implies two-phase segregation, whereas diffraction recently demonstrated that the system in equilibrium at about room temperature is actually a solid solution characterized by a mixed 8a/16c occupation.12 However, the conversion between two-phase segregation and solid solution is for Li4+xTi5O12 a gradual transition, where the initially micrometer 8a and 16c domains reduce in size with increasing temperature.12 At a certain stage, the domains will be of the order of nanometers, that is, much less than the coherence length of X-rays and neutrons. As a result, diffraction will only observe average occupations (note that for Li4+xTi5O12 the difference in lattice parameter is negligible, in particular having nanomixed domains), which is referred to as a solid solution. In addition, one should take into account that the Li+ substituting the Ti+3.4-+4 on the 16d sites introduces strong variations in the potential energy landscape experienced by the inserted Li. The distance of the 16d site to respectively the 8a and 16c sites is 3.45 and 2.95 Å. The difference in valence of the Ti and Li ions and the distance between the sites 16d and 16c introduces energetic changes of similar magnitude as that of simultaneous 8a and 16c occupancy and can therefore promote simultaneous 8a and 16c occupation in the neighborhood of a Li on 16d. Therefore, it is likely that at room temperature the Li4+xTi5O12 (0 < x
