Understanding fast ion dynamics in sodiated Li4Na x Ti5O12: from interfacial to extended Li+ and Na+ dynamics in its mixed-conducting solid solutions

Climate change and energy crises require the development of new sustainable materials to realise reliable electrochemical energy storage devices. Spinel-type Li4Ti5O12 (LTO) is one of the most promising anode materials not only for Li-based batteries, but also for those relying on sodium. While Li+ ion dynamics at the early stages of lithiation has been studied already previously, almost no data on the diffusion properties of Na+ ions can be found in the literature. Here, we used nucleus-specific 7Li and 23Na nuclear magnetic resonance (NMR) spectroscopy to quantify the motional processes in mixed-conducting Li4Na x Ti5O12 with x = 0.1, 0.5 and 1.5 on the angstrom length scale. Most importantly, our results reveal a strong increase in Li+ diffusivity in the early stages of chemical sodiation that is accompanied by a sharp decrease in activation energy when x reaches 0.5. The two-component 7Li NMR spectra point to the evolution of an interfacial solid solution at very low sodiation levels (x = 0.1). At x = 0.5, these regions emerge over almost the entire crystallite area, enabling rapid 8a-16c-8a Li+ exchange (0.4 eV), which leads to facile long-range ion transport. We direct the attention of the reader towards the initial formation of solid solutions in LTO-based anode materials and their capital impact on overall ion dynamics. In contrast to macroscopic electrochemical testing, NMR is uniquely positioned to detect and to resolve these exceptionally fast ion dynamics during the initial stages of sodiation. As these processes crucially determine the fast-charging performance of LTO-type batteries, our study lays the atomistic foundations to establish a general understanding of why two-phase materials such as LTO can act as an impressive insertion host for both Li and Na ions.


Introduction
Electrochemical energy storage devices, which power mobile phones or notebooks, are an integral part of daily life in industrialised countries [1][2][3]. Lithium batteries of various types and sizes are employed in many fields of electric storage ranging from mobile to stationary necessities. In particular, these fields do also include the transport sector, for which powerful large-scale systems are needed [4][5][6][7]. A gradual exhaustion of the world's lithium resources in the future, however, gives rise to thought about replacing Li as the ionic charge carrier in some of these systems. In particular, such considerations will affect the development of stationary, high-volume electrical storage systems. A highly abundant and, therefore, low-cost alternative would be sodium, Na.
Since the early stages of battery research, devices relying on ions such as Li + or Na + have been investigated in parallel. The commercialization of the first lithium-ion battery by Sony in 1991 [8,9] led, however, to a slowing down of research on Na-ion batteries. In the future, the market of the aforementioned with Li 2 TiO 3 that is almost invisible for XRD. We could not detect any other side phases or impurities of untreated LTO (see figure S1). Milling does not change the crystal structure; there are no mechanical transformations observed except those related to the broadening of the reflections due to size effects and were possibly strain introduced. Additionally, the low sodiation contents have only marginal influence on the positions of the Bragg reflections.

Sodiation procedure
Dimethoxyethane (DME), supplied by Fluka Chemicals, was mixed with Biphenyl in stoichiometric amounts to yield 1 M biphenyl-1,2-dimethoxyethane. To form a dark blue sodiating agent, approximately 2.3 g of sodium metal were added to 100 ml of the aforementioned 1 M biphenyl-DME solution. LTO was immersed into the solution at a specific molar ratio to obtain different sodiation levels. The calculated ratios were 0.1:1, 0.5:1 and 1.5:1 mol Na per mol LTO, hereafter referred to as x = 0.1, 0.5 and 1.5. The sodiation was carried out by stirring LTO in the reducing medium for several hours. The higher the sodium content, the more titanium ions get reduced, resulting in a darkening of the blue colour. Unless the sodiating agent is used in excess, the completion of the sodiation process is indicated by the reagent fading in colour. To remove all reagent residues, the sodiated powder was washed three times with DME and afterwards dried in a vacuum for 24 h. The Na content was verified by inductively coupled plasma emission spectroscopy; the standard deviation turned out to be 10%. The final sodiated LTO samples were then fire-sealed in quartz tubes with a length of approximately 2 cm. Quartz wool was used to centre the powder sample in the tube and to prevent it from heating during the sealing process.

NMR investigations
NMR measurements were carried out using an Avance III spectrometer (Bruker) that is connected to an Ultrashield 500 MHz widebore magnet with a magnetic field of 11.7 T. This field corresponds to Larmor frequencies of ω 0 /2π = 194 MHz and ω 0 /2π = 132 MHz for 7 Li and 23 Na, respectively. At a constant power output of 200 W, the π/2 pulse lengths varied with temperature in a range from 2 to 4.8 µs for 7 Li and from 2.2 to 2.9 µs for 23 Na. 23 Na and 7 Li NMR spin-lattice relaxation (SLR) rates, 1/T 1 ≡ R 1 , were acquired with the well-known saturation recovery pulse sequence, 10 × π/2 − t d − π/2 − acquisition (acq.) [42]. The variable delay time (t d ) was chosen such that the complete magnetization transients M z (t d ) were probed. The transients were either analysed with a single exponential M z (t d ) ∝ 1 − exp(−(t d /T 1 ) γ ′ ) or with a sum of two non-stretched exponentials. The stretching factor γ ′ = γ 1 ranged from 1 to 0, whereby γ 1 = 1 yields non-stretched functions.
Additionally, spin-lock SLR NMR measurements [33], were performed to investigate the temperature dependence of the corresponding 7 Li NMR rate 1/T 1ρ ≡ R 1ρ . This technique, π/2 p(t lock ) − acq., features a variable spin-lock pulse p(t lock ) and was introduced by Ailion and Slichter [42][43][44][45]. To ensure comparability, the spin-locking frequency, ν lock , was set to 33.3 kHz for all experiments. Transversal magnetization transients M ρ (t lock ) recorded as a function of the locking pulse length t lock were analysed with stretched exponentials according to M ρ (t lock ) ∝ exp(−(t lock /T 1ρ ) γ ), γ = γ 1ρ (see below). 6 Li magic angle spinning (MAS) NMR spectra were recorded using a 2.5 mm probe (Bruker) at a spinning frequency of 30 kHz. We accumulated 128 scans to obtain a single 1D NMR spectrum. To ensure full longitudinal relaxation of all magnetization components, the recycle delays were set to 600 s. Solid LiCl served as a reference to determine the NMR chemical shifts δ CS .

Results and discussion
3.1. 7 Li NMR spectra and motional narrowing of the central transition Recording 7 Li (spin-quantum number I = 3/2) NMR lines as a function of temperature gives first insights into the structural, electric and dynamic features of the samples with their varying Li content. In figure 2 the 7 Li NMR spectra of LTO samples with x = 0.1, x = 0.5 and x = 1.5 are shown. At low temperatures, that is, at 298 K, the line of Li 4 Na 0.1 Ti 5 O 12 is composed of a broad component (III) that mirrors the so-called quadrupole transitions (±3/2 ⇄ ±1/2) of a powder sample [46][47][48]. This signal is superimposed by the central line (±1/2 ⇄ ±1/2) that is mainly broadened because of homonuclear Li-Li magnetic dipolar interactions (signals I and II). Sufficiently rapid Li + exchange processes, characterised by jump rates 1/τ NMR in the kHz range, increasingly average these interactions with temperature [49]. This averaging process causes the central line to narrow, as is clearly seen figure 2(a). At temperatures at which 1/τ NMR reaches or exceeds the order of the width (full width at half maximum, FWHM) of the quadrupole component, the broad line (III) of the overall signal starts to narrow also. This narrowing process sets in at approximately 373 K (see figure 2(a)). (a) Crystal structure of Li4Ti5O12 crystallizing with spinel-type structure. Li ions occupy the 8a sublattice as well as sharing octahedral sites 16d with titanium ions. (b) Additional Li + or Na + ions enter the structure by occupying the empty 16c sites. (c), (d) Illustrations that highlight the empty 48f sites and 8b sites. The polyhedra 16c are connected to two 8a sites and to four 48f sites by face sharing. 16d shares common faces with 48f (four sites) and with two 8b sites. Jumping of a Li + ion involving the 16d sites is possible via the pathway 8a-16c-48f -16d(-8b), as also indicated by the arrows in yellow. See text for further explanation.

Very low sodiation levels (x = 0.1): formation of an interfacial solid solution
Most importantly, the central line of Li 4 Na 0.1 Ti 5 O 12 (figure 2(a)) reveals a so-called two-component narrowing process (see also the inset of figure 2(a)). We recognise that at 373 K the central transition is composed of two contributions (I and II). The narrow line (I) on top of the broader one (II) reflects Li + ions being much more mobile than the majority of Li + ions in LTO. Importantly, a non-sodiated sample (see the respective inset in figure 2(a)) does not show this component (see also below). Hence, we safely conclude that the introduction of Na + /e − significantly changes the Li + diffusion properties of LTO.
Assuming that the Na + ions occupy the empty 16c sites in the LTO framework, the neighbouring Li + ions on 8a, which are connected to 16c by face sharing, are immediately subjected to strong Coulomb repulsions. To escape from the 8a site, Li + jumps to the next empty 16c site. Again, on the new position it senses strong Li 8a -Li 16c interactions. Altogether, these local repulsions result in an overall frustrated situation [35] that gives rise to both strongly enhanced local and long-range Li + ion dynamics, see below [22,50]. The same 8a-16c diffusion pathway would be opened if Na + kicks off the Li + ions on 16d. The former 16d ions would occupy empty 16c sites leading to the same frustrated Li + cation arrangement.
As has been shown for Li 3.1 [LiTi]O 12 through 2D 6 Li MAS NMR exchange spectroscopy [23], the Li ions on 16d are much less mobile than those on 8a. Hence, we conclude that, also in the present case, the motional narrowing in Li 3 Na x [LiTi]O 12 with x = 0.1 is indeed predominantly governed by rapid 8a-16c Li + exchange processes driven by the strong repulsive Coulomb interactions [35].
The situation seen for Li 4 Na 0.1 Ti 5 O 12 is, however, not entirely comparable to that seen for Li 4.1 Ti 5 O 12 by some of us earlier [22]. In Li 4.1 Ti 5 O 12 the whole 7 Li NMR line is affected by the doping effect, giving rise to the formation of a solid solution at low x values [22]. Here, we see that the central 7 Li NMR line of Li 4 Na 0.1 Ti 5 O 12 is composed of two contributions (I and II). The broader line labelled II reflects the untouched LTO phase. Hence, not all of the ions in Li 4 Na 0.1 Ti 5 O 12 have access to fast exchange processes. The diffusion properties of most of them remain unaffected. This two-component line shape points to a segregation [24] of Na ions, most likely in the outer spheres, that is, in the interfacial regions of the particles (see the illustration in figure 2(b)). We still tend to ascribe the narrow line (I) to those ions located in a solid-solution-like region rather than to those residing in phases such as Na 6 [LiTi]O 12 and Li 7 [LiTi]O 12 [28]. These Li-rich [51] and Na-rich phases do not provide fast Li + ions, which will be discussed below.
For comparison and to put the present results into a broader context, two-component NMR line shapes have frequently been observed for a number of nanocrystalline ceramics that can be described by core-shell features with fast Li ions in the interfacial regions and slower ones in the crystalline bulk areas [52][53][54]. In contrast to these systems studied so far, the unsodiated, nanocrystalline LTO sample does not show such a two-component feature. Thus, as mentioned above, the narrow line shows up only when Na is inserted, which switches on cation-cation repulsions mainly involving the face-sharing 8a and 16c LiO 6 polyhedra (see figure 1(b)).

Na + insertion levels of x = 0.5: spatially extended solid-solution region through internal lithiation
For x = 0.5, the aforementioned situation of cation-cation repulsions escalates even more. In agreement with enhanced Li 8a -Li 16c dynamics due to increasing cation-cation Li + -Li + and Li + -Na + repulsions, we observe that the 7 Li NMR lines are subjected to strong motional narrowing effects (see figure 2(b) and its inset). To visualise these changes a better way, we plotted the FWHM of the three samples together with those of the unsodiated, microcrystalline LTO sample as a function of temperature (see figure 3). While motional narrowing of microcrystalline (and nanocrystalline) unsodiated LTO starts at relatively high temperatures, i.e. slightly below 400 K, the curve of the sample with x = 0.1 and especially that belonging to the sample with a Na content of x = 0.5 are clearly shifted towards lower temperatures. For x = 0.5 motion-induced narrowing of the central line does already start at a temperature below 300 K, indicating extremely fast Li + ion dynamics at these early stages of LTO sodiation. A separation into the lines I and II, as has been possible for x = 0.1, turns out to be difficult. Now, most, if not all of the Li + ions get involved in fast exchange processes, as would be the case for a spatially extended quasi solid solution (see the illustration in figure 2(b)). The same behaviour was observed for Li 4.1 Ti 5 O 12 and Li 4.3 Ti 5 O 12 previously by NMR [22] and recently confirmed by impedance spectroscopy by Pagani et al for thin films prepared by electrochemical lithiation [50]. Note that impedance spectroscopy is fraught with difficulties if one has to deal with mixed conducting (ionic-electronic) samples; a clear separation of ionic contributions to the overall conduction properties is needed. NMR, on the other hand, is able to directly sense ionic motions.
Here, we assume that the Na ions entering the structure, dislodge the Li + ions and force them to occupy sites farther away from the surface regions. This internal lithiation process results in extended areas with fast Li + diffusion. In this sense, Li + hopping essentially follows the principles of an interstitialcy diffusion mechanism involving the regular site 8a and the interstitial site 16c [35], as illustrated in figure 3 Li + diffusivity in Li 4 Na 0.5 Ti 5 O 12 is high enough to average the site-specific electric quadrupole interactions. Consequently, the corresponding quadrupolar NMR signal (III) disappears at higher T. Most likely, the rapid Li + ions sense an averaged, almost vanishing electric field gradient and are no longer exposed to quadrupole interactions giving rise to a large (mean) coupling constant. This behaviour has also been observed for lithiated LTO, but less pronounced [22].
As a side remark, the drastic increase in Li + diffusivity upon sodiation of LTO is exactly the opposite of what is seen for so-called mixed alkali glasses [55][56][57][58][59][60]. In glasses with a single charge carrier, such as Li + , a strong decrease in ionic conductivity is observed when a second one, e.g. Na, is added.

The multiphase regime at higher sodiation levels
For x = 1.5 the overall situation changes again. We observe a less pronounced NMR line-narrowing process at low T, see figure 2(c). The corresponding motional narrowing curve shifts back to higher temperatures ( figure 3). This observation shows that Li + ion diffusivity slows down again. We explain this decrease in Li + diffusivity by considering the following aspects. While Na ions on 16c destabilise Li + on 8a leading to rapid frustration-driven Li exchange processes, at the same time the Na + ions might block the 8a-16c-8a jump pathway if we assume a lower diffusivity of Na + as compared with Li + . Indeed, a lower diffusivity is seen by 23 Na NMR line shape measurements, as will be discussed below. The more Na ions enter the structure, the more 8a-16c-8a pathways, needed for through-going ion transport and effective averaging of the dipolar interactions, get blocked in the Na-rich regions of the solid solutions. At this insertion stage, we cannot exclude the involvement of other, alternative Li + diffusion pathways chosen by the ions. For example, it is possible that the empty tetrahedral sites 48f and 8b get involved in overall diffusion. The connection of these polyhedra with the Li bearing sites is illustrated in figure 1. While 8b is only connected to 16d (octahedral site) via face sharing, the 48f site is connected, again via face sharing, to both the Li 16c and the Li 16d sites, see below. Thus, the 48f site could indeed act as a suitable transition site to enable slow 16c-16d exchange processes coming into play at high x values. Such processes are expected to be characterised by higher activation energies than the 8a-16c-8a Li + jump process. Earlier results from NMR and broadband conductivity point in this direction [61]. Moreover, the stepwise decay of the 7 Li NMR line width with increasing temperature (see figure 3) could indeed serve as an argument for several diffusion pathways the Li + ions have access to in sodiated LTO. This behaviour, which includes a large distribution of activation energies, is in contrast to that of lithiated LTO. For lithiated LTO such steps in the NMR narrowing curves are absent [22]. This absence shows that, in comparison to lithiation, Na insertion has a two-fold effect on ion dynamics: it might block rapid diffusion pathways but could also open slower ones.
Besides a possible Na ion blocking effect that might occur at sufficiently high values of x, we must also consider the possible (macroscopic) phase changes of sodiated LTO that we briefly mentioned above. Such segregation effects, possibly also including the formation of nm-sized domain structures, are known for lithiated LTO [24]. In the case of electrochemically prepared samples, the exact behaviour will depend also on the (charging) conditions, that is, the C rate used to insert the Na ions. High C rates may result in kinetically stabilised metastable regions that differ from those obtained if sodiation is carried out chemically. Here, we focus on chemically sodiated samples and refer to the literature where such effects or differences have already been discussed [22,24] and studied [22,62]. At very low lithiation or sodiation levels we assume that the diffusion barriers probed by NMR (see below) are independent of the insertion route.
Here, we expect that with increasing sodiation the regions of the initially formed solid solution continuously subdivides into a Na-rich and a Li-rich region upon sodiation, as has also been suggested earlier [28]. In the (ideal) Na-rich region we deal with the rocksalt-type phase Na 6 [LiTi]O 12 in which the Na ions fully occupy the 16c sublattice leaving behind an empty 8a lattice. The Li-rich phase is Li 6 [LiTi]O 12 . As we showed earlier, the Li + diffusivity in this Li-7 phase, which is also formed when Li 4+x Ti 5 O 12 is lithiated up to x = 3, is much lower than in the original Li-4 phase [22, 23, 50, 51]. Its NMR motional narrowing  6 Li 1D exchange NMR spectra of lithiated Li 4+x Ti5O12. The spectra were taken from literature and refer to a microcrystalline sample [23]. Here, they serve for a comparison with the 6 Li spectra of sodiated LTO. (b) 6 Li 1D exchange NMR spectra of sodiated Li 4+x Ti5O12, this work. The first spectrum is identical to that on the left side. Values in ppm indicate the chemical shifts δCS of the individual NMR lines. Solid lines show the deconvolution of the total signal with appropriate Voigt functions. See text for further details.
curve [22] is added in figure 2(b) for comparison. In pure Na 6 [LiTi]O 12 , Li + occupies only the 16d sites that we identified as those sites that do not take part in rapid exchange processes (see above). Thus, in both phases, Na 6 [LiTi]O 12 and Li 6 [LiTi]O 12 [50,51], we suspect the Li ions on 16c and on 16d to be much less mobile than those on 8a, that is, in the solid solutions of Li 3 Na x [LiTi]O 12 (x < 1).
Taken together, the sample characterised by x = 1.5 is, most likely, a mixture of at least three regions: the solid solution Li 3 Na x [LiTi]O 12 as well as the phases Li 6 [LiTi]O 12 and Na 6 [LiTi]O 12 . The 7 Li NMR line observed is thus a superposition of various NMR lines reflecting the Li ions in the individual phases. Na ion blocking effects and phases with poor Li + diffusivity lead effectively to a decrease in overall Li + diffusivity for x = 1.5. The small schematics included in figure 2 help illustrate the evolution of these phases upon sodiation.

1D 6 Li MAS NMR revealing fast 8a Li ions
To support our conclusions on ion dynamics drawn, so far, from variable-temperature NMR line shape measurements, we recorded high-resolution 1D 6 Li MAS NMR spectra to resolve the Li ions in the various phases and their distinct, site-specific dynamic properties ( figure 4). The corresponding spectrum of LTO is composed of two lines [23,63]. The ratio of the areas under the lines reflect the 8a and 16d occupation levels. No other sites are occupied in unsodiated LTO by Li + . The signal around-0.85 ppm reveals a tiny amount of Li 2 TiO 3 , as has been discussed elsewhere [64]. This signal is also seen in the spectra shown in figure 4(b), slightly shifted towards-0.95 ppm (see arrows).
Upon sodiation (x = 0.1), we recognise that the line mirroring the 8a ions reduces in line width. Hence, besides elimination of the dipolar couplings through external MAS, internal exchange processes lead to further averaging of the residual dipolar broadening. Despite these effects, the line clearly resembles that of unsodiated LTO, supporting our interpretation that a surface-related Na-bearing solid-solution is formed at such low sodiation levels. At x = 0.1, many of the Li + ions in the bulk regions do not sense the effect of Na + on 16c.
Increasing x from 0.1 to 0.5 changes this situation drastically. The NMR line representing Li + on 8a is further narrowed revealing a strong elimination of dipolar interactions through rapid 8a-16c exchange processes. Li + ions on 16c give rise to a rather broad, and thus, less intense signal at negative ppm values, as they experience Fermi contact hyperfine interactions with the Ti 3+ centres generated. This feature is not shown here as it has been discussed for heavily lithiated LTO elsewhere [23]. Furthermore, we clearly see that significant 16c-16d Li + exchange is absent as we still observe an almost untouched 16d NMR signal that is not affected by any coalescence effects. This finding is in excellent agreement with the earlier 6 Li 2D MAS NMR experiments mentioned above [23]. The 6 Li NMR signal of Li 4 Na 0.5 Ti 4 O 12 is almost identical with that of Li 4.3 Ti 5 O 12 [23], for which extremely fast 8a-16c Li + exchange has been probed.
Increasing x in Li 4 Na x Ti 4 O 12 further does not change the 6 Li NMR spectrum much. Li in Li 7 Ti 5 O 12 produces a broadened signal shifted toward negative ppm values (not shown here for the sake of clarity). The Li + ions on 16d remain rather immobile on the NMR time scale. Hence, the 6

Diffusion-induced 7 Li SLR rates
To quantify our results in terms of mean activation energies that the Li + ions have to surmount while diffusing, we carried out variable-temperature 7 Li NMR SLR measurements. Such measurements sense the temporal magnetic spin fluctuations to which the ions are subjected to because of self-diffusion processes. These fluctuations are, roughly speaking, characterised by motional correlation rates 1/τ c on the MHz time scale. According to classical relaxation theory [37], the NMR rate 1/T 1 (1/T), which is proportional to 1/τ c , passes through a characteristic diffusion-induced rate peak whose flanks entail information on long-range (high temperature regime) and short-range (low-temperature regime) ion dynamics [51,65,66]. In the case of ordinary 1/T 1 NMR measurements, the slope of the so-called low-T flank is sensitive to local ion dynamics [67]. Here, the coupling of the spins with the paramagnetic Ti 3+ centres [22] does, however, govern the rates and masks any diffusion-induced contributions, which results in a weaker-than-activated temperature behaviour (see figure 5(a)). At temperatures below 300 K the longitudinal 7 Li NMR transients show even biexponential behaviour, which could either be a result of longitudinal relaxation driven by electric quadrupolar interactions [68,69] or, at least for x = 0.1, originate from fast and slow spin reservoirs, as suggested by the 7 Li NMR lines.
When switching to spin-lock 1/T 1ρ NMR, which is sensitive to spin fluctuations with rates in the kHz range, the diffusion-induced contributions dominate the primary NMR observable 1/T 1ρ , now giving access to the so-called low-T flank of the respective 1/T 1ρ (1/T) peak. At low T, non-diffusive background relaxation due to coupling with parametric centres (Curie-Weiss behaviour [70]) influence the experiments, while the rates 1/T 1ρ pass into the Arrhenius-type regimes at sufficiently high temperature. The lower this crossover temperature, the higher the Li + diffusivity in Li 4 Na x Ti 5 O 12 . We clearly see that, as compared to unsodiated LTO (x = 0), which has also been milled for 200 min in ethanol, the flank of Li 4 Na 0.1 Ti 4 O 12 is shifted towards a much lower crossover temperature. Simultaneously, the activation energy reduces from ca. 0.89 eV in pure LTO to 0.6 eV in the sodiated form. Worth mentioning, is that the spin-lock experiments do not point to two magnetically decoupled spin reservoirs, as might be expected from the two-component line shape of this sample. Hence, we conclude that effective spin-diffusion affects the underlying transversal magnetization transients, which can be very well approximated with stretched exponentials. The corresponding stretching factors γ ρ are shown in the upper graph of figure 5(b).
The 1/T 1ρ NMR flank of the sample characterised by x = 0.5 reveals a further decrease in slope resulting in an activation energy as low as approximately 0.4 eV. We recognise that the corresponding rates pass through a shallow maximum at T max = 390 K. At this temperature the mean motional correlation rate 1/τ c is given by [66] 1/τ c ≈ 2ω 1 with ω 1 /2π = 33.3 kHz, thus, resulting in a jump rate 1/τ (≈1/τ c ) of 4.2 × 10 5 s −1 .
The fact that we cannot detect a clear peak maximum in 1/T 1ρ (x = 0.5) could be explained by considering a superposition of several diffusion processes taking place between the available Li sites in LTO. This behaviour is in contrast to that seen for lithiated LTO where the rate 1/T 1ρ passes through a rate peak already at 350 K [22]. Increasing x to x = 1.5 slows Li + diffusion down again. The corresponding flanks belonging to Li 4 Na 1.5 Ti 4 O 12 shift back to higher temperatures. Simultaneously, their temperature behaviour becomes quite complex, likely revealing two temperature regimes pointing to activation energies of 0.29 eV and Figure 5. (a) 7 Li NMR 1/T1(1/T) rates recorded in the laboratory frame of reference at the frequency indicated. At low T, the transients were analysed with a sum of two non-stretched exponentials. (b) Variable-temperature 7 Li NMR relaxation rates (194 MHz (116 MHz, x = 0)) recorded in the rotating frame of reference by using a locking frequency ν lock in the order of 30 kHz. The sample labelled with x = 0 refers to unsodiated LTO that has been milled in ethanol for 200 min and then dried under the same conditions as applied for the sodiated samples. Crosses refer to a microcrystalline sample that has been investigated earlier by our group [22]. While the dashed lines are drawn to guide the eye, the solid lines represent Arrhenius fits to determine the activation energies indicated. For x = 0.5 (0.38 eV) the rates pass through a shallow maximum at 390 K. In the upper figure the corresponding stretching exponents γ1ρ are shown that characterise the deviation of the transversal magnetization transients from single exponential time behaviour. Values around 0.5 might be expected for the coupling of the spins with paramagnetic centres. Note that the rates referring to the sample with x = 1.5 have been shifted by one order of magnitude upwards for the sake of clarity. The dotted line shows the values without any offset. In excellent agreement with 7 Li NMR line shape measurements we see that Li + diffusivity is, for larger x values, slowed down, as is illustrated by the arrow connecting the distinct Arrhenius lines referring to x = 0, x = 0.5 and x = 1.5). 0.37 eV, respectively (see figure 5(b)). This behaviour points to the assumption that at high levels of x, the ions increasingly have access to further sites, and thus, diffusion pathways; figure 6(a) shows the connectivities of the (interstitial) octahedral and tetrahedral voids in LTO. Note that a value of 0.29 eV would be in agreement with local Li + 8a-16c Li + exchange processes [22,27].
Interpreting the 7 Li NMR response of this sample is further complicated by the fact that we have to take into account the following heteronuclear spin interaction. The Li spins in this sample, most likely, do not only sense their own spin-fluctuations but also those of the 23 Na spins and vice versa. For 23 Na (I = 3/2), with its large electric quadrupole moment, we expect strong electric quadrupolar interactions that will also govern NMR relaxation of the 7 Li nuclei. Indeed, the absolute values of the corresponding 1/T 1 23 Na NMR rates exceed the rates 1/T 1 of 7 Li by several orders of magnitude (see figure 6(b)).

23 Na NMR: SLR and line shapes
Here, the 23 Na 1/T 1 NMR transients of Li 4 Na 1.5 Ti 5 O 12 are clearly composed of two contributions, leading to two NMR rates 1/T 1,fast and 1/T 1,slow (see figure 6(b)). Fast 23 Na SLR NMR relaxation, characterised by an activation energy of 0.48 eV, likely mirrors Na + exchange according to the Na + pathway 16c-8a-16c ′ . The corresponding 23 Na NMR line shapes are show in figure S2. They reveal the beginning of motional narrowing at temperatures higher than 300 K (see also figure 3(a)).
The rate 1/T 1,slow , on the other hand, passes through a rate maximum located at T max ≈ 390 K. We tend to ascribe this feature to a 23 Na NMR relaxation process that is indirectly controlled by fast Li + jumps that occur in the direct neighbourhood of the Na + centres. Most likely, this diffusion-induced rate peak is caused by the localised but rapid Li + 8a-16c forward-backward jump processes in the vicinity to a 16c site that is occupied by Na + . Again, the corresponding activation energy of 0.24 eV is comparable to that probed by 7 Li spin-lock NMR (0.29 eV, see above) and thus, seems to be a reasonable value for such a rapid Li + exchange process. Figure 6. (a) Crystal structure of Li4Ti5O12 highlighting possible Na (and Li) diffusion pathways to explain the NMR SLR behaviour which points to multiple Li and Na diffusion pathways in heavily sodiated LTO. As an example, one might think about Na + exchange not only between 16c (via 8a) but also between the 16c and 16d sites using the empty tetrahedral sites (48f ) as transition states. (b) 23 Na NMR SLR rates of Li4N1.5Ti5O12 recorded in the laboratory frame of reference at a Larmor frequency of 132 MHz. 23 Na NMR yields two rates, 1/T 1i ≡ R 1i (i = fast, slow). Dashed lines serve as guides to the eye, whereas the solid line represents an Arrhenius fit to extract a mean activation energy of 0.48 eV for Na + self-diffusion, most likely describing the pathway 16c-8a-16c ′ . The rate R 1slow is expected to be indirectly controlled by rather rapid 7 Li spin-fluctuations such as local 8a-16c forward-backward jumps nearby a Na + (16c) centre. The upper graph includes the stretching exponents to characterise the 23 Na SLR NMR transients. Above ambient temperature, we need a sum of two stretched exponentials to satisfactorily parameterise the longitudinal recovery of the magnetization. For comparison, the 7 Li NMR 1/T1ρ (≡R1ρ) are also shown. See text for further discussion.
Unfortunately, variable-temperature 23 Na SLR of the samples with rather low amounts of Na do not show clear diffusion-induced contributions (see figure S3). In agreement with these changes, the 23 Na NMR lines do not change much in the temperature range from 60 • C to 140 • C. Therefore, Na + diffusivity in samples with x = 0.1 and x = 0.5 are much less mobile than those in the sample with x = 1.5. Furthermore, if we compare our 23 Na NMR lines with the situation seen for 7 Li, at the early stages of sodiation, the Li + ions turned out to be much more mobile than the Na + ions. In figure 3(a) we have included the corresponding 23 Na NMR motional narrowing curves; only for x = 1.5 are significant motional averaging effects seen. This observation underpins the idea of rapid Li + 8a-16c exchange processes, which are immediately initialised as soon as sodium ions enter the near-surface 16c sites.

Conclusion
We studied the influence of chemical Na insertion into the pentatitanate host Li 4 Na x Ti 5 O 12 on Li + diffusion. While Li + ion dynamics were studied by 7 Li NMR spectroscopy, 23 Na NMR helped us to obtain first insights into the Na + ion dynamics of a sample with x = 1.5. The present study is multifaceted, as it attempts to understand ion dynamics in a mixed ion-electron system that additionally provides two mobile cations. We tried to understand ion dynamics with a single, non-destructive, contactless nuclear method that is capable of selectively studying Li + and Na + hopping processes from the atomic-scale point of view. Future studies might also include muon spin measurements to underpin the current findings.
Here, Na insertion leads, already at the very early stages of sodiation, to a drastic enhancement of Li + ion dynamics because of 8a-16c Coulomb repulsions, which is accompanied by a significant decrease in activation energy from 0.83 eV (x = 0.) to 0.38 eV (x = 0.5). Compared to lithiated LTO, the increase does, however, start less pronounced and reaches a maximum diffusivity at values of approximately x = 0.5. Two-component 7 Li NMR line shape measurements point to the initial formation of interfacially located solid solutions that propagate over the whole crystallites with increasing sodiation level x. At larger insertions levels, we assume that besides the solid solution areas, Li-rich and Na-rich phases also form. These separate phases show lower Li + diffusivity, respectively, explaining the observed overall decrease in Li + ion diffusivity for x = 1.5. However, at low insertion levels, Li 4 Na x Ti 5 O 12 immediately turns into a fast Li + ion conductor with the Li + performing rapid exchange processes in a solid-solution like environment. At these insertion levels, the Na + ions on 16c are less mobile than the smaller Li + cations. We think that any foreign ion, be it mobile or immobile, will immediately switch on Coulomb repulsions, forcing the 8a Li ions to get involved in rapid exchange processes.
These rapid Li + ion dynamics in the solid-solution like regions explain the excellent suitability of LTO to act as fast-charging anode material. Hence, the pentatitanate should not be regarded as a material that only provides a two-phase insertion host, as seen in studies investigating its macroscopic electrochemical properties at progressed levels of lithiation or sodiation. Rather, interfacial properties and the existence of solid-solutions in LTO need to be considered, too.

Data availability statement
All data that support the findings of this study are included within the article (and any supplementary files).