1 Introduction and motivation
The mobility of small cations or anions in ionic crystals depend on numerous factors. On the one hand, point defects and polyhedral connections play a decisive part in enabling local jump processes and bulk ion transport. On the other hand, the morphology of the whole ceramic will determine migration of the charge carriers over long, i.e. macroscopic, distances. Disorder can be introduced through many different approaches such as radiation or bombardment techniques. A far more simple approach is to mechanically treat the coarse-grained samples in high-energy mills . Conveniently, high-energy ball milling is carried out at ambient temperature; it allows for the preparation of large quantities. In many cases, if only one component is treated phase pure nanocrystalline materials are obtained with large volume fractions of amorphous regions or at least disordered interfaces . The introduction of point defects and dislocations is, however, also expected for the crystalline cores of the nanocrystallites . So far, many examples have been reported documenting that the ionic conductivity of a poor conductor can significantly be enhanced when transforming the oxides or sulfides into a defect-rich nanocrystalline ceramics , . One may regard the excessive generation of defects, greatly exceeding the thermodynamic level, as a possibility to form materials with metastable properties concerning both defect concentrations and non-equilibrium local structures , , , . In general, the interfaces in nanostructured ceramics and nano-composites may govern macroscopic properties such as the ionic and electronic conductivity , , , , , , , , , , , , , , , , , .
Besides such top-down approaches the direct preparation of nanocrystalline or amorphous ceramic through wet chemical methods or electrochemical techniques is also possible. As an example, the ionic conductivity of sol–gel synthesis of nanocrystalline LiNbO3 is indeed enhanced compared to its single crystalline or microcrystalline form with μm-sized crystallites . Considering, however, the chemically identical samples prepared by heavy ball-milling their ion conductivity is much higher. Obviously, at least in the case of poorly conducting oxides the disordered if not completely amorphous regions are greatly responsible for the gradual transformation from a poor to a moderate or even highly conducting ion conductor , , , , , , , , .
Amorphous regions also immensely influence the electrochemical activity of otherwise poorly active materials. The different modifications of TiO2 belong to such a class of materials. Only downsizing the crystallite size unlocks the full potential of anatase, rutile or TiO2-B as anode materials , , , . The short diffusion lengths for both ions and electrons transform the transition metal oxide into powerful anode materials showing high rate capabilities and excellent specific charge capacities , . This also holds for mesoporous ,  and amorphous TiO2. In the following we will report on the preparation of amorphous TiO2 nanotubes via anodic etching , . The nanotubes, differing in lengths according to the synthesis conditions, have been investigated with respect to loading with Li and Na ions . Electrochemical investigations using cyclic voltammetry and galvanostatic cycling allowed us to reveal the underlying Na storage mechanism. Li nuclear magnetic resonance (NMR) has been used to evaluate the Li self-diffusion parameters of various electrochemically prepared, mixed-conducting LixTiO2 samples , , . For comparison, Li ion dynamics in mesoporous anatase was studied via spin-lock and stimulated echo NMR . It turned out that Li ion diffusion is unaffected by the phase transformation from anatase to orthorhombic TiO2 during Li uptake. This result is highly beneficial to enable stable cycling conditions in lithium-ion batteries.
The influence of structural disorder generated through ball milling on ion transport will be discussed for a range of model substances that include nanocrystalline Li2O2 , Na2O2 , the ternary oxides LiAlO2 , Li2TiO3 , LiTaO3 , , Li2CO3, as well as the glass former Li2B4O7 . Whereas Li ion transport in the materials mentioned above is isotropic, transition metal dichalcogenides such as SnS2 or TiS2 crystallize with a layered structure. Chemical lithiation enables the insertion of Li ions into the van der Waals gap between the SnS2 sheets. The Li ions are expected to diffuse quickly along two dimensions. Preliminary NMR results on LixSnS2 show how the diffusion parameters are altered when the material is exposed to mechanical treatment in ball mills. In contrast to microcrystalline LixSnS2 with its fast but spatially confined 2D diffusion , in nanocrystalline LixSnS2 the large number of Li ions in the disordered interfacial regions remarkably influence the NMR response. NMR line shapes point to a two-spin reservoir with fast and slow Li species, see also Ref. . Finally, the effect of high-energy ball-milling on ion transport in Li2B4O7 is shown. A significant difference is seen when comparing ionic conductivities of crystalline, nanocrystalline and amorphous Li2B4O7. The strategy of introducing structural disorder and stress is useful to transform a poor ion conductor into a moderate one. For very fast ion conductors the situation is, on the other hand, expected to be different.
2 Case studies: from oxides to peroxides and back again
2.1 Electrochemical performance and Li ion transport in various forms of TiO2
The different modifications of TiO2 represent promising anode materials that provide hosts to reversibly store small cations such as Li and Na. If present in nanostructured form good rate capabilities and discharge capacities as high as 250 mAh/g were reported , . Since such electrochemical properties might be linked also to ion dynamics several NMR studies took up the challenge to quantify Li self-diffusivity via, e.g. relaxometry, stimulated echo spectroscopy or even by 2D exchange spectroscopy , , , , . In the following some recent studies on amorphous TiO2 nanotubes, rutile nanorods and mesoporous TiO2 will be presented that deal with electrochemical properties, mechanisms and ion dynamics in these spatially confined structures.
2.1.1 Amorphous TiO2 nanotubes: synthesis, ionic diffusivity and the underlying storage mechanisms
The synthesis of anodic titania nanotubes , ,  follows a top-down approach, self-assembled TiO2 nanotubes are formed on titanium metal substrates by an anodic electrochemical oxidation process, called anodization. The anodization is usually done in two electrode cells at relatively high voltages, typically ranging from 10 to 200 V. To obtain the required nanotubular morphology, the anodization bath must also contain a Ti4+ complexing agent. The most used is F− with which Ti4+ is able to form the soluble [TiF6]2−, see Ref. . The formation of the tubes involves two opposite but balanced processes: (i) the electrochemical formation of TiO2 and (ii) the chemical etching of the formed oxide by the complexing agent. Under high electric field conditions the anodization results in highly regular layers consisting of parallel TiO2 nanotubes that grow from the Ti substrate.
Both aqueous-based and organic-based baths have been reported to yield highly regular nanotubular layers. While in aqueous baths the length of the nanotubes is somehow limited to 2–3 μm due to the faster fluoride etching of the electrochemically formed TiO2, in viscous organic-based baths, e.g. ethylene glycol, it is possible to grow very long nanotubes, sometimes longer than 1 mm , while keeping almost the same diameter over the entire length of the nanotubes, typically 80–120 nm. Thus, nanotube aspect ratios of 1:104 are easily achievable. Since the volume of the produced oxide is larger than the volume of the Ti metal from which it originated, the nanotubes are approximately 1.5 times longer than the corresponding thickness of the Ti layer consumed during anodization . An illustration of some typical anodic TiO2 nanotubes fabricated in ethylene glycol baths is presented in Figure 1.
Although the relation between the electrochemical conditions and the dimensions and geometry of the anodic titania nanotubes is a relatively complicated topic , , for a given bath, there is a direct connection between the voltage applied and the tube diameters. In principle, the higher the voltage, the larger the tube diameters are. By this method the diameters can easily be adjusted in practice between 30 and 120 nm.
One of the striking features of anodic TiO2 is its amorphous structure . In their pristine form, the nanotubes do not present any X-ray reflections in a diffraction experiment as illustrated in Figure 2. In fact, anodic titania is one of the very few known instances in which TiO2 occurs in its amorphous form. Their unique and tunable morphology doubled by the rare amorphous structure have attracted significant attention; many scientific and technological developments based on titania nanotubes have been brought forward in the last decade . One interesting development is related to the insertion in anodic TiO2 of ionic species such as H+ , Li+  and Na+  pertaining to the broader field of energy storage and conversion. Whereas earlier NMR studies focused on Li ion diffusion in crystalline nanotubes of TiO2, mainly TiO2-B, that were prepared by hydrothermal routes, so far less information is available on Li+ ion dynamics in amorphous titania nanotubes. Anodic etching allowed the preparation of relatively large quantities and, as mentioned above, according to the exact synthesis conditions both the length and the diameter of the tubes can be controlled. Li is then inserted either electrochemically in half cells with Li metal as anode material or chemically with n-BuLi in hexane.
For our first NMR experiments on amorphous TiO2 rather long tubes (250 μm, see Figures 2a) were synthesized. X-ray powder diffraction confirmed the amorphous structure of the material, Figure 2b, the corresponding pattern for the pristine sample only shows reflections of the Ti metal substrate. Interestingly, the tubes remain amorphous up to 200 °C, at higher temperatures they can be converted into anatase.
The typical morphology of the titania nanotube layers is shown in the inset of Figures 2a 3b. The rather long tubes were used as anode material to prepare LixTiO2 samples with the following compositions x=0.5, x=0.75 and x=1.0.
Variable-temperature 7Li NMR line shape measurements of these tubes revealed that Li ion diffusivity in the amorphous tubes is relatively slow. The rigid lattice line width, which is the line width at sufficiently low T where Li diffusivity has no effect on the NMR line shape, ranged from 12 to 16 kHz according to the amount of Li inserted per formula unit TiO2. Motional narrowing of the NMR line sets in if Li ion hopping processes reach jump rates that are comparable with the rigid lattice line width. At sufficiently high T these exchange processes start to average homonuclear and heteronuclear dipole–dipole interactions that are responsible for the broadening of the spectra at low T. In the case of LixTiO2 the Li+–Ti3+ interaction leads to further broadening effects. For all compositions motional averaging is seen to take effect on the line shape at temperatures higher than 300 K. This is why so-called spin-alignment echo (SAE) NMR , , , , , , , ,  proved to be a suitable way to characterize Li ion diffusivity in the tubes prepared (Figure 2a). The method works in the regime where spin–spin-relaxation rates are still unaffected by motional averaging processes . Here, the relatively poor ionic diffusivity as well as the coupling of the Li spins to paramagnetic centers like Ti3+ is reflected in a rigid-lattice relaxation time T20 of only 6 μs (see Figure 4a). An increase of T2 is seen at temperatures higher than 330 K. Around this temperature and at T>300 K the SAE NMR decay rates follow Arrhenius behavior with activation energies Ea ranging from 0.3 to 0.5 eV (see Figure 3a). Note that the data points referring to x=0.5 and x=1.0 were vertically shifted by 0.5 orders of magnitude each; the 7Li SAE NMR rates do not significantly depend on composition at low T if rather large values of x are considered. In general, SAE NMR is sensitive to slow Li ion hopping processes (<105 1/s) between electrically inequivalent Li sites. Usually the three-pulse sequence introduced by Jeener and Broekaert , , ,  is used to measure a two-time correlation functions S2 from which the decay rate 1/τSAE(T) can be deduced.
Interestingly, above 400 K the decay rates from stimulated echo NMR start to decrease again. If T2 is short enough this behavior can be traced back to averaging processes ,  that occur during the mixing period; such a scenario has quite recently been discussed in detail for fast ion jump processes in Li bearing oxide garnets . In these cases Li exchange processes may become too fast to be collected by SAE NMR. In the present case, however, we have to keep in mind the upper time window of SAE NMR, which is generally restricted by T2; for comparison with 1/T2 the SAE NMR rates 1/ττSAE are jointly plotted with the spin–spin and spin–lattice relaxation rates of Li0.75TiO2 in Figure 4a.
Interestingly, for the samples with x>0.5 we observed quite high activation energies by SAE NMR. Values a large as 0.5 eV are in good agreement with those reported for crystalline LixTiO2-B nanowires. Similarly, for mixed-conducting Li1.0TiO2, which was prepared by chemical lithiation, an activation energy of 0.58 eV was obtained (see Figure 4b). While SAE NMR is sensitive to slow Li+ exchange processes, which in many cases reflect long-range ion transport also accessible by DC conductivity measurements , SLR NMR is sensitive to more localized, short-range ion movements , , . As expected, if the low-T regime of a given 1/T1(1/T) rate peak is considered, much lower activation energies were probed through laboratory-frame 7Li SLR NMR , . For Li1.0TiO2 we were able to reach the beginning of the low-T flank of the diffusion-induced 1/T1(1/T) rate peak which resulted in 0.15 eV. Note that this flank was masked in the case of the electrochemically lithiated samples. Presumably, it was hidden by an increased Li–electron contribution to the overall spin–lattice relaxation rate. The electrochemically prepared samples are expected to contain minute amounts of fluorine from anodization. This F content will increase the electronic conductivity of the samples. As a result, coupling of the spins with conduction electrons shortens the overall T1 relaxation time which narrows the time window of time-domain NMR measurements. In extreme cases the diffusion-induced contributions to the overall spin–lattice relaxation rates are completely masked . In particular, due to the large volume fraction of interfacial regions of nanocrystalline TiO2 the spin–electron interactions with conductive carbon additives in contact with these surface regions can drastically shorten the T1 times, which also restricts the applicability of other NMR techniques that are limited by T1 such as rotating-frame SLR measurements (vide infra).
2.1.2 Crystalline TiO2 nanotubes crystallizing with the anatase structure
As noted above, the amorphous titania nanotubes convert into anatase at elevated T. Alternatively, anatase nanotubes can be prepared following a hydrothermal route. In Figure 5 the high-resolution (HR) transmission electron microscopy (TEM) images of hydrothermally synthesized nanocrystalline TiO2 tubes are shown. X-ray powder diffraction and 7Li NMR spectroscopy point to a highly crystalline material whose tubes crystallize with the anatase structure (Figure 6). By varying the synthesis conditions, e.g. the synthesis temperature, the molarity of the sodium hydroxide solution, the pH-value during the washing procedure or the temperature while calcination, either anatase or TiO2-B nanotubes can be obtained. If used as negative electrode material in lithium half cells the anatase tubes show excellent cycling behaviour. At C-rates of 1.5 C a relatively stable discharge capacity of 170 mAh/g is reached (see Figure 7); only a small capacity fade is seen with increasing cycle number. Even after 200 full cycles the Coulomb efficiency is close to 100 %.
To shed light on Li ion dynamics of TiO2 nanotubes, which were either treated with n-BuLi or lithiated electrochemically in Li half cells, we recorded 7Li NMR line shapes and spin–lattice relaxation rates. As an example, in Figure 8 the rates 1/T1 and 1/T1ρ of Li0.6TiO2 (TiO2-B) are shown. Li was inserted electrochemically using Swagelok cells; the final electrode contained 15 wt% binder (Kynar Flex 2801) and conducting additives [carbon black 15 wt% (Super P)].
Whereas for Li0.6TiO2 the rate 1/T1 only weakly depends on temperature, for the anatase tubes with x=0.3 and x≈0.13, which were chemically lithiated, 1/T1 reveals the shallow flank of a 1/T1(1/T) rate peak that is characterized by ca. 0.15 eV. Most likely, for LixTiO2 such a low activation energy has to be assigned to localized relaxation processes rather than to long-range ion transport. Li ions near the surface regions are expected to be involved in such processes. In all cases and irrespective of the final crystal structure of the titania nanotubes the corresponding spin-lock NMR transients, from which we extracted the rates 1/T1ρ, obey a rather complex behavior. At sufficiently high x values (x>0.1) we clearly observed a two-step decay behavior.
This behavior is exemplarily shown for the Li0.6TiO2-B in Figure 8b. Parameterizing the transients with a sum of two (stretched) exponentials results in the rates 1/T1ρ(s) and 1/T1ρ(f). The two-step behavior cannot be explained by the spin-properties of the 7Li nucleus as their difference greatly exceeds that usually expected for, e.g. quadrupolar relaxation. While 1/T1ρ(f) is close to 1/T2, independently measured through spin-echo experiments, the rate 1/T1ρ(s) is in the order of seconds. A significant temperature dependence is obviously masked because of, e.g. Li+–Ti3+ interactions, spin-diffusion, surface effects or the presence of a variety of (nm-sized) crystalline regions that differ, e.g. in Li content. The magnitude of 1/T1ρ(s) and its temperature independence resembles that expected for spin-diffusion that is, e.g. mediated through a spatially homogenous distribution of paramagnetic centers such as Ti3+. The NMR line shapes of all samples investigated point to very slow ion dynamics which is in line with the observations for amorphous titania nanotubes. Additional 7Li SAE NMR measurements are currently running in our labs to shed light on the origins of the two Li sub-ensembles seen in spin-lock NMR.
2.1.3 Li diffusion in rutile nanorods and their electrochemical behaviour
Slow Li ion diffusion was also found for nanostructured rutile whose electrochemical performance in Li-ion cells is comparable to that of the TiO2 nanotubes investigated. We studied both the cycling behaviour and the Li ion diffusivity of needlelike LixTiO2 crystallizing with the rutile structure. The powder used for the experiments was a commercial one that is characterized by small needles, ca. 40 nm in length and 10 nm in diameter, see Figures 9a and 10a. Earlier 7Li NMR spin–lattice relaxation and SAE measurements (see Figures 9 and 10) were performed on a sample with x=0.5 that was chemically lithiated by treatment in n-BuLi dissolved in hexane . SEM images and X-ray powder diffraction of the highly air-sensitive product confirmed that the rutile structure is fully retained during Li insertion. This contrasts with other modifications of TiO2 for which lithiation is accompanied with a phase transformation. For rutile such transformations are reported for samples with x>0.5.
As in the case of amorphous TiO2 nanotubes we took advantage of 7Li SAE NMR to characterize Li ion hopping in rutile Li0.5TiO2. Most interestingly, also for nanocrystalline, rutile Li0.5TiO2 the decay rates 1/τSAE are governed by non-diffusive effects until ca. 310 K. At higher T they discharge into an Arrhenius line that is once again characterized by an activation energy in the order of 0.5 eV. Significant motional line narrowing is recognized at 300–350 K (see inset of Figure 10b), thus at slightly higher temperatures than it was the case for amorphous TiO2 indicating faster ion dynamics in the structurally disordered samples. Note that for amorphous Li0.5TiO2 the activation energy derived from SAE NMR was only 0.3 eV. As also observed for the amorphous samples, the SAE NMR decay curves S2 could only be parameterized with stretched exponentials S2∝exp(−(tm/τSAE)γ), see Figure 10b. The beginning of the diffusion-controlled SAE NMR flank is associated with the beginning of the decrease of the exponent γ (0<γ≤1) that describes the deviation from single-exponential time behavior γ=1. This behavior is generally observed in SAE NMR if materials with a (large) distribution of decay rates are considered.
Despite the moderate to poor ion dynamics in rutile Li0.5TiO2 the nm-sized needles perform exceptionally well in lithium-ion cells; therefore, one might speculate whether surface and interface effects do significantly participate in facile Li storage. To test their electrochemical ability to work as anode material in cells (with Li metal as both counter and reference electrode) we prepared electrodes consisting of nano-Li0.5TiO2, binder (Kynar Flex 2801) and carbon powder (Super C 65); the weight ratio was 75:17:8. The cyclic voltammograms reveal a distribution of various redox processes (Figure 11b), at a scanning rate of 0.05 mV/s three distinct peaks are visible that indicate distinct insertion/de-insertion processes presumably associated with structural changes of the active material if electrochemically lithiated. Galvanostatic cycling at current rates ranging from 0.1C to 20C proves a credible rate capability (Figure 11a). For instance, at 1 C the decrease in charge capacity turned out to be marginal; even after 800 cycles the cell delivers a stable discharge capacity of more than 150 mAh/g.
2.1.4 Mesoporous TiO2 as long-lasting anode material
Mesoporous materials with an ordered 3D pore structure ensure superior storage capacities and facile Li insertion and removal. As mentioned above, these properties are inter alia related to short diffusion lengths of the nm-sized materials  as well as, see the discussion above, to the involvement of Li surface storage. Because of the large volume fraction of the interfacial regions this storage mechanism needs to be considered. Recently, excellent cycling behavior of a lithium-ion battery was achieved when mesoporous TiO2 with a 3D hierarchical pore structure was used as anode material . Even after extensive charging and discharging of the battery, the hierarchical pore structure was preserved throughout clearly illustrating the high stability of the anode, see the HR TEM images in Figure 12b that were taken from Ref. .
Initially, the mesoporous TiO2 crystallizes with tetragonal symmetry. Upon Li insertion the material transforms, however, into an orthorhombic form . Besides kinetic effects also Li diffusion properties are anticipated to govern the insertion and removal rates. To answer the important question if and to which extent Li self-diffusion changes as a function of Li content x in mesoporous LixTiO2, we used 7Li NMR relaxometry and 7Li SAE NMR to probe local activation energies and jump rates . As mentioned above, while 7Li SAE NMR is useful to probe rather slow Li motions with correlation rates lower than 105 Hz, 7Li NMR SLR measurements, in both the laboratory and rotating frame of reference are applicable to detect hopping processes with rates ranging from 105 Hz to 109 Hz , , . Owing to the relatively long 7Li NMR SLR rates of the samples in the rigid-lattice regime, we could detect the low-T flanks of the corresponding rate peaks. The key results are shown in Figures 3 and 4.
In Figure 12a 7Li NMR spin–lattice relaxation rates for two compositions x, i.e. two crystal structures, are shown that were recorded at 155 MHz and 78 MHz as well at a locking frequency of 14 kHz. The Arrhenius plot reveals that above 300 K the rates start to be mainly governed by ionic diffusion processes. Below that temperature non-diffusive origins control the rates. As expected, the more Ti3+ centers have been generated through the insertion of Li+/e− the larger the paramagnetic Li+–Ti3+ spin–spin interaction and the faster the longitudinal recovery in the low-T regime.
In the laboratory frame the diffusion-controlled rates follow Arrhenius behaviour that points to activation energies, Ea, of 0.37 eV (x=0.09) and 0.32 eV (x=0.74), respectively. Both the decrease in Ea and the slight increase in absolute values in the diffusion-induced regime indicate increased Li ion hopping processes in the sample with higher Li content. This view is supported by spin-lock NMR, see the upper part of Figure 12a. At first glance, one would expect a decrease in Li ion diffusivity if x is significantly increased from 0.09 to 0.74. Such a decrease could be the result of large Coulomb interactions at high x values with many interfering Li ions and a restricted number of vacant Li sites. The experimental results, however, point to the opposite direction: the dynamic parameters deduced from NMR turned out to be less influenced by the Li content than expected. If we consider surface effects and the fact that the crystal symmetry reversibly changes from tetragonal to orthorhombic when going from x=0.09–0.74 some solid arguments can be found being able to explain the current NMR response. The orthorhombic structure seems to facilitate Li ion migration which, on the other hand, is highly beneficial for the performance of the anode material that needs to easily accept and conduct Li ions at increased values of x.
The fact that Li bulk diffusivity is seen to increase rather than to decrease with increasing x in mesoporous LixTiO2 is also underpinned by 7Li SAE NMR measurements, Figure 13, see Ref. . Also from the point of view of SAE NMR correlation rates, the gradual transformation into orthorhombic LixTiO2 upon Li insertion, i.e. during charging the anode in a battery with full cell configuration, seems to have a positive effect on Li ion diffusivity (see Figure 12a and b).
By parameterizing the SAE decay curves, exemplarily shown in Figure 13a for x=0.09, we obtain temperature-dependent correlation rates 1/τSAE that start to be influenced by slow Li exchange processes at temperatures above 250 K. By careful subtraction of the almost temperature-independent and non-diffusive contributions to the SAE decay from the overall rates we ended up with purely diffusion-controlled rates 1/τ′SAE that follow Arrhenius-type behaviour. The straight lines in Figure 13b represent Arrhenius fits with activation energies of 0.48 eV (x=0.09), 0.44 eV (x=0.35), and 0.41 eV (x=0.74). These values are comparable with those from NMR relaxometry. They are higher than those from SLR NMR in the lab frame since laboratory-frame relaxation is able to gather also short-ranged (local) ion dynamics to which SAE NMR is less sensitive.
On the other hand, SAE NMR, although being able to characterize long-range ion transport, is insensitive to ion jump processes between electrically identic sites that albeit contribute to NMR relaxometry, e.g. in the rotating frame of reference. This fact might explain the higher activation energy seen via spin-lock NMR which obviously also probes ion hopping processes with even larger barriers the ions have to surmount (0.53 eV for the sample with x=0.74). It is, on the other hand, important to mention that the temperature ranges where the two techniques have been applied to measure ion dynamics do not coincide. Above 383 K the SAE decay curves start to be independent of temperature. Thus, at high temperatures, i.e. in the regime of ‘fast’ ion dynamics, SAE NMR is unable to produce reliable jump rates and activation energies.
A similar feature can be seen for the spin-lock rates of the sample with x=0.74. At high T, the rates follow an anomalous T behaviour that needs to be investigated in future studies. We suppose that it is related to the, to some extent irreversible, interaction of the active material with binders and carbon additives that are usually added to ‘ionically’ and electronically activate TiO2 to prepare a functioning battery anode. Nevertheless, in the T range of battery operation we have seen that at increased values of x the orthorhombic form of mesoporous TiO2 with its hierarchical pore structure represents a powerful anode material with slightly enhanced Li ion dynamics compared to the initially Li poor TiO2 with tetragonal symmetry.
2.1.5 Na insertion into amorphous TiO2 nanotubes: mechanistic details – differences between Li and Na
While the electrochemical reactions of nanostructured TiO2 with H+ and Li+ have been known for a while, the particularities of the electrochemical reaction of Na+ with anodic titania nanotubes are a more recent achievement. A cyclic voltammetry experiment investigating the Na+ insertion into amorphous TiO2 nanotubes (see Figure 14a) does not indicate a definite two-phase insertion mechanism as known for insertion of Li+ in crystalline forms of titania . A 2-phase mechanism would result in well-defined current peaks in the cyclic voltammogram. The very broad current response, however, hints to a one-phase mechanism that might instead be involved. Another feature is the relatively symmetrical response of the nanotubes with respect to Na+ electrochemical reaction when the sweep rate is increased, e.g. at 10 mV/s, contrasting with the asymmetric shape of the cyclic voltammogram recorded at relatively slow seep rates of, e.g. 0.5 mV/s.
In Figure 14b the current read at 1 V vs. Na+/Na has been plotted against the square root of the sweep rate for three different types of amorphous anodic titania nanotubes, see Ref. . Obviously, the nanotubes possess different outer diameters and lengths as follows: after anodization at 30 V for 2 h the nanotubes length was approximately 4.5 μm and 70 nm in diameter, at 40 V after 2 h 8 μm and 100 nm while at 50 V after 1 h the tubes were 9.1 μm long and 120 nm in diameter. For an electrochemical process limited by a mass transport phenomenon a Randles–Ševčík-type plot, as presented in Figure 14b, should be linear. However, even after any ohmic drops were eliminated, there is a clear deviation from this expected linearity. The deviation is always positive, i.e. the current is higher than expected. Moreover, the deviation magnitude increases with sweep rate. This observation proves that there is a process, contributing to Na+ storage, which is faster than solid-state diffusion in the walls of TiO2 nanotubes. This contributing process is commonly called pseudo-capacitive storage. Although a charge transfer takes place and a Ti4+ redox center is reduced to Ti3+ during electrochemical reaction with sodium, the corresponding Na+ ion does not diffuse into the bulk of the amorphous titania material. Instead, it adsorbs onto the titania/electrolyte interface region forming a somehow loose bound with the substrate while still compensating the negative charge of the mobile electron that has been injected into TiO2 conduction band. This interfacial storage mechanism is obviously not limited by ion diffusion in the solid-state since the Na+ ions reside on the surface of the material. The only mass transport limitation by diffusion occurs in the liquid state, i.e. chemical diffusion of the sodium species through the liquid electrolyte. Chemical diffusion in the liquid state can, however, safely be considered at least 4–6 orders of magnitude faster than the solid-state diffusion process and, thus, this process is significantly faster than its solid-state counterpart, as is clearly proven by the non-linear relationship observed in Figure 14b.
It is possible to separate the pseudo-capacitive and chemical diffusion process in the solid state by considering that diffusion should present a linear response on a Randles–Ševčík-type plot and that the pseudo-capacitive contribution adds to the diffusion process while being non-linear with respect to the sweep rate. By a relatively simple subtraction technique, detailed elsewhere , we found very high values of the pseudo-capacitance as shown in Figure 15a. The pseudo-capacitance is increasing as the potential of the electrode is driven towards more negative values, eventually reaching very high values around 1000 μF/cm2. Worth mentioning, this value is roughly two orders of magnitude higher than the usual double layer capacitance occurring in the absence of a faradaic process. This opens the path towards the use of anodic titania nanotubes in supercapacitors. While the pseudo-capacitive contribution of the anodic titania is very high, the Na+ diffusion into the walls of the nanotubes is very slow irrespective of the electrode potential at which it was measured as seen in Figure 15b. The chemical diffusion coefficient values are centered around 10−21 cm2/s which is 4–5 orders of magnitude lower than the corresponding Li+ diffusion coefficients in anatase TiO2 . Therefore, there is only a small amount of sodium diffusing into the walls of the titania nanotubes, most of the sodium storage capacity originates from the pseudo-capacitive processes. This feature is essentially different from Li+ insertion in TiO2, most of the Li+ is actually stored in the bulk regions of TiO2 below a certain electrode potential, typically lower than 1.5–1.7 V vs. Li+/Li.
2.2 Li ion diffusion in layer-structured (nanocrystalline) LixSnS2 with confined Li diffusion pathways
Macroscopic Li diffusion in nanostructured ceramics, such as TiO2, can be directed if the crystallites assume the shapes of tubes or rods. From the atomic scale point of view the elementary hopping processes have to be characterized in many cases by 3D diffusion unless diffusion of the ions is preferred along a special direction of the crystal structure. Apart from such anisotropic movements in materials offering 3D diffusion there are layer-structured and channel-structured ion conductors with significantly constraint migration pathways , , , , , , , . Lithium transition metal dichalcogenides represent a typical class of materials that offer 2D diffusion in their van-der-Waals gaps . Of course, besides intralayer diffusion, to a minor extent also interlayer hopping processes across the layers can take place. Considering sulfides, besides, e.g. LixTiS2 ,  and LixNbS2 , , the Sn-analogue, LixSnS2, constitutes another interesting model system not only to study the influence of dimensionality  but also the effect of structural disorder on a spatially confined diffusion process.
In Figure 16a 7Li NMR spin–lattice relaxation rates of three different LixSnS2 (x=0.17) samples, differing in morphology and mean crystallite size, are shown in an Arrhenius plot. With x=0.17 we ensured that mainly intralayer Li sites, i.e. those between the SnS2 sheets, have been occupied by the Li ions. The mobile Li ions were chemically introduced into SnS2 via treatment with n-BuLi in hexane. Microcrystalline LixSnS2 served as reference material to reveal the changes in diffusion-induced NMR spin-lock relaxation rates . NMR spin–lattice relaxation in Li0.17SnS2 with μm-sized crystallites turned out to be rather complex. We interpreted the appearance of two diffusion-induced rate peaks as a consequence of a heterogeneous distribution of Li ions in LixSnS2 that can be influenced by annealing . Soft thermal treatment is anticipated to homogenize the sample toward a uniform distribution of intercalants . After thermal annealing the low-T peak 1 (see Figure 16b) has significantly been decreased in intensity. We assume that this relaxation peak represents clustered Li ions near the surface-influenced regions having access to fast short-range motions.
If a nanocrystalline sample is studied that contains large volume fractions of amorphous LixSnS2 the NMR response clearly differs from that found for microcrystalline LixSnS2. At first the corresponding NMR line shapes of the nanocrystalline sample are composed of two contributions with quite different line widths (Figure 17). Thus, we have indeed to deal with a sample consisting of two spin reservoirs largely differing in ion dynamics, see also Ref. . The sharp line resembles that of microcrystalline Li0.17SnS2; most likely, the ions representing this line reflect those in the nanocrystalline grains. The broader line can then be assigned to those in the amorphous regions. The two spin ensembles are also visible in 7Li NMR spin-lock NMR transients which can only be parameterized with a sum of two single transients. The resulting rates are denoted as (fast, f) and (slow, s) in Figure 16a. Worth mentioning, the resulting broad NMR rate peak of the fast diffusing species resembles that obtained for microcrystalline LixSnS2 before annealing. The low-T activation energy is, however, much lower and the rate peak is shifted toward lower T as is illustrated by the horizontally drawn arrow in Figure 16a. This observation points to enhanced ion dynamics in the nanostructured form of LixSnS2.
An additional increase in Li ion diffusivity is seen if we consider a sample that has been prepared via mechanochemical reaction of Li2S and SnS2 in a planetary mill, see the corresponding 7Li NMR rates in Figure 16a. The shape of the Li NMR spectra do not reveal a pronounced structurally heterogeneous sample as discussed for the nanocrystalline sample before. We suppose that either defects introduced during the synthesize procedure are responsible for fast ionic diffusivity in the bulk or the surface-influenced regions. Heavy formation of amorphous regions, however, seems to slow down Li diffusivity at least in the case of layer-structured materials. Such materials already possess fast diffusion pathways being able to guide the ions also over long distances.
2.3 Enhancing ionic conductivity in poorly conducting ternary oxides and carbonates through structural disorder: LiAlO2, Li2TiO3, LiTaO3, Li4Ti5O12, and Li2CO3
Lithium aliuminate is, at least in its γ-modification, known as a very poor ionic conductor if at hand in a coarse-grained or single-crystalline form. The Li ions occupy tetrahedral voids that are connected by corner-sharing. Recently, Wiedemann et al. compared experimental results on Li ion translational dynamics in oriented LiAlO2 single crystals [orientations (100) and (001)] from (i) conductivity spectroscopy, (ii) mass tracer experiments as well as (iii) 7Li NMR measurements. Ion transport turned out to be fully ionic . For short-range Li ion dynamics 7Li NMR relaxation resulted in an activation energy of ca. 0.7 eV, see Ref.  for an overview and Ref.  for recent measurements on a powder sample. The value of 0.7 eV agrees with that derived from neutron diffraction data that indicated a curved pathway connecting two adjacent Li sites in LiAlO2 .
Long-range Li ion transport, on the other hand, has to be described with a higher activation energy , . Both secondary ion mass spectrometry (SIMS) and conductivity spectroscopy revealed essentially the same activation energies of ca. 1.20(5) eV and 1.12(1) eV, respectively . From 650 K to 750 K, which was the T range covered by the SIMS experiments, the diffusion coefficient DSIMS equals Dσ meaning that the corresponding Haven ratio is given by HR=1 . Note that in Ref.  the solid-state diffusion coefficient Dσ was estimated via the Nernst–Einstein equation by assuming that the number density of charge carriers is simply given by the lithium concentration of the oxide. Mechanical loss spectroscopy confirmed these diffusion coefficients and activation energies . Dynamic mechanical analysis, which is sensitive to ultraslow Li ion displacements, points to a Debye-like motional correlation that controls ion dynamics at low temperatures. Recently, activation energies of ca. 1.1 eV have also been found via sin–sin correlation functions probed with the help of 7Li stimulated echo NMR being sensitive to long-range transport, see Ref. .
Regarding microcrystalline powder samples a very similar activation energy of ca. 1.14 eV  is obtained from conductivity measurements for temperatures below 600 K (see Figure 18a), see also Ref.  for an overview. The low conductivities and diffusivities are highly welcome if LiAlO2 is used as, e.g. blanket material in fusion reactors. In such systems diffusion should be strictly prevented. The application of the oxide in electrochemical storage systems, however, requires much better ion diffusivities. For instance, LiAlO2 is considered to act as thin-film electrolyte in all-solid-state batteries prepared with the use of sputtering or other deposition techniques. Furthermore, it has been reported that the oxide can be used as coating for Lix(Ni, Co, Mn)O2-based cathodes ; Goodenough and co-workers  as well as Cheng et al.  have recently shown that during the preparation of the highly-conducting electrolyte Li7La3Zr2O12 (LLZO), doped with Al, the LLZO crystallites are often covered by an amorphous layer of LiAlO2. Such a grain-boundary phase can have a negative impact on long-range ion transport in such oxide electrolytes.
Thus, also from an application point of view it seems to be important to study Li ion diffusion parameters in structurally disordered LiAlO2. As is shown in Figure 18a high-energy ball milling significantly influences the DC conductivity of LiAlO2 which can be read off from the frequency independent plateaus of the underlying conductivity isotherms. While overall conductivity has increased by several orders of magnitude, the activation energy decreases from 1.14 eV down to 0.78 eV (Figure 18a), . The same effect is known for nanocrystalline LiTaO3 (see Figure 18b), which has been studied in detail via conductivity spectroscopy and 7Li NMR relaxometry in an earlier work .
In order to study the origins that cause the increase in conductivity, XRD, HR TEM and 27Al magic angle spinning (MAS) NMR were employed , see also Figures 19 and 20a. In the case of LiAlO2 powder XRD proves nanostructuring of the samples. While after 30 min a nanocrystalline ceramic of γ-LiAlO2 has been obtained, further milling leads to the formation of large amounts of amorphous material and structurally disordered δ-LiAlO2. The δ-form is a high-pressure modification of LiAlO2. This observation was confirmed by 27Al MAS NMR . The more δ-LiAlO2 is formed, the more intense the respective NMR signal at 15 ppm [referenced against Al(NO3) aqueous solution], which represents those Li ions residing on octahedral sites in the δ-modification. After 8 h of milling, LiAlO2 nanocrystallites are obtained that are embedded in an amorphous matrix of the aluminate (see the HR TEM image shown in Figure 19b). The higher diffusivity in LiAlO2 was also seen in 7Li NMR line shape measurements , see Figure 20b.
Compared to LiAlO2 the enhancement effect observed for LiTaO3 is somewhat stronger. As one might expect because of the similar structure parameters, the behaviour of LiTaO3 resembles that of nanocrystalline LiNbO3. For Li2TiO3, on the other hand, the total increase in conductivity is less pronounced. The latter is simply because the conductivity of microcrystalline Li2TiO3 is already higher than that of LiTaO3 and LiAlO2. The dashed lines in Figure 21a indicate the conductivities of LiAlO2 and LiTaO3 which were each milled for 8 h in the same planetary mill under the same conditions regarding the vial set and ball-to-powder ratio.
Quite recently, we studied the change in local structure of Li2TiO3 and LiTaO3 through (extended) X-ray absorption fine structure (EXAFS) measurements similar to earlier work on LiNbO3 . As an example, in Figure 21b EXAFS data and Fourier transforms are presented for un-milled and mechanically treated Li2TiO3. The XAS scans were collected for the appropriate edge (Ti K-edge and Ta L3-edge) at room temperature on beam line B18 at the Diamond Light Source (Oxfordshire). For Li2TiO3, ball-milling attenuates the EXAFS and we observed a decrease in the height of the Ti–Ti peak in the Fourier transform. Similar results were also obtained for ball-milled LiTaO3  that was treated in a planetary mill (Figure 22). In Figure 23a and b the conductivities of several samples as well as the corresponding isotherms of a sample milled for 30 min are shown.
For LiTaO3 the decrease in EXAFS is best seen for the Ta–O and Ta–Ta correlations at ca. 2.0 Å and 3.8 Å, respectively (Figure 22b). The effect was analyzed in two ways viz. as a change in the Debye–Waller factor σDW due to (microscopic) disorder and as the effect of amorphous regions introduced during milling. Considering the Debye–Waller factors, shown in the form of σ2DW vs. milling time, for all the correlations σ2DW almost doubles after the oxide has been treated for only 30 min (Figure 22a). It can be explained that already after short periods of milling the local structure around the Ta ions is somewhat distorted. With increasing milling the Ta–O Debye–Waller factors show only a gradual change whereas the Ta–Ta correlation, which is significantly larger, continues to increase steeply with increasing mechanical treatment. We assume that at the beginning of the milling process the local Ta–O octahedra are affected while the relative arrangement of the octahedra continues to change with further treatment. Such observation would be expected given that the strong Coulomb interaction between Ta5+ and O2− will maintain a relatively rigid local structure.
In an earlier study we used a shaker mill (SPEX 8000) equipped with a single ZrO2 ball (10 mm in diameter) and a zirconia vial to produce nanocrystalline LiTaO3. After 30 min of milling most of the local electric field gradients in the direct neighborhood of the Li nuclei are still comparable to those in un-milled, coarse-grained LiTaO3. Many hours of milling were needed to destroy the originally well-structured powder pattern. Interestingly, the largest increase in ion conductivity is seen when the sample is milled for 30 min. Obviously, considering ion dynamics in LiTaO3, (local) distortions, point defects, displacements and strain introduced during the first 30 min of milling is sufficient to have a remarkable effect on both short-range as well as long-range ion transport. Interestingly, the previous conductivity studies  revealed some subtle dependence of the microstructure on the time of ball-milling. The longer the milling time the more difficult it is to recover crystallinity by thermal annealing. Hence, the additional conductivity enhancement seen for longer milling times is presumably due to the increasing formation of amorphous fractions.
In the case of planetary mills the situation is similar but also entails some differences. For planetary mills, enabling heavy grinding, indeed the generation of amorphous materials is more likely. Although for both types of mills amorphous material is expected to be formed at longer milling times, planetary mills might already produce significant amounts of amorphous material at short milling times. In Figure 23a and b the conductivity results of such samples are shown; they were prepared in planetary mills equipped with up to 140 small milling balls with a diameter of 5 mm only. As can be clearly seen from the Arrhenius plots the ionic conductivity reached an upper limit already after 30 min. Considering the corresponding complex plane plots and capacities of the data, the DC plateaus in Figure 23b have to be characterized by capacities typically found for bulk responses that are already affected by the influence of the electrical response of grain boundaries (see Figure 24a).
Milling LiTaO3 for 30 min causes the activation energy to decrease from 0.85 eV to 0.67 eV. Simultaneously, the corresponding pre-factor of the Arrhenius relation increased by 1.5 orders of magnitude. Such an increase might be attributed to free volume generated and structural disorder generated. Longer milling times do not influence the Li ion conductivity further. Once again, after 30 min the extent of structural disorder, i.e. local defects and amorphous material, has already reached a critical level to generate a network of fast migration pathways. We expect the percolating amorphous regions to form such a network. This view is supported by the abrupt change of the corresponding 7Li NMR line shapes observed (Figure 24b). Already after 30 min of milling the 7Li NMR spectrum resembles that of a sample milled for 8 h rather than that of the source material. The samples produced in planetary mills can thus be regarded as heterogeneously disordered materials, i.e. they are composed of (defect-rich) crystalline grains being embedded in an amorphous matrix that ensures fast long-range ion transport.
According to this explanation we alternatively assumed that the attenuation seen in EXAFS of the samples prepared with planetary mills (Figure 22b) stems only from the amorphous material generated. If we take the Ta–Ta correlation as an indirect (relative) measure for the amount of amorphous LiTaO3 produced, milling for as little as 30 min is estimated to yield already ca. 25 % amorphous material. This parallels the ionic conductivity measurements of the same sample ball-milled for 30 min where the magnitude is four orders higher than that for an un-milled sample (see the data at 360 K). After 8 h of milling, EXAFS suggest that the amount of amorphous LiTaO3 has increased to approximately 60 %. This additional increase has, however, no further effect on the ionic conductivity presented in Figure 23a.
A similar steep increase in conductivity has recently been found for Li2CO3, see Figure 25. Lithium carbonate is an important constituent in the passivating interlayer, the so-called solid electrolyte interface (SEI), in liquid-based secondary lithium-ion batteries. During charging and discharging the battery the Li ions have to surmount this barrier of decomposition products. Thus, the ionic conductivity of its components is key to guarantee powerful cycling and rate capability, particularly if an SEI mainly composed of by Li2CO3 is considered. To mimic the presumably amorphous Li2CO3 formed inside a battery, we treated microcrystalline Li2CO3 to introduce defect structures and to push its conductivity to the upper reachable limit of ion dynamics. As has been seen for LiAlO2, Li2TiO3 and LiTaO3, σDC already increases by several orders of magnitude if treated for short times in planetary mills. The same effect is seen for the carbonate, Figure 25a. The increase in conductivity is accompanied by a decrease of the original activation energy (1 eV) of coarse-grained polycrystalline Li2CO3; after 2 h of milling it decreased to 0.66 eV. This value as well as the conductivities obtained almost coincide with those for LiTaO3 that served as an internal benchmark, see the dashed line in Figure 25a.
As compared to the oxides discussed so far, for the titanate Li5Ti4O12, which is a well-known zero-strain anode material for lithium-ion batteries, the effect of ball milling on Li+ dynamics is much lower. Although ionic conductivity in microcrystalline Li4Ti5O12 is poor , viz. in the order of 10−12 S cm−1 at 295 K (ca. 0.76 eV, depending on the defect chemistry and exact morphology , ), it is, however, by about 1 order of magnitude higher than that of Li2TiO3. Milling of Li4Ti5O12 for 4 h in a planetary mill causes σDC to increase by only 0.5 orders of magnitude (330K). The activation energy is reduced from 0.76 eV to 0.69 eV.
This relatively small effect can also be observed via 7Li NMR relaxometry and complementary line widths measurements. The results shown in Figure 26 refer to nanocrystalline Li4Ti5O12, which was prepared by high-energy ball milling in ethanol for 3 h. The open symbols in Figure 26a represent the 7Li NMR motional narrowing curve of nanocrystalline Li4Ti5O12. The curve resembles that of microcrystalline Li4Ti5O12, which is shown for comparison. The onset of motional narrowing for nano-Li4Ti5O12 is, however, shifted by 50 K toward lower temperatures revealing (slightly) enhanced ion diffusivity. Most interestingly, if Li is chemically inserted into nanocrystalline Li4Ti5O12 no drastic change of the motional narrowing (MN) curve is seen if x values of up to 0.3 are considered, Figure 26a. For micro-Li4Ti5O12 the same treatment in n-BuLi causes a significant enhancement of ion mobility – the corresponding MN curve is shifted by almost 150 K toward lower T . The situation for x being larger than 0.3 is more difficult to explain as the increased Li+–Ti3+ interactions additionally broaden the spectra. A significant dependence of Li ion diffusivity on x, as it has been documented for the unmilled form , , seems to be, however, absent.
The same characteristic for nanocrystalline Li4Ti5O12 and nano-Li4.1Ti5O12 is seen if we look at the 7Li NMR spin-lock relaxation rates presented in Figure 26b. The corresponding diffusion-induced relaxation rate peaks for x=0 and x=0.1 show up at essentially the same temperature. By coincidence it is what we also found for microcrystalline Li7Ti5O12. In contrast, the difference for microcrystalline Li4Ti5O12 and micro-Li4.1Ti5O12 is much larger. Hence, we conclude that in the case of Li4Ti5O12 the introduction of structural disorder is much less favorable for ionic diffusivity. By comparing the results for micro- and nanocrystalline Li4Ti5O12 from rotating-frame spin-lock NMR an interesting feature is revealed: although the rate peak of the nanocrystalline sample shifts to lower T, as is expected when comparing the respective MN curves, the low-T flank of nano-Li4Ti5O12 has to be characterized by a higher activation energy. This feature can only be explained by an enhanced pre-factor of the associated Arrhenius law. If x is increased from x=0 to x=0.1 we witness both a decrease of Ea (from 0.89 eV to 0.57 eV, see Figure 26b) and the associated pre-factor. Without any change of the pre-factor the position of the rate peak should have been changed to be in agreement with a higher mean activation energy.
2.4 Ionic conductivity in nanocrystalline Li2O2 and Na2O2 – the possible discharge products in Li- and Na-air batteries
Ionic conductivity and diffusivity in peroxides belongs to the white areas of materials science. Li2O2 and Na2O2 form during discharging a Li metal or Na metal oxygen battery. Elucidating the transport properties of the ionic and electronic charge carriers in these peroxides is of importance in the field of oxygen batteries. Considering the above derived conclusion that ion transport can be, in some cases, greatly enhanced if the poorly conducting oxides were mechanically treated, we tried the same approach to produce phase-pure nanocrystalline Li2O2 and Na2O2. Thus, we expect that with nanocrystalline, ball-milled Li2O2 a material with an upper limit of reachable ion conductivities is at hand. To determine these maximal conductivity parameters might also influence current battery research on metal oxygen systems.
Li2O2 crystallizes with the hexagonal space group P63/mmc and shows two crystallographically distinct Li sites (Wyckoff positions 2a and 2c). The covalently bonded O2 dimers are arranged in an alternating ABAB stacking. The trigonal prismatic Li ions in Li2O2 are in the same layer as the peroxide anions. The octahedrally coordinated ones reside between the peroxide layers. As revealed by impedance and conductivity spectroscopy Li ion transport in Li2O2 is extremely low , . In Figure 27a the corresponding overall conductivities of microcrystalline and nanocrystalline Li2O2 are compared with those of isostructural Na2O2 , see also Figure 27b. While high energy ball milling of Li2O2 causes the total conductivity to increase by approximately 2 orders of magnitude, in the case of Na2O2 the effect is much less pronounced. For micro-Li2O2 we obtained a very low conductivity of 3.4×10−13 S/cm at ambient temperature . High-energy ball-milling leads to an increase of σDC by ca. 2 orders of magnitude reaching 1.1×10−10 S/cm; correspondingly, the activation energy decreases from 0.89 eV to 0.82 eV. The electronic contribution to σ, which was measured via polarization experiments, turned out to be in the order of 9×10−12 S/cm. This values makes <10 % of the total conductivity. For ball-milled Na2O2 at ambient conditions the overall conductivity is in the order of 10−13 S/cm. Recent polarization experiments have shown that the partial electronic conductivity ranges between 7.6×10−14 S/cm and 1×10−13 S/cm. Thus, the total conductivity in the sodium analogue is to a non-negligible extent influenced by electronic charge transport.
The poor ionic conductivity of Li2O2 is also represented by 7Li NMR line shape measurements . Interestingly, the 7Li NMR lines of nano-Li2O2 undergo a pronounced heterogeneous motional narrowing upon heating the peroxide, see Figure 28a. The Gaussian shaped NMR line that is seen in the regime of the rigid lattice narrows such that a two-component line shape emerges. The narrow line on top of the broader one represents Li ions being mobile on the time scale defined by the line width at low T, i.e. these ions have access to diffusion processes being characterized by (mean) jump rates in the order of ca. 20 kHz. Most likely, the enhancement in conductivity can be traced back to the generation of a small spin reservoir with mobile Li ions; these are expected to reside in the direct neighborhood of defects generated or near the structurally disordered and defect-rich interfacial regions formed during mechanical treatment.
Through 7Li NMR relaxometry and stimulated echo measurements we could refine the picture presented by conductivity spectroscopy. Interestingly, the diffusion-induced NMR relaxation rates reveal much lower activation energies for Li ion dynamics in Li2O2 (0.22–0.24 eV, see Figure 28b). Obviously, the rates probe local or short-range motions rather than long-range ion transport. We may identify the fast subset of Li ions seen in line shape NMR to be responsible for the low Ea values deduced through relaxometry. The same seems to be the case for the 7Li SAE NMR decay rates that are shown in Figure 28b for comparison. At higher T we recognized another thermally activated process that is, in the case of T1 7Li NMR relaxation, governed by a higher activation energy of 0.47 eV. A similar increase in decay rates is also seen in SAE NMR (0.41 eV). Most likely, this process is influenced by polaron dynamics; such dynamics were, for example, studied by first-principle calculations by Radin and Siegel who calculated an activation energy of 0.42 eV .
In analogy to Li2O2 we started to analyze the poor Na ion diffusion in nano- and microcrystalline Na2O2, see Figure 27a. High-resolution (MAS) 23Na NMR measurements carried out at 132.25 MHz revealed the two magnetically inequivalent Na sites in Na2O2 as expected, see Figure 29a. The spectra shown were recorded at a spinning speed of 30 kHz, no reference was used to measure the chemical shift values; the more intense signal was simply referenced to 0 kHz. Krawietz et al. report chemical shifts of 4.8 and 9.9 ppm . Slow Na ion hopping between the two neighbored sites might be measure bale via 2D exchange NMR or SAE NMR. Preliminary 23Na SAE NMR decay curves of microcrystalline Na2O2 are shown in Figure 29b; to the best of our knowledge this is the first time that such curves are reported for 23Na. So far, the SAE technique has been successfully applied to 2H , , 9Be , ,  and the two Li isotopes (6Li and 7Li, , , , ). Extending the technique to the 23Na (I=3/2) nucleus is, however, limited because of the large quadrupole moment of the Na spin that hinders a non-selective excitation. In the present case, the 23Na SAE signal is a mixture of quadrupolar and dipolar contributions.
Although the 23Na SAE S2 curves recorded at fixed tp and variable tm sensitively depend on preparation time, they do not significantly vary with temperature. Hence, Na ion dynamics in microcrystalline Na2O2 is by far too poor to be detectable even with NMR methods designed to probe slow ion exchange. The curves recorded at short tp are clearly composed of three decay steps. While step III reflects the almost T independent T1 relaxation, step II is most likely driven by spin-diffusion effects. The first decay step seems to be associated with transversal spin–spin relaxation.
2.5 Glass formers: the influence on ball milling on ion transport in crystalline Li2B4O7
As has been illustrated above for several oxides, particularly for LiTaO3, LiAlO2 and Li2CO3, mechanical treatment can greatly enhance Li ion diffusivity and Li ion transport, respectively. Expectedly the same is true for glass formers such as Li2B4O7 that served as another model substance to quantify the effect of high-energy ball milling on DC conductivity , in a second step the transport parameters could directly be compared with those of the pure glass that was prepared by quenching a melt of Li2B4O7. For coarse-grained polycrystalline Li2B4O7 the conductivity isotherms revealed low DC-conductivities and a quite high activation energy of 1.05eV (see Figure 30). Milling in planetary mills has once again a drastic effect on ion transport. Interestingly, after 8 h of mechanical treatment we reached ionic conductivities that coincide with those of LiAlO2 also milled for 8 h. Increasing the milling time to 16 h results in an additional increase of σDC by 0.5 orders of magnitude. Comparing a 16-h ball-milled sample and glassy Li2B4O7 shows that there is still a large conductivity gap between the two samples, see Figure 30a.
X-ray powder diffraction suggested that the formation of amorphous Li2B4O7 is mainly responsible for the increase in ion dynamics. This view is supported by 11B MAS NMR (Figure 31b), cf. Ref. . Concerning ion dynamics, 7Li NMR line shapes revealed that in addition to the ions in the amorphous regions also those in the crystalline grains nano-Li2B4O7 do sense the effect of mechanical treatment; the motional narrowing curve depicted in Figure 30 b unveils the increase in ion dynamics seen in the wake of mechanical treatment. Presumably, defects introduced into the still crystalline grains also drastically influence local hopping processes. These local ion dynamics are characterized by only 0.3 eV as could be deduced from the low-T flank of the 7Li SLR NMR rate peak (see Figure 31a). For comparison, the flank for micro-Li2B4O7 is characterized by 0.5 eV.
Li2B4O7 and aluminosilicates easily form glasses if the materials are melted and quenched. Although plenty of studies can be found in literature that deal with ion transport phenomena and diffusion mechanisms in glasses only few report on the change of ion transport parameters if glasses were mechanically treated in shaker or planetary mills. At first glance one would expect no significant influence when an already disordered material is milled. So far only few reports, however, showed that high-energy ball-milling of glassy materials (LiAlSi2O6 (β-spodumene, ), LiBO2 , ) results in a decrease of the ionic DC conductivity, see also Ref. . The same effect was observed for β-eucryptite . This astonishing decrease was also confirmed by 7Li NMR spectroscopy. For a first interpretation a simple structural model was used to explain the observed trend . This effect is obviously caused by a mechanically induced structural relaxation of the non-equilibrium structure of the glass that was prepared by rapid thermal quenching . Such structural relaxation obviously causes the ionic charge carriers to slow down with respect to those residing in the unmilled glass matrix. Note that, influenced by the Löwenstein rule, for β-eucryptite, for example, stable and metastable forms with respect to the Al and Si ordering exist in certain temperature ranges. Ball-milling might largely influence local and long-range arrangements of the polyhedra. Hence, the structural arrangement in a quenched glass should not necessarily be identical with that of a milled sample.
Nanostructured materials are of large and ever growing interest due to their beneficial properties. In particular, nanocrystalline ceramics find applications as catalysts, sensors, adsorbents or new electrolytes and advanced electrode materials in electrochemical energy storage. We reviewed recent studies on lithium-ion dynamics and electrochemical activity of various classes of materials. Nanostructuring is essential for TiO2 to use the oxide as anode material in lithium-ion as well as sodium-ion batteries. We noticed marked differences in the storage mechanism when amorphous TiO2 nanotubes are used as active material; the electrochemical reaction with sodium is significantly affected by interfacial effects. Li NMR spectroscopy measurements point to slow Li ion self-diffusivity in the amorphous form. Similarly, poor to moderate ion dynamics also govern ion transport in the other forms of titania such as rutile nanorods or mesoporous TiO2. In the case of TiO2-B nanotubes a fast relaxing reservoir of spins is detected that might be ascribed to those ions being located in the surface-influenced regions.
The formation of nanocrystalline ceramics via high-energy ball-milling leads to ion conductors with, in many cases, greatly improved transport properties. By using both NMR and EXAFS we could show that for some of the samples prepared in planetary mills (LiAlO2, LiTaO3, Li2B4O7) the formation of amorphous material plays indeed a decisive role in explaining the enhancement seen. For some of the oxides studied an upper limit of σDC is seen for sufficiently long periods of milling. Besides amorphous structures, the introduction of defects into the bulk regions of the nanocrystallites has also to be considered if samples prepared in shaker mills are to be studied. It turned out that, aside from few exceptions (see, e.g. Li4Ti5O12, Li2O2), ion transport properties can be easily manipulated by tuning the degree of structural disorder. This strategy holds at least for oxides with low conductivities and, of course, depends on the exact crystal structure and bonding situations of the materials as well as their tendencies to form metastable modifications usually showing up at high temperatures or pressures. Fast ion conductors, on the other hand, may suffer rather than benefit from mechanically induced structural disorder.
We thank the Deutsche Forschungsgemeinschaft for financial support (FOR 1277, Mobility of Lithium Ions in Solids, sub-projects 7 and 1 (TP 7, TP 1), grant no. WI 3600 4-1(2) and 2-1(2)) over the last 6 years in the Research Unit ‘molife’. Moreover, additional financial support by the Austrian Federal Ministry of Science, Research and Economy, and the Austrian National Foundation for Research, Technology and Development (in the frame of the Christian-Doppler-Laboratory of Lithium Batteries: Ageing Effects, Technology and New Materials) is greatly appreciated.
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About the article
Published Online: 2017-06-29
Published in Print: 2017-07-26