A critical property of electrode materials is the ability to conduct Li through the host lattice. Li-ion mobility can be directly probed with INS and QENS, however only a few neutron studies report the direct measurement of Li dynamics mostly due to its moderate incoherent neutron-scattering cross section. Typically, each material has to be considered in order to determine whether the signal originates from Li, magnetism or other atoms. Usually, the hopping diffusion in Li-ion insertion electrodes is relatively slow compared to the timescale of INS and QENS in which case the local mobility is observed. As a consequence few studies exist that probe the Li motion directly. A different approach is to probe the Li diffusion in electrode materials with diffraction. Both the anisotropic contribution in the Debye-Waller factor and the deviation from harmonicity due to thermal motions at elevated temperatures can indicate the directionality of Li motion, which in turn may allow the identification of diffusion pathways. Both are illustrated here: anisotropy in the ADPs in combination with a maximum-entropy method (MEM) was used to identify the Li-ion trajectory in the positive-electrode material LiFePO4, and an — harmonicity of the ADPs revealed the Li-ion trajectory in the negative electrode material Li4Ti5O12.

Li12C60 fulleride is a good example where Li diffusion was studied using QENS and INS, quantifying the diffusional motion of Li-ions across a phase transition proposing a localized jump-diffusion model in the octahedral voids of the Li12C60 structure. This accounts for the changes in the vibrational density of states near the phase transition and results in a model of the dynamical behaviour [141]. Another QENS study revealed the diffusion coefficient of Li in a highly-oriented pyrolytic graphite electrode at high temperatures, deriving an activation energy of 0.35 eV [142]. Interestingly, the diffusion coefficient obtained is similar to that obtained using electrochemical methods despite the diffusion lengths measured by the two techniques differing by a factor of 15,000. Li diffusion is more frequently deter­mined indirectly using neutrons, and an example of this is the studies of anion dynamics to shed light on Li diffusion. Li-containing metal hydride systems have been investigated, such as in LiBH4 and LiAlH4, where translational modes of Li are linked with BH4 in the high-temperature form of LiBH4 [143]. Additionally, the disappearance of Li-containing lattice vibrations near phase transitions in these compounds is thought to be associated with the delocalisation of Li that enhances diffusivity. In this way, hydrogen-containing group dynamics can provide infor­mation on Li dynamics.

One QENS study describes alkali-ion diffusion (including for Li) in alkali — containing silicate melts [144], of interest for cathode materials based on silicates. This study used the decoupling of the incoherent (below 60 ps) and coherent neutron-scattering as a signature for Li-ion diffusion along channels in the immobile Si-O network. The relaxation times for Li were a factor of two smaller than for Na, indicating that Li-ion diffusivity is a factor of two larger, in agreement with con­ductivity data. QENS experiments have also been performed on single crystals of 7Li2MnCl4 (an inverse spinel-type structure), revealing a lack of anisotropy in the local Li motion [145]. Li-ions at 8a tetrahedral sites were shown to visit neigh­bouring 16c interstitial sites and jump back, but longer-range translational motion was outside the timescale used for the measurement.

Significant insight into Li diffusion can be gained from diffraction. Diffusion pathways can be identified by the anisotropy in ADPs in combination with MEMs. The exceptionally high discharge rate [47] observed in LiFePO4 indicates that ionic mobility in the LiFePO4 matrix is unusually fast. This has raised the question of how this is possible by the small polarons that are strongly localized at Fe sites in phase-separated LiFePO4 and FePO4 [146]. Morgan et al. [27] used the nudged elastic band method in calculations that show high Li ion mobility occurs in tunnels along the [010] direction, but reveal that hopping between tunnels is unlikely, confirmed by calculations of Islam et al. [108]. Fast one-dimensional conduction along the b-axis in the LiFePO4 Pnma structure was predicted by atomistic mod­elling [27, 108] and the first experimental proof of the diffusion trajectory came from Nishimura et al. [147] using NPD in combination with the MEM. To enhance the sensitivity towards Li 7LiFePO4 was prepared using 7Li-enriched Li2CO3 as the raw material. In this study the ADPs readily show the direction of the Li-trajectory towards adjacent Li-sites, with green ellipsoids in Fig. 7.13 representing the refined Li vibration (displacement parameters) and indicating preferred diffusion towards the face-shared vacant tetrahedra. This suggests a curved trajectory in the [010] direction, consistent with atomic modelling [27, 39].

To relate further the vibrational motions with diffusion, the material with the overall composition Li0.6FePO4 was heated to approximately 620 K. In this com­position Li06FePO4 forms a solid solution at a relatively low temperature, * 500 K, due to the unusual eutectoid as shown in the phase diagram in Fig. 7.13. This is confirmed as single phase by neutron diffraction. Thereby a large number of Li defects are introduced, that in combination with the higher thermal energy, enhances Li motion. Note that the Li trajectory in the solid solution should rep­resent both end members because the crystal symmetry does not change upon heating and Li insertion. In the refinement of the Li0.6FePO4 structure no reliable solution using harmonically-vibrating Li could be found. To evaluate the dynamic

disorder of the Li the MEM was used to estimate the nuclear-density distribution from neutron diffraction. By considering the entropy the most probable distributions of nuclear species can be evaluated, making it possible to evaluate not only the missing and overlapping reflections, but also the more complicated nuclear densi­ties. This approach applied to neutron diffraction data of Li06FePO4 at 620 K leads to the three-dimensional nuclear distribution of Li (Fig. 7.13). The observed dif­fusion along the [010] direction is consistent with the shape of the anisotropic thermal motions shown in Fig. 7.13 and atomistic modelling [27, 39]. Note that the Fe, P, and O atoms remain at their normal positions. The data show that the Li-ions move from one octahedral 4a site to the next via the intermediate tetrahedral vacant site. Along this trajectory the sites do not face-share with other occupied polyhedra. This is in contrast to, for instance, diffusion along the [001] direction where the intermediate octahedral position shares two faces with PO4 tetrahedra which will lead to higher activation energies.

Laumann et al. [148] investigated Li migration in commercial spinel Li4Ti5O12 using variable-temperature neutron diffraction. At 900 °C a marked deviation is observed in the linear dependence of the cell volume, O position, and anisotropic displacement parameters. Refinement of the Li occupancies resulted in almost complete 8a site occupation below 900 °C. However, at 900 °C a Li deficiency of approximately 14 % was observed, which was interpreted as the result of anhar — monic motions and migration of the Li-ions. Therefore, in the fitting procedure one isotropic anharmonic ADP was refined. Examination of the nuclear density revealed negative scattering-length density peaks next to the 16c site. In this way Li-ion occupancy at the 32e site was discovered and subsequent refinement of Li at the 32e sites results in the probability density shown in Fig. 7.14. This makes it possible to formulate the diffusion pathway. Rather than occupying the 16c as an intermediate site between two 8a sites, which introduces an unacceptably long Li-O bond, Li passes from the 8a site through the face of the surrounding O tetrahedron to the nearby 32e site. This is followed by switching to the adjacent 32e site where it is bonded to another O atom, and from where it can hop to the next tetrahedral

8a position. Effectively, this mechanism results in a number of short jumps along the [111] direction between adjacent 8a sites. The energy barriers can be approximated by assuming Boltzmann statistics for single-particle motion resulting in the one — particle potential shown in Fig. 7.14. These findings are consistent with nuclear magnetic resonance measurements indicating that the 16c site forms the saddle point of the barrier between two 8a sites [149]. In this way NPD is able to reveal the details of the three-dimensional long-range diffusion pathway in spinel Li4Ti5Oi2.