Evaluating lithium diﬀusion mechanisms in the complex spinel Li 2 NiGe 3 O 8 †

Lithium-ion diﬀusion mechanisms in the complex spinel Li 2 NiGe 3 O 8 have been investigated using solid-state NMR, impedance, and muon spectroscopies. Partial occupancy of migratory interstitial 12 d sites is shown to occur at lower temperatures than previously reported. Bulk activation energies for Li + ion hopping range from 0.43 (cid:2) 0.03 eV for powdered samples to 0.53 (cid:2) 0.01 eV for samples sintered at 950 1 C for 24 h, due to the loss of Li during sintering at elevated temperatures. A lithium diﬀusion coeﬃcient of 3.89 (cid:3) 10 (cid:4) 12 cm 2 s (cid:4) 1 was calculated from muon spectroscopy data for Li 2 NiGe 3 O 8 at 300 K.


Introduction
Since Sony's successful commercialisation of lithium-ion batteries (LIBs) in 1990, their numerous desirable properties have been widely reported. [1][2][3] However, despite becoming ubiquitous in modern society, several safety concerns still remain, predominantly related to the use of flammable and corrosive organic liquid electrolytes in close proximity to highly energetic electrode materials. [4][5][6] Whilst accidents are relatively rare, these liquid electrolytes can pose significant dangers to consumers and other end-users, as well as reputational damage for device manufacturers. 7 An all-solid-state battery utilising a solid electrolyte could alleviate many of these concerns, whilst offering improved shock resistance and durability. 8 To date, research has primarily focused on the development and optimisation of materials with room-temperature Li + ion conductivities (s i )o fZ10 À3 Sc m À1 ,i n order to compete with current commercial liquid electrolytes. 8 Several such materials exist, for instance thio-LISICONs (e.g., Li 10 GeP 2 S 12 , s i =1 . 2Â 10 À2 Sc m À1 ) and Li-stuffed garnets (e.g., Li 6.4 La 3 Zr 1.4 Ta 0.6 O 12 , s i =1 0 À3 Sc m À1 ). [9][10][11] Nevertheless, many of these candidate materials suffer a number of drawbacks, which are preventing their commercialisation. For example, thio-LISICONs are unstable in air and decompose at cell voltages 44Vvs. Li/Li + . 12,13 Many are also reported to react with lithium metal. 12 Li-stuffed garnets can undergo proton exchange (H + /Li + ), substantially reducing levels of Li + ion conductivity. 14,15 They are also widely reported to exhibit high interfacial resistance with electrode materials (up to B2000 O cm 2 ). 16 One solution to lowering this interfacial resistance is to use materials with the same crystal structure to enable lattice matching, for example by developing an all-spinel solid-state battery.
The spinel structure, AB 2 O 4 , has been studied extensively and is known to consist of cubic close packed O 2À anions, with A-site cations occupying an eighth of the tetrahedral sites and B-site cations filling half of the available octahedral sites for 'normal' spinels. 17,18 Depending on the cations present, the spinel structure may also be inverse ( O 4 ). Cubic spinels generally crystallise in the Fd% 3m space group. In Li-based spinels, Li + ion conductivity typically follows a two-step conduction mechanism involving Li ions in 8a tetrahedral sites hopping into empty 16c octahedral sites and then onto adjacent 8a sites, forming a three-dimensional 8a-16c-8a pathway for ionic migration 19 that means spinels often exhibit interesting and useful electrical properties. As a result, several manganese-based spinels have been considered as potential high voltage cathode materials (44.7 V vs. Li + /Li), e.g.,L i C o M n O 4 and LiNi 0.5 Mn 1.5 O 4 . [20][21][22] However, these are incompatible with current LIB cell designs due to the breakdown of organic electrolytes above ca. 4.5 V vs. Li + /Li. Spinel-based titanates such as Li 4 Ti 5 O 12 are currently of interest as anode materials in LIB applications, as they exhibit excellent dimensional stability during Li (de)intercalation. 23,24 In contrast, spinel-based materials for solid electrolyte applications have received considerably less attention, since they often incorporate redox active transition metals. One potential candidate material is Li 2 NiGe 3 O 8 ,previously reported by Kawai et al. to exhibit a modest Li + ion conductivity of B10 À7 Scm À1 at 63 1C(c omp ar a b l etot het etr a gon a lpha s eo f the Li-stuffed garnet Li 7 La 3 Zr 2 O 12 ) and which is electrochemically i n a c t i v eb e l o w5Vvs. Li + /Li. 25 Li 2 NiGe 3 O 8 can be described as an ordered or 'complex'  spinel in space group P4 3 32, with Li + ions occupying tetrahedral  8c sites, and 1 : 3 cation ordering of Ni and Ge on the 4b and 12d octahedral sites, respectively. 25 Conduction pathways in complex spinels are less well studied compared to normal spinels, but can involve additional steps depending on the nature of the ordering present. Previous work using variable-temperature time-of-flight neutron powder diffraction (ToF ND) indicated the presence of a second Li 12d octahedral site in Li 2 NiGe 3 O 8 at high temperatures (B350-850 1C), leading to the proposition of a three-dimensional 8c-12d-8c conduction pathway. 26 Theoretical studies by Nakayama et al. predicted the activation energy for this particular pathway to be 0.47 eV, lower than other previously proposed pathways. 19 An improved understanding of ionic diffusion mechanisms in spinel materials, and Li + ion conductors at large, is crucial if such materials are to be improved and optimised for use as solid electrolytes in all-solid-state LIBs. To this end, we have used a combination of techniques, including impedance, muon and solid-state NMR spectroscopies to enhance our understanding of the crystal structure of the complex spinel Li 2 Ni-Ge 3 O 8 and the Li + ion diffusion dynamics therein.

Synthesis and characterisation
Samples of Li 2 NiGe 3 O 8 were synthesised via traditional solid state methods. Stoichiometric amounts of Li 2 CO 3 (Sigma-Aldrich, 99%), NiO (Alfa Aesar, 99%) and GeO 2 (Sigma-Aldrich, 99.999%) were mixed and ground in an agate mortar and pestle, placed into Au boats and fired at 923 K for 5 hours. Prior to heating, the starting reagents were dried at either 453 (for Li 2 CO 3 ) or 773 K (for oxides) for 12 hours. The samples were then calcined at 1173 K for 36 hours, with intermediate regrinding. Identical specimens of Li 2 NiGe 3 O 8 were used for all XRD, impedance, solid-state NMR and mSR studies.
Samples were characterised by X-ray diffraction (XRD) using a Bruker D2 Phaser diffractometer with Cu Ka (l = 1.5418 Å) radiation. The ICDD's PDF-4+ database (2019 edition) and SIeve+ software were used for phase analysis. Rietveld refinements were performed using the GSAS-II software. 27

Impedance spectroscopy
Pellets of Li 2 NiGe 3 O 8 were prepared for impedance spectroscopy measurements by uniaxial pressing. Pellets were placed onto sacrificial powder in an alumina crucible and sintered at 1223 K for 6 or 24 hours, resulting in pellets with 66% and 81% density, respectively. Both pellet faces were polished and gold electrodes applied to each as a paste. Each pellet was then annealed at 1123 K for 2 hours. All heating steps described used heating/cooling rates of 5 1Cmin À1 . Impedance measurements were collected using a Solartron Analytical/Ametek ModuLab XM MTS system from 1 MHz to 30 mHz with a 100 mV applied AC voltage. Measurements were taken during heating from 336 to 541 K.

Solid-state NMR spectroscopy
Solid-state NMR spectra were acquired using a Bruker 500 Avance III HD spectrometer, equipped with a wide-bore 11.7 T Oxford magnet, using Larmor frequencies of 194.4 MHz for 7 Li (I = 3/2) and 73.6 MHz for 6 Li (I = 1). Powdered samples were packed into conventional 4.0 or 1.3 mm ZrO 2 rotors and magic-angle spinning (MAS) rates of 10 and 60 kHz were employed, respectively. Both 6 Li and 7 Li chemical shifts were referenced to 1 M LiCl (aq) .
Conventional 7 Li MAS NMR spectra were obtained using a single-pulse experiment with typical pulse lengths of 3 ms. 6 Li MAS NMR spectra were acquired using a Hahn echo experiment (90 x -t-180 y ) with a typical p/2 pulse length of 3 ms. Typical radiofrequency field strengths of 84 kHz were employed and an experimentally optimised recycle interval of 0.2 s was used for both 7 Li and 6 Li. Standard variable-temperature (VT) 6 Li MAS NMR experiments were completed between 260 and 412 K using conventional hardware and the parameters stated above. In all cases, temperatures were calibrated using the 1 H signal of MeOH; quoted temperatures thus reflect the true sample temperature during the experiment.
Additional static variable-temperature 6 Li NMR experiments were completed for Li 2 NiGe 3 O 8 over the temperature range 204 to 609 K using a Bruker 400 Avance III HD spectrometer, equipped with a wide-bore 9.7 T magnet, using a Larmor frequency of 58.9 MHz for 6 Li. The sample was packed into a 5.0 mm glass tube and placed into a Bruker 5.0 mm static probe. The static NMR spectra were acquired using a standard solid echo experiment (90 x -t-90 y ), with a typical p/2 pulse length of 5 ms. Here, t represents an echo delay of 200 ms between 197 and 542 K and 250 ms at 609 K. The interpulse delay was increased in order to acquire the whole echo at higher temperatures. Typical radiofrequency field strengths of 50 kHz were employed and the experimentally optimised recycle interval was 0.05 s. In all cases, true sample temperatures during experiments have been determined using a lead nitrate calibrant.

Muon spin relaxation (lSR) spectroscopy
All mSR measurements were performed using the EMU instrument at the ISIS pulsed muon facility. Around B1 g of sample was packed into a disk of 30 mm diameter and 1.5 mm thickness and sealed in a Ti sample holder with a B25 mmthickTifoilwindow. The sample was implanted with 3.2 MeV spin-polarised positive muons, and the out-coming positrons detected by 96 scintillator segments arranged in two circular arrays. Data were collected from 39-555 K using a closed cycle refrigerator under three different applied longitudinal magnetic fields (0, 5 and 10 G). Initial symmetry calibrations were conducted using a 20 G transverse magnetic field. Data analysis was conducted using the WiMDA program. 28 Collection of data in multiple longitudinal fields enabled (i) the controlled decoupling of interactions between the implanted muons and any local magnetic field distributions, and (ii) additional constraints in and hence more reliable results from the fitting process.

Results and discussion
Room-temperature powder XRD data for Li 2 NiGe 3 O 8 are shown in Fig. 1. Bragg peaks were indexed to the P4 3 32 space group, with no additional or missing reflections, giving a refined lattice parameter a = 8.1848(5) Å, in good agreement with previous reports. 25,26 Details of the corresponding Rietveld refinement and a list of refined structural parameters are given in the ESI. † AL i 2 NiGe 3 O 8 pellet sintered at 1223 K for 24 h showed small additional Bragg peaks which are likely caused by lithium volatilisation, resulting in the onset of thermal decomposition and formation of impurities. Despite a rigorous search of the 2019 edition of the ICDD PDF-4+ database, we were unable to identify the additional phases present. It is noted that these peaks were not observed in data collected for a pellet sintered at the same temperature for 6 h.

Lithium-ion conductivity analysis by impedance spectroscopy
Impedance data were collected for Li 2 NiGe 3 O 8 pellets sintered for 6 and 24 h. Owing to the lack of mixed valence Ni and Ge species in Li 2 NiGe 3 O 8 , the electrical conductivity is expected to be negligible, as previously reported. 19,25 Hence, the responses observed in impedance data are likely due to Li + ion conduction. The complex impedance spectra obtained in Fig. 2(a) show two partly resolved arcs followed by a low frequency spike.
Irrespective of the sintering time, the arc observed at higher frequencies has an associated capacitance of B3.1 Â 10 À12 F, indicative of bulk, intra-granular responses. The second, intermediate frequency arc, with capacitance B1 Â 10 À11 F, is attributed to the response from the grain boundary component. 29 Under both sintering conditions, a subsequent low-frequency Warburg spike, inclined at B501 to the horizontal axis, was observed with associated capacitance of B10 À6 F, indicative of complete or partial ion blocking at the electrode, representative of ionic conductivity in Li 2 NiGe 3 O 8 . 29 To extract conductivities from the arcs attributed to intragranular and grain boundary responses in the complex impedance spectra, fitting was performed using Z-View. Bulk conductivities were taken from the intersection of two manually fitted parallel RC semicircles, with errors calculated from the intersection of the semicircles with the Z 0 axis. The extracted bulk conductivities, as a function of inverse temperature, are shown in Fig. 2 25 Assuming all Li in the spinel unit cell contribute to diffusion, an intra-grain diffusion coefficient, D Li , of 2.26 Â 10 À13 cm s À1 can be estimated from impedance data at 336 K using the Nernst-Einstein equation: 30  It is evident from Fig. 2(a) and (b) that longer sintering times leads to a concomitant decrease in both bulk and grain boundary conductivities. This difference is attributed to the loss of lithium and subsequent formation of additional phases during sintering at temperatures close to the reported melting point of Li 2 NiGe 3 O 8 (1243 K). 25

Probing Li diffusion using solid-state NMR
Using solid-state NMR spectroscopy it is possible to probe both local structural changes and ion mobility. Both lithium nuclides ( 6 Li and 7 Li) are suitable for NMR spectroscopy, however, one is often preferred over the other, depending on the specific system under investigation. Typically, 7 Li is favoured because of its higher natural abundance (92.5%) when compared to 6 Li (7.5%). However, its large quadrupole moment can give rise to relatively broad lines when Li is in a low symmetry site. In such cases, 6 Li is often preferred because it can allow close or overlapped resonances to be resolved. Moreover, because of its smaller quadrupolar interaction, the 6  The variation in 6,7 Li chemical shift with coordination number is well reported for a variety of crystalline systems. 32 Typically, in diamagnetic systems, LiO 4 environments exhibit chemical shifts between d iso =0-3ppm,whilstLiO 6 environments are between À1a n d0p p m . 31,32 In paramagnetic systems, these shifts can be altered substantially by the presence of a paramagnetic species, i.e., the presence of an unpaired electron(s). 33,34 Based on the chemical shifts reported in the literature, coupled with the X-ray diffraction data presented here, and the relative intensities of each resonance, the resonance at d E À25 ppm is believed to correspond to the tetrahedral 8c site and the resonance at d E 0.0 ppm corresponds to the octahedral 12d site. Hence, at room temperature, it appears that small amounts of Li occupy the vacant octahedral site, which is in contrast to previous diffraction studies. 26 In the spectrum, the tetrahedral site is shifted from its expected position, indicating that it is directly affected by the presence of paramagnetic Ni 2+ , i.e., it is experiencing a Knight shift, although the shift observed here is relatively small when compared to similar reported systems where the resonance can be shifted by several hundreds of ppm. 33,34 A fast spinning (60 kHz) 7 Li MAS NMR spectrum was also acquired for Li 2 NiGe 3 O 8 (shown as an inset in Fig. 3(a)), which revealed the presence of two resonances, one broad resonance at d = À25.3 ppm, belonging to the tetrahedral Li site and a sharper resonance at d = À3.9 ppm corresponding to the octahedral Li site. It is noted that the extra resolution afforded by faster MAS rates indicates that a Knight shift is also observed for the octahedral site. At slower MAS rates the lineshape is broadened, which hinders the extraction of an accurate shift for this site. Again, the intensities indicate that a small quantity of Li is occupying the octahedral sites. To verify the quantity of Li on each site, the spectrum was fitted to determine the approximate ratio of tetrahedral to octahedral sites. It is noted that this is somewhat challenging based on the broadened nature and overlap of the two sites. Occupancies of 0.024 and 0.976 were obtained for the octahedral and tetrahedral sites, respectively (Fig. S4, ESI †). This is in good agreement with the slow spinning (10 kHz) 7 Li MAS NMR spectrum.
Initial variable-temperature 6 Li MAS NMR studies of Li 2 Ni-Ge 3 O 8 were completed over the temperature range 260 to 412 K. The corresponding spectra are shown in Fig. 4(a). Between 260 and 357 K, a single broad resonance is observed. As the temperature is increased to 379 K a second resonance appears at d = À1.1 ppm, indicating the presence of a second Li site, believed to correspond to the octahedral Li site. The appearance of this site upon heating indicates diffusion of the Li ions from the tetrahedral 8c site onto one of the three neighbouring vacant 12d octahedral sites via a hopping mechanism. The presence of a second site is in good agreement with previous high temperature (B350-850 1C) ToF ND structural studies of Li 2 NiGe 3 O 8 . 26 However, the solid-state NMR data presented Fig. 3 (a) 7 Li and (b) 6 Li MAS NMR spectra acquired for Li 2 NiGe 3 O 8 . In (a), two different MAS rates were used, 10 and 60 kHz, respectively. In (b), a MAS rate of 10 kHz was used and an expansion of the central transition is also shown as a comparison. All spinning sidebands are denoted by *.
indicate that Li diffusion onto the octahedral site(s) occurs at lower temperatures than previously reported. 26 In fact, our 7 Li MAS NMR data (vide supra) suggest that, even at room temperature, some of the vacant octahedral 12d sites are occupied. However, owing to relatively poor signal-to-noise in the VT 6 Li MAS NMR spectra, it is challenging to accurately determine the precise temperature at which Li ions become mobile and move between the 8c and 12d sites.
As the temperature is increased, there is an obvious, yet gradual, linear change in chemical shift of the resonance corresponding to the tetrahedral site, towards more positive values. For example, the resonance is centred at d = À31.3 ppm at 260 K and moves to d = À17.2 ppm at 412 K. This is in contrast to the trend expected with increasing temperature for a paramagnetic system.
Typically, as temperature is increased, Li chemical shift values move to lower (or more negative) values, thereby obeying Curie-Weiss behaviour. 35 As stated earlier, a Knight shift is observed for the tetrahedral site in the 7 Li MAS NMR spectrum obtained at room temperature. This indicates that the tetrahedral Li site is closer in the structure to the paramagnetic Ni 2+ centre. In contrast, the resonance assigned to the octahedral 12d site exhibits a very small change in chemical shift, moving from d = À1.1 ppm to d = À0.9 ppm, with increasing temperature.
It is noted that, owing to the relatively low intensity and broad nature of the resonance, it is challenging to accurately determine the precise chemical shift observed. However, the resonance is not shifted to the same extent as that corresponding to the tetrahedral Li site. This suggests that the octahedral 12d site is positioned further away from the Ni 2+ in the structure and therefore does not experience the same effect of the paramagnetic species, i.e., no significant Knight shift. As temperature is increased and Li ions increasingly migrate from the tetrahedral site onto the octahedral site they move further and further away from the paramagnetic species. As a result, their chemical shift changes (becoming more positive). In Li 2 NiGe 3 O 8 , the octahedral Li site is B4 Å from the Ni centre, compared to a separation of B3.2 Å between the tetrahedral site to the Ni centre. Similar VT 7 Li MAS NMR experiments were completed between 260 and 357 K and the same trend in chemical shift was observed, Fig. S5 in the ESI. † Hence, the VT 6 Li and 7 Li MAS NMR data are in good agreement.
To further investigate Li + ion mobility in Li 2 NiGe 3 O 8 , additional static variable-temperature 6 Li NMR experiments were completed over a greater temperature range (204 to 609 K). It is noted that, due to hardware limitations, it is not possible to acquire 6 Li MAS NMR data over this temperature range. The VT static 6 Li NMR spectra obtained are shown in Fig. 4(b). Below room temperature, a single broad and relatively featureless lineshape is observed. As the temperature is increased, line narrowing is observed, indicative of Li + ion mobility within Li 2 NiGe 3 O 8 , in good agreement with the VT 6 Li MAS NMR data.
The variation in 6 Li chemical shift and full width at half maximum (FWHM) with increasing temperature are shown in Fig. 5, where a linear change in chemical shift is observed and a gradual narrowing of the resonance is also observed, again indicative of Li ion motion. In contrast to the MAS NMR data, it was not possible to resolve distinct Li sites or the individual contributions from the 8c tetrahedral and 12d octahedral Li sites in the observed lineshape. In this instance, the 6 Li NMR data is only capable of identifying the presence of Li + ion mobility within Li 2 NiGe 3 O 8 and not the precise contribution of each site. To gain further insight into the ion mobility, 6 Li T 1 measurements were attempted for Li 2 NiGe 3 O 8 using a saturation recovery experiment. However, owing to the paramagnetic nature of the sample, the relaxation properties of the system were too fast and could not be accurately measured. Similarly, using the VT NMR data acquired, and analysis of the corresponding FWHM, attempts were made to obtain an activation energy for Li migration. Unfortunately, due to a combination of hardware limitations and the specific characteristics of the system under investigation, we were unable to acquire the full motional narrowing curve for Li 2 NiGe 3 O 8 (Fig. 5(b)). Hence, we were unable to obtain an activation energy.

Investigation of intra-grain diffusion by lSR
To explore Li + ion diffusion in greater depth, muon spectroscopy, mSR, was used. Positively charged muons, m + , have a lifetime of 2.197 ms and are 100% spin polarised. They can be implanted B200 mm into a sample and are expected to reside near oxygen sites. [36][37][38][39] The m + spin can precess depending on the different magnetic fields it experiences, such as external applied fields, fields from nearby nuclei, or those from unpaired electrons in paramagnetic species. The diffusion of Li + ions leads the m + to undergo a spin flip due to the inherent nuclear magnetic moment of lithium. When the m + decays, the positron produced is most likely to be emitted in the direction of the m + spin at decay. By recording the positrons emitted from opposite sides of the sample, the asymmetry of positrons can then be followed as a function of time and the evolution of the muon spin ensemble deduced.
Muon decay asymmetry data collected in longitudinal magnetic fields of 0, 5 and 10 G at various temperatures were fitted using WiMDA. For each temperature point, data from all three fields were fitted to a single model using Keren's analytic generalisation of the Abragam function, multiplied by an exponential relaxation term to account for the presence of paramagnetic Ni. 40 Example fitted data for Li 2 NiGe 3 O 8 at room temperature are shown in Fig. 6.
From the different fits, the calculated fluctuation rate, n, and local magnetic field distribution, D, were extracted and their variation with temperature is shown in Fig. 7(a) and (b). The fluctuation rate shows a plateau at lower temperatures, followed by an Arrhenius-like increase due to thermally activated diffusion of lithium ions above B300 K. This increase in fluctuation rate continues to 421 K; the subsequent decrease observed at higher temperatures is likely indicative of Li + ions hopping at rates too fast for mSR to capture. 36,37 The values obtained for D, Fig. 7(b), support this hypothesis; D is constant, within errors, at low temperatures, due to the slow rate of lithium hopping, but then shows a significant decrease from B380 K related to the effect of motional narrowing, where Li + ions are moving quickly and their nuclear spins differ from point to point within the sample. Above 442 K, lithium diffusion coefficients become too large for the muons to capture, and D values plateau again.

Elucidating diffusion mechanisms
The lithium ion diffusion coefficient for Li 2 NiGe 3 O 8 can be calculated using the equation: where N i is the number of accessible Li sites in the ith path, Z n,i is the vacancy fraction of the destination sites in the ith path, S i is the hopping distance between sites, and n is the fluctuation rate at 300 K, and assumed to be related to Li + ions hopping between 8c and 12d crystallographic sites, as reported previously. 26,41 Fig. 5 Variation in (a) 6 Li chemical shift and (b) full width at half maximum (FWHM) with increasing temperature for the 6 Li static NMR data obtained for Li 2 NiGe 3 O 8 . The corresponding spectra are shown in Fig. 4(b).  Based on the findings obtained using mSR and solid-state NMR spectroscopy, additional analysis was conducted on the crystal structural refinements, using the ToF ND data previously reported by our group. 26 Therein, refinements conducted on room temperature data had indicated within standard statistical approaches that the 8c site was fully and solely occupied by Li; occupancy of the 12d migratory interstitial had only been noted where datasets had been collected at temperatures above ambient conditions. This does not preclude the possibility of very low concentrations of lithium hopping between the two sites at, or close to, ambient conditions -such results would merely be statistically indistinguishable from the fully ordered structure reported. This assumption is in good agreement with the 6,7 Li MAS NMR and mSR data presented ( Fig. 3 and 7). Therefore, in order to calculate the true diffusion coefficient at 300 K, refined occupancies of both the 8c and 12d sites from 350 r T/1C r 850 were linearly extrapolated (Fig. S6, ESI †) to give proposed fractional occupancies, or Z n,i , of 0.97 and 0.03 for the 8c and 12d sites respectively at 300 K (Table S2, ESI †). This is in good agreement with the occupancies obtained from the 7 Li MAS NMR data (vide supra).
The hopping distance, S i ,inLi 2 NiGe 3 O 8 can be calculated by considering that an ion hopping between the 8c and 12d sites likely passes through three saddle points (SP) along the way, in the LiO 4 tetrahedral and LiO 6 octahedral faces, and an empty tetrahedral site. Once in the 12d site, Li + ions can hop to one of two neighbouring 8c sites (one of which is the original 8c site). A reasonable hopping distance of 2.95 Å can thus be calculated from the distances between the 8c-SP1-SP2-SP3-12d sites along this proposed conduction pathway (Fig. 8).
By following these assumptions, the calculated diffusion coefficient, D Li , for Li 2 NiGe 3 O 8 at 300 K is found to be 3.89 Â 10 À12 cm 2 s À1 (Table S2, ESI †). This is in good agreement with the figure extracted from impedance spectroscopy data, and is similar to values reported for other spinel-type materials, e.g., Li 4 Ti 5 O 12 which has a diffusion coefficient, D Li of between 3.2 Â 10 À11 to 4.0 Â 10 À12 cm 2 s À1 , depending on the technique used and precise degree of lithiation. 42,43 By comparison, other solid electrolyte candidate materials based on the Li-stuffed garnet structure, e.g.,Li 6.5 Al 0.25 La 2.92 Zr 2 O 12 , with a faster ionic conductivity and shorter hopping distance (1.67 Å), has a Li + ion diffusion coefficient of 4.62 Â 10 À11 cm 2 s À1 . 39 An activation energy of 0.43 AE 0.03 eV for lithium hopping in our powdered sample of Li 2 NiGe 3 O 8 was calculated from an Arrhenius plot of log D Li over the thermally activated region (Fig. 9), in good agreement with the value obtained from EIS data on a pellet sintered for 6 h (0.46 AE 0.01 eV), but considerably lower than that observed after a 24 h sinter (0.53 AE 0.01 eV). This is further evidence that long dwell times at temperatures close to the melting point result in Li loss through volatilisation. As a result, additional studies aimed at identifying less extreme consolidation methods are currently underway. Length-scale dependent ion dynamics are well known in the literature with LiFePO 4 being a particular prominent example, 44 where the activation energy changes several-fold and the diffusion constant by several orders-of-magnitude. In Li 2 NiGe 3 O 8 the change in activation energy is far less pronounced.

Conclusions
Lithium-ion diffusion mechanisms in the complex spinel Li 2 Ni-Ge 3 O 8 have been investigated using a range of complementary techniques. Building on previous reports of an 8c-12d-8c conduction pathway, using mSR and 6,7 Li solid-state NMR spectroscopy, we have shown that Li + ion hopping becomes thermally activated at B300 K, resulting in partial occupancy of the migratory interstitial site at lower temperatures than previously reported. A lithium diffusion coefficient of 3.89 Â 10 À12 cm 2 s À1 at 300 K and an activation energy for lithium hopping of 0.43 AE 0.03 eV were determined using mSR on powdered samples. This energy is considerably lower than that observed for sintered pellets (0.46 AE 0.01 and 0.53 AE 0.01 eV,  depending on the sintering conditions), suggesting that the investigation of an alternate consolidation route, avoiding Li volatilisation, may be worthwhile. This work also highlights the necessity of using multiple complementary techniques, such as impedance spectroscopy, solid-state NMR and mSR, as local probes in order to gain a more complete understanding of hopping mechanics in important ionic conductors.

Conflicts of interest
There are no conflicts to declare.