Anomalies in Bulk Ion Transport in the Solid Solutions of Li7La3M2O12 (M = Hf, Sn) and Li5La3Ta2O12

Cubic Li7La3Zr2O12(LLZO), stabilized by supervalent cations, is one of the most promising oxide electrolyte to realize inherently safe all-solid-state batteries. It is of great interest to evaluate the strategy of supervalent stabilization in similar compounds and to describe its effect on ionic bulk conductivity σ′bulk. Here, we synthesized solid solutions of Li7–xLa3M2–xTaxO12 with M = Hf, Sn over the full compositional range (x = 0, 0.25...2). It turned out that Ta contents at x of 0.25 (M = Hf, LLHTO) and 0.5 (M = Sn, LLSTO) are necessary to yield phase pure cubic Li7–xLa3M2–xTaxO12. The maximum in total conductivity for LLHTO (2 × 10–4 S cm–1) is achieved for x = 1.0; the associated activation energy is 0.46 eV. At x = 0.5 and x = 1.0, we observe two conductivity anomalies that are qualitatively in agreement with the rule of Meyer and Neldel. For LLSTO, at x = 0.75 the conductivity σ′bulk turned out to be 7.94 × 10–5 S cm–1 (0.46 eV); the almost monotonic decrease of ion bulk conductivity from x = 0.75 to x = 2 in this series is in line with Meyer–Neldel’s compensation behavior showing that a decrease in Ea is accompanied by a decrease of the Arrhenius prefactor. Altogether, the system might serve as an attractive alternative to Al-stabilized (or Ga-stabilized) Li7La3Zr2O12 as LLHTO is also anticipated to be highly stable against Li metal.


■ INTRODUCTION
Garnet-type Li 7 La 3 Zr 2 O 12 (LLZO), if stabilized in its cubic modification by aliovalent doping, belongs to the most promising solid electrolytes 1 for all-solid-state batteries (ASSBs). 2,3 Despite of its high Li-ion conductivity in the mS cm −1 range, 4,5 LLZO has attracted great attention because of its nonflammability, high chemical and electrochemical stability, as well as its mechanical robustness. 2,6 Unfortunately, the pure cubic phase (Ia3d no. 230) is thermodynamically not stable at room temperature; at ambient temperature, the tetragonal modification is present (space group: I4 1 /acd no. 142), which shows a much lower ionic conductivity, see Figure 1a. 7−10 The cubic form can, however, be stabilized by the introduction of supervalent cations, such as Ta, substituting, for example, the Zr ions. 2 Further elegant doping strategies have been reported as well including Fdoping 11 and Ce-doping. 12 As a typical example, Li 7−x La 3 Zr 2−x Ta x O 12 (LLZTO) with x ≈ 0.6 shows ionic conductivities ion the order of 1 mS cm −1 . 13,14 In contrast to Al-stabilized LLZO, where Al 3+ occupies part of the Li sites residing on 24d and 96h, 15 in LLZTO the Li sublattice remains untouched. In all LLZO compounds, the exact Li content also influences the dynamic properties. As an example, for Li 7−3x Ga x La 3 Zr 2 O 12 an amount of 6.25 (x = 0.25) Li ions per formular unit (pfu) turned out to guarantee high Li ion conductivities with values on the order of 1 mS cm −1 at 20°C . 13,16 Apart from pure tetragonal LLZO, other tetragonal phases such as Li 7 La 3 Hf 2 O 12 (LLHO) 17,18 and Li 7 La 3 Sn 2 O 12 (LLSO) 19 also exist which might be transformed into powerful electrolytes by substitution strategies 2 using supervalent cations. Such investigations are expected to be helpful in refining our understanding of ionic conduction in garnet-type electrolytes. Previous studies have shown that Nb, Ta, and Al stabilize the cubic form of the LLSO phase; 17,19,20 another investigation showed that Ta is also able to stabilize cubic-LLHO 21,22 at ambient temperature. To the best of our knowledge, no study so far is available in literature that systematically looked at the change of bulk ionic conductivities of the two solid solutions of Li 7−x La 3 Hf 2−x Ta x O 12 (LLHTO) and Li 7−x La 3 Sn 2−x Ta x O 12 (LLSTO) over the full compositional range. Here, we synthesized two series of samples with x values ranging from x = 0 to x = 2.
In the present study, we took advantage of a ceramic sintering approach and systematically investigated the connections between phases, Li content, microstructure and Li + transport properties by using powder X-ray diffraction (PXRD), scanning electron microscopy (SEM), and broadband impedance and conductivity spectroscopy. The goal was to provide a complete picture of the change in lattice constants, density and Li ion conductivity, i.e., activation In tetragonal LLHTO (and LLSTO) the purple dodecahedra correspond to two distinctly coordinated La 3+ ions (8b and 16e), and the violet octahedra show the coordination spheres of Hf 4+ (Sn 4+ ) residing on 16c. While the blue spheres correspond to octahedrally coordinated Li + on 8a, the orange ones represent 6-fold coordinated Li + on 32g and the red ones represent 6fold coordinated Li + on 16f. In the illustration of cubic-LLHTO (cubic-LLSTO), the purple dodecahedra reflect the coordination sphere of the La 3+ ions (A-site, 24c), and the violet octahedra represent the spheres of Hf 4+ (and Sn 4+ ) corresponding to the B-site (16a Then, they were uniaxially pressed under a force of 5−10 kN to prepare pellets with diameters of 10 mm. These pellets were calcined at 850°C for 4 h; the heating rate to reach the target temperature was 5°C/min, and after 4 h the pellets were allowed to cool down to room temperature in the furnace. Afterward, the samples were mixed with isopropanol and milled in a Fritch Pulverisette 7 ball mill for a time period of 2 h (5 min at 500 rpm (12 times) with breaks for 5 min between the milling periods). Finally, the powders were again isostatically pressed (5−10 kN) to prepare pellets (d = 10 mm) for the sintering step. Sintering was carried out at 1100°C , and the sintering period was 4 h; again, we used a heating rate of 5°C/min. Importantly, the bottom of the crucible was covered with ZrO 2 powder to reduce possible contamination with Al from the crucible. A so-called "bottom-pellet" with a height of approximately 1 mm, which was prepared from the original material, was put onto the powder. On top of the bottom-pellet, we placed the pressed samples for further sintering. The pellets themselves were covered by a "cap-pellet" to prevent Li loss during sintering. The density was calculated from the unit cell parameters shown in Table 1 and the respective molecular weight of each composition. The relative shrinkage and relative density were determined by the relative shrinkage of the sample diameter and the relative change of the sample dimensions before and after sintering, respectively.
To identify the main phases and any side phases as well as crystal symmetries and unit cell dimensions, powder X-ray diffraction (PXRD) measurements were carried out using a Bruker D8 Advance diffractometer that operates with Cu K α radiation. Data were collected at angles of 2θ ranging from 10°t o 80°. The patterns were analyzed by Rietveld refinement with the program X'Pert HighScore Plus V3.0 (PANalytical).
Scanning electron microscopy (SEM) analysis was carried out by using an SEM ZEISS Ultra 55 device. Small polycrystalline chips, taken from the larger pellets, were embedded in an epoxy resin. The surface was ground and subsequently polished using sand paper with 4000 grit. The surface was coated with a 5−10 nm thin layer of Au/Pd. For the analysis carried out at 15 kV, special attention was paid to extra phases, grain sizes, grain boundaries, and textures. We used both a secondary electron detector (SE) and a backscattered electron detector (BSE) to investigate the ceramic samples.
For the impedance measurements, the sintered pellets with a diameter of approximately 10 mm and a thickness of about 1 mm were used. Au electrodes (100 nm in thickness) were applied on both sides of the pellet utilizing a Leica EM SCD 050 sputter device. Impedance spectra were recorded with a Novocontrol Concept 80 broadband dielectric spectrometer The Journal of Physical Chemistry C pubs.acs.org/JPCC Article covering a frequency range from 10 mHz to 10 MHz; we measured conductivity spectra from 173 to 453 K in steps of 20 K. No optical change of the Au electrodes were observed after the measurements, assuming that at least for temperatures of up to 453 K the electrolyte/Au interface seems to be chemically stable. A QUATRO cryosystem (Novocontrol) controlled the temperature in the sample cell (BDS 1200, Novocontrol). The measurements were carried out under a stream of freshly evaporated N 2 gas to avoid any influence of water or oxygen.

■ RESULTS AND DISCUSSION
In Figure 1b, the PXRD patterns of the solid solutions of LLHTO and LLSTO are shown. It can be clearly seen that, in our case, for LLHTO an amount of x = 0.25 is necessary to fully stabilize the cubic modification. Similar observations were reported by Gupta et al., who managed to stabilize LLHTO with a Ta amount corresponding to x = 0.2. 22 We also see that with increasing x the cubic phase remains the stable polymorph. The corresponding reflections become narrower revealing that the samples have to be characterized by a higher degree of crystallinity and a larger average grain size. For the LLSTO counterpart, we observe a similar behavior. The only difference compared to LLHTO is that a Ta content of x = 0.50 is needed to fully stabilize the cubic phase. At x = 0.25, the corresponding pattern shows that a mixed phase consisting of both tetragonal and cubic LLHTO is present. This finding is different than a previous report; Deviannapoorani et al. showed that an amount of x = 0.25 is sufficient to stabilize the cubic phase. 25 Changes in the synthesis conditions may, however, serve as an explanation for this finding as they can cause non-negligible changes in the overall properties of oxide garnets.
The change of the cell parameters, a (and c), as a function of x of the two solid solutions is shown in Figure 1c. Within the cubic phase regime, we observe Vegard's behavior, that is, a linearly decreases with x. It decreases from 12.953 to 12.819 Å (LLHTO) and from 12.902 to 12.819 Å in the case of LLSTO; see also Table 1. The origin of the decrease is 2-fold and originates (i) from the replacement of the larger octahedrally coordinated (IV) cations Hf 4+ (r VI = 0.85 Å) 26 and Sn 4+ (r VI = 0.83 Å) 26 by the smaller Ta 5+ cations (r VI = 0.78 Å) 26 as well as (ii) from the reduction of the Li + content. Since Hf is a bit larger than Sn, the increase of the lattice parameter a with x is slightly steeper as compared to the behavior observed for the LLSTO series.
In Figure 2a,b the relative shrinkages and the relative densities of the LLHTO and LLSTO pellets are shown. Data have been determined after the final sintering step. To estimate the behavior illustrated, three samples were each sintered simultaneously. It turned out that the shrinkage of the pellets was very sensitive to their position in the furnace. This sensitivity resulted in non-negligible scattering of the data points. Data shown refer to those pellets that were placed at the same position in the furnace. We see that the relative shrinkage of the pellets because of the final sintering step reaches approximately 15% for x = 1.0; at this composition, ρ rel is given by 87%. Afterward, we recognize a decrease in shrinkage. For LLSTO, we see that at around x = 1.0 less dense samples as compared to LLHTO were obtained. The largest shrinkage is observed for a Ta content of x = 0.50. The density of the samples correlates well with the relative shrinkage of those samples. For LLSTO, ρ rel reaches about 85% at x = 0.25. Similar values have been reported by Hamao et al. 20 Our values are, however, lower than those presented by Deviannapoorani et al., who managed to increase the density of some samples to values as high as 94%. 25 In Figure 2c, the corresponding SEM-BSE pictures of the two series of samples are shown. In agreement with the result from Figure 2a,b we see that at x = 1 and x = 1.25 LLHTO has to be characterized by only a small volume fraction of pores. For LLSTO, on the other hand, relatively dense samples are For the latter two samples, we see a high-frequency semicircle (see Figure 3a) followed by a semiarc in the intermediate frequency range. While the first refers to a bulk electrical relaxation process, the one appearing at lower frequencies mirrors electrical relaxation either influenced by grain boundary (g.b.) regions or by surface layers (interfacial effects). We attribute the increase seen at even lower frequencies to strong polarization effects that occur when the ionic charge carriers pile up in front of the ion-blocking electrodes applied. 27 In Figure 3a, we used the equivalent circuit indicated to approximate the location curves of the tetragonal samples. The bulk process can be well parametrized with a resistor (R bulk ) connected in parallel to a so-called constant phase element (CPE). The capacitance C of the high-frequency arc is given by C = R ((1−n)/n) Q 1/n , where n is an empirical fitting parameter (0 < n ≤ 1) and Q is the numerical value of the admittance |1/Z| at the angular frequency ω = 1 rad s −1 . 28 For the bulk response, we obtained C values in the pF range (4.9 and 6.7 pF), whereas the response of the second semicircle is given by capacitances being in the order of 70 nF (= 7 × 10 −8 F ≈ 10 −7 F). The value 10 −8 F lies at the upper limit of capacitances commonly attributed to g.b. effects. 29 As mentioned before, surface layers and/or polarization at the sample/|electrode interface may also contribute to this electrical response. Here, we cannot exclude the formation of a thin decomposition layer at the electrolyte/| electrode surface. One might also think about a thin layer of Li 2 CO 3 that leads to this electrical response. 30 If liberally interpreting this response simply in terms of g.b. effects, the associated resistance would be only by a factor of 3−4 larger than that of the respective bulk responses. Hence, in any case in LLHO and LLSO no strong ion-blocking grain boundary regions seem to be present. It seems that for some samples its volume fraction is too low to be detectable for sintered samples consisting of sufficiently large crystallites. For cation-mixed (x = 1.0) cubic-LLSTO, as well as for the corresponding Hf-analogue (see inset), we see that these semicircles even disappear. Note that the relative density of the Hf-containing sample Li 7−x La 3 Hf 2−x Ta x O 12 with x = 1.0 is the highest seen in the series prepared, cf. Figure 2b. At the same time, this sample reveals the highest bulk ion conductivity, as will be discussed below. Hence, we conclude that detrimental g.b. effects are largely reduced for samples that are characterized by both a high density as well as by a large Hf/Ta mixing ratio. Thus, cation mixing does not only influence bulk properties but seems to help in both reducing g.b. resistances and densifying. Whether the first is a consequence simply because of a higher density or whether g.b. in cation mixed samples shows higher conductivities needs to be clarified, see below.
The joint or interrelated influence of cation-mixing and density on both bulk and interfacial properties is also seen if we consider cubic-LLSTO; although the sample with x = 0.75 exhibits a high ionic conductivity (vide inf ra), its relative density, within error margins, is somewhat lower than that of LLSTO with x = 1.0. The lower density for some Sn-bearing samples (see Figure 2b), especially those characterized by x ranging from 0.5 to 1.0, might serve as an explanation for the additional small semicircle that appears at intermediate frequencies; see Figure 3b. Its capacitance of 8.8 nF (x = 0.5, LLSTO) is an indication of very thin g.b. regions, whose resistance do only marginally affect the overall electrical conductivity; see Figure 3b. The shape of the plot for x = 0.75 looks very similar. The associated apex frequency of the intermediate semicircle is by 2.5 orders of magnitude shifted toward lower frequencies. This shift points to the fact that mainly long-range ion dynamics is affected by this response, supporting its assignment to g.b. effects. As mentioned above, for LLSTO with x = 1.0 any g.b. effects originating from a lower density seem to be overcompensated by the beneficial influence of Sn/Ta cation mixing as the intermediate semicircle does almost disappear. Here, we assume that the grain boundary regions in heavily mixed but less dense LLSTO are less resistive than in nonmixed samples.
Coming back to the location curves shown in Figure 3b, we conclude that the strong increase of −Z″ IM observed in the Nyquist plots seen in the low-frequency region represents an interfacial relaxation process in front of the ion-blocking Au electrodes. Most likely, this process is, again, either caused by direct electrode polarization or by a thin interphase formed at the Au/electrolyte interface. Visual inspection of the Au/ electrolyte region does not show any obvious changes.
In the following, we will mainly focus on bulk properties and their change with composition of the two series studied. Importantly, compared to the tetragonal samples, for cubic-Li 7−x La 3 Sn 2−x Ta x O 12 , as well as for the Hf-analogue (see Figure 3a,b), we recognize an immense decrease of the bulk resistance from the MΩ to the kΩ range if x reaches values around 0.75 and 1.0, respectively (see also below). The corresponding semicircle seen in the high-frequency region is characterized by capacitances on the order of few pF, thus clearly pointing to a bulk response.
The same features of several electrical relaxation processes are also found if we take a look at the conductivity isotherms σ′(ν). 31 Here, σ′ denotes the real part of the complex conductivity σ. As an example, in Figure 4a the isotherms for Li 7−x La 3 Sn 2−x Ta x O 12 with x = 0.75 are displayed. This sample shows the highest ionic conductivity in the LLSTO series. In the region of very low frequencies, electrode (or interfacial) polarization is evident that proceeds stepwise. 32 This process also includes a shallow plateau seen as an inflection point at ν = 1 Hz if we consider the isotherm recorded at ϑ = 20°C (regime I). 30 This interface-controlled electrical relaxation process passes into a so-called direct current (dc) plateau (σ′ bulk ) being, in the present case, characteristic for bulk ionic conduction (regime II). The intermediate semicircle, discussed above for the LLSTO (x = 0.5, Figure 3b) is also present for the sample with x = 0.75. Because of its low resistivity, it is hidden in the dc plateau in the σ′(ν) representation. By increasing the frequency further, the dc plateau reaches its dispersive regime (III), which is responsible for short-range, The Journal of Physical Chemistry C pubs.acs.org/JPCC Article nonsuccessful (forward−backward) jump events. 27 For comparison, in Figure 4b the corresponding behavior of the real part, ε′, of the complex permittivity ε is also shown. Again, in agreement with the Nyquist analyses, the isotherms reveal that the decrease in σ′(ν) at low frequencies is, most likely, caused by polarization effects near the sample/electrode surface as the drop for the isotherm seen at 100 Hz corresponds to permittivities ε′ in the order of 10 6 . Of course, the different sources for electrical relaxation, especially the one assigned to the bulk response, are also observed when −Z″ IM and M″ IM are plotted versus frequency ν. Here, M″ IM denotes the imaginary part of the complex electrical modulus M. The corresponding spectra, which were recorded at 20°C, are shown in Figure 3c for the cubic samples with the highest ionic conductivities, that is, for x = 1.0 (LLHTO) and x = 0.75 (LLSTO). The M″ IM peaks (see arrows) appearing in the high-frequency range refer to both the bulk semicircle in the Nyquist representation and to the dc plateau in the σ′(ν) plot. Since the amplitude of M″ IM , here denoted as M″ max , is inversely proportional to 1/C, bulk responses are more prominent in the modulus representation as compared to those with lower capacitances. 31 In general, while −Z″ IM (ν) pronounces electrical relaxation originating from grain boundaries or interfacial effects M″ IM (ν) is used to shed light on bulk relaxation. Here, for the Hf-bearing sample M″ IM (ν) passes through a maximum at relatively high characteristic frequencies of 10 7 Hz. For the Sn-containing sample, the peaks shift toward lower frequencies, in agreement with the lower ionic bulk conductivity; see also Figures 4a and 5.
For cubic-Li 6.0 La 3 Hf 1.0 Ta 1.0 O 12 , a second, much shallower, M″ IM (ν) peak appears at ν = 4 Hz; the corresponding real part, ε′, of the complex permittivity ε takes values on the order of 10 5 . For comparison, for the Sn-bearing cubic samples Li 5.75 La 3 Sn 1.25 Ta 0.75 O 12 the permittivity reaches values of almost 10 6 in this region, indicating a process that is influenced by interfacial effects near or directly in front of the ion-locking electrodes applied. In general, permittivity values of this order of magnitude correspond to capacitances C with values in the nF range.
In addition, for LLHTO (x = 1.0) the ε′(ν) isotherm reveals a plateau at 1 kHz characterized by ε′ = 10 4 . This feature is less seen for the LLSTO sample, again indicating that different interfacial processes affect the dielectric properties in this frequency range. We suppose that Sn-containing LLSTO interacts differently with the Au electrode, possibly pointing to a weaker electrochemical stability if in contact with metal electrodes. As a side note, two samples also differ in bulk permittivities. For cubic-Li 6.0 La 3 Hf 1.0 Ta 1.0 O 12 , we obtain ε′(∞) values well below 50. 33 In the case of the Sn-containing cubic Li 7−x La 3 Sn 2−x Ta x O 12 sample (x = 0.75), we see that ε′ reaches a value of 20 for the M″(ν) peak appearing at 10 6 Hz.
As mentioned above, analyzing the Nyquist curves with appropriate equivalent circuits, see Figure 3, leads to the resistance R bulk , which can be studied as a function of both temperature T and composition x. The specific bulk conductivities σ′ bulk have been calculated according to σ′ bulk = 1/R bulk × (d/A), where d denotes the thickness of the pellets and A is their area. The temperature dependence of σ′ bulk is shown using an Arrhenius representation that plots log 10 (σ′ bulk (T)T) versus 1000/T, see Figure 5a, and T denotes the absolute temperature in K. In all cases, we observe linear behavior, that is, we calculated the activation energies E a according to the relationship σ′ bulk T = σ 0 exp(−E a /(k B T)), where k B is Boltzmann's constant. The conductivity values obtained for ambient conditions, that is, for ϑ = 20°C, as well as the corresponding activation energies E a are included in Table 1, which also lists the Arrhenius prefactors σ 0 . The change of σ′ bulk , E a , and σ 0 for the two series of Li 7−x La 3 M 2−x Ta x O 12 investigated is presented in Figure 5b. For Li 7−x La 3 Hf 2−x Ta x O 12 , we see that starting from tetragonal symmetry the ionic conductivity increases from 2 × 10 −6 S cm −1 to values being 2 orders of magnitude higher than the initial one. The sample with x = 1.0 exhibits the highest density; at 20°C, σ′ bulk is given as 1.9 × 10 −4 S cm −1 .
For larger values of x, it decreases again reaching about 8 × 10 −7 S cm −1 for the ordered Li 5 La 3 Ta 2 O 12 sample. The maximum in bulk ion conductivity for the sample with the largest degree of Hf/Ta site disorder and 6Li pfu corresponds to a minimum in activation energy (0.46 eV). Interestingly, tetragonal Ta-free LLSO also shows a very low ionic conductivity, and its activation energy (0.49 eV) is comparable to that seen for the sample with x = 1.0. However, the corresponding prefactor σ 0 of Li 7 La 3 Hf 2 O 12 is 2 orders of magnitude lower than that of Li 6.0 La 3 Hf 1.0 Ta 1.0 O 12 .
It is worth noting that two conductivity anomalies are seen for the compositions x = 0.5 and x = 1.5; see Figure 5b. In each case, we observed an undershoot of σ′ bulk of more than 1 order of magnitude. The associated activation energies of the two Li 7−x La 3 Hf 2−x Ta x O 12 samples are higher than expected and take a value of 0.66 eV. In qualitative agreement with the socalled Meyer−Neldel rule, 23,24 which relates E a with the prefactor σ 0 , we recognize that, at least for the sample with x = 0.5, the prefactor is 1 order of magnitude higher than expected for this sample; see the dashed line that serves to guide the eye for the continuous change of σ 0 . A small increase in σ 0 is also seen for x = 1.5. Obviously, these Li compositions are energetically less favored for long-range ion transport. Similar trends have been observed for Al-stabilized LLZO and explained in terms of order−disorder phenomena of the Li sublattice; 34 see also ref 19.
For the series with Sn, a similar behavior is seen. The maximum in ionic bulk conductivity is reached at x = 0.75 (8 × 10 −5 S cm −1 ). For x values larger than x = 0.75, we observed a continuous decrease in σ′ bulk and an increase in activation energy finally reaching a value of almost 0.7 eV at x = 2. If we disregard the anomaly at x = 1.0, this increase in E a is accompanied by a monotonic increase of the Arrhenius prefactor spanning a range of about 1.5 orders of magnitude, a behavior that is again in agreement with the rule introduced by Meyer and Neldel (MN). This empiric compensation rule links the prefactor τ 0 −1 of the Arrhenius relation for the ionic Li + jump rate τ −1 (= τ 0 −1 exp(−E a /(k B T)) with the overall activation energy E a according to τ 0 −1 ≈ τ MN −1 exp(E a /Δ MN ). Here, we used τ 0 −1 ∝ σ 0 and plotted log 10 (σ 0 ) versus E a ; see Figure 6. The dashed line in the Meyer−Neldel plot of Figure  6 shows a linear fit excluding the anomalies at x = 0.5 and x = 1.0 (vide infra). The fit yields E MN ≈ 0.06 eV; this value translates into an isokinetic temperature of T iso = E MN /k B ≈ 700 K. We see for cubic Li 7−x La 3 Sn 2−x Ta x O 12 that the prefactors are larger for the tetragonal forms. A difference of up to 2 orders of magnitude in the prefactor has recently been also seen if results from tetragonal Li 7 La 3 Zr 2 O 12 are compared with those from cubic Li 6 La 3 ZrTaO 12 . 10 σ 0 contains several parameters that might be responsible for this increase. For instance, a higher number of mobile charge carriers N c , an increased (mean) attempt frequency, as well as an increased activation entropy ΔS, being the sum of the migration and formation entropy, could be made responsible for this enhancement; see below.
As for the series with Hf, the LLTSO series also reveals two prefactor anomalies (Figure 5c). The samples with x = 1.5 and x = 0.5, in particular, show activation energies and prefactors that are higher than expected by the dashed line in Figure 5c. Again, the noticeable drop in conductivity for the Li 7−x La 3 Sn 2−x Ta x O 12 sample with x = 0.5 is reflected by a somewhat higher activation energy and a considerably larger prefactor, partly compensating the decrease in σ′ bulk . The shallow anomaly in E a and τ 0 −1 seen for x = 1.0 is hidden in σ′ bulk if values at 20°C are considered; it is, however, seen at temperatures different from ϑ = 20°C.  The original Ta-free sample crystallizing with tetragonal symmetry, Li 7 La 3 Sn 2 O 12 , shows a very low ionic conductivity and a relatively high activation energy of about 0.57 eV. The latter is higher than that seen for the Hf-analogue. As both tetragonal samples show similar prefactors (see also Figure 6), the higher conductivity in tetragonal Li 7 La 3 Hf 2 O 12 (note that σ′ bulk exceeds that of the Sn-analogue by a factor of 10) turned out to be a direct consequence of the lower activation energy for Li + transport.
Most interestingly, the Sn-containing sample characterized by x = 0.25, which still crystallizes partly with tetragonal symmetry, reveals an unexpectedly high ionic conductivity in the order of 10 −4 S cm −1 (8 × 10 −5 S cm −1 ). The activation energy (0.44 eV) of this sample, being a mixture of cubic and tetragonal LLSTO, is the lowest one seen in the Li 7−x La 3 Sn 2−x Ta x O 12 series. As the prefactor does not change much as compared to that found for x = 0 (see Figure 5c and Figure 6), the increase in σ′ bulk is again solely due to the lowering of the overall activation energy. Note that this sample shows the highest relative density (85%) of its series. We assume that this sample has to be characterized by a high degree of lattice distortion as the corresponding PXRD reflections turned out to be broader than those seen in the patterns belonging to the pure tetragonal and pure cubic samples.
The above-mentioned anomalies in ionic conductivity are also evident if we use the electric modulus formalism to analyze our data. The corresponding curves M″(ν) are shown for selected compositions of the two series in Figure 7a,b. Importantly, the decrease in characteristic electric relaxation frequencies τ M −1 , which correspond to the frequencies at which the M″ peaks appear, reveals almost quantitatively the same trend as σ′ bulk does. As an example, τ M −1 (x = 0.5) increases from 1 kHz to τ M −1 (x = 1.0) = 100 kHz (Figure 7a). The same increase by 2 orders of magnitude is seen for σ′ bulk (− 40°C ). As τ M −1 is proportional to the Li + hopping rate and σ′ bulk is directly proportional to both the electric mobility μ of the Li + ions and the number density of charge carriers N c , this finding indicates that the drops in ionic conductivity at x = 0.5 and x = 1.0 are mainly caused by a change in charge carrier mobility μ rather than by a decrease in N c . Indeed, τ M −1 (1/T) of the sample with x = 0.5 yields 0.60 (0) eV, which is only slightly lower than 0.63 (1) eV from the analysis of σ′ bulk T. The marginal increase of E a from 0.60 to 0.63 eV is usually explained, as implied by weak electrolyte models, by an increase of N c which obeys the Arrhenius law N c ∝ exp(−E N / k B T)). 35 Hence, if we assume similar attempt frequencies for the samples of the Li 7−x La 3 Sn 2−x Ta x O 12 series (Figure 7b), the reason for the anomalies seen is likely caused by a change in activation entropy ΔS to which τ 0 −1 (and σ 0 ) are proportional (τ 0 −1 ∝ exp(ΔS/k B )). In addition, with x approaching x = 2 the modulus peaks increasingly become broader and asymmetric in shape reflecting strong deviations from Debye relaxation. For comparison, the widths δ M (in orders of magnitude) of the peaks belonging to the tetragonal samples are closer to Debye relaxation. In general, for the latter δ M, D = 1.14 is expected. 36 Finally, we compare our results with those presented in literature for similar compositions x. In our study, the peak conductivity values are given by approximately 2 × 10 −4 S cm −1 (LLHTO, x = 1.0) and by about 0.8 × 10 −4 S cm −1 (LLSTO, x = 0.75). These values are somewhat lower as compared to those reported earlier: 3.5 × 10 −4 S cm −1 (LLHTO, x = 0.45) 22 and 2.41 × 10 −4 S cm −1 (LLSTO, x = 0.45). 21 Such differences may have various origins. Bulk properties and interfacial ion transport is expected to be influenced by sintering procedures, final Li compositions, the defect chemistry, and the element distribution in the ceramics. As an example of how sintering temperatures and sintering periods will influence the total conductivity of garnet ceramics, we refer to Deviannapoorani et al. who reported an increase in total conductivity by more than 3 orders of magnitude, that is, reaching 2.41 × 10 −4 S cm −1 after increasing the density from 75% to 94%. 25 This finding clearly shows that changes in porosity and thus morphology of the samples will greatly influence ion dynamics related to g.b. regions in garnet-type samples. Chen et al. clearly pointed out how the density of pellets does also affect bulk properties. 37 For example, bulk properties may be affected by lattice strain expected to be alleviated the longer the sintering or annealing periods were chosen. As mentioned above, we witnessed a non-negligible interplay of densification and the ratio of cation mixing, most likely affecting both interfacial and bulk ion dynamics.

■ CONCLUSIONS
We synthesized two attractive series of garnet-type ceramics that, depending on the Ta content, crystallize either with tetragonal or cubic symmetry: Li 7−x La 3 Hf 2−x Ta x O 12 and Li 7−x La 3 Sn 2−x Ta x O 12 . The samples were characterized by Xray diffraction to identify the phases formed. We used broadband impedance and conductivity spectroscopy to The shift in frequencies Δτ max −1 mirrors the difference Δσ′ bulk . (b) Starting from tetragonal Li 7 La 3 Sn 2 O 12 , ion dynamics increases by more than 2 orders of magnitude at −40°C. The mixed cubic/ tetragonal sample (x = 0.25) reveals almost the same rapid ion exchange processes as the cubic sample characterized by x = 0.75. However, for the tetragonal samples and for the samples with low x values, the widths of the peaks, δ M = 1.43 (in orders of magnitude), point to electrical relaxation being comparable to Debye relaxation (δ M, D = 1.14); the peaks significantly broaden and become increasingly asymmetric with x reaching x = 2 (δ M = 2). This finding points to a larger distribution of electrical relaxation rates in Ta-rich LLZO-type garnets.
The Journal of Physical Chemistry C pubs.acs.org/JPCC Article study bulk ion dynamics and correlate the findings with microstructure, that is, relative density, and Li content. The latter was varied from x = 0 to x = 2. For the Li 7−x La 3 Hf 2−x Ta x O 12 series, the cubic sample with x = 1.0 revealed the highest bulk ionic conductivity σ′ bulk . Since Li 7−x La 3 Hf 2−x Ta x O 12 is expected to have high electrochemical stability, further improvement of its conductivity could result in an attractive alternative to Al-stabilized Li 7 La 3 Zr 2 O 12 , which is currently discussed to play the major role in future battery applications relying on oxide electrolytes. For the Sn-analogue, σ′ bulk passes through a maximum at x = 0.75. Interestingly, a mixed sample (x = 0.25) being both cubic and tetragonal has to be characterized by a relatively high ionic conductivity almost reaching 10 −4 S cm −1 at 20°C. The activation energy of this sample, which is characterized by a relatively low Arrhenius prefactor, turned out to be rather low (0.44 eV). Importantly, the relative density of this sample takes the highest value of this series reaching about 85%.
Adjusting the total conductivity in LLZO-based garnets is based on the complex interplay of crystal symmetry, composition, site preferences, and defects on the one hand and morphology as well as interfacial properties on the other hand. Here, we followed the change in bulk ionic conductivity as a function of Li content in the cubic phase regime. In qualitative agreement with the trend predicted by the empirical Meyer−Neldel rule, we observe two conductivity anomalies for which a pronounced decrease in activation energy is accompanied with an increase in the Arrhenius-prefactor. For both series investigated, at x = 0.5 the ionic conductivity is lower than expected. As we look at bulk ion dynamics, such a trend can only partly be explained by variations in morphology or porosity of the samples. Here, we find evidence that that order−disorder effects of the Li sublattice are responsible for this observation.
For the Li 7−x La 3 Sn 2−x Ta x O 12 series, we observe Meyer− Neldel behavior over a large compositional range, that is, an increase in activation energy is accompanied by an increase of the conductivity prefactor σ 0 . Comparing results obtained for cubic and tetragonal samples revealed that in garnet-type LLSTO (and in LLTO) with noncubic symmetry the Arrhenius prefactors are by tendency lower than those of their cubic counterparts with cation disorder on the B-site 16a. Most likely, this change is due to different attempt frequencies and/or to a change of the Li + activation entropy that enters σ 0 . The highest activation energies and prefactors are found for cubic Li 5 La 3 Ta