Figure 1

XRPD of Li${}_7$La${}_3$Zr${}_2$O${}_{12}$ proving its tetragonal symmetry at room temperature. Vertical lines indicate intensities and diffraction angles calculated on the basis of the neutron diffraction study of Awaka et al. (Ref. 13).Reuse & Permissions

Figure 2

(Left) ${}^6\mathrm{Li}$ MAS NMR spectrum of garnet-type Li${}_7$La${}_3$Zr${}_2$O${}_{12}$ recorded at ${\nu }_{\mathrm{rot}}=30\hspace{0.5em}\mathrm{kHz}$ and a resonance frequency of 88 MHz. The solid line shows a spectrum obtained from 16 scans which were accumulated at an interval of 2400 s; for the second spectrum (dashed line) 12 scans were accumulated and the delay time was set to 9000 s so that full ${}^6\mathrm{Li}$ NMR SLR is ensured (see text). The main signal can be attributed to Li ions occupying the distorted octahedral sites 16$f$ and 32$g$. The signal with much lower intensity reflects Li ions residing in the tetrahedral interstices. (Right) ${}^6\mathrm{Li}$ MAS NMR recorded with the same relaxation delays but at 73 MHz and ${\nu }_{\mathrm{rot}}=39\hspace{0.5em}\mathrm{kHz}$. Up to 64 scans were accumulated.Reuse & Permissions

Figure 3

Temperature-variable ${}^7\mathrm{Li}$ NMR spectra of polycrystalline garnet-type Li${}_7$La${}_3$Zr${}_2$O${}_{12}$ recorded at a resonance frequency of 155 MHz. The spectra were obtained directly from the FIDs of the ${}^7\mathrm{Li}$ SLR NMR measurements in the laboratory frame of reference. The insets (a), (b), and (c) represent NMR spectra obtained after Fourier transformation of ${}^7\mathrm{Li}$ NMR spin-alignment echoes beginning from their top. See text for further details.Reuse & Permissions

Figure 4

${}^7\mathrm{Li}$ NMR line widths $\delta$ of the central line versus temperature. The dashed line represents a fit according to Eq. (2) with no restrictions for the adjustable parameters. The solid line shows the same fit, however, with $E_a$ being fixed at 0.5 eV. (Inset) Arrhenius plot of the correlation rates ${\tau }_a^{-1}$ of Eq. (2). The solid line shows a fit according to the corresponding Arrhenius relation and yields $E_a\approx 0.43\mathrm{\hspace{0.5em}}\mathrm{eV}$.Reuse & Permissions

Figure 5

${}^7\mathrm{Li}$ NMR SLR rates of garnet-type Li${}_7$La${}_3$Zr${}_2$O${}_{12}$ recorded in both the laboratory ($•$) and the rotating frame of reference ($°$). The solid lines show fits according to Eqs. (3) and (4). Data points marked with a dot were excluded from the fit (see text for further details). The dashed-dotted line illustrates the deviation of the rate peak $R_{1\hspace{0.5em}\varrho }(1/T)$ from simple BPP-type behavior characterized by $\beta =2$.Reuse & Permissions

Figure 6

Temperature dependence of the ${}^7\mathrm{Li}$ NMR SSR rates $R_2$ of Li${}_7$La${}_3$Zr${}_2$O${}_{12}$. The dashed line represents a fit according to an Arrhenius law yielding an activation energy of 0.50(3) eV. For comparison, the rates $R_1$ of Fig. 5 are shown, too.Reuse & Permissions

Figure 7

${}^7\mathrm{Li}$ NMR SLR rates $R_1$ as well as $R_{1\varrho }$ recorded at ${\omega }_1/2\pi =30\hspace{0.5em}\mathrm{kHz}$ and at 77 and 155 MHz. The solid lines represent a global fit according to Eqs. (3) and (4). The dashed-dotted line indicates the position of the SSR rates $R_2$ shown in Fig. 6. At higher $T$ the $R_2$ rates follow the behavior of $R_{1\hspace{0.5em}\varrho }$. Note that the fitting functions were modified such that dipolar relaxation is taken into account (see text for further details). Furthermore, ${\omega }_1$ was replaced by an effective locking frequency ${\omega }_{\mathrm{eff}}$ taking into account the coupling of the Li spins with paramagnetic centers. The data points marked by dots were excluded from the fit.Reuse & Permissions

Figure 8

(a) Impedance spectra ${\sigma }^{\prime }(\nu )$ of Li${}_7$La${}_3$Zr${}_2$O${}_{12}$ recorded at the temperatures indicated. The spectra are composed of different contributions reflecting electrode polarization, grain boundary, and bulk response (see, e.g., the highlighted spectra recorded at 298 K). The latter becomes most evident at low temperatures and merges into a dispersive regime at higher frequencies. ${\sigma }_{\mathrm{dc}}^{\prime }$ of the bulk response is read out at the corresponding inflexion points. The uncertainty is somewhat less than half an order of magnitude (see also Fig. 9). At the lowest frequencies and highest temperatures, polarization effects showing up being characteristic for metallic electrodes blocking Li-ion transport. (b) Impedance spectra ${\sigma }^{\prime }(\nu )$ of Li${}_7$La${}_3$Zr${}_2$O${}_{12}$ obtained after sintering the pellet at 1148 K. For comparison, the spectrum recorded at 298 K recorded before annealing is also shown. (c) ${\sigma }_{\mathrm{dc}}^{\prime }$ (plotted as ${\sigma }_{\mathrm{dc}}^{\prime }T$ vs $1/T$) of the bulk response [see (b), sintered sample] as well as of the low-frequency conductivity plateau of the nonsintered sample [cf. panel (a)]. The solid line shows a fit according to ${\sigma }_{\mathrm{dc}}^{\prime }T\propto \exp [-E_a/(k_{\mathrm{B}}T)]$, yielding $E_a=0.47(2)\hspace{0.5em}\mathrm{eV}$ (bulk). The dashed line corresponds to $E_a=0.87(2)\hspace{0.5em}\mathrm{eV}$. For comparison, the data published recently by Awaka et al. are also shown (Ref. 13).Reuse & Permissions

Figure 9

Temperature dependence of the Li jump rate in garnet-type Li${}_7$La${}_3$Zr${}_2$O${}_{12}$ as obtained from various NMR methods as well as ionic conductivity measurements. The jump rates deduced from $R_1$ NMR measurements were obtained at two different Larmor frequencies (see Sec. 3c1). For comparison, the conductivity data of Awaka et al. (Ref. 13), which were converted into Li jump rates according to Eq. (12), are also included. See Ref. 13 for details concerning these data points.Reuse & Permissions