Li-ion diffusion in ${\mathrm{Li}}_4{\mathrm{Ti}}_5{\mathrm{O}}_{12}$ and ${\mathrm{LiTi}}_2{\mathrm{O}}_4$ battery materials detected by muon spin spectroscopy

Lithium diffusion in spinel ${\mathrm{Li}}_4{\mathrm{Ti}}_5{\mathrm{O}}_{12}$ and ${\mathrm{LiTi}}_2{\mathrm{O}}_4$ compounds for future battery applications has been studied with muon spin relaxation (${\mu }^{+}\mathrm{SR})$. Measurements were performed on both thin-film and powder samples in the temperature range between 25 and 500 K. For ${\mathrm{Li}}_4{\mathrm{Ti}}_5{\mathrm{O}}_{12}$ and above about $\sim 200\mathrm{K}$, the field distribution width ($\mathrm{\Delta })$ is found to decrease gradually, while the field fluctuation rate ($\nu )$ increases exponentially with temperature. For ${\mathrm{LiTi}}_2{\mathrm{O}}_4$, on the contrary, the $\mathrm{\Delta }\left(T\right)$ curve shows a steplike decrease at $\sim 350\mathrm{K}$, around which the $\nu \left(T\right)$ curve exhibits a local maximum. These behaviors suggest that ${\mathrm{Li}}^{+}$ starts to diffuse above around 200 K for both spinels. Assuming a jump diffusion of ${\mathrm{Li}}^{+}$ at the tetrahedral $8a$ site to the vacant octahedral $16c$ site, diffusion coefficients of ${\mathrm{Li}}^{+}$ at 300 K in the film samples are estimated as $(3.2\pm 0.8)\times {10}^{-11} {\mathrm{cm}}^2$/s for ${\mathrm{Li}}_4{\mathrm{Ti}}_5{\mathrm{O}}_{12}$ and $(3.6\pm 1.1)\times {10}^{-11} {\mathrm{cm}}^2$/s for ${\mathrm{LiTi}}_2{\mathrm{O}}_4$. Further, some small differences are found in both thermal activation energies and Li-ion diffusion coefficients between the powder and thin-film samples.

Figure 1

The relationship between the distribution of the implanted muons in the ${\mathrm{Li}}_4{\mathrm{Ti}}_5{\mathrm{O}}_{12}$ film [i.e., normalized stopping distribution ($N_{\mathrm{SD}}\left)\right]$ and the energy of the muon beam ($E_{\mu }^{\mathrm{imp}})$. The distribution was simulated by the computer program TRIMSP, in which we used the density of ${\mathrm{Li}}_4{\mathrm{Ti}}_5{\mathrm{O}}_{12}$ as 3.29 g/${\mathrm{cm}}^3$ and that of ${\mathrm{MgAl}}_2{\mathrm{O}}_4$ as 3.65 g/${\mathrm{cm}}^3$.

Figure 2

The ZF and LF-${\mu }^{+}\mathrm{SR}$ spectra for the ${\mathrm{Li}}_4{\mathrm{Ti}}_5{\mathrm{O}}_{12}$ film obtained at (a) $T=150$ K using a cryostat and (b) $T=400$ K using an oven at $\mathrm{S}\mu \mathrm{S}$ of PSI. Solid lines represent the best fit using Eq. (1).

Figure 3

The temperature dependencies of (a) the field distribution width ($\mathrm{\Delta })$, (b) the field fluctuation rate ($\nu )$, (c) the exponential relaxation rate of the KT signal ($\lambda )$, and (d) magnetic susceptibility ($\chi =M/H)$ for the film and powder sample of ${\mathrm{Li}}_4{\mathrm{Ti}}_5{\mathrm{O}}_{12}$. The data were obtained by fitting the time spectrum with Eq. (1). The magnetization ($M)$ for the powder sample was measured with a field cooling mode under $H=10$ KOe using a SQUID magnetometer (MPMS, Quantum Design).

Figure 4

The temperature variation of (a) ZF- and (b) wTF-${\mu }^{+}\mathrm{SR}$ spectrum for the ${\mathrm{Li}}_4{\mathrm{Ti}}_5{\mathrm{O}}_{12}$ powder sample. In (a), each data point is shifted by 0.025 for clarity of display. The data were obtained at ISIS of RAL.

Figure 5

The temperature dependencies of (a) $\mathrm{\Delta }$, (b) $\nu$, and (c) $\lambda$ for the ${\mathrm{LiTi}}_2{\mathrm{O}}_4$ film. The data were obtained by fitting the time spectrum using Eq. (1). The scales of both axes in (a)–(c) are the same to those in Fig. 3 for comparison.

Figure 6

The relationship between $\nu$ and inverse temperature for (a) the ${\mathrm{Li}}_4{\mathrm{Ti}}_5{\mathrm{O}}_{12}$ film and powder and (b) the ${\mathrm{LiTi}}_2{\mathrm{O}}_4$ film. The numbers in (a) and (b) represent the thermal activation energy $E_a$ estimated by fitting the data with $\nu ={\nu }_0+Aexp(-E_a/k_{\mathrm{B}}T)$ in the temperature range between 50 and 350 K. For ${\mathrm{LiTi}}_2{\mathrm{O}}_4$, since ${\nu }_0=0$ below 200 K, we fitted the data in the temperature range between 200 and 325 K.

Figure 7

The monoclinic supercell for first-principles calculations of ${\mathrm{Li}}_4{\mathrm{Ti}}_5{\mathrm{O}}_{12}$. The optimized lattice parameters are $a=10.4850\AA , b=6.0277\AA , c=14.9396\AA$, and $\beta =89.{6036}^{\circ }$.

Figure 8

The temperature dependence of $D_{\mathrm{Li}}$ for ${\mathrm{Li}}_4{\mathrm{Ti}}_5{\mathrm{O}}_{12}$ and ${\mathrm{LiTi}}_2{\mathrm{O}}_4$ films estimated with a conventional approach (case 1). Note that points above $T_{\max }$ are omitted since their values are too low due to the artificial effect caused by the insufficient time scale of ${\mu }^{+}\mathrm{SR}$ at high temperatures and are hereby not valid for obtaining true values of $D_{\mathrm{Li}}$.

Figure 9

The temperature dependencies of (a) $\mathrm{\Delta }$ and (b) the reduced ${\chi }^2$ (${\chi }^2/N$, where $N$ is the degree of freedom), and (c) the relationship between $\mathrm{\Delta }$ and inverse temperature for the powder sample of ${\mathrm{Li}}_4{\mathrm{Ti}}_5{\mathrm{O}}_{12}$. For the case 2, we fixed $\mathrm{\Delta }=0.1641\times {10}^6 {\mathrm{s}}^{-1}$ in the whole temperature range measured. The number in (c) represents $E_a$.

Figure 10

The ZF- and LF-${\mu }^{+}\mathrm{SR}$ spectra for the powder sample of ${\mathrm{Li}}_4{\mathrm{Ti}}_5{\mathrm{O}}_{12}$ obtained at (a) 150, (b) 300, and (c) 300 K in ISIS. Solid lines represent the best fit with Eq. (1) using a temperature-dependent $\mathrm{\Delta }$ (case 1) and a temperature-independent $\mathrm{\Delta }$ (case 2). At 150 K, $\mathrm{\Delta }=0.1641\times {10}^6 {\mathrm{s}}^{-1}$ for both cases, while, at 300 K, $\mathrm{\Delta }=0.1286\times {10}^6 {\mathrm{s}}^{-1}$ for case 1 and $\mathrm{\Delta }=0.1641\times {10}^6 {\mathrm{s}}^{-1}$ for case 2.