Estimation of the concentration and mobility of mobile Li⁺ in the cubic garnet-type Li₇La₃Zr₂O₁₂

Abstract

LLZ) lithium ion conductors with the garnet-like structure are promising candidates for applications in all solid-state lithium ion batteries. Due to the complexity of the structure and the distribution of Li + , it was difficult to get information on the true concentration of mobile Li + , n c , and their mobility. In this report, we estimate for the first time the values of n c from the analysis of the conductivity spectra at different temperatures. We found that only a small fraction of Li + contributes to the conduction process. n c is found to be independent of temperature with an average value of 3.17 Â 10 21 cm À3 , which represents 12.3% only of the total Li + content in LLZ garnets. Comparing the conduction parameters of LLZ with Li 6 BaLa 2 Ta 2 O 12 (LBLT) and Li 5 La 3 Ta 2 O 12 (LLT) garnets indicates that the mobility of Li + plays a prominent role in the conductivity enhancement in LLZ garnet materials. The diffusion coefficient of LLZ at room temperature has a value of 1.33 Â 10 À8 cm 2 s À1 , which is comparable with other fast Li + conductors.

Evaluating lithium diffusion mechanisms in the complex spinel Li2NiGe3O8

“…For both samples, the data follows typical Arrhenius-type behaviour, enabling activation energies to be calculated. The pellet sintered for 6 h exhibited an activation energy of 0.46 AE 0.01 eV, whilst the pellet fired for 24 h showed a higher value, 0.53 AE 0.01 eV, closer to that previously reported by Kawai et al (0.55 eV) for Li 2 NiGe 3 O 8 sintered for 24 h. 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 D ¼ 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.…”

Effect of Sm3+ Substitutions on the Lithium Ionic Conduction and Relaxation Dynamics of Li5+2xLa3Nb2−xSmxO12 Ceramics

“…It is suggested that Sm 3+ substitutions in LLN garnets will force Li + ions at 24d sites to leave their positions and move to occupy 48 g/96 h octahedral sites [33][34][35]. This process will allow more vacant 24d sites, which are essential for 3D diffusion process through the 24d-96h-48g-96h-24d chain pathway, as illustrated in Figure 6 [27,[33][34][35][36]. The relaxation dynamics of the LLN-Sm ceramics are studied by the complex electric modulus M * (ω), which can be expressed as follows [37]:…”

Origin of the enhanced Li+ ionic conductivity in Gd+3 substituted Li5+2xLa3Nb2−xGdxO12 lithium conducting garnets

“…The crossover frequency o c usually represents the true hopping frequency, o H , of the mobile ions. [29][30][31][32] Therefore, we analyzed the conductivity spectra of the investigated materials with eqn (2) in order to determine the values of s dc and o c at different temperatures.…”

“…Both the concentration n c and the hopping frequency o H of mobile Li + could be thermally activated and are expressed as follows, [29][30][31][32]…”