Local Structure and Li Ion Dynamics in Garnet Li7-2xGaxLa3Zr2O12 Solid Electrolytes
Authors: Jalem Randy , Nakayama Masanobu 
Published: February 2020

One of the key component in solid-state Li ion rechargeable Li ion batteries is the solid electrolyte. Garnet Li7-xGaxLa3Zr2O12 is one of the solid electrolyte systems that has been reported to demonstrate conductivity values that almost reaches the level of conventional organic-based electrolytes (~10-3 S/cm).1 Interestingly, the dopant cation in this system, Ga3+, occupies Li sites and can directly impede Li ion movement. Meanwhile, experimental results were inconclusive and not unanimous in ascertaining the actual site preference and distribution of Ga3+ in the 24d tetrahedral (Td) and 48g/96hoctahedral (Oh) crystallographic sites. In this work, we attempted to clarify the aforementioned issues by performing computational modelling, emphasizing on the Ga dopant coordination environment and the effects of Ga towards the Li ion transport process.
To study the local environment for Ga3+, we calculated the NMR parameters (chemical shift ∂iso, asymmetry factor ηQ, quadrupolar coupling CQ) at the two distinct Li sites using the augmented plane-wave method implemented in WIEN2k. Prior to NMR parameter fitting, model cells for the doped garnet (with Ga at the tetrahedral and octahedral cage, respectively) and several relevant Ga-containing compounds were relaxed by DFT using VASP. Meanwhile, we also analyzed the energy distribution with respect to Ga3+occupancy by uniformly sampling the Li-Ga-vacancy configurations within a 3 x 3 x 3 garnet supercell using fitted Buckingham interatomic potentials and GULP. For Li ion transport study, we employed molecular dynamics by using DL_POLY.
Structural information of DFT-relaxed models showed good agreement with experimental results; ~1% difference for lattice constants and < 5% difference for volume. The calculated NMR parameters are as follows: ∂iso,Ga@Td = 231.7 ± 9.30 ppm, ηQ,Ga@Td = 0.4860 ± 0.0053, CQ,Ga@Td = 11.82 ± 0.34 MHz; ∂iso,Ga@Oh = 53.8 ± 9.30 ppm, ηQ,Ga@Oh = 0.4496 ± 0.0053, CQ,Ga@Oh = 5.84 ± 0.34 MHz. For the chemical shift ∂iso for the Td environment (four-fold coordination), our result is consistent with MAS NMR results for Ga-doped garnets (207 ± 10 and 244 ppm).1,2 On the other hand, the calculated asymmetry parameter ηQ is larger than the experimental value for the 24d tetrahedral cage (0.05 ± 0.05)1. However, when compared with the experimental value for LiGaO2 (0.37) in which Ga3+ also sits in a tetrahedral cage,3 our calculated value for ηQ
is comparable, indicating that Ga may coordinate assymetrically as well in the 24d tetrahedral cage in the garnet Li sublattice. Based from configuration sampling for Li-Ga-vacancy arrangements (16,000 random configurations of 3 x 3 x 3 supercells, sampling for all-Td, all-Oh, and intermediate distribution for Ga), we found that the energy variation is small (< 15 meV/atom) which means that Ga has no site occupancy preference. Furthermore, Ga can exist in a four-fold coordination inside the octahedral cage (eg., when at the 96hsite). Hence, the inconsistency in experiments may be resolved by viewing the dopant Ga as sitting in a four-fold coordination environment either at the tetrahedral or the octahedral Li cage of the garnet structure.
Our molecular dynamics results4 have shown that the first-nearest-neighbor site of Ga is energetically inaccessible for a migrating Li due to strong repulsion, possibly forming defect clusters according to the following association reactions: i) Ga··
Li + V'Li → {Ga··
LiV'
Li
}·, {Ga··
LiV'
Li
}· + V'Li → {Ga··
Li2V'
Li
}X, 2Ga··
Li + 4V'Li → {2Ga··
Li4V'Li}X. We also confirmed the stabilization effect of Ga for the high-conductivity cubic phase (from the low-conductivity tetragonal phase) as evidenced in the calculated thermal expansion profiles. Two distinct regions for conductivity were observed for 0 ≤ x ≤ 0.30 in Li7-xGaxLa3Zr2O12: an abrupt rise followed linear decrease for 0 ≤ x ≤ 0.10 (owing to competing effects of tetragonal → cubic transition and decreasing Li concentration) and a flattrend for 0.10 ≤ x ≤ 0.30 (due to increasing accessible Li vacancies which are crucial for initiating concerted Li motion).
REFERENCES

1 Bernuy-Lopez et al., Chem. Mater. 2014, 26, 3610−3617.

2Rettenwander et al., Inorg. Chem. 2014, 53, 6264−6269.

3Ash et al., Magn. Reson. Chem. 2006, 44, 823−831.

4 Jalem et al., Chem. Mater. 2015, 27, 2821–2831.