The Role of THz Phonons in the Ionic Conduction Mechanism of $Li_7La_3Zr_2O_{12}$ Polymorphs

TL;DR

The study addresses the role of THz phonons in Li+ ionic conduction within LLZO polymorphs and whether phonon–ion coupling can be leveraged to enhance conduction. It employs laser-driven ultrafast impedance spectroscopy (LUIS) to resonantly excite THz phonons ($0.5-7.5$ THz) and monitor Li+ hopping with picosecond resolution. The main finding is that THz excitation produces a longer impedance perturbation in the tetragonal, ordered, vacancy-poor Li+ sublattice than in the cubic, disordered one, suggesting phonon-mediated cooperative hopping is more effective in ordered systems; 400/800 nm excitation, by contrast, yields rapid relaxation, indicating a non-thermal mechanism. The work highlights a path to engineer dynamic lattice factors to improve solid-state ionic conductivity by populating room-temperature THz phonon modes.

Abstract

Superionic conduction in solid-state materials is governed not only by static factors, such as structure and composition, but also by dynamic interactions between the mobile ion and the crystal lattice. Specifically, the dynamics of lattice vibrations, or phonons, have attracted interest because of their hypothesized ability to facilitate superionic conduction. However, direct experimental measurement of the role of phonons in ionic conduction is challenging due to the fast intrinsic timescales of ion hopping and the difficulty of driving relevant phonon modes, which often lie in the low-energy THz regime. To overcome these limitations, we use laser-driven ultrafast impedance spectroscopy (LUIS). LUIS resonantly excites phonons using a THz field and probes ion hopping with picosecond time resolution. We apply LUIS to understand the dynamical role of phonons in $Li_7La_3Zr_2O_{12}$ (LLZO). When in its cubic phase (c-LLZO), this garnet-type solid electrolyte has an ionic conductivity two orders of magnitude greater than its tetragonal phase (t-LLZO). T-LLZO is characterized by an ordered and filled $Li^+$ sublattice necessitating synchronous ion hopping. In contrast, c-LLZO is characterized by a disordered and vacancy-rich $Li^+$ sublattice, and has a conduction mechanism dominated by single hops. We find that, upon excitation of phonons in the 0.5-7.5 THz range, the impedance of t-LLZO experiences a longer ion hopping decay signal in comparison to c-LLZO. The results suggest that phonon-mediated ionic conduction by THz modes may lead to larger ion displacements in ordered and fully occupied mobile ion sublattices as opposed to those that are disordered and vacancy-rich. Overall, this work highlights the interplay between static and dynamic factors that enables improved ionic conductivity in otherwise poorly conducting inorganic solids.

Figures (4)

• Figure 1: Conduction pathway of (a) tetragonal and (b) cubic Li7La3Zr2O12.Li+ migrates across the LLZO framework of ZrO6 and LaO8 polyhedra, depicted in blue and purple, respectivelyLogeat2012Chen2012, in the first column. The ions move through a 3D pathway characterized by individual loops, highlighted by the outlined Li+ atoms, connected by junctions as shown in the second columnAwaka2011Meier2014. In the third column, one such hoop is shown to illustrate the order and fully occupied Li+ sublattice of t-LLZO compared to the disordered and vacancy-rich Li+ sublattice of c-LLZOAwaka2009Awaka2011.
• Figure 2: Laser-driven ultrafast impedance spectroscopy (LUIS). Broadband 0.5-7.5 THz radiation is directed toward a 300 $\mu$m thick and 1 mm wide LLZO pellet. Orthogonally, a gigahertz (GHz) AC (blue) is transmitted to the pellet from a signal generator via a high frequency coaxial cable, a vertical launch, and finally, a gold pin which interfaces with the pellet. Impedance mismatch at that interface, in an otherwise impedance-matched system, causes a portion of the GHz signal (orange) to be reflected back through the high frequency coaxial cable and is sampled by a real-time oscilloscope. When the THz excitation causes a change in the LLZO's impedance, the perturbed GHz signal back-reflection is captured by the real-time oscilloscope.
• Figure 3: THz-field-induced perturbations in (a) t-LLZO and (b) c-LLZO impedances. The rise and decay of a perturbation in the reflected GHz signal by t-LLZO (a) and c-LLZO (b), representing their change in impedance as a result of resonantly exciting phonons between 0.5-7.5 THz by a THz field (744 kV/cm). The purple and blue signals are the root-mean-square averages of amplitude-demodulated spectra. The solid black lines are the exponentially modified Gaussian fit of each spectrum from which the decay time constant is extracted, which is $\sim$900 ps and $\sim$390 ps for t-LLZO and c-LLZO, respectively. The spectra have been shifted vertically so that the center of the GHz carrier is at 0, and horizontally so that time zero corresponds to the THz impulse.
• Figure 4: Raman spectrum of (a) t-LLZO and (b) c-LLZO. The Raman-active modes between 2.25-7.5 THz (75-250 cm-1).