Identifying the Phonon Contributions to Li+ Hop in La0.5Li0.5TiO3 Solid Electrolyte

Abstract

Ion diffusion is important in a variety of applications, yet fundamental understanding of the interaction of lattice vibrations (phonons and vibrational motifs) and the mobile species in solids is still missing. Particularly, for Li super ionic conductors (LISICONs), several studies have reported on the important role of the poly-anion octahedral rotations (rocking modes) in facilitating solid-state Li+ ion migration.[1], [2] However, direct calculation of the contribution of these rocking modes to the Li+ hop is missing, and the provided arguments in these reports are mostly based on establishing correlations between different properties of the rocking modes and the migration properties of the hopping Li+ ion without directly quantifying the contribution of the rocking modes to the Li+ hop. For instance, rocking modes have been argued to be able to (i) provide a softer lattice environment for Li+ ion vibration,[3] (ii) increase the bottleneck area of diffusion (4-O square area),[2] (iii) induce additional force on the carrier sublattice,[1] and (iv) maintain a relatively constant coordination number for Li+ ion during its hop[1] – all conducive to Li+ hop in the lattice. Although insightful, we still lack understanding of the exact vibrational frequencies (density of states) of the rocking modes, and, more importantly, the degree of their contribution to Li+ hop with respect to other phonon modes in the structure. In this work, using a combination of ab initio nudged elastic band (NEB) and lattice dynamics calculations based on the recently proposed formalism,[4] we identify the direct contributions of all phonons, including the rocking ones, to Li+ hop in the perovskite solid-state Li+ conductor Li0.5La0.5TiO3 (LLTO).We set up our NEB Li+ hop calculations considering (i) different orderings of the LLTO lattice,[5] and (ii) different Li+ hopping mechanisms (single and concerted (cooperative)) that can occur in the LLTO lattice.2 To sample such a high degree of complexity, we performed 22 independent NEB calculations of Li+ hop in three different LLTO structures with distinct Li|La orderings and based on two different ion hop mechanisms (single and concerted). Our calculations determined that the following two groups of vibrational modes dominate the contributions to the Li+ hop in the LLTO lattice: (i) rocking modes, and (ii) modes that induce large vibrational energies on the hopping Li+ along its hopping direction. Specifically, our results confirmed that the top 5% (10%) contributing modes to the Li+ hop in the LLTO lattice were responsible for 48% (61%) of the total contributions to the Li+ hop, and the two rocking and highly energetic modes comprised >95% (>85%) of these top 5% (10%) contributing modes. Notable from our calculations was that the rocking modes were only present in the < 5.5 THz frequency region, and in this < 5.5 THz frequency region, they comprised 33% of the vibrational modes and contributed 50% to all the possible contributions to the Li+ hop in this low frequency THz region. Moreover, through static modal excitement calculations, we determined that highly contributing rocking modes of vibration were important in solid-state Li+ ion migration because of their ability to (i) increase the O-4 square bottleneck area of conduction[6] and (ii) amplify the force on the hopping Li+ ion. In summary, our observations demonstrated the strong importance of the THz vibrational region to Li+ hop in the lattice, which can be accessible for further explorations using THz spectroscopy techniques to deepen our understanding of the relation between solid-state transport of Li+ and different vibrational motifs in the lattice.