Lattice Dynamics Signature for Sodium Superionic Conductors

Sodium superionic conductors (SICs) are the most important component in sodium-based batteries. However, the knowledge derived from known Li-SICs cannot be straightforwardly transferred to design and discover Na-SICs. For a long time, tremendous experimental and theoretical studies have been devoted to material chemistry and transition and hopping theory, while the role of lattice vibrations, i.e., phonons, received little attention. We explore key lattice dynamics features that influence the thermal motion of Na⁺ ions, focusing on the accuracy of capturing the real dynamics and calculating the mean squared displacement (MSD) of Na⁺ ions using large supercells rather than small primitive cells, a critical point that has been overlooked in literature. With the improved approach, for the first time, we established a quantitative and strong positive correlation between the MSDs and the diffusion coefficients on 1,106 structures. We further presented the significance of other phonon features such as the Debye frequency and the center phonon partial density of state (PDOS) of Na⁺ ions in impacting ion diffusion process. Lower Debye frequency and lower center PDOS of Na⁺ ions closer to the Debye frequency, and better match of the vibrations between moving Na⁺ ions and hosting sub-lattice in the low frequency range facilitate free motion of Na⁺ ions within the lattice, reinforcing the link between lattice dynamics and ionic mobility. We also provide phonon mode level analysis of contribution to MSDs of Na⁺ ions. Only a limited number of extremely low frequency acoustic and low-lying optic phonon modes are primarily responsible for the large MSDs of Na⁺ ions and thus contributing their hopping in the lattice, while the majority of phonon modes have little contribution to ion migration. Our research is expected to advance the discovery and design of novel sodium superionic conductors that can be used as electrolytes in sodium all-solid-state-battery applications, such as by incorporating these lattice dynamics features into machine learning algorithms and workflows.