The nonexistence of a paddlewheel effect in superionic conductors

Since the 1980s, the paddlewheel effect has been suggested as a mechanism to boost lithium-ion diffusion in inorganic materials via the rotation of rotor-like anion groups. However, it remains unclear whether the paddlewheel effect, defined as large-angle anion group rotations assisting Li hopping, indeed exists; furthermore, the physical mechanism by which the anion-group dynamics affect lithium-ion diffusion has not yet been established. In this work, we differentiate various types of rotational motions of anion groups and develop quaternion-based algorithms to detect, quantify, and relate them to lithium-ion motion in ab initio molecular dynamics simulations. Our analysis demonstrates that, in fact, the paddlewheel effect, where an anion group makes a large angle rotation to assist a lithium-ion hop, does not exist and thus is not responsible for the fast lithium-ion diffusion in superionic conductors, as historically claimed. Instead, we find that materials with topologically isolated anion groups can enhance lithium-ion diffusivity via a more classic nondynamic soft-cradle mechanism, where the anion groups tilt to provide optimal coordination to a lithium ion throughout the hopping process to lower the migration barrier. This anion-group disorder is static in nature, rather than dynamic and can explain most of the experimental observations. Our work substantiates the nonexistence of the long-debated paddlewheel effect and clarifies any correlation that may exist between anion-group rotations and fast ionic diffusion in inorganic materials.