RETRACTED: Relating critical phonon occupation to activation barrier in fast lithium-ion conductors

Phonon-based (vibrational) theories of ion transport are likely key to developing new design strategies for solid-state ionic conductors. However, they are not often utilized because it is difficult to ascertain which vibrational frequencies are important, even in describing fundamental parameters such as the activation barrier. This is perpetuated by the fact that it is difficult to tune vibrational frequencies directly, without changing the chemical structure, in order to study underlying phonon relations. Using isotopic substitution of 6Li for 7Li, we are able to change the mobile ion vibrations in the two exemplary ion conductors Li10SnP2S12 and Li6PS5Cl without altering their structure. Using a combination of nuclear magnetic resonance spectroscopy and ab initio molecular dynamics simulations to characterize temperature-dependent ion transport, it is demonstrated that the isotopic substitution of 6Li for 7Li increases the activation barrier for Li-ion transport. The magnitude of this isotope effect cannot be explained by changes in the zero-point vibrational energy alone. Therefore, we propose that the observed change in the activation barrier is related to the differences in the average critical phonon occupation needed to overcome the activation barrier. Our hypothesis is supported by an analytical model, based on the physics of quantum harmonic oscillators, that gives good agreement with the experimental results. Thus, isotopic substitution provides unique insights into the vibrational perspective and frequency dependence of the activation barrier in fast Li-ion conductors.