Relating Critical Phonon Occupation to Activation Barrier in Fast Lithium-Ion Conductors

The families of Li₁₀(Ge/Sn)P₂S₁₂ and Li₆(P/Sb)S₅X (X = Cl, Br, I) are, so far, the only Li⁺ compounds exceeding 10 mS cm^-1 at room temperature. The structure and transport of these materials has been widely investigated, and the ionic conductivities have been pushed continually higher, reaching values reasonable for solid state battery operation. From a structural perspective, however, they are markedly different, making them excellent model systems to compare in fundamental investigations. For example, if isotopic substitutions have any impact on ionic transport, known as kinetic isotope effects.<br/><br/>By using a combination of nuclear magnetic resonance spectroscopy and ab initio molecular dynamics to characterize temperature-dependent ion transport, it is demonstrated that the isotopic substitution of ⁶Li for ⁷Li increases the thermodynamic activation barrier for Li-ion transport in Li₁₀SnP₂S₁₂ and Li₆PS₅Cl. Although previous studies in Li⁺ conductors have indicated that lower vibrational frequencies generally result in lower activation barriers, we find that the lower average vibrational frequency of the ⁷Li⁺ ions results in a larger thermodynamic activation barrier. Unlike the case of proton conductors, the magnitude of the kinetic isotope effect cannot be explained by changes in the zero-point vibrational energy. We propose that the observed changes in activation barrier are related to the differences in critical phonon occupation needed to overcome the local barrier to transport. Our hypothesis is supported by an analytical model, based on the physics of quantum harmonic oscillators, that gives good agreement with experiment. Thus, the kinetic isotope effect provides unique insights into the vibrational perspective and frequency dependence of the activation barrier in these fast Li⁺ ionic conductors.