Ion Jump Motion as the Background for Muon Diffusion in Battery Materials Research Using $\hat{I}¼$SR

Abstract

Numerical simulations of muon spin relaxation ($\hat{I}¼$SR) in ion diffusion were performed using the {\sl extended} Kubo-Toyabe (KT) relaxation function $G_z^{\mathrm{EA}}(t)$ that incorporates an Edwards-Anderson type autocorrelation function for the jump motion of ions. The analysis of the generated $\hat{I}¼$SR spectra using the conventional KT function $G_z^{\mathrm{KT}}(t;\hat{I}{”}_{\mathrm{KT}},\hat{I}{½}_{\mathrm{KT}})$ (mimicking the previous analysis procedure) suggest that the anomalous peak in the fluctuation rate $\hat{I}{½}_{\mathrm{KT}}$ around a specific temperature $T^{\ast }$ and associated decrease of the linewidth $\hat{I}{”}_{\mathrm{KT}}$ above $T^{\ast }$, often observed in the previous $\hat{I}¼$SR studies on ion diffusion, originate from the sharp increase in the ion jump rate $\hat{I}{½}_{\mathrm{i}}$ against that of the muon $\hat{I}{½}_{\hat{I}}¼$ with increasing temperature. This indicates that a more detailed reanalysis of the vintage data using $G_z^{\mathrm{EA}}(t)$ is useful for the proper evaluation of $\hat{I}{½}_{\mathrm{i}}$ and $\hat{I}{½}_{\hat{I}}¼$. Meanwhile, it also suggests that the $\hat{I}¼$SR results showing no such anomaly convey little information on ion diffusion.

5 pages, 3 figures