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Ion Jump Motion as the Background for Muon Diffusion in Battery Materials Research Using $μ$SR

Ryosuke Kadono

Abstract

It is shown by numerical simulations of muon spin relaxation ($μ$SR) spectra and analysis of these using the Kubo-Toyabe relaxation function $G_z^{\rm KT}(t)$ that the anomalous peak in the fluctuation rate $ν_{\rm KT}$ around a specific temperature $T^*$ and associated decrease of the linewidth $Δ_{\rm KT}$ above $T^*$, often observed in the previous $μ$SR studies on ion diffusion, originate from the sharp increase in the ion jump rate $ν_{\rm i}$ against that of the muon $ν_μ$ with increasing temperature. This indicates that a more detailed reanalysis of the vintage data using the "extended" Kubo-Toyabe relaxation function $G_z^{\rm EA}(t)$ incorporating the jump motion of both ions and implanted muon (which was also used to simulate the $μ$SR spectra) is useful for the proper evaluation of $ν_{\rm i}$ and $ν_μ$. Meanwhile, it also suggests that the $μ$SR results showing no such anomaly convey little information on ion diffusion.

Ion Jump Motion as the Background for Muon Diffusion in Battery Materials Research Using $μ$SR

Abstract

It is shown by numerical simulations of muon spin relaxation (SR) spectra and analysis of these using the Kubo-Toyabe relaxation function that the anomalous peak in the fluctuation rate around a specific temperature and associated decrease of the linewidth above , often observed in the previous SR studies on ion diffusion, originate from the sharp increase in the ion jump rate against that of the muon with increasing temperature. This indicates that a more detailed reanalysis of the vintage data using the "extended" Kubo-Toyabe relaxation function incorporating the jump motion of both ions and implanted muon (which was also used to simulate the SR spectra) is useful for the proper evaluation of and . Meanwhile, it also suggests that the SR results showing no such anomaly convey little information on ion diffusion.

Paper Structure

This paper contains 3 equations, 3 figures, 1 table.

Figures (3)

  • Figure 1: Temperature dependences of jump frequencies for ions ($\nu_{\rm i}$) and muon ($\nu_\mu$) assumed for the simulation of $\mu$SR spectra. The main panel shows these in semi-log scale against inverse temperature, while inset shows a magnified view of the region relevant to $\mu$SR in linear scale.
  • Figure 2: (a) Linewidth $\Delta_{\rm KT}$ and fluctuation frequency $\nu_{\rm KT}$, and (b) associated $\chi^2$ versus ion jumping frequency $\nu_{\rm i}$ (in logarithmic scale) obtained by fitting the time spectra (ZF and LF=1 mT) generated by $G_z^{\rm EA}(t)$ (with $\Delta=0.3$ MHz, $Q=0.8$) using the conventional KT function. (c) $Q$ dependence of $\Delta_{\rm KT}$ and $\nu_{\rm KT}$ at $\nu_{\rm i}=3.3$ MHz. Examples of the simulated ZF and LF spectra (EA) and those obtained by curve fitting (KT) are shown for (d) $\nu_{\rm i}=0.12$ MHz, (e) 3.3 MHz, and (f) 45 MHz.
  • Figure 3: (a) Linewidth $\Delta_{\rm KT}$ and (b) fluctuation frequency $\nu_{\rm KT}$ versus temperature obtained by fitting the time spectra (ZF and LF=1 mT) generated by $G_z^{\rm EA}(t)$ (with $\Delta=0.3$ MHz, $Q=0.8$) using the conventional KT function. Dashed line in (a) is the best fit using Eq.(\ref{['tsm']}), and those in (b) are $\nu_{\rm i}$ and $\nu_\mu$ given by Eqs. (\ref{['nui']}) and (\ref{['num']}) (see the inset of Fig. \ref{['nuimu']}).