Relationship between local hydride ion dynamics and ionic conductivity in LaH$_{3-2x}$O$_x$ inferred from muon study

Abstract

We performed muon spin rotation and relaxation ($μ$SR) experiments to investigate the microscopic mechanism behind the high ionic conductivity ($σ$) exhibited by hydride (H$^-$) ions in lanthanum hydroxide LaH$_{3-2x}$O$_x$. The $μ$SR spectra observed at 5--300 K in a sample with $x\approx0.25$ consist primarily of two components which are attributed to muons occupying tetrahedral (Tet) and octahedral (Oct) sites common to H$^-$. The spectra also indicate that muons at the Oct sites (Mu$_{\rm O}$) appear nearly stationary in the time scale of $μ$SR ($\sim$10$^{-5}$ s), whereas those at the Tet sites (Mu$_{\rm T}$) are subject to the fluctuating local fields. The cusp-like peak in the fluctuation rate around 160 K and the decrease in linewidth at higher temperatures probed by Mu$_{\rm T}$ suggest that the jump motion of both Mu$_{\rm T}$ (via the vacant Oct sites) and surrounding Oct-site H$^-$ contributes to spin relaxation and that the fluctuation frequency is widely distributed. These results indicate that the implanted Mu behave as Mu$^-$ and that the jump motion of Mu$^-$/H$^-$ is restricted by the availability of nearby vacant sites. On the other hand, the activation energy for the jump is estimated to be 0.11(3) eV, which is significantly different from $\sim$1.3 eV evaluated from the temperature dependence of $σ$ at high temperatures ($\gtrsim400$ K). In our attempt to resolve this discrepancy, we discuss problems inherent in interpreting $σ$ using the Arrhenius equation, and demonstrate that the behavior of H$^-$ ions can be better explained as a viscous fluid exhibiting a glass transition.

Figures (6)

• Figure 1: Schematic crystal structures of LaH$_{3-y}$ for (a) $y=1$ (fluorite structure) where H occupies tetrahedral (Tet) sites, and (b) the octahedral sites to be occupied by H for $y<1$ in addition to the Tet sites (not shown). Thus, the $\alpha$-BiF$_3$ structure with $y < 1$ can be regarded as a structure where the fluorite structure (a) and the rock salt structure (b) mutually interpenetrate. In the case of LaH$_{3-2x}$O$_x$, oxygen preferentially occupies the Tet site.
• Figure 2: $\mu$SR time spectra observed in LaH$_{2.5}$O$_{0.25}$ at (a) 5.3 K, (b) 110 K, (c) 160 K, (d) 175 K, (e) 210 K, and (f) 300 K, where the solid curves are results of global fits using Eq. (\ref{['asys']}) with common parameters through four spectra ($\mu_0H_{\rm LF} = 0$, 0.5, 1, and 3 mT) at each temperature. Dashed lines indicate the background level ($A_{\rm b}\approx0.05$) estimated from calibration measurements.
• Figure 3: Temperature dependence of the parameters in Eq. (\ref{['asys']}) deduced by curve fits: (a) Partial asymmetry $A_1$ for the component reprodiced by the sum of static GKT and dynamical LKT functions, $A_2$ for that with no relaxation, and the total asymmetry $A_0$ ($=A_1+A_2$). (b) The fractional yield for the component reproduced by the static GKT function (the rest represented by the dynamical LKT function). (c) The static linewidth for the GKT function ($\Delta$) and for the dynamical LKT function ($\Lambda_{\rm eff}$). (d) The fluctuation rate $\nu_{\rm eff}$ of the internal magnetic field for the dynamical LKT function. The dashed curve in (c) is the best fit with Eq. (\ref{['QT']}).
• Figure 4: Ion conductivity of LaH$_{3-2x}$O$_x$ at $x=0.24$ plotted against $T$ on a linear scale (a) and on a logarithmic scale against $1/T$ (b) (after Ref. Fukui:19). Dashed lines are fits using Eqs. (\ref{['VFT']}) and (\ref{['JG']}). Inset in (a): DSC curves measured for the present sample ($x\approx0.25$), where the onset of an endothermic reaction is inferred at $T_{\rm g}\approx440$ K in the second loop which is relatively free from the strain effect of the sample prepared by high pressure synthesis. The dashed line shows extrapolated baseline.
• Figure 5: (a) Lorentzian Kubo-Toyabe (LKT) function under a zero external magnetic field, where the fluctuation of local field at a rate $\nu$ (normalized by the linewidth $\Lambda$) is incorporated by strong collision approximation. (b) Lorentzian density distribution function, where $x=\gamma_\mu H/\Lambda$: dashed lines shows possible cutoffs to remove unphysical property (not considered in this study). (c) LKT function with $\Lambda$ replaced with $\Lambda'=2\Lambda^2/\nu_{\rm f}$, where $\nu_{\rm f}\gtrsim\Lambda$, and (d) the corresponding $n(x)$.