Dielectric response ofNaβ-alumina: Evidence for a "glass transition"

Electrical modulus ($M^{\prime \prime }$) data for melt-grown $\mathrm{Na}\beta$-alumina between 92 and 151 K is fitted in terms of the fractional-exponential-decay formalism with a fractional exponent $n$. Above 120 K the exponent $n$ decreases rapidly with increasing temperature, whereas the $M^{\prime \prime }$ peak frequency shifts with temperature as predicted by the Williams-Landel-Ferry relation. The behavior of $n$ and $M^{\prime \prime }$ is similar to that observed for glasses near their glass transition, which suggests that $\mathrm{Na}\beta$-alumina undergoes a "glass transition" near 120 K. It is also shown that the recent low-frequency-response model of Ngai yields the observed $n\left(T\right)\mathrm{}$, $M^{\prime \prime }(\omega ,T)$ behavior and leads to the determination of the microscopic activation energy for ${\mathrm{Na}}^{+}$ -ion motion of 0.059 eV.