Low-temperature dielectric susceptibility of Li, Na, K, and Agβ-alumina

Crystalline Na, K, Li, and Ag $\beta$-alumina show glasslike variations of the dielectric susceptibility with temperature and frequency provided the measuring field is directed along the conducting planes. Only Li $\beta$-alumina shows variations of the dielectric susceptibility perpendicular to the conducting planes. The data are discussed in terms of the tunneling-states model of amorphous materials. The estimated average tunneling distances are ≲ 0.3 Å.