Measurement of mechanical and electrical relaxations in β-alumina

Abstract

Mechanical relaxations in single-crystal Na β-alumina were studied by measuring the attenuation of longitudinal ultrasonic waves propagating parallel to the conduction planes over the frequency range 50–240 MHz. Broad, thermally activated attenuation peaks were observed which were attributed to the motion of Na + ions in the conduction planes. These results are compared with literature data on (a) internal friction and (b) electrical relaxations. A combined Arrhenius plot of the relaxation times obtained from all measurements showed excellent agreement between the electrical and mechanical relaxation results. Least-squares analysis gave a prefactor of 1×10 13 Hz and an activation energy of 0.166 eV. However, there was some evidence of curvature in the data which, if confirmed would lead to a slightly smaller prefactor and activation energy. The difficulty of measuring electrical relaxations in solid electrolytes is pointed out and the possible validity of using the complex electric modulus formalism to obtain ion hopping frequencies is discussed.