Disorder in β’’-aluminas: Dielectric relaxation and x-ray absorption

\ensuremath{\beta}''-aluminas substituted with rare-earth elements (Pr, Nd, Er, and Tb) and Sn have been studied using near-edge and extended x-ray-absorption fine structure (NEXAFS and EXAFS). In addition, dielectric-relaxation (DR) measurements have been made on Na--\ensuremath{\beta}-, Na--\ensuremath{\beta}''-, and Na-Er--\ensuremath{\beta}''-alumina. Both the DR and EXAFS results confirm that disorder, particularly in the conduction plane, in the vicinity of the rare-earth ions is a key feature of the \ensuremath{\beta}''-aluminas. The NEXAFS studies show that the rare-earth ions are ionized to trivalency and are highly localized; in contrast, Sn is clearly divalent, as in SnO.