Host lattices and superionic properties in<i>β</i>- and β’’-alumina. I. Structures and local correlations

Abstract

Long-range and local orders for ion-rich \ensuremath{\beta}- and \ensuremath{\beta}''-alumina are determined from conventional crystal-structure determinations and x-ray diffuse scattering. Both materials exhibit composition close to 1.66 ${\mathrm{Na}}^{+}$ per unit plane cell with a compensation mechanism exclusively due to ${\mathrm{Mg}}^{2+}$. The ionic distribution, \ensuremath{\simeq}0.66 BR (Beevers-Ross) [or Na(1)] ion and \ensuremath{\simeq}1 mO (mid-oxygen) [or Na(2)] ion per unit plane cell, remains almost unchanged from room temperature to 320?deC. The thermal behavior of the ${\mathrm{Na}}^{+}$ ions is interpreted by a Thomchick-MacKelvey model which accounts for a strong anharmonicity of the potential wells at low temperature and a quasi-pure-harmonic vibration at high temperature. This results in a thermally induced flattening of the potential wells. Both materials exhibit the same local-order-type two-dimensional (2D) (a \ensuremath{\surd}3 -a \ensuremath{\surd}3 ) supercell consistent with the ionic distribution observed. Examination of the diffraction functions accounts for the quasi-2D long-range order observed in ion-rich \ensuremath{\beta}-alumina for the limited coherence length (BR\ensuremath{\rightleftarrows}a BR fault) (Beevers-Ross\ensuremath{\rightleftarrows}anti--Beevers-Ross) in \ensuremath{\beta}''-alumina, and for the microscopic homogeneity of the two materials. The conduction channel is strongly constricted in ion-rich \ensuremath{\beta}-alumina, whereas in \ensuremath{\beta}''-alumina at high temperature the lowering of the conduction slab thickness favors a high ionic mobility. both local- and long-range-order arguments lead to a localized model for the ionic distribution even for \ensuremath{\beta}''-alumina at high temperature in contradiction with the results deduced only from average structure determination.