Host lattices and superionic properties in<i>β</i>- and β’’-alumina. II. Homogeneity ranges and conductivities

Abstract

From structural results previously reported the equilibrium conditions for ion-ion correlations in \ensuremath{\beta}-alumina are obtained. This provides a theoretical confirmation of the Beevers-Ross--mid-oxygen (BR-mO) model stability which whatever is the composition (1(5/3)) reveals itself to correspond to a lower energy than the BR--anti-BR (BR-aBR) model as indicated by experimental results. Under these conditions \ensuremath{\beta}''-alumina appears as a further lowering of energy by a polarization of the host lattice by the conducting ions. This model is used to calculate the respective homogeneity range of \ensuremath{\beta}-alumina 1.00--1.56 ${\mathrm{Na}}^{+}$ formula unit (fu) and of \ensuremath{\beta}''-alumina 1.56--1.66 ${\mathrm{Na}}^{+}$/fu in agreement again with experimental results. Ion-rich \ensuremath{\beta}-alumina (\ensuremath{\rho}\ensuremath{\simeq}1.60 ${\mathrm{Na}}^{+}$/fu) appears to be a quenched metastable phase. The model also establishes that concentrations \ensuremath{\rho}&gt;(5/3) cannot be reached because they should require much too high energies. Path probability method is used as a basis for the interpretation of the conductivity equation which solves in a simple model for \ensuremath{\beta}-alumina in agreement with published results. For \ensuremath{\beta}''-alumina the structural change observed in the temperature range 300--600 K is driven by the progressive destruction of a two-dimensional antiferroelectric order. This results in a two terms activation energy: a temperature-independent hopping term and a dissociation term whose temperature dependence is parametrized by the coherence-length variation.