Host lattices and superionic properties inβ- and β’’-alumina. II. Homogeneity ranges and conductivities

From structural results previously reported the equilibrium conditions for ion-ion correlations in β-alumina are obtained. This provides a theoretical confirmation of the Beevers-Ross–mid-oxygen (BR-mO) model stability which whatever is the composition (1<ρ<(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 β’ ’-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 β-alumina 1.00–1.56 ${\mathrm{Na}}^{+}$ formula unit (fu) and of β’ ’-alumina 1.56–1.66 ${\mathrm{Na}}^{+}$/fu in agreement again with experimental results. Ion-rich β-alumina (ρ≃1.60 ${\mathrm{Na}}^{+}$/fu) appears to be a quenched metastable phase. The model also establishes that concentrations ρ>(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 β-alumina in agreement with published results. For β’ ’-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.