Application of the path-probability method to conduction problems ofβ- andβ′′-alumina

The values of the adjustable parameters used in the path-probability method developed by Sato and Kikuchi are determined for Na—$\beta$-alumina by fitting these parameters to the experimental conductivity and tracer diffusivity data. These values are used to analyze the temperature-dependent Haven ratio of Na—$\beta$-alumina, the low conductivity of stoichiometric Na—$\beta$-alumina, and the nonlinear $\ln \left(\sigma T\right)$ vs $\frac{1}{T}$ behavior of Na—${\beta }^{\prime \prime }$-alumina. A discussion of the results based on potential-energy calculations is given.