Diffusion and ionic conductivity in sodium beta alumina

Measurements of sodium tracer diffusion (D_t) and ionic conductivity (σ) have been made on the same single crystals of sodium beta-alumina of composition 1.23 Na₂0.11 Al₂O₃. The σ- measurements were made over the temperature 390–660 K using reversible (liquid sodium) electrodes. A fit to the conductivity data gives $\text{σT = 2470}\text{exp}\text{(?0.142}\text{eV}\text{kT}\text{)Ω}{}^{\mathrm{?1}}\text{cm}{}^{\mathrm{?1}}\text{K}$. The D_t, measurements employed two techniques, i.e. nondestructive profiling over the temperature range 210–750 K and cation exchange over the temperature range 505–970 K. The results of the two techniques were in close agreement and can be expressed as $\text{D = 2.12 ×10}{}^{\mathrm{?4}}\text{exp}\text{(?0.169}\text{eV}\text{kT}\text{)}\text{cm}{}^2\text{sec}{}^{\mathrm{?1}}$ for T>520K and $\text{D = 2.45 × 10}{}^{\mathrm{?4}}\text{exp}\text{(?0.164}\text{eV}\text{kT}\text{)}\text{cm}{}^2\text{sec}\text{470}\text{K}$. The “transition” region between 470 and 520 K is not observed in the conductivity measurements. Silver cation exchange was used to determine the number of mobile sodium ions. A comparison of D_t and σ data yielded a Haven ratio that is temperature dependent, ranging in value from 0.45 at 870 K to 0.35 at 370 K.