Determination of diffusivity of sodium in liquid tin using Na-ß″ alumina

Abstract

Diffusivity of sodium in molten tin was determined using an electrochemical cell of the type Na/Na-β″-Al₂O₃/(Na)Sn where Na-β″-Al₂O₃, which is a sodium-ion conductor, was the solid electrolyte. Using the above cell in which a small amount of sodium dissolved in tin was transported through β″-Al₂O₃ upon application of an external voltage, and using a known solution to Fick's second law for appropriate boundary conditions, the diffusivity was determined to be

$$D{\text{ = 4}}{\text{.4 }}\left( {\begin{array}{*{20}c} {{\text{ + 1}}{\text{.0}}} \\ {{\text{ - 0}}{\text{.5}}} \\ \end{array} } \right){\text{ x 10}}^{{\text{ - 4}}} {\text{ exp }}\left( {{\text{ - }}\frac{Q}{{RT}}} \right){\text{ cm}}^{\text{2}} {\text{ sec}}^{{\text{ - 1}}} $$

withQ = 16320 J mol⁻¹ over a range of temperatures from 240 to 440° C. From the solution to Fick's second law, it was shown that first term approximations, which have often been used in the past, lead to an estimate of diffusivity which is about a factor of 2 too high indicating that more terms should be considered. The diffusivity was also determined using a transient technique in which the decay in voltage upon removal of externally applied voltage was recorded as a function of time. The diffusivity so determined, in which it was assumed that the only polarization was the concentration polarization, was higher than the previous method. The difference between the two diffusivities became smaller with increasing temperature. These experiments thus suggested that interfacial or activation polarization must also be present.