# Self-Diffusion in Molten Sodium Chloride: A Test of the Applicability of the Nernst-Einstein Equation

Alina Z. Borucka, J. O'M. Bockris, J. A. Kitchener

## Abstract

Self-diffusion coefficients of sodium and chlorine in molten sodium chloride have been determined by the capillary method with the aid of $^{22}$Na and $^{36}$Cl radio-tracers. The results can be represented by the expressions D$_{\text{Na}}$ = 8 $\times$ 10$^{-4}$ exp (-4000/RT) and D$_{\text{Cl}}$ = 33 $\times$ 10$^{-4}$ exp (-8500/RT). These values, when inserted in the Nernst-Einstein equation ($\Lambda$ = (F$^{2}$/RT) (D$_{+}$+D$_{-}$)), lead to a value of the equivalent conductance, A, which is about 40% greater than that observed experimentally. The evidence that the diffusion coefficients of Na$^{+}$ and Cl$^{-}$ are similar in magnitude and that the activation energies are much smaller than the heat of vaporization of liquid sodium chloride, support the conclusions, derived from other evidence, that the free volume in the molten salt consists largely of holes, analogous to vacant lattice sites. On the basis of this model, the discrepancy in the Nernst-Einstein relation can readily be interpreted in terms of two diffusion mechanisms, one being normal vacancy diffusion of single ions, and the other a process in which no net charge is displaced in a unit step. It is suggested that the latter is the Seitz-Dienes mechanism of consecutive jumps of cation and anion in coupled vacancies. The interpretation mentioned enables the individual mobilities of Na$^{+}$ and Cl$^{-}$ ions to be determined, and hence their transport numbers can be calculated (t$_{\text{Na}}{}^{+}$ = 0$\cdot$71, t$_{\text{Cl}}{}^{-}$ = 0$\cdot$29 at 935 degrees C). The individual diffusion coefficients of the ions and of the coupled vacancies are in reasonable agreement with the Stokes-Einstein equation.