Self-Diffusion and Ionic Conductivity in Sodium Bromide

Abstract

The self-diffusion coefficient ${D}_{\mathrm{Br}}$ of radioactive bromide ions in sodium bromide (melting point 755\ifmmode^\circ\else\textdegree\fi{}C) has been measured in the temperature range 360-688\ifmmode^\circ\else\textdegree\fi{}C, and the ionic conductivity of sodium bromide in the range 340-600\ifmmode^\circ\else\textdegree\fi{}C. At high temperatures, above 450\ifmmode^\circ\else\textdegree\fi{}C, the results of the diffusion measurements are quantitative and are expressible as ${D}_{\mathrm{Br}}=50{e}^{\ensuremath{-}\frac{2.02}{\mathrm{kT}}}$ ${\mathrm{cm}}^{2}$/sec. A comparison of diffusion and conductivity measurements yields the following results. The activation energy for migration of a Na-ion vacancy is 0.80\ifmmode\pm\else\textpm\fi{}0.03 ev. The activation energy for the formation of a separated Na-ion vacancy and a Br-ion vacancy is 1.68 ev. The activation energy for the migration of a Br-ion vacancy is 1.18 ev. The transport numbers for the salt can be expressed as ${n}_{\mathrm{Br}}=11.5{e}^{\ensuremath{-}\frac{0.36}{\mathrm{kT}}}$. At lower temperatures the diffusion coefficient contains a large experimental uncertainty. It is shown, however, that the measured values can only be higher than the actual diffusion coefficients. Comparison of the measured diffusion coefficient of the bromide ion with the diffusion coefficient of the sodium ion calculated from the ionic conductivity shows that the diffusion coefficient of the bromide ion is not more than 2-3 percent as large as the diffusion coefficient of the sodium ion, whence it must be concluded that in the whole temperature range investigated there is no evidence for the presence of pairs of vacancies.