Effective Mass of Ions in Fused Salts

It is obvious that the values of the transport numbers of the ions in the fused salts involve various informations concerning the interaction between ions. The quantitative or semi-quantitative analysis of the results, however, is very few and insufficient nowadays. Here the present author wants to propose a new method of analysis as well as the experimental results for the alkali metal nitrates, the alkali metal chlorides and others in fused state. In the present analysis the "effective mass" of the ion plays the important role. From the definition, it can easily be seen t-/t+=μ-/μ+, (1) where ti is the transpor number and μi is the mobility of the ion. i= + or - refer to the cation and anion respectively. Based on the simple model of the electrical conduction by the ionic transportation, the relation mi ui = ZieEτi is obtained immediately, where mi is the effective mass, ui is the average velocity and Ze is the charge (Zi is the valency) of the ion, and τi is the mean of the time between collisions which the ion suffers in its course of the conduction within the sample. If it can be assumed that ui =μiE, the relation (1) becomes t-/t+=m+/m-. (2) By the use of the Nernst-Einstein relation (u/ZF=D/RT, F : Faraday Constant), it can be shown that the similar relation holds for the diffusion coefficient D of the ion. D-/D+=m+/m-. (3) The "effective mass" mi of the ion introduced in the above involves all the effect of the interactions between a particular ion and its surroundings. The detailed analysis of these effects will require very complicated theoretical treatments. One may guess, however, that the effective mass m is proportional to the bare mass of the ion, and the relation (2) may be written in a form t-/t+=n(mo+/mo-), n=β+/β-. (4) Where n is the ratio of the effective mass constant βi (mi =βiim). The values of n are obtained from the data for ti and mi