On the Fluctuation Model of Diffusion in Liquid Metals

Abstract

In this paper further considerations has been given to the fluctuation model of diffusion, and equations have been derived which express the self-diffusivity of liquid metals as a function of temperature and pressure. For liquid metals which are characterized by pair potentials which are relatively deep compared with k T, D is predicted to vary in a linear fashion with T at constant volume. At constant pressure, the apparent activation energy is predicted to be equial to R T+R(β/β)T2 where β is the isothermal compressibility and β' is its temperature derivative. Further, the variation in the logarithm of D with respect to pressure is predicted to be equal to [ (1/2.3)β] (∂β/∂P) T . A test of the equations for liquid mercury shows good correlation between theory and experiment. For liquid metals which are characterized by a shallow well in terms of the pair potential, no simple statements can be made concerning the nature of the temperature dependence, and simple approximations cannot be made. A test of the derived equations is made for liquid sodium which fits this case and for which good pair potential data exist, and good agreement is obtained at 373 °K. The temperature dependence of D as a function of T at constant volume is derived, but cannot be tested because of insufficient experimental data. The case of thermodiffusion is discussed, and it is shown that experimental values of the heat of transport are consistent with predictions of the theory.