Diffusion in metals: the flux of history

Abstract

It is 150 years since the first equation was proposed for the rate of flow of a constituent by diffusion. Alternative equations have been proposed over the years for this basic, underlying flux, i.e. excluding the various complications that vie to bog down the subject. A brief commentary is offered on the alternative equations available for this Fick's first law of diffusion, and their consequences for the time dependency of local concentration (Fick's second law) and chemical interdiffusion of a mutual solution. It is suggested that, while the preferred choice for the flux equation is rather more debatable than is commonly assumed, the actual differences between the rival formulations might be rather less than would be expected.

Oxygen Diffusion Model using the THERMOCHIMICA Module in Moose/Bison

“…Modeling of species diffusion in multicomponent systems is a challenging and still an open science problem [7,8]. For simple systems, a Fick's law [7] approximation is commonly used that assumes that the concentration gradients are the driving forces of diffusion.…”