Chapter 3 - Fick's Laws of Diffusion

Abstract

Diffusion is governed by Fick's laws. Fick's first law, also known as the “flux equation,” describes the flux of matter resulting from a given concentration gradient and diffusion coefficient. The concentration gradient is the thermodynamic driving force for diffusion, and the kinetics are governed by the diffusion coefficient, also known as the diffusivity. Fick's second law, also known as simply the “diffusion equation,” is derived from Fick's first law and the conservation of matter. The diffusion equation describes the evolution of concentration profiles in space and time. Additional driving forces for diffusion can include electrical potential gradients, thermal gradients, magnetic fields, and applied stresses. The diffusion coefficient typically has an Arrhenius dependence on temperature. If more than one diffusion mechanism is present in a system, the temperature dependence of the diffusivity can be described by a summation of Arrhenius terms, each with its own activation barrier. Interdiffusion involves the simultaneous diffusion of two different species. If the net flux is zero, then the interdiffusion process can be described using a single diffusion coefficient. On the other hand, if the net flux is non-zero, then two separate diffusion coefficients must be used, one for each species. An example of interdiffusion with a non-zero net flux is the Kirkendall effect. Various experimental techniques exist to measure chemical concentration profiles and deduce the value of the diffusion coefficient. In the case of self-diffusion, radioactive tracer isotopes can be employed.