Fick’s Laws

Abstract

Atoms and molecules are not completely immobile within a solid material. They move by jumping into vacancies or interstitial sites in the crystal lattice. The laws describing their motion were discovered by Adolf Fick in the mid-19th century, modelled on analogous laws for the flow of heat (Fourier’s law) and electricity (Ohm’s law). According to Fick’s first law, the rate at which atoms move is proportional to the concentration gradient, with the diffusion coefficient defined as the constant of proportionality. Fick’s second law generalises the first law to a wide range of situations and is called the diffusion equation. This chapter examines a number of characteristic diffusion profiles; the difference between self, intrinsic, inter- and tracer diffusion coefficients; the Kirkendall effect and porosity formation when different components move at different speeds; and the Arrhenius temperature dependence of diffusion. Fick was a physiologist and derived his laws initially to describe the flow of blood through the heart. He made advances in anatomy, physiology and medicine, developing methods of monitoring blood pressure, muscular power, corneal pressure and glaucoma. He lived at the time of Bismarck’s post-Napoléonic unification of Germany and the associated flowering of German science, engineering, medicine and culture.