Diffusion - History of Diffusion in Physics

History of Diffusion in Physics

In technology, diffusion in solids was used long before the theory of diffusion was created. For example, the cementation process that produces steel from the iron includes carbon diffusion and was described already by Pliny the Elder, the diffusion of colours of stained glasses or earthenwares and Chinas was well known for many centuries.

In modern science, the first systematic experimental study of diffusion was performed by Thomas Graham. He studied diffusion in gases and the main phenomenon was described by him in 1831-1833:

"...gases of different nature, when brought into contact, do not arrange themselves according to their density, the heaviest undermost, and the lighter uppermost, but they spontaneously diffuse, mutually and equally, through each other, and so remain in the intimate state of mixture for any length of time.”

The measuments of Graham allowed James Clerk Maxwell to derive in 1867 the coefficient of diffusion of CO₂ in air. The error is less than 5%.

In 1855, Adolf Fick, the 26-year old anatomy demonstrator from Zürich proposed his law of diffusion. He used Graham's research and his goal was "the development of a fundamental law, for the operation of diffusion in a single element of space". He declared a deep analogy between diffusion and conduction of heat or electricity and created the formalism that is similar to Fourier's law for heat conduction (1822) and Ohm's law for electrical current (1827).

Robert Boyle demonstrated diffusion in solids in 17th century by penetration of Zinc into a copper coin. Nevertheless, diffusion in solids was not systematically studied till the second part of the 19th century. William Chandler Roberts-Austen, the well-known British metallurgist, studied systematically solid state diffusion on the example of gold in lead in 1896. He has been the former assistant of Thomas Graham and this connection inspired him:

"... My long connection with Graham's researches made it almost a duty to attempt to extend his work on liquid diffusion to metals."

In 1858, Rudolf Clausius introduced the concept of the mean free path. In the same year, James Clerk Maxwell developed the first atomistic theory of transport processes in gases. The modern atomistic theory of diffusion and Brownian motion was developed by Albert Einstein, Marian Smoluchowski and Jean-Baptiste Perrin. The role of Ludwig Boltzmann in the development of the atomistic backgrounds of the macroscopic transport processes was great. His Boltzmann equation serves more than 140 years as a source of ideas and problems in mathematics and physics of transport processes.

In 1920-1921 George de Hevesy measured self-diffusion using radioisotopes. He studied self-diffusion of radioactive isotopes of lead in liquid and solid lead.

Yakov Frenkel (or, sometimes, Jakov or Jacov) proposed in 1926 and then elaborated the idea of diffusion in crystals through local defects (vacancies and interstitial atoms). He introduced several mechanisms of diffusion and found rate constants from experimental data. Later, this idea was developed further by Carl Wagner and Walter H. Schottky. Nowadays, it is universally recognized that atomic defects are necessary to mediate diffusion in crystals.

The ideas of Frenkel represent diffusion process in condensed matter as an ensemble of elementary jumps and quasichemical interactions of particles and defects. Henry Eyring with co-authors applied his theory of absolute reaction rates to this quasichemical representation of diffusion. The analogy between reaction kinetics and diffusion leads to various nonlinear versions of Fick's law.