A Commentary on: “Diffusion of Carbon in Austenite with a Discontinuity in Composition”

CONSIDER an allotropic transition between two phases in a pure substance. The phases are said to be in equilibrium when they have identical free energies. Pure ice and water coexist at precisely 273.15 K (0 C) and 1 atm of pressure. When this system consists of a mixture of common salt and H2O, the ice and water become solid and liquid solutions, respectively, but can still coexist in equilibrium, albeit under different circumstances. Yet, it has been known for many centuries that these impure phases have different chemical compositions, water being richer in salt than in ice. The astonishing fact is that there is no tendency for the salt to diffuse from the water into the ice to homogenize concentrations, no matter how long the mixture is observed. With solutions, it is not the free energy of the individual phases that must be equal for equilibrium to be achieved; rather the chemical potentials of the components (H2O and NaCl) must be uniform everywhere. This potential can be paraphrased as the mean free energy of a component in a solution of given composition. If all the potentials in the system are uniform, then there is no driving force for diffusion irrespective of spatial variations in concentration. When attempting to validate his laws of diffusion, the physiologist Fick used water and salt to conduct experiments. The diffusion flux, he proposed, depends on the concentration gradient. However, at some stage, it was realized that it should depend on the negative gradient of the chemical potential. A flux driven in this manner would lead to a reduction in free energy, which after all, is what is required for any process to occur spontaneously. I am not sure when this realization came about, but Darken refers to an 1888 article by Nernst on osmotic pressure. But the real motivation for Darken’s 1949 article was to demonstrate experimentally that ‘‘for a system of more than two components it is no longer necessarily true that a given element tends to diffuse towards a region of lower concentration.’’ The chemical potential gradient of that element may have a different sign to its concentration gradient. When dealing with a single phase, the chemical potential gradient has the same sign as an activity gradient so that the latter sometimes is used in describing diffusion. As pointed out by Darken, evidence for such diffusion could be found in a 1931 article by Hartley on ‘‘the distribution of a molecular solute [acetone] in a solvent [water] containing a gradient of concentration of a second solute [salt].’’ But he wanted to demonstrate this in the solid state; it should be borne in mind that the nature of diffusion in solids was, at the time, the subject of much debate. Proof for the vacancy mechanism for substitutional diffusion only just had been presented by Simgelkas and Kirkendall to an audience, which was not entirely receptive. The samples that Darken fabricated were similar to those in earlier work in which dissimilar steels were joined together to study diffusion. However, his goal was to realize the role of chemical potential gradients rather than to measure diffusion coefficients. Darken welded together two steels with similar carbon concentrations but different silicon concentrations. The choice of silicon as a substitutional solute seems to have been based on work by Smith, whose article on the activity of carbon in ternary steels predates that of Darken but is referred to by him as unpublished work. Smith demonstrated experimentally that silicon dramatically increases the activity of carbon in austenite, more so than manganese. The composition of the silicon-rich side of the weld was such that the whole of the diffusion couple would be austenitic at the heat-treatment temperature. It was understood that substitutional solutes would diffuse at a rate that is much less than the interstitial carbon so the carbon could be considered to migrate within an essentially fixed distribution of silicon. Darken succeeded in demonstrating the ‘‘uphill diffusion’’ of carbon and at the same time proved that although as a consequence of this diffusion, the carbon concentration changed discontinuously at the weld junction, the activity did not. He pointed out that Smoluchowski did not observe a similar partitioning of carbon in a diffusion couple containing a discontinuity of cobalt concentration, implying that the influence of cobalt on the activity of carbon is small in comparison with that of silicon. We now know that this is, in fact, the case. H.K.D.H. BHADESHIA, Professor, is with Materials Science and Metallurgy, University of Cambridge, Cambridge, UK. Contact e-mail: hkdb@cam.ac.uk *L.S. Darken, Trans. AIME, 1949, vol. 180, pp. 430–38. Article published online May 1, 2010