On a relationship between grain boundary free energy, grain boundary segregation, and grain boundary diffusion

TL;DR

This paper re-derives and extends the Borisov equation linking grain boundary free energy and diffusion, clarifying its assumptions and applicability for impurity and complex diffusion mechanisms.

Contribution

It provides a rigorous re-derivation of the Borisov model, correcting errors and extending it to impurity and complex diffusion mechanisms.

Findings

Re-derivation clarifies the assumptions behind the Borisov equation.

Extensions to impurity diffusion and complex mechanisms are proposed.

Discussion on testing the key assumptions of the model.

Abstract

We present a detailed analysis of the universal relationship between grain boundary (GB) free energy and GB self-diffusion coefficient derived by Borisov et al. (1964). This relationship was expressed by a simple equation that was used in many publications to predict GB energies on the basis of experimental diffusion data. Meanwhile, the physical assumptions and approximations underlying the Borisov model are poorly understood. As a result, the Borisov equation was often used outside its intended limits. Here, we re-derive the Borisov equation from ground up, identifying its underlying assumptions, correcting some errors and inconsistencies, and extending the original model to the case of impurity diffusion and diffusion by the interstitialcy and interstitial-dumbbell mechanisms. The meaning of the key assumption of the Borisov model, related to the free energy of the activated complex, is discussed, and ways to test this assumption are proposed.