Solute Diffusion in Grain Boundaries – Outside the Scope of Fisher Model

Abstract

Thermodynamic and kinetic models are developed for grain boundary segregation and diffusion with regards to the possible complexes formation in grain boundary. The equilibrium state for ideal solutions can be described by the equilibrium constants b and K. The first corresponds to the pure segregation, i.e. the exchange A and B atoms between grain boundary and the bulk. The second represents the equilibrium of the reaction of the complexes formation in grain boundary. The segregation isotherm and diffusion profiles are calculated. It is shown that both b and K equilibrium constants define completely dependence of the total grain boundary concentration of B atoms on the bulk concentration and distribution of B atoms between two states: free (pure exchange) and tied (in the complexes). Segregation in both forms (free B atoms and tied B atoms) decreases grain boundary diffusivity in comparison with the absence of segregation.