Statistical and structural effects during solute-atom segregation to grain boundaries

Mean field theory of a rigid grain boundary segregation in binary mixture is developed on the basis of local equilibrium and geometrical considerations. The application of the Guggenheim adsorption isotherm equation to the problem of internal interfaces is proved to be valid for the case of regular substitutional solid solution. The segregation coefficient is found to be a function of a new interaction constant which yields the relative stability of an interface between a crystal made of pure solute and a crystal of pure solvent, with respect to the stability of grain boundaries in solvent and solute materials. Three typical structures are obtained when a local miscibility gap is formed and two other structures when the bulk tends to order. Segregation can stabilize new boundary structures which may involve changes in the intergranular translation, faceting, etc.