Influence of grain boundaries on the distribution of components in binary alloys

Based on the free-energy density functional method (the Cahn–Hilliard equation), a phenomenological model that describes the influence of grain boundaries on the distribution of components in binary alloys has been developed. The model is built on the assumption of the difference between the interaction parameters of solid solution components in the bulk and at the grain boundary. The difference scheme based on the spectral method is proposed to solve the Cahn–Hilliard equation with interaction parameters depending on coordinates. Depending on the ratio between the interaction parameters in the bulk and at the grain boundary, temperature, and alloy composition, the model can give rise to different types of distribution of a dissolved component, namely, either depletion or enrichment of the grain-boundary area, preferential grainboundary precipitation, competitive precipitation in the bulk and at the grain boundary, etc.