Reaction-diffusion model of surface and grain boundary segregation kinetics

Small amounts of impurities normally present within crystalline solid mater ials tend to segregate near the surfaces of pores. A mathematical model for the surface segregation kinetics is proposed. An analytical solution is ob tained for the evolution of the impurity's surface concentration, induced b y an instantaneous change of the material's temperature. For times, signifi cantly exceeding the characteristic diffusion time, when the segregation pr ocess is controlled by the bulk diffusion, the segregation kinetic curve re duces to the McLean's expression. For times, which are short compared to th e reaction time, segregation is shown to be entirely controlled by the surf ace reaction kinetics. The effect of the grain boundary parameters on the s egregation of impurities on surfaces of small pores is studied. The analyse s are performed for grains and pores of plane, cylindrical and spherical sh apes. The results calculated for surface segregation kinetics are fitted wi th experimental data for segregation of silver in copper and sulfur in Fe-6 at.%Si, available from the literature. This allowed calculation of the surf ace reaction constant and the segregation length, appearing in the model. T hese quantities showed the Arrhenius temperature dependence. (C) 2000 Publi shed by Elsevier Science Ltd.