Reaction-diffusion model of surface and grain boundary segregation kinetics

T. Gambaryan-Roisman, E. Litovsky, M. Shapiro*, A. Shavit

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

5 Scopus citations


Small amounts of impurities normally present within crystalline solid materials tend to segregate near the surfaces of pores. A mathematical model for the surface segregation kinetics is proposed. An analytical solution is obtained for the evolution of the impurity's surface concentration, induced by an instantaneous change of the material's temperature. For times, significantly exceeding the characteristic diffusion time, when the segregation process is controlled by the bulk diffusion, the segregation kinetic curve reduces to the McLean's expression. For times, which are short compared to the reaction time, segregation is shown to be entirely controlled by the surface reaction kinetics. The effect of the grain boundary parameters on the segregation of impurities on surfaces of small pores is studied. The analyses are performed for grains and pores of plane, cylindrical and spherical shapes. The results calculated for surface segregation kinetics are fitted with experimental data for segregation of silver in copper and sulfur in Fe-6at.%Si, available from the literature. This allowed calculation of the surface reaction constant and the segregation length, appearing in the model. These quantities showed the Arrhenius temperature dependence. (C) 2000 Published by Elsevier Science Ltd.

Original languageEnglish
Pages (from-to)4135-4151
Number of pages17
JournalInternational Journal of Heat and Mass Transfer
Issue number22
StatePublished - 2000
Externally publishedYes


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