INTERFACE SCIENCE 11, 21–31, 2003 c  2003 Kluwer Academic Publishers. Manufactured in The Netherlands. Grain Boundary Diffusion and Linear and Non-Linear Segregation of Ag in Cu SERGIY DIVINSKI, MAIK LOHMANN AND CHRISTIAN HERZIG Institut f ¨ ur Materialphysik, Universit¨ at M ¨ unster, Wilhelm-Klemm-Str. 10, D-48149 M¨ unster, Germany Abstract. Ag grain boundary (GB) diffusion was measured in the Cu-0.2at%Ag alloy in a wide temperature range from 473 to 970 K. The direct measurements of Ag GB diffusivity D alloy gb under conditions of the Harrison C regime revealed that D alloy gb is almost identical to D pure gb determined earlier for Ag diffusion in high-purity Cu (Divinski, Lohmann, and Herzig, 2001). The penetration profiles determined in the Harrison B regime showed a complex, multi-stage shape. This diffusion behavior can be rationalized assuming that besides GBs significantly covered by segregated Ag atoms, some fraction of GBs remains almost free from Ag atoms in the studied temperature interval. The total amount of “pure” GBs drastically decreases with decreasing temperature. This hypothesis was proven by measurements of Ag GB diffusion in Cu near 5 bicrystals, which allowed us to analyze in detail the non-linear segregation of Ag in Cu GBs. Keywords: Cu, Cu(Ag) alloy, grain boundary diffusion, grain boundary segregation, non-linear segregation 1. Introduction Grain boundary (GB) diffusion and segregation phe- nomena play an important role in various technologi- cal applications. A knowledge of segregation behavior of solutes in pure Cu and Cu alloys is important in view of their increased applications in microelectronic devices. Investigation of solute GB diffusion presents an elegant way to determine equilibrium segregation char- acteristics in the dilute limit by applying the Harrison [1] B and C regime GB diffusion measurements in the same material [2]. This approach has already been successfully applied to several Cu- and Ag-based sys- tems, see e.g. [3–5]. In [6] this approach was ap- plied to Ag diffusion in high-purity Cu. GB dif- fusion measurements in the B regime provide the value of the triple product P = s · δ · D gb , whereas the GB diffusivity D gb can be directly determined in C regime conditions. Existing estimates, coming from B and C regime GB self-diffusion measure- ments [7, 8], indicate that the GB width δ can be well approximated as δ ≃ 5 × 10 -10 m in FCC met- als, e.g. Ag. Then the segregation factor s can be determined as s = P δ · D gb . (1) The determination of P from GB diffusion pene- tration profiles assumes that the segregation factor s , which is defined as the ratio of the solute concentra- tions in the GB c gb and in the bulk c v (0) just near the GB, s = c gb c v (0) , (2) does not change along the corresponding part of the penetration profile. This means that in the case of im- purity GB diffusion in a pure metal the tracer concen- trations c gb and c v (0) have to be sufficiently small to sat- isfy the dilute limit conditions. The equilibrium value of the segregation factor s will thus be determined. In Ref. [6] the absolute concentrations of the Ag tracer atoms in Cu GBs, c gb , were calculated from the measured specific radiotracer activity of the section. It was shown that c gb ≪ 1 at the penetration profile depths where the GB diffusivity P was evaluated.