Numerical Analysis of Observations on Diffusion Induced Recrystallization in the Ni(Cu) System using A Kinetic Model

Abstract

Considering the effect of the friction force due to volume diffusion of a solute on the driving force, a new kinetic model has been proposed for diffusion induced recrystallization (DIR) in the A(B) system in which solute B atoms diffuse into a pure A metal or a binary A-B alloy. The energy balance model [M. Kajihara and W. Gust: Scr. Mater. 38 (1998) 1621] has been combined with the columnar geometry and boundary diffusion model [C. Li and M. Hillert: Acta Metall. 29 (1981) 1949] and the extended model [Y. Kawanami et al.: ISIJ Int. 37 (1997) 921] in order to describe mathematically the growth rate of the fine grain region (DIR region) formed by DIR as a function of the reaction time. DIR in the Ni(Cu) system was experimentally observed by Kawanami et al. [Y. Kawanami et al.: Mater. Trans., JIM 39 (1998) 218] at 923 and 1023 K. The new model has been utilized to analyze their observations theoretically. According to the observations, the migration rate v of the moving boundary gradually decreases with increasing reaction time. However, the decrease in the migration rate v is negligible during a small time interval of Δt = 1 s at the experimental reaction times. Thus, the value of v was assumed to be constant at each time step with At = 1 s in order to simplify the analysis. Using the mobility M of the moving boundary as the fitting parameter, the thickness of the DIR region was calculated as a function of the reaction time by a numerical technique. The calculation gives values of M = 3.73 x 10 -17 and 1.51 x 10 -15 m 4 /Js at 923 and 1023 K, respectively, and thus M 0 = 1.03 m 4 /Js and Q M = 290 kJ/mol for M = M 0 exp(-Q M /RT). The temperature dependence of the mobility indicates that the grain boundary migration may be governed by the solute drag effect for which the volume diffusion of the solute along the moving direction in the untransformed matrix ahead of the moving boundary has the most important role.