Kinetic equation describing the annealing process of copper

During the annealing process of cold-drawn copper with small amounts of impurities a multiple-sigmoidal behavior has been found, related to the overlapping of two or more process steps, corresponding to a simultaneous recrystallization of the copper matrix and the impurities placement processes. A kinetic equation is introduced to describe the overall process by means of an auto-catalytic kinetic model which could also be extended to describe any annealing process presenting a multi-sigmoidal character. C 2005 Springer Science + Business Media, Inc.