Ostwald ripening of precipitates during two successive heat treatments performed at different temperatures

Two-stage Ostwald ripening of precipitates has been investigated experimentally and theoretically. A nickel-base alloy in which spherical nano-scale precipitates of the γ′-phase form served as a model system. Each specimen was heat treated at two successive temperatures T1 and T2 in the range 949–1119 K. Thus, monodal as well as bimodal precipitate dispersions were produced. On the basis of an equation published by Wagner, Lifshitz, and Slyozov for isothermal ageing, the function r(t1,T1,t2,T2)¯ is modeled, where r(t1,T1,t2,T2)¯ is the average precipitate radius after double ageing and ti is the ageing time at Ti. In the case of bimodal γ′-precipitate dispersions, two average radii are considered. The agreement between measured and calculated values for r(t1,T1,t2,T2)¯ is within 7%, which is about the same accuracy as that of experimental data determined by transmission electron microscopy. The quoted agreement holds for monodal γ′-precipitate dispersions as well as for each γ′-population of bimodal dispersions.