A critique of activation energies for nucleation growth and overall transformation kinetics

The nucleation, growth and overall transformation kinetics of a model precipitation reaction, based in part upon the proeutectoid ferrite reaction in FeC alloys, are calculated as a function of temperature in an "A-2 A/O B" alloy. The apparent activation energy for each type of kinetics is computed as a function of temperature. At low undercoolings these energies (Q's) become negative; they vary markedly with temperature, particularly at low and intermediate undercoolings; under some conditions Q becomes roughly constant at large undercoolings. Comparison of the apparent Q's at large undercoolings (low temperatures) with Q's for diffusion in the matrix and the product phases suggests in some instances control of transformation by diffusion in the matrix, in others control by means of diffusion within the precipitate; while in many cases there is no physical unit process in the example system which has a Q anywhere near that computed from the activation plots. Qualitative consideration of the equations for nucleation, growth and overall transformation kinetics makes clear the lack of meaning which any apparent Q must have because two or more important factors, particularly driving force and mobility or diffusivity, are simultaneously operative, each of which has a different, and oppositely directed real or apparent Q of its own. The conclusion is thus reached that the widespread practice of determining activation energies for nucleation, for growth and especially for overall transformation kinetics should be terminated on the ground that not only are the results obtained meaningless but also can readily be misleading.