Generalized additivity rule and isokinetics in diffusion-controlled growth

Validity of traditional additivity rule in diffusion-controlled growth is discussed. This process has a memory of thermal history due to temperature-dependent interface concentrations. When the thermodynamics is involved, the application of additivity rule should be carefully considered. By introducing a thermal history-related function, generalized isokinetic hypothesis and additivity rule involving the thermal history-dependent instantaneous reaction rate are proposed. According to the exact solutions of diffusion-controlled growth, the generalized additivity rule is analyzed, discussed, and applied well.