Generalized additivity rule and isokinetics in diffusion-controlled growth
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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.
KeywordsThermal History Additivity Rule Continuous Cool Isothermal Transformation Diffusion Field
The authors gratefully acknowledge the financial supports from the National Basic Research Program of China (973 Program, 2011CB610403), the Natural Science Foundation of China (51071127 and 51134011), the China National Fund for Distinguished Young Scientists (51125002), and the Fundamental Research Fund of Northwestern Polytechnical University (JC20120223). S.J. Song is also grateful to the Ministry of Education Fund for Doctoral Students Newcomer Awards of China and the Excellent Doctorate Foundation of Northwestern Polytechnical University (CX201008 and DJ201303).
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