Interfacial reaction rates and free energy of cubic clusters

Abstract

A new formulation of interfacial reaction rates for clusters in binary alloys is presented. It accounts for the matrix structure and the topological properties of the clusters at the atomic scale. It is shown that the probabilities per unit time that a solute atom be captured or released by a cluster are functions not only of the partition function but also of a transition function. The principles of calculation of these functions are general but only the case of cubic clusters is treated here (results can be used for L₁₂ clusters in fcc matrices). Exact calculations have been done for small clusters (size<10), followed by a Monte-Carlo sampling method for intermediate sizes as a function of temperature and interaction energy (a material characteristic). Finally, it is shown that generic results can be extrapolated at higher cluster size in a large range of temperature and/or interaction energy.

Acknowledgements

This work results from numerous fruitful discussions during the joint research program “CPR Precipitation” (Arcelor, Alcan – Pechiney, CNRS and CEA). The author is especially grateful to G. Martin for his constructive criticisms and encouraging remarks and to E. Clouet for enriching discussions and his KMC data. Discussions about KMC simulations and Ising models with A. Finel, F. Soisson and M. Athenes have been very helpful to achieve this work.

Notes

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Additional information

Notes on contributors

J. Lepinoux *

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