Phenomenological coefficients in a concentrated alloy for the dumbbell mechanism

Abstract

We present an adaptation of the self-consistent mean field (SCMF) theory to calculate the transport coefficients in a concentrated alloy for diffusion by the dumbbell mechanism. In this theory, kinetic correlations are accounted for through a set of effective interactions within a non-equilibrium distribution function of the system. Transport coefficients are calculated for the FCC and BCC multicomponent concentrated alloys for simple sets of jump frequencies, including different stabilities of the different defects. A first approximation leads to an analytical expression of the Onsager coefficients in a binary alloy, and a second approximation provides a more accurate prediction. The results of the SCMF theory are compared with existing models and available Monte Carlo simulations, and an interpretation of the set of effective interactions in terms of a competition between jump frequencies is proposed.

Acknowledgements

The authors are grateful to J.L. Bocquet, A. Barbu, G. Martin, C. Hin and A.B. Lidiard for their valuable support and comments. Private communications from J.L. Bocquet were particularly appreciated. This work was funded by the joint program SMIRN (CEA, EDF, CNRS).

Notes

†Throughout this paper, we call non-interacting a system without interactions involving the substitutional atoms. As we will see, a particular set of jump frequencies can take into account different stabilities of the dumbbells of different compositions, which is equivalent to speaking of thermodynamic interactions between both atoms inside the dumbbell. Nevertheless, non-interacting alloys in this study are characterized by the absence of short-range or long-range order.

†The link with the macroscopic transport phenomenology for a cubic symmetry states: , where is expressed in atoms per time and area units, a is the lattice parameter and V_at the atomic volume.