A self-consistent mean field calculation of the phenomenological coefficients in a multicomponent alloy with high jump frequency ratios

Abstract

We present an improvement of the self-consistent mean field (SCMF) approximation of the L _ij which extends its applications to alloys presenting high jump frequency ratios. The theory uses a vacancy–atom exchange model which depends on temperature and local composition through thermodynamic and kinetic parameters. Kinetic correlations due to the vacancy mechanism are represented by a time-dependent effective Hamiltonian. In the case of high jump frequency ratios it is shown that long return paths of the vacancy need to be considered, which is shown to be equivalent to introducing many-body long-range effective interactions. We compare this theory to existing formalisms and Monte Carlo simulations for systems both without and with atomic interactions.

Acknowledgements

The authors thank J.-L. Bocquet, G. Martin and A. B. Lidiard for their support and judicious comments. This work was funded by the joint research program ‘SMIRN’ between EdF, CNRS and CEA.

Notes

† Throughout this section, quantities that are a function of the configuration n will be marked by the ‘hat’ sign: stands for H(n). Moreover, the species indices are denoted in capital letters A,B,… when the sum includes the vacancies, and in Greek characters α,β,… when the sum runs over chemical species only.