Intrinsic diffusion coefficients have been calculated for a solid solution binary fcc metal alloy with vacancies using grand canonical and kinetic Monte Carlo (MC) methods for a variety of model Hamiltonians. Model Hamiltonians include a kinetically and thermodynamically ideal case, solute-vacancy attraction and repulsion, and solute-solute attraction and repulsion. These model Hamiltonians are chosen to have constant average activation energies in order to focus on contributions from other thermodynamic and kinetic factors. The thermodynamic factor calculated using MC is compared to a mean-field regular solution model. It is shown that the mean-field model accurately predicts the thermodynamic factors for each model alloy Hamiltonian except for the alloys with a solute-solute interaction and concentration that are in the spinodal region (as predicted by the regular solution model). The MC determined concentration-dependent intrinsic diffusion coefficients are compared to values determined from the dilute five-frequency model and Darken and Manning analytical approximations. The results indicate that for a solid solution with known average barriers and vacancy concentration, Darken and Manning approximation-based analytic expressions and mean-field theory can be used to predict concentration-dependent diffusion coefficients within a factor of approximately three, provided the system is outside of the spinodal region. The good accuracy of this approximate approach follows from the fact that the thermodynamic factor is the main contribution to the concentration dependence of the diffusion constants, and that this thermodynamic factor is well described by mean-field theory.
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We gratefully acknowledge financial support from the DOE Nuclear Engineering Research Initiative Program (NERI), award number DE-FC07-06ID14747.
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Swoboda, B., Van der Ven, A. & Morgan, D. Assessing Concentration Dependence of FCC Metal Alloy Diffusion Coefficients Using Kinetic Monte Carlo. J. Phase Equilib. Diffus. 31, 250–259 (2010). https://doi.org/10.1007/s11669-010-9706-8
- diffusion constant
- diffusion modeling
- metallic alloys
- Monte Carlo simulations
- thermodynamic modeling