Journal of Phase Equilibria and Diffusion

, Volume 31, Issue 3, pp 250–259 | Cite as

Assessing Concentration Dependence of FCC Metal Alloy Diffusion Coefficients Using Kinetic Monte Carlo

  • B. Swoboda
  • A. Van der Ven
  • D. MorganEmail author
Basic and Applied Research


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.


diffusion constant diffusion modeling metallic alloys Monte Carlo simulations thermodynamic modeling 



We gratefully acknowledge financial support from the DOE Nuclear Engineering Research Initiative Program (NERI), award number DE-FC07-06ID14747.


  1. 1.
    R.E. Howard and A.B. Lidiard, Matter Transport in Solids, Rep. Prog. Phys., 1964, 27, p 161-240.CrossRefADSGoogle Scholar
  2. 2.
    A. Van der Ven, J.C. Thomas, Q. Xu, B. Swoboda, and D. Morgan, Nondilute Diffusion from First Principles: Li Diffusion in LixTiS2, Phys. Rev. B: Condens. Matter Mater. Phys., 2008, 78, p 104306.ADSGoogle Scholar
  3. 3.
    J.R. Manning, Correlation Factors for Diffusion in Nondilute Alloys, Phys. Rev. B, 1971, 4(4), p 1111-1121.CrossRefADSGoogle Scholar
  4. 4.
    A.B. Lidiard, Impurity Diffusion in Crystals (Mainly Ionic Crystals with the Sodium Chloride Structure), Philos. Mag., 1955, 46, p 1218-1237Google Scholar
  5. 5.
    A.D. LeClaire and A.B. Lidiard, Correlation Effects in Diffusion in Crystals, Philos. Mag., 1956, 1(6), p 518-527 (8th series).Google Scholar
  6. 6.
    A.D. LeClaire, Solute Diffusion in Dilute Alloys, J. Nucl. Mater., 1978, 69-70(1-2), p 70-96CrossRefADSGoogle Scholar
  7. 7.
    V. Barbe and M. Nastar, Phenomenological Coefficients in a Concentrated Alloy for the Dumbbell Mechanism, Philos. Mag., 2006, 86(23), p 3503-3535CrossRefADSGoogle Scholar
  8. 8.
    V. Barbe and M. Nastar, Phenomenological Coefficients in a Dilute BCC Alloy for the Dumbbell Mechanism, Philos. Mag., 2007, 87(11), p 1649-1669CrossRefADSGoogle Scholar
  9. 9.
    A. Van der Ven and G. Ceder, First Principles Calculation of the Interdiffusion Coefficient in Binary Alloys, Phys. Rev. Lett., 2005, 94, p 045901.CrossRefADSGoogle Scholar
  10. 10.
    A. Van der Ven and G. Ceder, Vacancies in Ordered and Disordered Binary Alloys Treated with the Cluster Expansion, Phys. Rev. B: Condens. Matter. Mater. Phys., 2005, 71, p 054102-1-054102-2.ADSGoogle Scholar
  11. 11.
    A.R. Allnatt and E.L. Allnatt, Computer Simulation Study of the Manning Relations and Related Approximations in a Strictly Regular Solution Model, Phil. Mag. A, 1991, 64(2), p 341-353CrossRefADSGoogle Scholar
  12. 12.
    A.R. Allnatt and E.L. Allnatt, Comparison of Computer Simulated and Theoretical Tracer Diffusion Coefficients for a Strictly Regular Solution Model of a Concentrated Alloy, Phil. Mag. A, 1992, 66(1), p 165-171CrossRefADSGoogle Scholar
  13. 13.
    A. Van der Ven, G. Ceder, M. Asta, and P.D. Tepesch, First-Principles Theory of Ionic Diffusion with Nondilute Carriers, Phys. Rev. B: Condens. Matter. Mater. Phys., 2001, 64(18), 184307-1-184307-17.ADSGoogle Scholar
  14. 14.
    G.K. Boreskov, Heterogeneous Catalysis, Nova Science Publishers Inc., New York, 2003Google Scholar
  15. 15.
    J.M. Yeomans, Statistical Mechanics of Phase Transitions. Clarendon Press/Oxford University Press, Oxford, New York, 1992.Google Scholar
  16. 16.
    J.M. Sanchez and D.d. Fontaine, The FCC Ising Model in the Cluster Variation Approximation, Phys. Rev. B, 1978, 17(7), p 2926-2936CrossRefMathSciNetADSGoogle Scholar
  17. 17.
    A. Van der Ven, H.C. Yu, G. Ceder, and K. Thornton, Vacancy Mediated Substitutional Diffusion in Binary Crystalline Solids, Progr. Mater. Sci., 2010, 55(2), p 61-105.CrossRefGoogle Scholar
  18. 18.
    A.R. Allnatt, Einstein and linear response formulae for the phenomenological coefficients for isothermal matter transport in solids, J. Phys. C: Solid State, 1982, 15, p 5605-5613CrossRefADSGoogle Scholar
  19. 19.
    Y. Kakuda, E. Uchida, and N. Imai, A New Model of the Excess Gibbs Energy of Mixing for a Regular Solution, Proc. Jpn. Acad. Ser. B, 1994, 70(10), p 163-168CrossRefGoogle Scholar
  20. 20.
    A.R. Allnatt and A.B. Lidiard, Atomic Transport in Solids, Cambridge University Press, Cambridge, 1993CrossRefGoogle Scholar
  21. 21.
    L.S. Darken, Diffusion, Mobility and their Interrelation Through Free Energy in Binary Metallic Systems, Trans. AIME, 1948, 175, p 184-201.Google Scholar
  22. 22.
    G.E. Murch, Chemical Diffusion in Highly Defective Solids, Phil. Mag. A, 1980, 41(2), p 157-163CrossRefADSGoogle Scholar
  23. 23.
    R. Kutner, Chemical Diffusion in the Lattice Gas of Non-Interacting Particles, Phys. Lett. A, 1981, 81(4), p 239-240CrossRefADSGoogle Scholar
  24. 24.
    L.K. Moleko, A.R. Allnatt, and E.L. Allnatt, A Self-Consistent Theory of Matter Transport in a Random Lattice Gas and Some Simulation Results, Phil. Mag. A, 1989, 59(1), p 141-160CrossRefADSGoogle Scholar
  25. 25.
    I.V. Belova and G.E. Murch, Collective Diffusion in the Binary Random Alloy, Phil. Mag. A, 2000, 80(3), p 599-607CrossRefADSGoogle Scholar

Copyright information

© ASM International 2010

Authors and Affiliations

  1. 1.University of Wisconsin-MadisonMadisonUSA
  2. 2.University of MichiganAnn ArborUSA

Personalised recommendations