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Journal of Phase Equilibria and Diffusion

, Volume 32, Issue 4, pp 302–308 | Cite as

Effect of the Compositional Strain on the Diffusive Interface Thickness and on the Phase Transformation in a Phase-Field Model for Binary Alloys

  • Mohsen Asle ZaeemEmail author
  • Haitham El Kadiri
  • Sinisa Dj. Mesarovic
  • Mark F. Horstemeyer
  • Paul T. Wang
Basic and Applied Research

Abstract

A Cahn-Hilliard phase-field—elasticity model was used to study the effect of compositional strain on the diffusive interface thickness and on the solid state phase transformations in binary alloys. Compositional strain was introduced using the Vegard’s law. Mixed order finite element analyses and analytical solutions of an infinite diffusion couple with a flat interface were used to track the phase-field interface morphology. Both analytical and numerical calculations showed a substantial rate-increasing effect of compositional strain on the interface thickness, especially for low energy barrier values. Compositional strain was found to cause substantial patterning of single precipitates during their evolution in a parent matrix and significantly change the equilibrium size of the precipitates. Results show a considerable influence of compositional strain on the coarsening kinetics of coherent precipitates.

Keywords

compositional strain finite element interface thickness phase-field model precipitate 

References

  1. 1.
    L.Q. Chen, Phase-Field Models for Microstructure Evolution, Annu. Rev. Mater. Res., 2002, 32, p 113-140CrossRefGoogle Scholar
  2. 2.
    N. Moelans, B. Blanpain, and P. Wollants, An Introduction to Phase-Field Modeling of Microstructure Evolution, Calphad, 2008, 32(2), p 268-294CrossRefGoogle Scholar
  3. 3.
    B. Echebarria, R. Folch, A. Karma, and M. Plapp, Quantitative Phase-Field Model of Alloy Solidification, Phys. Rev. E, 2004, 70(6), p 061604ADSCrossRefGoogle Scholar
  4. 4.
    S. Torabi, J. Lowengrub, A. Voigt, and S. Wise, A New Phase-Field Model for Strongly Anisotropic Systems, Proc. R. Soc. A, 2009, 465, p 1337-1359MathSciNetADSzbMATHCrossRefGoogle Scholar
  5. 5.
    M. Selzer, B. Nestler, and D. Danilov, Influence of the Phase Diagram on the Diffuse Interface Thickness and on the Microstructure Formation in a Phase-Field Model for Binary Alloy, Math. Comput. Simul., 2010, 80(7), p 1428-1437MathSciNetzbMATHCrossRefGoogle Scholar
  6. 6.
    J.W. Cahn and J.E. Hilliard, Free Energy of a Nonuniform System. I. Interfacial Free Energy, J. Chem. Phys., 1958, 28, p 258-267ADSCrossRefGoogle Scholar
  7. 7.
    J.W. Cahn, On Spinodal Decomposition, Acta Metall., 1961, 9, p 795-801CrossRefGoogle Scholar
  8. 8.
    A.G. Khachaturyan, Theory of Structural Transformations in Solids, Wiley, New York, 1983Google Scholar
  9. 9.
    F.C. Larche and J.W. Cahn, Thermochemical Equilibrium of Multiphase Solids Under Stress, Acta Metall. Mater., 1978, 26, p 1579-1589CrossRefGoogle Scholar
  10. 10.
    F.C. Larche and J.W. Cahn, Phase Changes in a Thin Plate with Non-Local Self-Stress Effects, Acta Metall. Mater., 1992, 40, p 947-955CrossRefGoogle Scholar
  11. 11.
    P.H. Leo, J.S. Lowengrub, and H.J. Hou, A Diffuse Interface Model for Microstructural Evolution in Elastically Stressed Solids, Acta Mater., 1998, 46(6), p 2113-2130CrossRefGoogle Scholar
  12. 12.
    L.Q. Chen, Y. Wang, and A.G. Khachaturyan, Transformation-Induced Elastic Strain Effect on Precipitation Kinetics of Ordered Intermetallics, Philos. Mag. Lett., 1991, 64(5), p 241-251ADSCrossRefGoogle Scholar
  13. 13.
    J.W. Cahn and R. Kobayashi, Exponentially Rapid Coarsening and Buckling in Coherently Self-Stressed Thin Plates, Acta Metall. Mater., 1995, 43, p 931-944CrossRefGoogle Scholar
  14. 14.
    D.Y. Li and L.Q. Chen, Computer Simulation of Morphological Evolution and Rafting of γ′ Particles in Ni-based Superalloys Under Applied Stresses, Scripta Mater., 1997, 37(9), p 1271-1277CrossRefGoogle Scholar
  15. 15.
    P.-R. Cha, D.-H. Yeon, and S.-H. Chung, Phase-Field Study for the Splitting Mechanism of Coherent Misfitting Precipitates in Anisotropic Elastic Media, Scripta Mater., 2005, 52(12), p 1241-1245CrossRefGoogle Scholar
  16. 16.
    D.-H. Yeon, P.-R. Cha, J.-H. Kim, M. Grant, and J.-K. Yoon, A Phase Field Model for Phase Transformation in an Elastically Stressed Binary Alloy, Model. Simul. Mater. Sci. Eng., 2005, 13, p 299-319ADSCrossRefGoogle Scholar
  17. 17.
    H. El Kadiri, M.F. Horstemeyer, and D.J. Bammann, A Theory for Stress-Driven Interfacial Damage Upon Cationic-Selective Oxidation of Alloys, J. Mech. Phys. Solids, 2008, 56, p 3392-3415ADSzbMATHCrossRefGoogle Scholar
  18. 18.
    A.R. Denton and N.W. Ashcroft, Vegards’s Law, Phys. Rev. A, 1991, 43, p 3161-3164ADSCrossRefGoogle Scholar
  19. 19.
    F.C. Larche and J.W. Cahn, A Linear Theory of Thermochemical Equilibrium of Solids Under Stress, Acta Metall., 1973, 21, p 1051-1063CrossRefGoogle Scholar
  20. 20.
    M. Asle Zaeem and S.Dj. Mesarovic, Finite Element Method for Conserved Phase Fields: Stress-Mediated Diffusional Phase Transformation, J. Comp. Phys., 2010, 229(24), p 9135-9149ADSzbMATHCrossRefGoogle Scholar
  21. 21.
    M. Asle Zaeem and S.Dj. Mesarovic, Investigation of Phase Transformation in Thin Film Using Finite Element Method, Solid State Phenom., 2009, 150, p 29-41CrossRefGoogle Scholar
  22. 22.
    M. Asle Zaeem and S.Dj. Mesarovic, Morphological Instabilities in Thin Films: Evolution Maps, Comput. Mater. Sci., 2011, 50(3), p 1030-1036CrossRefGoogle Scholar
  23. 23.
    W.C. Johnson, On the Growth of an Intermediate Phase in Coherently Stressed Thin Plates, Acta Mater., 2000, 48, p 1021-1032CrossRefGoogle Scholar
  24. 24.
    W. Ostwald, On the Supposed Isomerism of Red and Yellow Mercury Oxide and the Surface Tension of Solid Substances, Z. Phys. Chem., 1900, 34, p 495-503Google Scholar

Copyright information

© ASM International 2011

Authors and Affiliations

  • Mohsen Asle Zaeem
    • 1
    Email author
  • Haitham El Kadiri
    • 1
    • 2
  • Sinisa Dj. Mesarovic
    • 3
  • Mark F. Horstemeyer
    • 1
    • 2
  • Paul T. Wang
    • 1
  1. 1.Center for Advanced Vehicular SystemsMississippi State UniversityStarkvilleUSA
  2. 2.Mechanical Engineering DepartmentMississippi State UniversityStarkvilleUSA
  3. 3.School of Mechanical and Materials EngineeringWashington State UniversityPullmanUSA

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