Skip to main content
SpringerLink
Log in

Calibration of a multi-phase field model with quantitative angle measurement

  • HTC 2015
  • Published:
Journal of Materials Science Aims and scope Submit manuscript

Abstract

Over the last years, the phase-field method has been established to model capillarity-induced microstructural evolution in various material systems. Several phase-field models were introduced and different studies proved that the microstructure evolution is crucially affected by the triple junction (TJ’s) mobilities as well as the evolution of the dihedral angles. In order to understand basic mechanisms in multi-phase systems, we are interested in the time evolution of TJ’s, especially in the contact angles in these regions. Since the considered multi-phase systems consist of a high number of grains, it is not feasible to measure the angles at all TJ’s by hand. In this work, we present a method enabling the localization of TJ’s and the measurement of dihedral contact angles in the diffuse interface inherent in the phase-field model. Based on this contact angle measurement method, we show how to calibrate the phase-field model in order to satisfy Young’s law for different contact angles.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6

Similar content being viewed by others

References

  1. Boettinger W, Warren J, Beckermann C, Karma A (2002) Phase-field simulation of solidification 1. Ann Rev Mater Res 32(1):163–194

    Article  Google Scholar 

  2. Cogswell DA, Carter WC (2011) Thermodynamic phase-field model for microstructure with multiple components and phases: the possibility of metastable phases. Phys Rev E 83(6):061602–061615. doi:10.1088/0965-0393/17/7/073001

    Article  Google Scholar 

  3. Nestler B, Choudhury A (2011) Phase-field modeling of multi-component systems. Curr Opin Solid State Mater Sci 15(3):93–105

    Article  Google Scholar 

  4. Cahn JW, Hilliard JE (1958) Free energy of a nonuniform system. I. Interfacial free energy. J Chem Phys 28(2):258–267

    Article  Google Scholar 

  5. Kobayashi R (1993) Modeling and numerical simulations of dendritic crystal growth. Phys D 63:410–423

    Article  Google Scholar 

  6. Langer JS (1986) Models of pattern formation in first-order phase transitions. Directions in condensed matter. World Scientific, Singapore, pp 165–186

    Google Scholar 

  7. Kim SG, Kim WT, Suzuki T (1999) Phase-field model for binary alloys. Phys Rev E 60:7186–7198

    Article  Google Scholar 

  8. Plapp M (2011) Unified derivation of phase-field models for alloy solidification from a grand-potential functional. Phys Rev E 84:031601–031616

    Article  Google Scholar 

  9. Garcke H, Nestler B, Stoth B (1999) A multiphase field concept: numerical simulations of moving phase boundaries and multiple junctions. SIAM J Appl Math 60(1):295–315. doi:10.1137/S0036139998334895

    Article  Google Scholar 

  10. Nestler B, Garcke H, Stinner B (2005) Multicomponent alloy solidification: phase-field modeling and simulations. Phys Rev E 71:041609–041615

    Article  Google Scholar 

  11. Chen LQ, Yang W (1994) Computer simulation of the domain dynamics of a quenched system with a large number of nonconserved order parameters: the grain-growth kinetics. Phys Rev B 50(21):15752–15759

    Article  Google Scholar 

  12. Fan D, Chen LQ (1997) Computer simulation of grain growth using a continuum field model. Acta Mater 45(2):611–622

    Article  Google Scholar 

  13. Garcke H, Nestler B, Stoth B (1998) On anisotropic order parameter models for multi-phase systems and their sharp interface limits. Phys D 115(1):87–108

    Article  Google Scholar 

  14. Steinbach I, Pezzolla F (1999) A generalized field method for multiphase transformations using interface fields. Phys D 134(4):385–393

    Article  Google Scholar 

  15. Steinbach I, Pezzolla F, Nestler B, Seeßelberg M, Prieler R, Schmitz G, Rezende J (1996) A phase field concept for multiphase systems. Phys D 94(3):135–147

    Article  Google Scholar 

  16. Warren JA, Kobayashi R, Lobkovsky AE, Carter WC (2003) Extending phase field models of solidification to polycrystalline materials. Acta Mater 51(20):6035–6058

    Article  Google Scholar 

  17. Lu Y, Zhang L, Zhou Y, Chen Z, Zhang J (2013) Phase-field study for texture evolution in polycrystalline materials under applied stress. J Mater Sci Technol 29(10):999–1004

    Article  Google Scholar 

  18. Ravash H, Vleugels J, Moelans N (2014) Three-dimensional phase-field simulation of microstructural evolution in three-phase materials with different diffusivities. J Mater Sci 49(20):7066–7072. doi:10.1007/s10853-014-8411-0

    Article  Google Scholar 

  19. Ahmed K, Allen T, El-Azab A (2015) Phase field modeling for grain growth in porous solids. J Mater Sci. doi:10.1007/s10853-015-9107-9

    Google Scholar 

  20. McKenna I, Gururajan M, Voorhees P (2009) Phase field modeling of grain growth: effect of boundary thickness, triple junctions, misorientation, and anisotropy. J Mater Sci 44(9):2206–2217. doi:10.1007/s10853-008-3196-7

    Article  Google Scholar 

  21. Moelans N, Wendler F, Nestler B (2009) Comparative study of two phase-field models for grain growth. Comput Mater Sci 46(2):479–490

    Article  Google Scholar 

  22. Johnson A, Voorhees P (2014) A phase-field model for grain growth with trijunction drag. Acta Mater 67:134–144

    Article  Google Scholar 

  23. Gottstein G, King A, Shvindlerman L (2000) The effect of triple-junction drag on grain growth. Acta Mater 48(2):397–403

    Article  Google Scholar 

  24. Caroli C, Misbah C (1997) On static and dynamical Young’s condition at a trijunction. J Phys I 7(10):1259–1265

    Google Scholar 

  25. Guo W, Steinbach I (2010) Multi-phase field study of the equilibrium state of multi-junctions. Int J Mater Res 101(4):382–388. doi:10.3139/146.110298

    Article  Google Scholar 

  26. Holm E, Srolovitz DJ, Cahn J (1993) Microstructural evolution in two-dimensional two-phase polycrystals. Acta Metall Mater 41(4):1119–1136

    Article  Google Scholar 

  27. Wheeler AA, Boettinger WJ, McFadden GB (1992) Phase-field model for isothermal phase transitions in binary alloys. Phys Rev E 45:7424–7451

    Article  Google Scholar 

  28. Choudhury A, Nestler B (2012) Grand-potential formulation for multicomponent phase transformations combined with thin-interface asymptotics of the double-obstacle potential. Phys Rev E 85:021602–021618

    Article  Google Scholar 

  29. Moelans N, Blanpain B, Wollants P (2008) An introduction to phase-field modeling of microstructure evolution. Calphad 32(2):268–294

    Article  Google Scholar 

  30. Vondrous A, Selzer M, Hötzer J, Nestler B (2014) Parallel computing for phase-field models. Int J High Perform C 28(1):1–12. doi:10.1177/1094342013490972

    Article  Google Scholar 

  31. Stinner B, Nestler B, Garcke H (2004) A diffuse interface model for alloys with multiple components and phases. SIAM J Appl Math 64(3):775–799

    Article  Google Scholar 

  32. Chen Y, Ye X (2011) Projection onto a simplex, arXiv preprint arXiv:1101.6081, pp 1–7

  33. Wendler F, Becker JK, Nestler B, Bons PD, Walte NP (2009) Phase-field simulations of partial melts in geological materials. Comput Geosci 35(9):1907–1916

    Article  Google Scholar 

  34. Adams BL, Ta’Asan S, Kinderlehrer D, Livshits I, Mason D, Wu CT, Mullins W, Rohrer G, Rollett A, Saylor D (1999) Extracting grain boundary and surface energy from measurement of triple junction geometry. Interface Sci 7(3–4):321–337

    Article  Google Scholar 

  35. Stinner B (2006) Derivation and analysis of a phase field model for alloy solidification, Dissertation, University of Regensburg

Download references

Author information

Authors and Affiliations

  1. Institut für Angewandte Materialien, Computational Materials Science (IAM-CMS), Karlsruhe Institute of Technology (KIT), Haid-und-Neu-Str. 7, 76131, Karlsruhe, Germany

    Johannes Hötzer, Marouen Ben Said, Marco Berghoff, Marcus Jainta, Georges Barthelemy, Nikolay Smorchkov, Daniel Schneider, Michael Selzer & Britta Nestler

  2. Institute of Materials and Processes, Karlsruhe University of Applied Sciences, Moltkestrasse 30, 76133, Karlsruhe, Germany

    Johannes Hötzer, Oleg Tschukin, Michael Selzer & Britta Nestler

Authors
  1. Johannes Hötzer
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Oleg Tschukin
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Marouen Ben Said
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Marco Berghoff
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Marcus Jainta
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Georges Barthelemy
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. Nikolay Smorchkov
    View author publications

    You can also search for this author in PubMed Google Scholar

  8. Daniel Schneider
    View author publications

    You can also search for this author in PubMed Google Scholar

  9. Michael Selzer
    View author publications

    You can also search for this author in PubMed Google Scholar

  10. Britta Nestler
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Johannes Hötzer.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Hötzer, J., Tschukin, O., Said, M.B. et al. Calibration of a multi-phase field model with quantitative angle measurement. J Mater Sci 51, 1788–1797 (2016). https://doi.org/10.1007/s10853-015-9542-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10853-015-9542-7

Keywords

Search

Navigation