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Phase field analysis of the growth of fast and slow crystallites

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Abstract

Using an advancement of a phase field model of multi-grain crystallization developed by Moelans et al., a system of governing equations describing the evolution of multiple crystals in rapidly solidifying samples is formulated. The dynamics of the moving interface is analysed, and an analytical solution in form of traveling wave is obtained for the phase field profile and its velocity.

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References

  1. L. Granasy, T. Pusztai, J.A. Warren, J. Phys.: Condens. Matter 16, R1205 (2004)

    ADS  Google Scholar 

  2. R. Folch, M. Plapp, Phys. Rev. E 72, 011602 (2005)

    Article  ADS  MathSciNet  Google Scholar 

  3. D.A. Cogswell, W.C. Carter, Phys. Rev. E 83, 061602 (2011)

    Article  ADS  Google Scholar 

  4. I. Steinbach, L. Zhang, M. Plapp, Acta Mater. 60, 2689 (2012)

    Article  Google Scholar 

  5. L. Zhang, I. Steinbach, Acta Mater. 60, 2702 (2012)

    Article  Google Scholar 

  6. D. Fan, L.Q. Chen, Acta Mater. 45, 611 (1997)

    Article  Google Scholar 

  7. N. Moelans, B. Blanpain, P. Wollants, Phys. Rev. B 78, 024113 (2008)

    Article  ADS  Google Scholar 

  8. N. Moelans, B. Blanpain, P. Wollants, Phys. Rev. Lett. 101, 025502 (2008)

    Article  ADS  Google Scholar 

  9. N. Moelans, Acta Mater. 59, 1077 (2011)

    Article  Google Scholar 

  10. Y. Fu, J. Michopoulos, B. Gnanasekaran, Comput. Mater. Sci. 155, 457 (2018)

    Article  Google Scholar 

  11. D.V. Alexandrov, I.G. Nizovtseva, I.V. Alexandrova, Int. J. Heat Mass Transfer. 128, 46 (2019)

    Article  Google Scholar 

  12. I. Nizovtseva, D. Alexandrov, Philos. Trans. R. Soc. A 377, 20180214 (2019)

    Article  Google Scholar 

  13. I. Nizovtseva, P. Galenko, M. Rettenmayr, K. Reuther, J. Exp. Theor. Phys. 154, 124 (2018)

    Google Scholar 

  14. P. Galenko, D. Jou, Phys. Rev. E 71, 046125 (2005)

    Article  ADS  Google Scholar 

  15. D. Danilov, V. Lebedev, P. Galenko, J. Non-Equilib, Thermodyn. 39, 93 (2014)

    Google Scholar 

  16. I. Nizovtseva, N. Moelans, A. Ivanov, Eur. Phys. J. Special Topics 229, 453 (2020)

    Google Scholar 

  17. H. Ravash, J. Vleugels, N. Moelans, J. Mater. Sci. 52, 13852 (2017)

    Article  Google Scholar 

  18. A. Salhoumi, P. Galenko, Physica A 447, 161 (2016)

    Article  ADS  MathSciNet  Google Scholar 

  19. I. Nizovtseva, P. Galenko, D. Alexandrov, J. Phys. A: Math. Theor. 49, 435201 (2016)

    Article  ADS  Google Scholar 

  20. D. Alexandrov, G. Dubovoi, A. Malygin, I. Nizovtseva, L. Toropova, Russ. Metall. (Metally) 2, 127 (2017)

    Article  ADS  Google Scholar 

  21. I. Nizovtseva, P. Galenko, Philos. Trans. R. Soc. A 376, 20170202 (2016)

    Article  ADS  Google Scholar 

  22. P. Galenko, V. Ankudinov, Acta Mater. 168, 203 (2019)

    Article  Google Scholar 

  23. H. Jones, Rep. Prog. Phys. 36, 1425 (1973)

    Article  ADS  Google Scholar 

  24. O. Gusakova, P. Galenko, V. Shepelevich, D. Alexandrov, M. Rettenmayr, Philos. Trans. R. Soc. A 377, 20180204 (2019)

    Article  ADS  Google Scholar 

Download references

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Authors and Affiliations

  1. Ural Federal University, Department of Theoretical and Mathematical Physics, Laboratory of Multi-Scale Mathematical Modeling, 620000, Ekaterinburg, Russia

    Irina G. Nizovtseva & Dmitri V. Alexandrov

  2. Friedrich-Schiller-Universität Jena, Otto Schott Institute of Materials Research, 07743, Jena, Germany

    Irina G. Nizovtseva, Klemens Reuther & Markus Rettenmayr

  3. KU Leuven, Department of Materials Engineering (MTM), 3001, Leuven, Belgium

    Nele Moelans

Authors
  1. Irina G. Nizovtseva
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  2. Nele Moelans
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  3. Klemens Reuther
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  4. Markus Rettenmayr
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  5. Dmitri V. Alexandrov
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Corresponding author

Correspondence to Irina G. Nizovtseva.

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Nizovtseva, I.G., Moelans, N., Reuther, K. et al. Phase field analysis of the growth of fast and slow crystallites. Eur. Phys. J. Spec. Top. 229, 433–437 (2020). https://doi.org/10.1140/epjst/e2019-900135-3

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  • DOI: https://doi.org/10.1140/epjst/e2019-900135-3

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