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Phase-field method of materials microstructures and properties

  • Phase-Field Method and Its Applications
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Abstract

The phase-field method has become the main computational technique for modeling and predicting the microstructure evolution in materials science and engineering. Its versatility and ability to capture complex microstructure phenomena under different processing conditions make it a valuable tool for researchers and engineers in advancing our understanding and engineering of materials microstructures and properties. This issue of MRS Bulletin is focused on a few recent success stories of applying the phase-field method to understanding, discovering, and designing mesoscale structures and for guiding the design of experiments to optimize properties or discover new phenomena or functionalities. We hope this issue will inspire increasing future focus on utilizing the phase-field method to guide experimental synthesis and characterization for desirable properties.

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References

  1. L.-Q. Chen,  Annu. Rev. Mater. Res. 32, 113 (2002)

    CAS  Google Scholar 

  2. K. Thornton, J. Agren, P.W. Voorhees, Acta Mater. 51(19), 5675 (2003)

    CAS  Google Scholar 

  3. H. Emmerich, Adv. Phys. 57(1), 1 (2008)

    CAS  Google Scholar 

  4. N. Moelans, B. Blanpain, P. Wollants, CALPHAD 32(2), 268 (2008)

    CAS  Google Scholar 

  5. I. Singer-Loginova, H.M. Singer, Rep. Prog. Phys. 71(10), 32 (2008)

    Google Scholar 

  6. Y.Z. Wang, J. Li, Acta Mater. 58(4), 1212 (2010)

    CAS  Google Scholar 

  7. B. Nestler, A. Choudhury, Curr. Opin. Solid State Mater. Sci. 15(3), 93 (2011)

    CAS  Google Scholar 

  8. I. Steinbach,  Annu. Rev. Mater. Res. 43, 89 (2013)

    CAS  Google Scholar 

  9. M.R. Tonks, L.K. Aagesen, Annu. Rev. Mater. Res. 49, 79 (2019)

    CAS  Google Scholar 

  10. D. Tourret, H. Liu, J. Llorca, Prog. Mater. Sci. 123, 19 (2022)

    Google Scholar 

  11. Y.H. Zhao, NPJ Comput. Mater. 9(1), 25 (2023)

    Google Scholar 

  12. A.A. Wheeler, W.J. Boettinger, G.B. McFadden, Phys. Rev. A 45(10), 7424 (1992)

    CAS  PubMed  Google Scholar 

  13. R. Kobayashi, Physica D 63(3–4), 410 (1993)

    Google Scholar 

  14. L.-Q. Chen, W. Yang, Phys. Rev. B 50(21), 15752 (1994)

    CAS  Google Scholar 

  15. R. Kobayashi, J.A. Warren, W.C. Carter, Physica D 140(1–2), 141 (2000)

    Google Scholar 

  16. C.E. Krill, L.-Q. Chen,  Acta Mater. 50(12), 3057 (2002)

    CAS  Google Scholar 

  17. N. Moelans, B. Blanpain, P. Wollants, Phys. Rev. B 78, 2 (2008)

    Google Scholar 

  18. L. Gránásy, G.I. Tóth, J.A. Warren, F. Podmaniczky, G. Tegze, L. Rátkai, T. Pusztai, Prog. Mater. Sci. 106, 51 (2019)

    Google Scholar 

  19. Y. Wang, L.-Q. Chen, A.G. Khachaturyan, Acta Metall. Mater. 41(1), 279 (1993)

    CAS  Google Scholar 

  20. J.Z. Zhu, A.J. Ardell, S.H. Zhou, Z.K. Liu, L.-Q. Chen, Acta Mater. 52(9), 2837 (2004)

    CAS  Google Scholar 

  21. H. Liu, Y. Gao, J.Z. Liu, Y.M. Zhu, Y. Wang, J.F. Nie, Acta Mater. 61(2), 453 (2013)

    CAS  Google Scholar 

  22. Y. Wang, A.G. Khachaturyan, Acta Mater. 45(2), 759 (1997)

    CAS  Google Scholar 

  23. V.I. Levitas, D.L. Preston, D.W. Lee, Phys. Rev. B 68, 13 (2003)

    Google Scholar 

  24. M. Mamivand, M.A. Zaeem, H. El Kadiri, Comput. Mater. Sci. 77, 304 (2013)

    CAS  Google Scholar 

  25. L.-Q. Chen, J. Am. Ceram. Soc. 91(6), 1835 (2008)

    CAS  Google Scholar 

  26. J.-J. Wang, B. Wang, L.-Q. Chen, Annu. Rev. Mater. Res. 49(1), 127 (2019) 

    CAS  Google Scholar 

  27. J.J. Sun, S. Shi, Y. Wan, J. Wang, Acta Mech. 234(2), 283 (2023)

    Google Scholar 

  28. Z.-H. Shen, J.-J. Wang, J.-Y. Jiang, S.X. Huang, Y.-H. Lin, C.-W. Nan, L.-Q. Chen, Y. Shen, Nat. Commun. 10, 1843 (2019)

  29. T.Q. Bui, X.F. Hu, Eng. Fract. Mech. 248, 33 (2021)

    Google Scholar 

  30. Y.L. Li, S. Hu, X. Sun, M. Stan, NPJ Comput. Mater. 3, 16 (2017)

    Google Scholar 

  31. T.Q. Ansari, Z. **ao, S. Hu, Y. Li, J.-L. Luo, S.-Q. Shi, NPJ Comput. Mater. 4, 38 (2018)

  32. I. Bellemans, N. Moelans, K. Verbeken, Crit. Rev. Solid State Mater. Sci. 43(5), 417 (2018)

    CAS  Google Scholar 

  33. Q. Wang, G. Zhang, Y. Li, Z. Hong, D. Wang, S. Shi, NPJ Comput. Mater. 6(1), 176 (2020)

  34. E. Meca, V.B. Shenoy, J. Lowengrub, Phys. Rev. E 88, 5 (2013)

    Google Scholar 

  35. J. Berry, S. Zhou, J. Han, D.J. Srolovitz, M.P. Haataja, Nano Lett. 17(4), 2473 (2017)

  36. K. Momeni, Y. Ji, Y. Wang, S. Paul, S. Neshani, D.E. Yilmaz, Y.K. Shin, D. Zhang, J.-W. Jiang, H.S. Park, S. Sinnott, A. van Duin, V. Crespi, L.-Q. Chen, NPJ Comput. Mater. 6(1), 22 (2020)

  37. D.M. Anderson, G.B. McFadden, A.A. Wheeler, Annu. Rev. Fluid Mech. 30, 139 (1998)

    Google Scholar 

  38. J. Kim, Commun. Comput. Phys. 12(3), 613 (2012)

    Google Scholar 

  39. A. Karma, D.A. Kessler, H. Levine, Phys. Rev. Lett. 87, 4 (2001)

    Google Scholar 

  40. C. Kuhn, R. Muller, Eng. Fract. Mech. 77(18), 3625 (2010)

    Google Scholar 

  41. C. Miehe, F. Welschinger, M. Hofacker, Int. J. Numer. Methods Eng. 83(10), 1273 (2010)

    Google Scholar 

  42. M.J. Borden, C.V. Verhoosel, M.A. Scott, T.J.R. Hughes, C.M. Landis, Comput. Methods Appl. Mech. Eng. 217, 77 (2012)

  43. X.Q. Wang, Q. Du, J. Math. Biol. 56(3), 347 (2008)

    PubMed  Google Scholar 

  44. J.S. Lowengrub, A. Ratz, A. Voigt, Phys. Rev. E 79, 3 (2009)

    Google Scholar 

  45. D.Y. Shao, W.J. Rappel, H. Levine, Phys. Rev. Lett. 105, 10 (2010)

    Google Scholar 

  46. F. Ziebert, I.S. Aranson, NPJ Comput. Mater. 2, 16019 (2016)

    Google Scholar 

  47. W. Kohn, L.J. Sham,  Phys. Rev. 140(4A), 1133 (1965)

    Google Scholar 

  48. K.R. Elder, N. Provatas, J. Berry, P. Stefanovic, M. Grant, Phys. Rev. B 75, 064107 (2007)

  49. L.-Q. Chen, Y.H. Zhao, Prog. Mater. Sci. 124, 34 (2022)

    Google Scholar 

  50. J.D. van der Waals, Arch. Neerland. Sci. Exact. Nat. 28, 121 (1895)

    Google Scholar 

  51. V.L. Ginzburg, L.D. Landau, Soviet Phys. JETP 20(12), 1064 (1950)

    CAS  Google Scholar 

  52. J.W. Cahn, J.E. Hilliard, J. Chem. Phys. 28(2), 258 (1958)

    CAS  Google Scholar 

  53. S.M. Allen, J.W. Cahn, Acta Metall. 27(6), 1085 (1979)

    CAS  Google Scholar 

  54. T. Yang, B. Wang, J.-M. Hu, L.-Q. Chen, Phys. Rev. Lett. 124, 107601 (2020)

  55. K. Ji, A.J. Clarke, J.T. McKeown, A. Karma, MRS Bull. 49(6) (2024). https://doi.org/10.1557/s43577-024-00717-6

  56. D. Wang, J. Zhu, T. Zhang, Y. Wang, MRS Bull. 49(6) (2024). https://doi.org/10.1557/s43577-024-00721-w

  57. I. Steinbach, M. Uddagiri, H. Salama, M.A. Ali, O. Shchyglo, MRS Bull. 49(6) (2024). https://doi.org/10.1557/s43577-024-00715-8

  58. R. Li, Y. Zhang, N. Moelans, V. Yadav, D. Juul Jensen, MRS Bull. 49(6) (2024). https://doi.org/10.1557/s43577-024-00716-7

  59. E. Martínez-Pañeda, MRS Bull. 49(6) (2024). https://doi.org/10.1557/s43577-024-00715-8

  60. Y. Zhao, T. **n, S. Tang, H. Wang, X. Fang, H. Hou, MRS Bull. 49(6)(2024). https://doi.org/10.1557/s43577-024-00720-x

  61. F. Li, B. Wang, L.-Q. Chen, MRS Bull. 49(6) (2024). https://doi.org/10.1557/s43577-024-00692-y

  62. J.-M. Hu, MRS Bull. 49(6) (2024). https://doi.org/10.1557/s43577-024-00699-5

  63. W.B. Andrews, K. Thornton, MRS Bull. 49(6) 2024. https://doi.org/10.1557/s43577-024-00732-7

  64. Y. Shi, F. Xue, L.-Q. Chen, Europhys. Lett. 120, 4 (2017)

    Google Scholar 

  65. Y. Shi, V. Gopalan, L.-Q. Chen, Phys. Rev. B 107, 20 (2023)

    Google Scholar 

  66. Y.U. Wang, Y.M. **, A.M. Cuitiño, A.G. Khachaturyan, Acta Mater. 49(10), 1847 (2001)

  67. S.Y. Hu, Y.L. Li, L.-Q. Chen, J. Appl. Phys. 94(4), 2542 (2003)

    CAS  Google Scholar 

  68. C. Shen, Y. Wang, Acta Mater. 52(3), 683 (2004)

    CAS  Google Scholar 

  69. L.Y. Liang, L.-Q. Chen, Appl. Phys. Lett. 105, 26 (2014)

    Google Scholar 

  70. S.G. Kim, Acta Mater. 55(13), 4391 (2007)

    CAS  Google Scholar 

  71. B. Echebarria, R. Folch, A. Karma, M. Plapp, Phys. Rev. E 70, 061604 (2004)

  72. A. Karma, W.J. Rappel, Phys. Rev. E 53(4), R3017 (1996)

    CAS  Google Scholar 

  73. J. Zhang, A.F. Chadwick, D.L. Chopp, P.W. Voorhees, NPJ Comput. Mater. 9, 166 (2023)

  74. V. Feyen, N. Moelans, Acta Mater. 256, 119087 (2023)

    CAS  Google Scholar 

  75. M. Plapp, Phys. Rev. E 84, 3 (2011)

    Google Scholar 

  76. A.F. Chadwick, P.W. Voorhees, Acta Mater. 211, 116862 (2021)

    CAS  Google Scholar 

  77. A. Finel, Y. Le Bouar, B. Dabas, B. Appolaire, Y. Yamada, T. Mohri, Phys. Rev. Lett. 121, 025501 (2018)

  78. R. Darabi, E. Azinpour, A. Reis, J.C. de Sa, Appl. Math. Model. 122, 572 (2023)

  79. N. Moelans, Acta Mater. 59(3), 1077 (2011)

    CAS  Google Scholar 

  80. J. Eiken, B. Böttger, I. Steinbach, Phys. Rev. E 73, 6 (2006)

    Google Scholar 

  81. A. Malik, J. Odqvist, L. Höglund, S. Hertzman, J. Ågren, Metall. Mater. Trans. A 48(10), 4914 (2017)

  82. N. Warnken, D. Ma, A. Drevermann, R.C. Reed, S.G. Fries, I. Steinbach, Acta Mater. 57(19), 5862 (2009)

  83. W. Yan, J. Melville, V. Yadav, L. Yang, K. Everett,  M.S. Kesler, A.R. Krause, M.R. Tonks, J.B. Harley, Mater. Des. 222, 111032 (2022)

  84. V. Oommen, K. Shukla, S. Goswami, R. Dingreville, G.E. Karniadakis, NPJ Comput. Mater. 8, 190 (2022)

  85. Y.A. Coutinho, N. Vervliet, L. De Lathauwer, N. Moelans, NPJ Comput. Mater. 6, 2 (2020)

  86. Y.C. Yabansu, P. Steinmetz, J. Hötzer, S.R. Kalidindi, B. Nestler, Acta Mater. 124, 182 (2017)

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Funding

The authors thank X. Cheng for preparing the figure of this editorial. L.-Q.C.’s effort is supported by the US Department of Energy, Office of Science, Basic Energy Sciences, under Award No. DE-SC0020145 as part of the Computational Materials Sciences Program. L.-Q.C. also appreciates the generous support from the Donald W. Hamer Foundation through a Hamer Professorship at Penn State. N.M. acknowledges the support by the HORIZON EUROPE European Research Council (101123107—μTWIN).

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  1. Materials Research Institute and Department of Materials Science and Engineering, The Pennsylvania State University, University Park, USA

    Long-Qing Chen

  2. Department of Materials Engineering, KU Leuven, Leuven, Belgium

    Nele Moelans

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  1. Long-Qing Chen
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L.-Q.C. and N.M. co-wrote the editorial.

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Correspondence to Nele Moelans.

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Chen, LQ., Moelans, N. Phase-field method of materials microstructures and properties. MRS Bulletin 49, 551–555 (2024). https://doi.org/10.1557/s43577-024-00724-7

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