Author:
Steinbach Ingo,Salama Hesham
Abstract
AbstractThe chapter introduces the meaning of Phase Field from the aspect of thermodynamics on the one hand and numerics of moving boundary solutions on the other hand. A moving boundary solution here means the evolution, motion, of grain boundaries, phase boundaries or surfaces in multicrystalline materials as described by a set of partial differential equations. The thermodynamic aspect relates to the concept of an order parameter, identifying a phase, in thermodynamics in general. Here the interfaces, grain- or phase boundaries and surfaces, are described by a gradient contribution in the free energy functional, the gradient of the phase field when the order changes between different grains. The history of both approaches is reviewed shortly considering their pros and cons.
Publisher
Springer Nature Switzerland
Reference24 articles.
1. G. Caginalp, E. Socolovsky, Phase field computations of single-needle crystals, crystal growth, and motion by mean curvature. SIAM J. Sci. Comput. 15 (1994). https://doi.org/10.1137/0915007
2. G. Caginalp, W. Xie, Mathematical models of phase boundaries in alloys: phase field and Sharp interface, in Motion by Mean Curvature and Related Topics: Proceedings of the International Conference held at Trento, Italy, 20–24, 1992, ed. by G. Buttazzo, A. Visintin. (De Gruyter, 2011), pp. 43–62. https://doi.org/10.1515/9783110870473.43
3. J.E. Cahn, J.E. Hilliard, Free energy of a nonuniform system. I. Interfacial free energy. J. Chem. Phys. 28, 258–267 (1958)
4. L.-Q. Chen, Y. Zhao, From classical thermodynamics to phase-field method. Progress Mater. Sci. 124, 100868 (2022). ISSN:0079-6425. https://doi.org/10.1016/j.pmatsci.2021.100868
5. F. Gibou, R. Fedkiw, S. Osher, A review of level-set methods and some recent applications. J. Comput. Phys. 353, 82–109 (2018). ISSN:0021-9991. https://doi.org/10.1016/j.jcp.2017.10.006