[SY-I1] Coarse-grained, three-dimensional modeling of defects at low-angle grain boundaries with the amplitude expansion of the phase field crystal model
The Phase-Field Crystal (PFC) approach describes the dynamics of the local atomic probability density on atomic length scales and diffusive time scales [1]. It generally requires a fine spatial discretization, which limits the application of the method to small systems. The so-called amplitude expansion of the PFC model (APFC) is known to solve this issue, as it accounts for the evolution of the slowly varying amplitudes of the atomic probability density [2]. However, a limited number of parameters are present in the model and this poses some restrictions in the quantitative description of material properties. Moreover, the application of this model to three-dimensional systems has not been extensively explored.
We illustrate the modeling of defects at low-angle grain boundaries (GBs) forming between tilted crystals by means of the APFC model in two and three dimensions. This is achieved through a Finite Element Method with advanced numerical features such as adaptive mesh refinement exploiting the features of the APFC approach. Moreover, an extension of the model to control the energy of defects and GBs is proposed [3]. The possibility to describe dislocation networks at planar and spherical grain boundaries is illustrated for different lattice symmetries, namely triangular/honeycomb in 2D as well as body-centered cubic and face-centered cubic in 3D. The dynamics of spherical grain boundaries is also addressed in detail. In particular, the anisotropic shrinkage of spherical grain is addressed, revealing general qualitative features independent of the specific rotational axis and crystal symmetry [4] in agreement with recent atomistic calculations.
[1] K. R. Elder, M. Katakowski, M. Haataja, and M. Grant, Phys. Rev. Lett. 88, 245701 (2002)
[2] N. Goldenfeld, B. P. Athreya, and J. A. Dantzip, Phys. Rev. E 72, 020601 (2005)
[3] M. Salvalaglio, R. Backofen, A. Voigt, K. R. Elder, Phys. Rev. E 78, 184104 (2017)
[4] M. Salvalaglio, R. Backofen, K. R. Elder, A. Voigt, arXiv:1803.03233
We illustrate the modeling of defects at low-angle grain boundaries (GBs) forming between tilted crystals by means of the APFC model in two and three dimensions. This is achieved through a Finite Element Method with advanced numerical features such as adaptive mesh refinement exploiting the features of the APFC approach. Moreover, an extension of the model to control the energy of defects and GBs is proposed [3]. The possibility to describe dislocation networks at planar and spherical grain boundaries is illustrated for different lattice symmetries, namely triangular/honeycomb in 2D as well as body-centered cubic and face-centered cubic in 3D. The dynamics of spherical grain boundaries is also addressed in detail. In particular, the anisotropic shrinkage of spherical grain is addressed, revealing general qualitative features independent of the specific rotational axis and crystal symmetry [4] in agreement with recent atomistic calculations.
[1] K. R. Elder, M. Katakowski, M. Haataja, and M. Grant, Phys. Rev. Lett. 88, 245701 (2002)
[2] N. Goldenfeld, B. P. Athreya, and J. A. Dantzip, Phys. Rev. E 72, 020601 (2005)
[3] M. Salvalaglio, R. Backofen, A. Voigt, K. R. Elder, Phys. Rev. E 78, 184104 (2017)
[4] M. Salvalaglio, R. Backofen, K. R. Elder, A. Voigt, arXiv:1803.03233