Maik Punke: A hybrid multiscale phase-field crystal, amplitude phase-field crystal approach - elastic properties and numerical studies

Vortragender/Speaker: Maik Punke (Institute of Scientific Computing)
Ansprechpartner/Contact: Dr. Simon Praetorius

Titel/Title:
A hybrid multiscale phase-field crystal, amplitude phase-field crystal approach - elastic properties and numerical studies

Zusammenfassung/Abstract:
The modeling of crystalline materials requires the resolution of microscopic details on large length and time scales to guarantee the description of lattice-dependent features as well as the dynamics of solidification. The so-called phase-field crystal (PFC) model emerged as a prominent framework to model crystalline systems. Indeed, it describes crystalline materials through a continuous order parameter related to the atomic number density and its dynamic at relatively large (diffusive) time scales. The amplitude expansion of the PFC model (APFC) was developed to further overcome the length scale limitations in the PFC framework. Herein, the continuous density in PFC models is replaced by the amplitudes of the minimum set of Fourier modes (wave vectors) for a given crystal symmetry.
We propose a multiscale model with local PFC accuracy and APFC length scale limitations. In our hybrid multiscale approach, the PFC and APFC models are coupled through Dirichlet conditions by penalty terms within the spectral framework. We showcase the model capabilities via selected numerical investigations which focus on the energetic and elastic properties of two-dimensional crystals. Furthermore, runtime and accuracy comparisons with the standard PFC and APFC models are made.