Multiscale Modeling and Simulation of Ferroelectric Materials

• Applicant: Professor Dr.-Ing. Paul Steinmann
• Subject Area: Mechanics ; Applied Mechanics, Statics and Dynamics
• Term: from 2019 to 2024
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 414986811

• Final Report Year: 2025

Final Report Abstract

Through the research work carried out in the project, the extension to an established atomisticto-continuum multiscale method was formulated facilitating the study of ferroelectric behavior using numerical simulations. It allowed for conducting numerical experiments at much larger length scales than currently possible using purely atomistic simulations. The simulations of ferroelectric materials revealed several interesting insights as mentioned in the following. Investigating the onset of ferroelectricity in free standing ultrathin films, it is found that the out-of-plane ferroelectricity is suppressed in films with thickness 10 or less than 10 unit cells, indicating that there exists a critical thickness for the emergence of ferroelectricity. Earlier was also found that the ultrathin films exhibit ferroelectric hysteresis loop (albeit asymmetrical due to surface relaxations). The study of the use of cutoffbased methods to evaluate long-range Coulomb interactions concluded that relevant physical quantities of ionic systems can be computed accurately under the limitation that the system is charge neutral and crystalline in structure. This finding allowed studying ferroelectric crystals using the Wolf summation method greatly reducing computational complexity in evaluating long-range Coulomb interactions. Finally, the examination of surface and strain effects in ferroelectric barium titanate revealed interesting electric polarization structures aiding in real-world applications. The source code implementing the method is made available allowing researchers to explore, use the source code and further the research in understanding important phenomena in ionic crystals.

Publications

• Cutoff-Based Modeling of Coulomb Interactions for Atomistic-to-Continuum Multiscale Methods. Multiscale Science and Engineering, 1(4), 299-317.
  Boddu, Vishal; Davydov, Denis; Eidel, Bernhard & Steinmann, Paul
  
• DEAL.II-QC: a C++ program library to conduct coarse-grained atomistic simulations using the fully nonlocal quasicontinuum method”. Version v0.1.0. In: (Apr. 2022).
  Vishal Boddu & Denis Davydov
  
• “DEAL.II-QC: a C++ program library to conduct coarse-grained atomistic simulations using the fully nonlocal quasicontinuum method”. Version v0.1.0.
  Vishal Boddu & Denis Davydov