<p>The quasicontinuum (QC) method has been established as an important tool to bridge atomistic and continuum descriptions. Though numerous variants of the QC method have been developed, till date the QC method has not been applied to ionic crystals to the same extent as it has been applied to simple crystals, such as metals. However, most multi-functional crystalline materials that are indispensable in various scientific and technological applications, have a multilattice structure and consist of ions interacting via the long-range Coulomb potential. Developing and extending the QC method for such ionic crystals is a significant leap in broadening the applicability of the method as this will allow simulating material behavior that is not possible or practical with molecular mechanics due to the enormous computational costs involved.To achieve this, we propose an extension to the QC method to model and simulate ionic crystals on multiple length scales with seamless transition from atomistics to the continuum. In doing so, a new approach for imposing kinematic constraints (on all the basis atoms of a unit cell) is realized in a fully nonlocal QC setting. In addition, a cutoff-based method is used for coarse-graining Coulomb interactions in ionic crystals owing to their charge-ordering property. The proposed method is employed to simulate surface effects of a ferroelectric nanocube such that the region near surfaces are modeled with an atomistic resolution and the interior with a coarse-grained resolution. As a result, the electric polarization profile of the nanocube is numerically determined for the first time in a QC setting.</p>

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A Fully Nonlocal Quasicontinuum Method for Ionic Crystals

  • Vishal Boddu,
  • Denis Davydov,
  • Paul Steinmann

摘要

The quasicontinuum (QC) method has been established as an important tool to bridge atomistic and continuum descriptions. Though numerous variants of the QC method have been developed, till date the QC method has not been applied to ionic crystals to the same extent as it has been applied to simple crystals, such as metals. However, most multi-functional crystalline materials that are indispensable in various scientific and technological applications, have a multilattice structure and consist of ions interacting via the long-range Coulomb potential. Developing and extending the QC method for such ionic crystals is a significant leap in broadening the applicability of the method as this will allow simulating material behavior that is not possible or practical with molecular mechanics due to the enormous computational costs involved.To achieve this, we propose an extension to the QC method to model and simulate ionic crystals on multiple length scales with seamless transition from atomistics to the continuum. In doing so, a new approach for imposing kinematic constraints (on all the basis atoms of a unit cell) is realized in a fully nonlocal QC setting. In addition, a cutoff-based method is used for coarse-graining Coulomb interactions in ionic crystals owing to their charge-ordering property. The proposed method is employed to simulate surface effects of a ferroelectric nanocube such that the region near surfaces are modeled with an atomistic resolution and the interior with a coarse-grained resolution. As a result, the electric polarization profile of the nanocube is numerically determined for the first time in a QC setting.