Abstract
In this paper, we derive a continuum variational model for a two-dimensional deformable lattice of atoms interacting with a two-dimensional rigid lattice. The starting point is a discrete atomistic model for the two lattices which are assumed to have slightly different lattice parameters and, possibly, a small relative rotation. This is a prototypical example of a three-dimensional system consisting of a graphene sheet suspended over a substrate. We use a discrete-to-continuum procedure to obtain the continuum model which recovers both qualitatively and quantitatively the behaviour observed in the corresponding discrete model. The continuum model predicts that the deformable lattice develops a network of domain walls characterized by large shearing, stretching and bending deformation that accommodates the misalignment and/or mismatch between the deformable and rigid lattices. Two integer-valued parameters, which can be identified with the components of a Burgers vector, describe the mismatch between the lattices and determine the geometry and the details of the deformation associated with the domain walls.
Original language | English (US) |
---|---|
Article number | 20170612 |
Journal | Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences |
Volume | 474 |
Issue number | 2209 |
DOIs | |
State | Published - 2018 |
Externally published | Yes |
Keywords
- Bilayer graphene
- Discrete-to-continuum modelling
- Domain wall
- Ginzburg–Landau energy
- Heterostructure
- Moiré pattern
ASJC Scopus subject areas
- General Mathematics
- General Engineering
- General Physics and Astronomy