The local strain distribution in bilayer materials: A multiscale study
Recent studies show that small geometric changes can result in dramatic changes in physical properties and need to be carefully evaluated. In this regard, We calculate the distribution of local strains in bilayer graphene and two configurations of hexagonal BN (h-BN), which is different from previous studies that focus on homogeneous strains in such materials. We consider a mismatch of one lattice parameter and calculate how strain distributes without external stresses. This problem is equivalent to finding the core structure of a type of dislocation profuse in structural materials. The strain distribution is transformed into the core distribution of a dislocation, which is calculated by a new formulation proposed by us. The new formulation finds new lower-energy states for the 2D materials. Our results show the strain of one-lattice mismatch in bilayer graphene forms two Lorentz peaks with half widths of $117b-120b$ (edge component) and $67b-80b$ (screw component), where $b$ is the lattice constant. The case for bilayer h-BN is slightly more complicated but the results are also presented. Our analytic solutions, which is based on the new formulation with more freedom in structural relaxation, provide the basis for the next-step study of their electronic properties.