“Interface dislocations in grain boundaries and 2D heterostructures using Smith normal bicrystallography”
Crystal interfaces exist in diverse materials systems in the form of grain and phase boundaries in three-dimensional (3D) polycrystals and as heterointerfaces in two-dimensional (2D) heterostructures. Interfaces significantly influence the mechanical response of a material as observed in phenomena such as superplasticity and creep in polycrystals and the much sought-after electromechanical coupling in 2D materials that is responsible for correlated electron physics. This talk is motivated by the central role interface plasticity plays in diverse crystalline systems. Recognizing interface dislocations as the primary carriers of interface plasticity, we will present a unified mathematical framework to construct interface dislocations in an arbitrary heterointerface. Our framework is driven by the Smith normal form (SNF) for integer matrices which enables us to systematically explore the bicrystallography of interfaces. Analogous to the definition of a bulk dislocation, which relies on the translational symmetry of a 3D lattice, the framework results in a translation symmetry of the interface that is integral to the definition of interface dislocations. Central to our framework are two lattices — coincident site lattice (CSL) and the displacement shift complete lattice (DSCL) — derived from the two lattices that constitute an interface. The CSL and the interface dislocations in 2D heterointerfaces are commonly referred to as the moir´e superlattice and strain solitons, respectively. In 3D GBs, bicrystallography informs that a step in the boundary possibly accompanies an interface dislocation, and together, they are referred to as a disconnection. We will demonstrate the application of SNF bicrystallography to a) enumerate disconnection modes in arbitrary rational GBs, and quantify their energetics, and b) to study interface dislocations in bilayer graphene with a significant twist (> 10◦). The constructive nature of the framework lends itself to an algorithmic implementation based exclusively on integer matrix algebra.
