We apply the method to accurately predict shear coupling factors of [0 0 1] symmetric tilt grain boundaries in Cu. Particular attention is paid to the boundaries where the dislocation-based disconnection nucleation model produces incorrect nucleation barriers. We demonstrate that the method can accurately compute the energy barriers and predict the shear coupling factors for the low-temperature regime. In addition, the NEB trajectories reveal interesting phenomena such as the dissociation of a higher energy mode into lower energy modes, and in some cases, shear coupling being mediated by partial disconnections wherein the GB structure temporarily changes to a metastable state before reverting back to its original structure.

The DFK and DD models are motivated by molecular dynamics simulations of friction in heterodeformed BG. In particular, we note that interface dislocations formed during structural relaxation translate in unison when a heterodeformed BG is subjected to shear traction, leading us to the hypothesis that the kinetic properties of interface dislocations determine the friction drag coefficient of the interface. The constitutive law of the DFK model comprises the generalized stacking fault energy of the AB stacking, a scalar displacement drag coefficient, and the elastic properties of graphene, which are all obtained from atomistic simulations. Simulations of the DFK model confirm our hypothesis, since a single choice of the displacement drag coefficient, fitted to the kinetic property of an individual dislocation in an atomistic simulation, predicts interface friction in any heterodeformed BG. In addition, we develop a DD model to derive an analytical expression for the friction coefficient of heterodeformed BG. While the DD model is analytically tractable and numerically more efficient, the drag at dislocation junctions must be explicitly incorporated into the model. By bridging the gap between dislocation kinetics at the microscale and interface friction at the macroscale, the DFK and DD models enable a high-throughput investigation of strain-engineered vdW heterostructures.

To reveal the translational invariance of the heterointerface responsible for the formation of such dislocations, we derive the translational symmetry of the GSFE of a 2D heterostructure using the notions of coincident site lattices (CSLs) and displacement shift complete lattices (DSCLs). The workhorse for this exercise is a recently developed Smith normal form bicrystallography framework. Next, we construct a bicrystallography-informed and frame-invariant Frenkel–Kontorova model, which can predict the formation of strain solitons in arbitrary 2D heterostructures, and apply it to study a heterostrained, large-twist bilayer graphene system. Our mesoscale model is found to produce results consistent with atomistic simulations.

Two sets of numerical experiments are performed to explore the effect of grain boundary anisotropy on the evolution of microstructure features. In the first experiment, we focus on abnormal grain growth and find that grain boundary anisotropy introduces a statistical preference for certain grain orientations. This leads to changes in the overall grain size distribution from the isotropic case. In the second experiment, we examine the texture development and growth of twin grain boundaries at different initial microstructures. We find that both phenomena are more pronounced when the initial microstructure has a dominant fraction of high-angle grain boundaries. Our results suggest effective grain boundary engineering strategies for improving material properties.

We first apply these results to explore coincidence relations in arbitrary phase boundaries, and study interface dislocations. In particular, we demonstrate the framework for a phase boundary formed by a strained hexagonal lattice and a square lattice. As a second application, we show how to enumerate all possible (geometric) disconnection modes in arbitrary rational grain boundaries, including glide and non-glide modes in both STGBs and asymmetric-tilt grain boundaries (ATGBs). The constructive nature of the framework lends itself to an algorithmic implementation based exclusively on integer matrix algebra to construct all interfaces that admit CSLs up to a prescribed size, and determine disconnection modes in grain boundaries. We demonstrate the use of SNF bicrystallography on selected bicrystal misorientation axes/angles in face-centered cubic (fcc), body-centered cubic (bcc), and hexagonal (hex) lattices.

Key features of surface reconstruction include the formationof straight and pyramidal facets of size∼100 nmin width and∼10 nmin height. In addition,discontinuities in facet directions under a single graphene flake distributed over two grains highlightthe strong crystallographic influence on surface reconstruction.In this paper, we present an atomistically informed continuum model of a graphene-metal in-terface in three dimensions. Graphene is modeled as an elastic surface that is in contact with arigid metal substrate. Due to the weak van der Waals interaction between graphene and metal, thekinematics of the model incorporates sliding of graphene. However, since we assume that grapheneis always in contact with the substrate, its normal displacement is mediated by surface diffusion ofmetal atoms. Based on evidence from recent molecular dynamics simulations and experiments, wemodel the interfacial energy to include in-plane elasticity and bending energy of graphene, and aninteraction energy that depends on the orientation of graphene relative to the substrate. We comparethe predictions of our model with surface reconstructions observed during the CVD of graphene onforged thin film palladium polycrystals. As we continue to unravel the atomic scale mechanismsresponsible for surface reconstruction during CVD, we expect the current continuum frameworkand its generalizations will serve to bridge the atomic- and the meso-scales.

We validate the model by demonstrating the Herring angle and the von Neumann–Mullins relations as shown in the figure on the left. In addition, we also generalize the KWC model, which was originally restricted to grain boundary energies of the Read–Shockley type, to incorporate grain boundary energies that respect the bicrystallography of grain boundaries. This allows us to study grain microstructure evolution in a two-dimensional face-centered cubic copper polycrystal with crystal symmetry-invariant grain boundary energy

Most models developed in the last two decades to study recovery, recrystallization and grain growth have employed the phase field method, and do not model the entire problem in a unified framework. More importantly, they do not model the underlying plastic deformation/shape change that accompanies grain boundary motion. Therefore, phenomena such as dynamic grain nucleation and shear induced grain boundary motion, which play an important role during recrystallization, are beyond the reach of these models.

Stain gradient elasticity (SGE), proposed by Mindlin [1964], is a generalization of classical elasticity to include intrinsic length scales through the dependence of the energy density on strain and its gradient. In other words, SGE includes corrections to the energy corresponding to deformation modes that correspond to strain gradients. The above figure shows such deformation modes in a cubic crystal. Despite its potential, SGE has not gained traction in the engineering community primarily due to the following two issues. First, due to the large number of elastic constants, the theory appears to lack the simplicity of classical elasticity. Second, due to the lack of an explicit relationship between the elastic constants and the underlying atomistic structure, multiscale models that involve gradient elasticity have not been developed.

In addition, I have proposed new definitions for the energy density and the heat flux vector. These definitions avoid the ambiguous decomposition of energy among particles present in the original IK framework. Additionally, in our study of the non-uniqueness of the atomistic stress tensor, we derived a discrete analog of the Helmholtz decomposition for symmetric stress tensors. The above figure shows the decomposition of the yy-component of the Cauchy stress in a plate with a hole, subjected to uniaxial loading under plane strain conditions. The discrete decomposition of the atomistic stress tensor has potential applications in identifying various defect structures in amorphous materials. On the other hand, the conventional Helmholtz decomposition, which is extensively used in fluid mechanics to identify various features such as vortices and critical points of fluid flow, can also be used for feature detection. Since the discrete decomposition proposed in this work includes the geometry and discreteness of the crystal, it results in a superior resolution of defects compared to the resolution obtained using conventional Helmholtz decomposition.