Atomistically-informed continuum modeling and isogeometric analysis of 2D materials over holey substrates

This work develops, discretizes, and validates a continuum model of a molybdenum disulfide (MoS$_2$) monolayer interacting with a periodic holey silicon nitride substrate via van der Waals (vdW) forces. The MoS$_2$ layer is modeled as a geometrically nonlinear Kirchhoff-Love shell, and vdW forces are modeled by a Lennard-Jones potential, simplified using approximations for a smooth substrate topography. The material parameters of the shell model are calibrated by comparing small-strain tensile and bending tests with atomistic simulations. This model is efficiently discretized using isogeometric analysis (IGA) for the shell structure and a pseudo-time continuation method for energy minimization. The IGA shell model is validated against fully-atomistic calculations for several benchmark problems with different substrate geometries. The continuum simulations reproduce deflections, strains and curvatures predicted by atomistic simulations, which are known to strongly affect the electronic properties of MoS$_2$, with deviations well below the modeling errors suggested by differences between the widely-used reactive empirical bond order and Stillinger-Weber interatomic potentials. Agreement with atomistic results depends on geometric nonlinearity in some cases, but a simple isotropic St. Venant-Kirchhoff model is found to be sufficient to represent material behavior. We find that the IGA discretization of the continuum model has a much lower computational cost than atomistic simulations, and expect that it will enable efficient design space exploration in strain engineering applications. This is demonstrated by studying the dependence of strain and curvature in MoS$_2$ over a holey substrate as a function of the hole spacing on scales inaccessible to atomistic calculations. The results show an unexpected qualitative change in the deformation pattern below a critical hole separation

A KIM-compliant potfit for fitting sloppy interatomic potentials : application to the EDIP model for silicon

Fitted interatomic potentials are widely used in atomistic simulations thanks to their ability to compute the energy and forces on atoms quickly. However, the simulation results crucially depend on the quality of the potential being used. Force matching is a method aimed at constructing reliable and transferable interatomic potentials by matching the forces computed by the potential as closely as possible, with those obtained from first principles calculations. The potfit program is an implementation of the force-matching method that optimizes the potential parameters using a global minimization algorithm followed by a local minimization polish. We extended potfit in two ways. First, we adapted the code to be compliant with the KIM Application Programming Interface (API) standard (part of the Knowledgebase of Interatomic Models Project). This makes it possible to use potfit to fit many KIM potential models, not just those prebuilt into the potfit code. Second, we incorporated the geodesic Levenberg–Marquardt (LM) minimization algorithm into potfit as a new local minimization algorithm. The extended potfit was tested by generating a training set using the KIM Environment-Dependent Interatomic Potential (EDIP) model for silicon and using potfit to recover the potential parameters from different initial guesses. The results show that EDIP is a “sloppy model” in the sense that its predictions are insensitive to some of its parameters, which makes fitting more difficult. We find that the geodesic LM algorithm is particularly efficient for this case. The extended potfit code is the first step in developing a KIM-based fitting framework for interatomic potentials for bulk and two-dimensional materials. The code is available for download via https://www.potfit.net

Atomistically-informed continuum modeling and isogeometric analysis of 2D materials over holey substrates

This work develops, discretizes, and validates a continuum model of a molybdenum disulfide (MoS2) monolayer interacting with a periodic holey silicon nitride (Si3N4) substrate via van der Waals (vdW) forces. The MoS2 layer is modeled as a geometrically nonlinear Kirchhoff–Love shell, and vdW forces are modeled by a Lennard-Jones (LJ) potential, simplified using approximations for a smooth substrate topography. Both the shell model and LJ interactions include novel extensions informed by close comparison with fully-atomistic calculations. The material parameters of the shell model are calibrated by comparing small-strain tensile and bending tests with atomistic simulations. This model is efficiently discretized using isogeometric analysis (IGA) for the shell structure and a pseudo-time continuation method for energy minimization. The IGA shell model is validated against fully-atomistic calculations for several benchmark problems with different substrate geometries. Agreement with atomistic results depends on geometric nonlinearity in some cases, but a simple isotropic St.Venant–Kirchhoff model is found to be sufficient to represent material behavior. We find that the IGA discretization of the continuum model has a much lower computational cost than atomistic simulations, and expect that it will enable efficient design space exploration in strain engineering applications. This is demonstrated by studying the dependence of strain and curvature in MoS2 over a holey substrate as a function of the hole spacing on scales inaccessible to atomistic calculations. The results show an unexpected qualitative change in the deformation pattern below a critical hole separation

ColabFit Exchange: open-access datasets for data-driven interatomic potentials

Data-driven (DD) interatomic potentials (IPs) trained on large collections of first principles calculations are rapidly becoming essential tools in the fields of computational materials science and chemistry for performing atomic-scale simulations. Despite this, apart from a few notable exceptions, there is a distinct lack of well-organized, public datasets in common formats available for use with IP development. This deficiency precludes the research community from implementing widespread benchmarking, which is essential for gaining insight into model performance and transferability, while also limiting the development of more general, or even universal, IPs. To address this issue, we introduce the ColabFit Exchange, the first database providing open access to a large collection of systematically organized datasets from multiple domains that is especially designed for IP development. The ColabFit Exchange is publicly available at \url{https://colabfit.org/}, providing a web-based interface for exploring, downloading, and contributing datasets. Composed of data collected from the literature or provided by community researchers, the ColabFit Exchange consists of 106 datasets spanning nearly 70,000 unique chemistries, and is intended to continuously grow. In addition to outlining the software framework used for constructing and accessing the ColabFit Exchange, we also provide analyses of data, quantifying the diversity and proposing metrics for assessing the relative quality and atomic environment coverage of different datasets. Finally, we demonstrate an end-to-end IP development pipeline, utilizing datasets from the ColabFit Exchange, fitting tools from the KLIFF software package, and validation tests provided by the OpenKIM framework

Atomic and electronic reconstruction at van der Waals interface in twisted bilayer graphene

Control of the interlayer twist angle in two-dimensional (2D) van der Waals (vdW) heterostructures enables one to engineer a quasiperiodic moir\'e superlattice of tunable length scale. In twisted bilayer graphene (TBG), the simple moir\'e superlattice band description suggests that the electronic band width can be tuned to be comparable to the vdW interlayer interaction at a 'magic angle', exhibiting strongly correlated behavior. However, the vdW interlayer interaction can also cause significant structural reconstruction at the interface by favoring interlayer commensurability, which competes with the intralayer lattice distortion. Here we report the atomic scale reconstruction in TBG and its effect on the electronic structure. We find a gradual transition from incommensurate moir\'e structure to an array of commensurate domain structures as we decrease the twist angle across the characteristic crossover angle, $\theta_c$ ~1\deg. In the twist regime smaller than $\theta_c$ where the atomic and electronic reconstruction become significant, a simple moir\'e band description breaks down. Upon applying a transverse electric field, we observe electronic transport along the network of one-dimensional (1D) topological channels that surround the alternating triangular gapped domains, providing a new pathway to engineer the system with continuous tunability

Hybrid continuum mechanics and atomistic methods for simulating materials deformation and failure

Many aspects of materials deformation and failure are controlled by atomic-scale phenomena that can be explored using molecular statics and molecular dynamics simulations. However, many of these phenomena involve processes on multiple length scales with the result that full molecular statics/molecular dynamics simulations of the entire system are too large to be tractable. In this review, we discuss hybrid models that perform molecular statics/molecular dynamics simulations "without all the atoms," aimed at retaining atomistic detail at a fraction of the computational cost. These methods couple a fully atomistic model in critical regions to regions described by less-expensive continuum methods where they can provide an adequate representation of the important physics. We give an overview of the challenges such models present, with a focus on recent work to address issues of dynamics and finite (non-zero) temperature