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Continuum scaling laws often break down when materials approach atomic length scales, reflecting changes in their underlying physics and the opportunities to access unconventional properties. These continuum limits are evident in two-dimensional materials, where there is no consensus on their bending stiffnesses or how they scale with thickness. Through combined computational and electron microscopy experiments, we measure the bending stiffness of graphene, obtaining 1.2–1.7 eV for a monolayer. Moreover, we find that the bending stiffness of few-layer graphene decreases sharply as a function of bending angle, tuning by almost 400% for trilayer graphene. This softening results from shear, slip and the onset of superlubricity between the atomic layers and corresponds with a gradual change in scaling power from cubic to linear. Our results provide a unified model for bending in two-dimensional materials and show that their multilayers can be orders of magnitude softer than previously thought, among the most flexible electronic materials currently known. The bending stiffness of few-layer graphene is shown to decrease significantly with the bending angle due to shear and slip between the atomic layers, which culminate in superlubric behaviour as the bending angle further increases.

Electrolytes play a critical role in designing next-generation battery systems, by allowing efficient ion transfer, preventing charge transfer, and stabilizing electrode-electrolyte interfaces. In this work, we develop a differentiable geometric deep learning (GDL) model for chemical mixtures, DiffMix, which is applied in guiding robotic experimentation and optimization towards fast-charging battery electrolytes. In particular, we extend mixture thermodynamic and transport laws by creating GDL-learnable physical coefficients. We evaluate our model with mixture thermodynamics and ion transport properties, where we show improved prediction accuracy and model robustness of DiffMix than its purely data-driven variants. Furthermore, with a robotic experimentation setup, Clio, we improve ionic conductivity of electrolytes by over 18.8% within 10 experimental steps, via differentiable optimization built on DiffMix gradients. By combining GDL, mixture physics laws, and robotic experimentation, DiffMix expands the predictive modeling methods for chemical mixtures and enables efficient optimization in large chemical spaces. Electrolytes play a critical role in designing next generation battery systems. Here, the authors developed a differentiable geometric deep-learning model for chemical mixtures and applied it in guiding a robot to design fast-charging battery electrolytes.

An amendment to this paper has been published and can be accessed via a link at the top of the paper.An amendment to this paper has been published and can be accessed via a link at the top of the paper.

Since its monolayer exfoliation in 2004, graphene has been the focus of intense study revealing a multitude of exciting properties that allow for studying fundamental physics and new engineering devices. In particular, monolayer graphene has unique mechanical properties such as high in-plane strength but very low flexural rigidity. This causes in-plane strains to be accommodated through out-of-plane deformation enabling engineering complex 3D deformation of graphene-based on patterned in-plane strain. In addition, monolayer graphene only weakly bonds with itself enabling non-lattice stacking between two graphene layers or graphene and an arbitrary crystalline surface. Non-lattice stacking has created a whole new sub-field called moir ́e engineering, which takes advantage of the larger scale periodicity caused by two periodic interfaces. An exciting possibility of moir ́e engineering is to enable new physics such as the unconventional superconductivity found in twisted bilayer graphene. Common between these are dislocations. Dislocations can be used to a pattern in plane strain and describe the mismatch between two lattices. Dislocations are topological defects that add an extra half-plane of atoms causing a large strain at the core of the dislocation. Dislocations have been studied for both their role in out-of-plane deformation in mono-layer graphene and periodicity in moir ́e superlattices. However, the effect of out-of-plane deformation and weak interlayer bonding on the mechanics of dislocations has not been fully studied. We focus on how dislocation mechanics appear in grain boundary migration and moir ́e patterns. For grain boundary migration, while the structure and energy of dislocations in single layer graphene have been studied, grain boundary dislocations, which nucleate when grain boundaries form kinks and disconnections, are important to understand structure evolution during annealing. However, it is uncertain how these dislocations are impacted by the out-of-plane deformation observed at edge dislocations in graphene. Or, while it has long been suggested that moir ́e patterns are arrays of inter-layer dislocations, there has not been a rigorous connection to dislocation topology nor a formal presentation of a linear elastic theory of dislocation between two 2D materials. In this thesis, we address these two dislocations by defining their topology and developing continuum dislocation models to isolate the mechanics of dislocations in graphene systems from atomistic calculations. This thesis focuses on understanding the mechanics of displacement shift complete (DSC) dislocations and interlayer dislocations. DSC dislocations are dislocations that govern the migration of grain boundaries in graphene. The mechanics of DSC dislocations are studied with both atomistic and continuum models to understand the thermodynamic and kinetic barriers of grain boundary migration. The DSC dislocation model is used to show how the grain boundary structure can be controlled through external shears of graphene. The study of DSC dislocations includes how DSC dislocations and grain boundaries can be used to control 3D deformation in graphene. The control of 3D deformation using topological defects is expanded at the end of the thesis by exploring the computational techniques that would enable the precise control of topological defects in graphene. Interlayer dislocations are dislocations between graphene and another crystalline material. The mechanics of interlayer dislocations are studied using twist and stretch moiré superlattices of bilayer graphene. The topology of interlayer dislocations is presented for 1D and 2D networks of dislocations. Continuum mechanics models utilize the dislocation topology to find the structure and energetics of dislocations; these are validated with atomistic simulations. The continuum dislocation model is applied to understand the structural relaxation of dislocations in twist moiré superlattices that give rise to a structural transition at small rotation angles. Furthermore, the line and junction energies of arbitrary sense interlayer dislocations is presented. The energetics show that screw interlayer dislocations and their junctions are more favorable than edge interlayer dislocations. The mechanics of interlayer dislocations and in-plane dislocations–including DSC dislocations–are combined to develop a moiré engineering technique. The moiré engineering technique is based on how the long-range strain field of in-plane dislocations alters the interlayer dislocation network revealed in the moiré pattern. The moiré engineering technique is developed with mechanistic atomic scale models that are brought to the nanoscale with bond convolution simulations to show the moiré patterns of topological defects in the graphene lattice. The moiré engineering technique is applied to in-operando scanning tunneling microscopy to reveal the atomic structure of grain boundaries thus enabling real-time analysis and decision making regarding growth conditions. In conclusion, this thesis focuses on the understanding of dislocation mechanics in graphene. Two dislocations, the DSC dislocation formed during grain boundary migration of monolayer graphene and the interlayer dislocation present between graphene and another crystalline material, are studied. The mechanics are studied by developing continuum models that find the structure and energy of each dislocation by comparing them to atomistic simulations. Finally, the dislocations mechanics are utilized to develop a moiré engineering technique that enables probing the dislocation structure of graphene grain boundaries.

Central to interatomic potential efficiency is the radial envelope function that enables linear scaling with computational cost by defining a local neighborhood of atoms. This has enabled MLIPs to revolutionize materials science over the past decade by providing DFT accuracy with linear scaling computational cost in molecular dynamics workflows. However, MLIPs still have a relatively high computational cost compared to empirical interatomic potentials, preventing them from transforming molecular dynamics workflows. A central issue is that MLIPs use relatively large cutoff radii, converging to 6A over the last few years. The large cutoffs prioritize accuracy of any material over efficiency in any particular region of phase space, capturing dispersion effects and low density materials at the expense of increased computational cost in higher density materials. Past work has aimed to address this with KNN graph sparsification, which, while significantly reducing cost, has the drawback of breaking energy conservation. In this work, we propose higher-order envelope functions that prune local atomic neighborhoods through physically inspired geometric functions to provide the memory and efficiency benefits of KNN graph sparsification while eliminating non-conservative energy dynamics. Through numerical experiments on solids and liquids with 5-8A cutoffs, we show that triplet envelope functions complement radial envelope functions by doubling training and inference speed, tripling memory efficiency, and increasing simulation stability while not impacting accuracy or data efficiency for the most common 6A cutoff. Moreover, experiments with 8A radial cutoffs show triplet envelope functions create a pathway to larger cutoff radii for efficiently and accurately modeling open structures with large interatomic distances, showing a promising new direction for engineering MLIP efficiency.

Machine learning interatomic potentials (MLIPs) are promising surrogates for quantum mechanics evaluations in ab-initio molecular dynamics simulations due to their ability to reproduce the energy and force landscape within chemical accuracy at four orders of magnitude less cost. While developing uncertainty quantification (UQ) tools for MLIPs is critical to build production MLIP datasets using active learning, only limited progress has been made and the most robust method, ensembling, still shows low correlation between high error and high uncertainty predictions. Here we develop a rigorous method rooted in statistics for determining an error cutoff that distinguishes regions of high and low UQ performance. The statistical cutoff illuminates that a main cause of the poor UQ performance is due to the machine learning model already describing the entire dataset and not having any datapoints with error greater than the statistical error distribution. Second, we extend the statistical analysis to create an interpretable connection between the error and uncertainty distributions to predict an uncertainty cutoff separating high and low errors. We showcase the statistical cutoff in active learning benchmarks on two datasets of varying chemical complexity for three common UQ methods: ensembling, sparse Gaussian processes, and latent distance metrics and compare them to the true error and random sampling, showing that the statistical cutoff is generalizable to a variety of different UQ methods and protocols and performs similarly to using the true error. Importantly, we conclude that utilizing this uncertainty cutoff enables using significantly lower cost uncertainty quantification tools such as sparse gaussian processes and latent distances compared to ensembling approaches for generating MLIP datasets at a fraction of the cost.

We develop a continuum dislocation description of twist and stretch moire superlattices in 2D material bilayers. The continuum formulation is based on the topological constraints introduced by the periodic dislocation network associated with the moire structure. The approach is based on solving analytically for the structural distortion and displacement fields that satisfy the topological constraints, and which minimize the total energy. The total energy is described by both the strain energy of each individual distorted layer, and a Peierls-Nabarro like interfacial contribution arising from stacking disregistry. The dislocation core emerges naturally within the formalism as a result of the competition between the two contributions. The approach presented here captures the structure and energetics of twist and stretch moire superlattices of dislocations with arbitrary direction and character, without assuming an analytical solution a priori, with no adjustable parameters, while accounting naturally for dislocation-dislocation image interactions. In comparisons to atomistic simulations using classical potentials, the maximum structure deviation is 6%, while the maximum line energy deviation is 0.019 eV/Angstrom. Several applications of our model are shown, including predicting the variation of structure with twist angle, and describing dislocation line tension and junction energies.

Electrolytes mediate interactions between the cathode and anode and determine performance characteristics of batteries. Mixtures of multiple solvents are often used in electrolytes to achieve desired properties, such as viscosity, dielectric constant, boiling point, and melting point. Conventionally, multi-component electrolyte properties are approximated with linear mixing, but in practice, significant deviations are observed. Excess quantities can provide insights into the molecular behavior of the mixture and could form the basis for designing high-performance electrolytes. Here we investigate the excess density of commonly used Li-ion battery solvents such as cyclic carbonates, linear carbonates, ethers, and nitriles with molecular dynamics simulations. We additionally investigate electrolytes consisting of these solvents and a salt. The results smoothly vary with mole percent and are fit to permutation-invariant Redlich-Kister polynomials. Mixtures of similar solvents, such as cyclic-cyclic carbonate mixtures, tend to have excess properties that are lower in magnitude compared to mixtures of dissimilar substances, such as carbonate-nitrile mixtures. We perform experimental testing using our robotic test stand, Clio, to provide validation to the observed simulation trends. We quantify the structure similarity using SOAP fingerprints to create a descriptor for excess density, enabling the design of electrolyte properties. To a first approximation, this will allow us to estimate the deviation of a mixture from ideal behavior based solely upon the structural dissimilarity of the components.

Interlayer rotation angle couples strongly to the electronic states of twisted van der Waals layers. However, not every angle is energetically favorable. Recent experiments on rotation-tunable electronics reveal the existence of a discrete set of angles at which the rotation-tunable electronics assume the most stable configurations. Nevertheless, a quantitative map for locating these intrinsically preferred twist angles in twisted bilayer system has not been available, posing challenges for the on-demand design of twisted electronics that are intrinsically stable at desired twist angles. Here we reveal a simple mapping between intrinsically preferred twist angles and geometry of the twisted bilayer system, in the form of geometric scaling laws for a wide range of intrinsically preferred twist angles as a function of only geometric parameters of the rotating flake on a supporting layer. We reveal these scaling laws for triangular and hexagonal flakes since they frequently appear in chemical vapor deposition growth. We also present a general method for handling arbitrary flake geometry. Such dimensionless scaling laws possess universality for all kinds of two-dimensional material bilayer systems, providing abundant opportunities for the on-demand design of intrinsic \"twistronics\". For example, the set of increasing magic-sizes that intrinsically prefers zero-approaching sequence of multiple magic-angles in bilayer graphene system can be revealed.

Safe, all-solid-state lithium metal batteries enable high energy density applications, but suffer from instabilities during operation that lead to rough interfaces between the metal and electrolyte and subsequently cause void formation and dendrite growth that degrades performance and safety. Inspired by the morphogenetic control of thin lamina such as tree leaves that robustly grow into flat shapes -- we propose a range of approaches to control lithium metal stripping and plating. To guide discovery of materials that will implement these feedback mechanisms, we develop a reduced order model that captures couplings between mechanics, interface growth, temperature, and electrochemical variables. We find that long-range feedback is required to achieve true interface stability, while approaches based on local feedback always eventually grow into rough interfaces. All together, our study provides the beginning of a practical framework for analyzing and designing stable electrochemical interfaces in terms of the mechanical properties and the physical chemistry that underlie their dynamics.