Understanding Defects in Amorphous Silicon with Million-Atom Simulations and Machine Learning.

The structure of amorphous silicon (a-Si) is widely thought of as a fourfold-connected random network, and yet it is defective atoms, with fewer or more than four bonds, that make it particularly interesting. Despite many attempts to explain such "dangling-bond" and "floating-bond" defects, respectively, a unified understanding is still missing. Here, we use advanced computational chemistry methods to reveal the complex structural and energetic landscape of defects in a-Si. We study an ultra-large-scale, quantum-accurate structural model containing a million atoms, and thousands of individual defects, allowing reliable defect-related statistics to be obtained. We combine structural descriptors and machine-learned atomic energies to develop a classification of the different types of defects in a-Si. The results suggest a revision of the established floating-bond model by showing that fivefold-bonded atoms in a-Si exhibit a wide range of local environments-analogous to fivefold centers in coordination chemistry. Furthermore, it is shown that fivefold (but not threefold) coordination defects tend to cluster together. Our study provides new insights into one of the most widely studied amorphous solids, and has general implications for understanding defects in disordered materials beyond silicon alone.

Modelling atomic and nanoscale structure in the silicon-oxygen system through active machine learning.

Silicon-oxygen compounds are among the most important ones in the natural sciences, occurring as building blocks in minerals and being used in semiconductors and catalysis. Beyond the well-known silicon dioxide, there are phases with different stoichiometric composition and nanostructured composites. One of the key challenges in understanding the Si-O system is therefore to accurately account for its nanoscale heterogeneity beyond the length scale of individual atoms. Here we show that a unified computational description of the full Si-O system is indeed possible, based on atomistic machine learning coupled to an active-learning workflow. We showcase applications to very-high-pressure silica, to surfaces and aerogels, and to the structure of amorphous silicon monoxide. In a wider context, our work illustrates how structural complexity in functional materials beyond the atomic and few-nanometre length scales can be captured with active machine learning.

High-dimensional order parameters and neural network classifiers applied to amorphous ices.

Amorphous ice phases are key constituents of water's complex structural landscape. This study investigates the polyamorphic nature of water, focusing on the complexities within low-density amorphous ice (LDA), high-density amorphous ice, and the recently discovered medium-density amorphous ice (MDA). We use rotationally invariant, high-dimensional order parameters to capture a wide spectrum of local symmetries for the characterization of local oxygen environments. We train a neural network to classify these local environments and investigate the distinctiveness of MDA within the structural landscape of amorphous ice. Our results highlight the difficulty in accurately differentiating MDA from LDA due to structural similarities. Beyond water, our methodology can be applied to investigate the structural properties and phases of disordered materials.

Geometrically frustrated interactions drive structural complexity in amorphous calcium carbonate.

Amorphous calcium carbonate is an important precursor for biomineralization in marine organisms. Key outstanding problems include understanding the structure of amorphous calcium carbonate and rationalizing its metastability as an amorphous phase. Here we report high-quality atomistic models of amorphous calcium carbonate generated using state-of-the-art interatomic potentials to help guide fits to X-ray total scattering data. Exploiting a recently developed inversion approach, we extract from these models the effective Ca⋯Ca interaction potential governing the structure. This potential contains minima at two competing distances, corresponding to the two different ways that carbonate ions bridge Ca2+-ion pairs. We reveal an unexpected mapping to the Lennard-Jones-Gauss model normally studied in the context of computational soft matter. The empirical model parameters for amorphous calcium carbonate take values known to promote structural complexity. We thus show that both the complex structure and its resilience to crystallization are actually encoded in the geometrically frustrated effective interactions between Ca2+ ions.

Robustness of Local Predictions in Atomistic Machine Learning Models.

Machine learning (ML) models for molecules and materials commonly rely on a decomposition of the global target quantity into local, atom-centered contributions. This approach is convenient from a computational perspective, enabling large-scale ML-driven simulations with a linear-scaling cost and also allows for the identification and posthoc interpretation of contributions from individual chemical environments and motifs to complicated macroscopic properties. However, even though practical justifications exist for the local decomposition, only the global quantity is rigorously defined. Thus, when the atom-centered contributions are used, their sensitivity to the training strategy or the model architecture should be carefully considered. To this end, we introduce a quantitative metric, which we call the local prediction rigidity (LPR), that allows one to assess how robust the locally decomposed predictions of ML models are. We investigate the dependence of the LPR on the aspects of model training, particularly the composition of training data set, for a range of different problems from simple toy models to real chemical systems. We present strategies to systematically enhance the LPR, which can be used to improve the robustness, interpretability, and transferability of atomistic ML models.

Surface effects on the crystallization kinetics of amorphous antimony.

Elemental antimony (Sb) is regarded as a promising candidate to improve the programming consistency and cycling endurance of phase-change memory and neuro-inspired computing devices. Although bulk amorphous Sb crystallizes spontaneously, the stability of the amorphous form can be greatly increased by reducing the thickness of thin films down to several nanometers, either with or without capping layers. Computational and experimental studies have explained the depressed crystallization kinetics caused by capping and interfacial confinement; however, it is unclear why amorphous Sb thin films remain stable even in the absence of capping layers. In this work, we carry out thorough ab initio molecular dynamics (AIMD) simulations to investigate the effects of free surfaces on the crystallization kinetics of amorphous Sb. We reveal a stark contrast in the crystallization behavior between bulk and surface models at 450 K, which stems from deviations from the bulk structural features in the regions approaching the surfaces. The presence of free surfaces intrinsically tends to create a sub-nanometer region where crystallization is suppressed, which impedes the incubation process and thus constrains the nucleation in two dimensions, stabilizing the amorphous phase in thin-film Sb-based memory devices.

Coarse-grained versus fully atomistic machine learning for zeolitic imidazolate frameworks.

Zeolitic imidazolate frameworks are widely thought of as being analogous to inorganic AB2 phases. We test the validity of this assumption by comparing simplified and fully atomistic machine-learning models for local environments in ZIFs. Our work addresses the central question to what extent chemical information can be "coarse-grained" in hybrid framework materials.

Cross-platform hyperparameter optimization for machine learning interatomic potentials.

Machine-learning (ML)-based interatomic potentials are increasingly popular in material modeling, enabling highly accurate simulations with thousands and millions of atoms. However, the performance of machine-learned potentials depends strongly on the choice of hyperparameters-that is, of those parameters that are set before the model encounters data. This problem is particularly acute where hyperparameters have no intuitive physical interpretation and where the corresponding optimization space is large. Here, we describe an openly available Python package that facilitates hyperparameter optimization across different ML potential fitting frameworks. We discuss methodological aspects relating to the optimization itself and to the selection of validation data, and we show example applications. We expect this package to become part of a wider computational framework to speed up the mainstream adaptation of ML potentials in the physical sciences.

Machine-learned acceleration for molecular dynamics in CASTEP.

Machine learning (ML) methods are of rapidly growing interest for materials modeling, and yet, the use of ML interatomic potentials for new systems is often more demanding than that of established density-functional theory (DFT) packages. Here, we describe computational methodology to combine the CASTEP first-principles simulation software with the on-the-fly fitting and evaluation of ML interatomic potential models. Our approach is based on regular checking against DFT reference data, which provides a direct measure of the accuracy of the evolving ML model. We discuss the general framework and the specific solutions implemented, and we present an example application to high-temperature molecular-dynamics simulations of carbon nanostructures. The code is freely available for academic research.

Spin Glass Behavior in Amorphous Cr2 Ge2 Te6 Phase-Change Alloy.

The layered crystal structure of Cr2 Ge2 Te6 shows ferromagnetic ordering at the two-dimensional limit, which holds promise for spintronic applications. However, external voltage pulses can trigger amorphization of the material in nanoscale electronic devices, and it is unclear whether the loss of structural ordering leads to a change in magnetic properties. Here, it is demonstrated that Cr2 Ge2 Te6 preserves the spin-polarized nature in the amorphous phase, but undergoes a magnetic transition to a spin glass state below 20 K. Quantum-mechanical computations reveal the microscopic origin of this transition in spin configuration: it is due to strong distortions of the CrTeCr bonds, connecting chromium-centered octahedra, and to the overall increase in disorder upon amorphization. The tunable magnetic properties of Cr2 Ge2 Te6 can be exploited for multifunctional, magnetic phase-change devices that switch between crystalline and amorphous states.

Simulations in the era of exascale computing.

Exascale computers - supercomputers that can perform 1018 floating point operations per second - started coming online in 2022: in the United States, Frontier launched as the first public exascale supercomputer and Aurora is due to open soon; OceanLight and Tianhe-3 are operational in China; and JUPITER is due to launch in 2023 in Europe. Supercomputers offer unprecedented opportunities for modelling complex materials. In this Viewpoint, five researchers working on different types of materials discuss the most promising directions in computational materials science.

How to validate machine-learned interatomic potentials.

Machine learning (ML) approaches enable large-scale atomistic simulations with near-quantum-mechanical accuracy. With the growing availability of these methods, there arises a need for careful validation, particularly for physically agnostic models-that is, for potentials that extract the nature of atomic interactions from reference data. Here, we review the basic principles behind ML potentials and their validation for atomic-scale material modeling. We discuss the best practice in defining error metrics based on numerical performance, as well as physically guided validation. We give specific recommendations that we hope will be useful for the wider community, including those researchers who intend to use ML potentials for materials "off the shelf."

Structure and Bonding in Amorphous Red Phosphorus.

Amorphous red phosphorus (a-P) is one of the remaining puzzling cases in the structural chemistry of the elements. Here, we elucidate the structure, stability, and chemical bonding in a-P from first principles, combining machine-learning and density-functional theory (DFT) methods. We show that a-P structures exist with a range of energies slightly higher than those of phosphorus nanorods, to which they are closely related, and that the stability of a-P is linked to the degree of structural relaxation and medium-range order. We thus complete the stability range of phosphorus allotropes [Angew. Chem. Int. Ed. 2014, 53, 11629] by now including the previously poorly understood amorphous phase, and we quantify the covalent and van der Waals interactions in all main phases of phosphorus. We also study the electronic densities of states, including those of hydrogenated a-P. Beyond the present study, our structural models are expected to enable wider-ranging first-principles investigations-for example, of a-P-based battery materials.

Exploring the configurational space of amorphous graphene with machine-learned atomic energies.

Two-dimensionally extended amorphous carbon ("amorphous graphene") is a prototype system for disorder in 2D, showing a rich and complex configurational space that is yet to be fully understood. Here we explore the nature of amorphous graphene with an atomistic machine-learning (ML) model. We create structural models by introducing defects into ordered graphene through Monte-Carlo bond switching, defining acceptance criteria using the machine-learned local, atomic energies associated with a defect, as well as the nearest-neighbor (NN) environments. We find that physically meaningful structural models arise from ML atomic energies in this way, ranging from continuous random networks to paracrystalline structures. Our results show that ML atomic energies can be used to guide Monte-Carlo structural searches in principle, and that their predictions of local stability can be linked to short- and medium-range order in amorphous graphene. We expect that the former point will be relevant more generally to the study of amorphous materials, and that the latter has wider implications for the interpretation of ML potential models.

Indirect learning and physically guided validation of interatomic potential models.

Machine learning (ML) based interatomic potentials are emerging tools for material simulations, but require a trade-off between accuracy and speed. Here, we show how one can use one ML potential model to train another: we use an accurate, but more computationally expensive model to generate reference data (locations and labels) for a series of much faster potentials. Without the need for quantum-mechanical reference computations at the secondary stage, extensive reference datasets can be easily generated, and we find that this improves the quality of fast potentials with less flexible functional forms. We apply the technique to disordered silicon, including a simulation of vitrification and polycrystalline grain formation under pressure with a system size of a million atoms. Our work provides conceptual insight into the ML of interatomic potential models and suggests a route toward accelerated simulations of condensed-phase systems.

Designing Inorganic Semiconductors with Cold-Rolling Processability.

While metals can be readily processed and reshaped by cold rolling, most bulk inorganic semiconductors are brittle materials that tend to fracture when plastically deformed. Manufacturing thin sheets and foils of inorganic semiconductors is therefore a bottleneck problem, severely restricting their use in flexible electronic applications. It is recently reported that a few single-crystalline 2D van der Waals (vdW) semiconductors, such as InSe, are deformable under compressive stress. Here it is demonstrated that intralayer fracture toughness can be tailored via compositional design to make inorganic semiconductors processable by cold rolling. Systematic ab initio calculations covering a range of van der Waals semiconductors homologous to InSe are reported, leading to material-property maps that forecast trends in both the susceptibility to interlayer slip and the intralayer fracture toughness against cracking. GaSe is predicted, and experimentally confirmed, to be practically amenable to being rolled to large (three quarters) thickness reduction and length extension by a factor of three. The fracture toughness and cleavage energy are predicted to be 0.25 MPa m0.5 and 15 meV Å-2 , respectively. The findings open a new realm of possibility for alloy selection and design toward processing-friendly group-III chalcogenides for practical applications.

Unraveling Crystallization Mechanisms and Electronic Structure of Phase-Change Materials by Large-Scale Ab Initio Simulations.

Ge-Sb-Te ("GST") alloys are leading phase-change materials for digital memories and neuro-inspired computing. Upon fast crystallization, these materials form rocksalt-like phases with large structural and vacancy disorder, leading to an insulating phase at low temperature. Here, a comprehensive description of crystallization, structural disorder, and electronic properties of GeSb2 Te4 based on realistic, quantum-mechanically based ("ab initio") computer simulations with system sizes of more than 1000 atoms is provided. It is shown how an analysis of the crystallization mechanism based on the smooth overlap of atomic positions kernel reveals the evolution of both geometrical and chemical order. The connection between structural and electronic properties of the disordered, as-crystallized models, which are relevant to the transport properties of GST, is then studied. Furthermore, it is shown how antisite defects and extended Sb-rich motifs can lead to Anderson localization in the conduction band. Beyond memory applications, these findings are therefore more generally relevant to disordered rocksalt-like chalcogenides that exhibit self-doping, since they can explain the origin of Anderson insulating behavior in both p- and n-doped chalcogenide materials.

Cluster Fragments in Amorphous Phosphorus and their Evolution under Pressure.

Amorphous phosphorus (a-P) has long attracted interest because of its complex atomic structure, and more recently as an anode material for batteries. However, accurately describing and understanding a-P at the atomistic level remains a challenge. Here, it is shown that large-scale molecular-dynamics simulations, enabled by a machine-learning (ML)-based interatomic potential for phosphorus, can give new insights into the atomic structure of a-P and how this structure changes under pressure. The structural model so obtained contains abundant five-membered rings, as well as more complex seven- and eight-atom clusters. Changes in the simulated first sharp diffraction peak during compression and decompression indicate a hysteresis in the recovery of medium-range order. An analysis of cluster fragments, large rings, and voids suggests that moderate pressure (up to about 5 GPa) does not break the connectivity of clusters, but higher pressure does. The work provides a starting point for further computational studies of the structure and properties of a-P, and more generally it exemplifies how ML-driven modeling can accelerate the understanding of disordered functional materials.