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Training interatomic potentials for spin-polarized systems continues to be a difficult task for the molecular modeling community. In this note, a proof-of-concept, random initial spin committee approach is proposed for obtaining the ground state of spin-polarized systems with a controllable degree of accuracy. The approach is tested on two toy models of elemental sulfur where the exact optimal spin configuration can be known. Machine-learning potentials are trained on the resulting data, and increasingly accurate fits with respect to the ground state are achieved, marking a step towards machine-learning force fields for general bulk spin-polarized systems., Comment: The supporting data will be uploaded at https://doi.org/10.17863/CAM.112212 after the publication is accepted

Chiral crystals, like chiral molecules, cannot be superimposed onto their mirror images -- a fundamental property that has been linked to interesting physical behavior and exploited in functional devices. Among the simplest inorganic systems with crystallographic chirality, elemental tellurium adopts crystal structures with right- or left-handed chains. However, understanding the formation mechanisms of those structures has been difficult due to the rapid crystallization of Te, which reaches the spatial and temporal resolution limits of even the most advanced experiments. Here, we report ultra-large-scale, quantum-mechanically accurate simulations that reveal mechanisms of crystallization and the origin of crystallographic chirality in solid Te. We identify a characteristic, disordered cube-like structural motif -- a transient bonding environment with only nanosecond lifetime -- that enables both the rapid crystallization of Te and mediates chirality transfer. Based on the resulting microscopic understanding, we are able to explain the switching behavior of Te-based electrical devices.

Machine-learning-based interatomic potentials enable accurate materials simulations on extended time- and lengthscales. ML potentials based on the Atomic Cluster Expansion (ACE) framework have recently shown promising performance for this purpose. Here, we describe a largely automated computational approach to optimizing hyperparameters for ACE potential models. We extend our openly available Python package, XPOT, to include an interface for ACE fitting, and discuss the optimization of the functional form and complexity of these models based on systematic sweeps across relevant hyperparameters. We showcase the usefulness of the approach for two example systems: the covalent network of silicon and the phase-change material Sb$_{2}$Te$_{3}$. More generally, our work emphasizes the importance of hyperparameter selection in the development of advanced ML potential models.

The structure of amorphous silicon (a-Si) has been studied for decades. The two main theories are based on a continuous random network and on a `paracrystalline' model, respectively -- the latter being defined as showing localized structural order resembling the crystalline state whilst retaining an overall amorphous network. However, the extent of this local order has been unclear, and experimental data have led to conflicting interpretations. Here we show that signatures of paracrystallinity in an otherwise disordered network are indeed compatible with the existing body of experimental observations for a-Si. We use quantum-mechanically accurate, machine-learning-driven simulations to systematically sample the configurational space of quenched a-Si, thereby allowing us to elucidate the boundary between amorphization and crystallization. We analyze our dataset using structural and local-energy descriptors to show that paracrystalline models are consistent with experiments in both regards. Our work provides a unified explanation for seemingly conflicting theories in one of the most widely studied amorphous networks.

Graphene oxide (GO) materials are widely studied, and yet their atomic-scale structures remain to be fully understood. Here we show that the chemical and configurational space of GO can be rapidly explored by advanced machine-learning methods, combining on-the-fly acceleration for first-principles molecular dynamics with message-passing neural-network potentials. The first step allows for the rapid sampling of chemical structures with very little prior knowledge required; the second step affords state-of-the-art accuracy and predictive power. We apply the method to the thermal reduction of GO, which we describe in a realistic (ten-nanometre scale) structural model. Our simulations are consistent with recent experimental findings and help to rationalise them in atomistic and mechanistic detail. More generally, our work provides a platform for routine, accurate, and predictive simulations of diverse carbonaceous materials.

Main-group layered binary semiconductors, in particular, the III-VI alloys in the binary Ga-Te system are attracting increasing interest for a range of practical applications. The III-VI semiconductor, monoclinic gallium monotelluride (m-GaTe), has been recently used in high-sensitivity photodetectors/phototransistors and electronic memory applications due to its anisotropic properties yielding superior optical and electrical performance. Despite these applications, the origin of such anisotropy, namely the complex structural and bonding environments in GaTe nanostructures remain to be fully understood. In the present work, we report a comprehensive atomic-scale characterization of m-GaTe by state-of-the-art element-resolved atomic-scale microscopy experiments, enabling a direct measure of the in-plane anisotropy at the sub-Angstrom level. We show that these experimental images compare well with the results of first-principles modeling. Quantum-chemical bonding analyses provide a detailed picture of the atomic neighbor interactions within the layers, revealing that vertical Ga-Ga homopolar bonds get stronger when they are distorted and rotated, inducing the strong in-plane anisotropy. Beyond GaTe, using a systematic screening over the Materials Project database, we identify four additional low-symmetric layered crystals with similar distorted tetrahedral patterns, namely, GeP, GeAs, SiP, and SiAs. We thereby confirm the homopolar-bond-induced anisotropy is a more generic feature in these layered van-der-Waals materials., Comment: Accepted in Small Science

Machine-learned force fields have transformed the atomistic modelling of materials by enabling simulations of ab initio quality on unprecedented time and length scales. However, they are currently limited by: (i) the significant computational and human effort that must go into development and validation of potentials for each particular system of interest; and (ii) a general lack of transferability from one chemical system to the next. Here, using the state-of-the-art MACE architecture we introduce a single general-purpose ML model, trained on a public database of 150k inorganic crystals, that is capable of running stable molecular dynamics on molecules and materials. We demonstrate the power of the MACE-MP-0 model - and its qualitative and at times quantitative accuracy - on a diverse set problems in the physical sciences, including the properties of solids, liquids, gases, chemical reactions, interfaces and even the dynamics of a small protein. The model can be applied out of the box and as a starting or "foundation model" for any atomistic system of interest and is thus a step towards democratising the revolution of ML force fields by lowering the barriers to entry., Comment: 119 pages, 63 figures, 37MB PDF

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 (HDA), 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 characterisation of local oxygen environments. We train a neural network (NN) 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.

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.

The structure of amorphous silicon 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 show that atomistic machine-learning methods can reveal the complex structural and energetic landscape of defects in amorphous silicon. We study an ultra-large-scale, quantum-accurate structural model containing a million atoms, and more than ten thousand defects, allowing reliable defect-related statistics to be obtained. We combine structural descriptors and machine-learned local atomic energies to develop a universal classification of the different types of defects in amorphous silicon. The results suggest a revision of the established floating-bond model by showing that fivefold-coordinated atoms in amorphous silicon exhibit a wide range of local environments, and 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 modelling and understanding defects in disordered materials beyond silicon alone.

Machine learning (ML) based interatomic potentials have transformed the field of atomistic materials modelling. However, ML potentials depend critically on the quality and quantity of quantum-mechanical reference data with which they are trained, and therefore developing datasets and training pipelines is becoming an increasingly central challenge. Leveraging the idea of "synthetic" (artificial) data that is common in other areas of ML research, we here show that synthetic atomistic data, themselves obtained at scale with an existing ML potential, constitute a useful pre-training task for neural-network interatomic potential models. Once pre-trained with a large synthetic dataset, these models can be fine-tuned on a much smaller, quantum-mechanical one, improving numerical accuracy and stability in computational practice. We demonstrate feasibility for a series of equivariant graph-neural-network potentials for carbon, and we carry out initial experiments to test the limits of the approach.

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 allow for the identification and post-hoc interpretation of contributions from individual chemical environments and motifs to complicated macroscopic properties. However, even though there exist practical justifications for these decompositions, only the global quantity is rigorously defined, and thus it is unclear to what extent the atomistic terms predicted by the model can be trusted. Here, 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 LPR on the aspects of model training, particularly the composition of training dataset, 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.

Zeolitic imidazolate frameworks are widely thought of as being analogous to inorganic AB$_{2}$ 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.

Amorphous calcium carbonate (ACC) is an important precursor for biomineralisation in marine organisms. Among the key outstanding problems regarding ACC are how best to understand its structure and how to rationalise its metastability as an amorphous phase. Here, we report high-quality atomistic models of ACC generated by 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$\boldsymbol\cdots$Ca interaction potential governing ACC formation. This potential contains minima at two competing distances, corresponding to the two different ways in which carbonate ions bridge Ca$^{2+}$-ion pairs. We reveal an unexpected mapping to the Lennard-Jones--Gauss (LJG) model normally studied in the context of computational soft-matter, with the empirical LJG parameters for ACC taking values known to promote structural complexity. In this way we show that both the complex structure of ACC and its resilience to crystallisation are actually encoded in the geometrically-frustrated effective interactions between Ca$^{\boldsymbol 2+}$ ions.

The layered crystal structure of Cr2Ge2Te6 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, we demonstrate that Cr2Ge2Te6 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 Cr2Ge2Te6 could be exploited for multifunctional, magnetic phase-change devices that switch between crystalline and amorphous states.

Machine-learning models are increasingly used to predict properties of atoms in chemical systems. There have been major advances in developing descriptors and regression frameworks for this task, typically starting from (relatively) small sets of quantum-mechanical reference data. Larger datasets of this kind are becoming available, but remain expensive to generate. Here we demonstrate the use of a large dataset that we have "synthetically" labelled with per-atom energies from an existing ML potential model. The cheapness of this process, compared to the quantum-mechanical ground truth, allows us to generate millions of datapoints, in turn enabling rapid experimentation with atomistic ML models from the small- to the large-data regime. This approach allows us here to compare regression frameworks in depth, and to explore visualisation based on learned representations. We also show that learning synthetic data labels can be a useful pre-training task for subsequent fine-tuning on small datasets. In the future, we expect that our open-sourced dataset, and similar ones, will be useful in rapidly exploring deep-learning models in the limit of abundant chemical data.

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 which extract the nature of atomic interactions from reference data. Here, we review the basic principles behind ML potentials and their validation for atomic-scale materials modeling. We discuss 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".

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 bond-ing in a-P from first principles, combining machine-learning and density-functional theo-ry (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 phos-phorus. 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.

Quantum-accurate computer simulations play a central role in understanding phase-change materials (PCMs) for advanced memory technologies. However, direct quantum-mechanical simulations are necessarily limited to simplified models, containing no more than a few hundred or a thousand atoms. Machine learning (ML) based potential models that are "trained" on quantum-mechanical data are an emerging alternative approach, currently evolving from highly specialised to more widely applied simulation tools. Here we show that a universal, compositionally flexible ML model can describe a wide range of flagship Ge-Sb-Te PCMs under real device conditions, including non-isothermal heating and chemical disorder which are relevant for memory applications. The speed of the ML model enables atomistic simulations of multiple thermal cycles and delicate operations for neuro-inspired computing, namely, cumulative SET and iterative RESET. A device-scale capability demonstration (40 x 20 x 20 nm3) shows that the new ML potential can directly describe technologically relevant processes in PCM-based memory products. In a wider context, our work demonstrates how ML-driven materials simulations are now entering a stage where they can guide architecture design for high-performance electronic devices.

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.

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 electronics applications. It was recently reported that a few single-crystalline two-dimensional van der Waals (vdW) semiconductors, such as InSe, are deformable under compressive stress. Here we demonstrate that intralayer fracture toughness can be tailored via compositional design to make inorganic semiconductors processable by cold rolling. We report systematic ab initio calculations covering a range of van der Waals semiconductors homologous to InSe, leading to material-property maps that forecast trends in both the susceptibility to interlayer slip and the intralayer fracture toughness against cracking. GaSe has been 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. Our findings open a new realm of possibility for alloy selection and design towards processing-friendly group-III chalcogenides for flexible electronic and thermoelectric applications.

Machine learning (ML) based interatomic potentials are emerging tools for materials 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 existing, 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 machine learning of interatomic potential models, and it suggests a route toward accelerated simulations of condensed-phase systems and nanostructured materials.

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 we show 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. Our 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.

Chalcogenide phase-change materials (PCMs) are regarded as the leading candidate for storage-class non-volatile memory and neuro-inspired computing. Recently, using the $TiTe_2$/$Sb_2Te_3$ material combination, a new framework - phase-change heterostructure (PCH), has been developed and proved to effectively suppress the noise and drift in electrical resistance upon memory programming, largely reducing the inter-device variability. However, the atomic-scale structural and chemical nature of PCH remains to be fully understood. In this work, we carry out thorough ab initio simulations to assess the bonding characteristics of the PCH. We show that the $TiTe_2$ crystalline nanolayers do not chemically interact with the surrounding $Sb_2Te_3$, and are stabilized by strong covalent and electrostatic Ti-Te interactions, which create a prohibitively high barrier for atomic migrations along the pulsing direction. We also find significant contrast in computed dielectric functions in the PCH, suggesting possible optical applications of this class of devices. With the more confined space and therefore constrained phase transition compared to traditional PCM devices, the recently introduced class of PCH-based devices may lead to improvements in phase-change photonic and optoelectronic applications with much lower stochasticity during programming., Comment: 11 pages, 5 figures

We present an accurate machine learning (ML) model for atomistic simulations of carbon, constructed using the Gaussian approximation potential (GAP) methodology. The potential, named GAP-20, describes the properties of the bulk crystalline and amorphous phases, crystal surfaces and defect structures with an accuracy approaching that of direct ab initio simulation, but at a significantly reduced cost. We combine structural databases for amorphous carbon and graphene, which we extend substantially by adding suitable configurations, for example, for defects in graphene and other nanostructures. The final potential is fitted to reference data computed using the optB88-vdW density functional theory (DFT) functional. Dispersion interactions, which are crucial to describe multilayer carbonaceous materials, are therefore implicitly included. We additionally account for long-range dispersion interactions using a semianalytical two-body term and show that an improved model can be obtained through an optimisation of the many-body smooth overlap of atomic positions (SOAP) descriptor. We rigorously test the potential on lattice parameters, bond lengths, formation energies and phonon dispersions of numerous carbon allotropes. We compare the formation energies of an extensive set of defect structures, surfaces and surface reconstructions to DFT reference calculations. The present work demonstrates the ability to combine, in the same ML model, the previously attained flexibility required for amorphous carbon [Phys. Rev. B, 95, 094203, (2017)] with the high numerical accuracy necessary for crystalline graphene [Phys. Rev. B, 97, 054303, (2018)], thereby providing an interatomic potential that will be applicable to a wide range of applications concerning diverse forms of bulk and nanostructured carbon., Comment: The following article has been accepted by The Journal of Chemical Physics. After it is published, it will be found at https://publishing.aip.org/resources/librarians/products/journals/

Amorphous carbon (a-C) materials have diverse interesting and useful properties, but the understanding of their atomic-scale structures is still incomplete. Here, we report on extensive atomistic simulations of the deposition and growth of a-C films, describing interatomic interactions using a machine learning (ML) based Gaussian Approximation Potential (GAP) model. We expand widely on our initial work [Phys. Rev. Lett. 120, 166101 (2018)] by now considering a broad range of incident ion energies, thus modeling samples that span the entire range from low-density ($sp^{2}$-rich) to high-density ($sp^{3}$-rich, "diamond-like") amorphous forms of carbon. Two different mechanisms are observed in these simulations, depending on the impact energy: low-energy impacts induce $sp$- and $sp^{2}$-dominated growth directly around the impact site, whereas high-energy impacts induce peening. Furthermore, we propose and apply a scheme for computing the anisotropic elastic properties of the a-C films. Our work provides fundamental insight into this intriguing class of disordered solids, as well as a conceptual and methodological blueprint for simulating the atomic-scale deposition of other materials with ML-driven molecular dynamics.

Much of our understanding of complex structures is based on simplification: for example, metal-organic frameworks are often discussed in the context of "nodes" and "linkers", allowing for a qualitative comparison with simpler inorganic structures. Here we show how such an understanding can be obtained in a systematic and quantitative framework, by combining atom-density based similarity (kernel) functions and unsupervised machine learning with the long-standing idea of "coarse-graining" atomic structure. We demonstrate how the latter enables a comparison of vastly different chemical systems, and use it to create a unified, two-dimensional structure map of experimentally known tetrahedral AB2 networks - including clathrate hydrates, zeolitic imidazolate frameworks (ZIFs), and diverse inorganic phases. The structural relationships that emerge can then be linked to microscopic properties of interest, which we exemplify for structural heterogeneity and tetrahedral density.

Machine learning driven interatomic potentials, including Gaussian approximation potential (GAP) models, are emerging tools for atomistic simulations. Here, we address the methodological question of how one can fit GAP models that accurately predict vibrational properties in specific regions of configuration space, whilst retaining flexibility and transferability to others. We use an adaptive regularization of the GAP fit that scales with the absolute force magnitude on any given atom, thereby exploring the Bayesian interpretation of GAP regularization as an "expected error", and its impact on the prediction of physical properties for a material of interest. The approach enables excellent predictions of phonon modes (to within 0.1-0.2 THz) for structurally diverse silicon allotropes, and it can be coupled with existing fitting databases for high transferability. These findings and workflows are expected to be useful for GAP-driven materials modeling more generally., Comment: 11 pages, 6 figures, 2 tables; submitted to The Journal of Chemical Physics

Structurally disordered materials continue to pose fundamental questions, including that of how different disordered phases ("polyamorphs") can coexist and transform from one to another. As a widely studied case, amorphous silicon (a-Si) forms a fourfold-coordinated, covalent random network at ambient conditions, but much higher-coordinated, metallic-like phases under pressure. However, a detailed mechanistic understanding of the liquid-amorphous and amorphous-amorphous transitions in silicon has been lacking, due to intrinsic limitations of even the most advanced experimental and computational techniques. Here, we show how machine-learning (ML)-driven simulations can break through this long-standing barrier, affording a comprehensive, quantum-accurate, and fully atomistic description of all relevant liquid and amorphous phases of silicon. Combining a model system size of 100,000 atoms (ten-nanometre length scale) with a prediction accuracy of a few meV per atom, our simulations reveal a remarkable, three-step transformation sequence for a-Si under increasing external pressure. First, up to 10-11 GPa, polyamorphic low- and high-density amorphous (LDA and HDA) regions are found to coexist, rather than appearing sequentially. Then, we observe a structural collapse into a distinct, very-high-density amorphous (VHDA) phase at 12-13 GPa, reminiscent of the dense liquid but being formed at a much lower temperature. Finally, our simulations indicate the transient nature of this VHDA phase: it rapidly nucleates crystallites at 13-16 GPa, ultimately leading to the formation of a poly-crystalline, simple-hexagonal structure, consistent with experiments but not seen in earlier simulations.

We generate representative structural models of amorphous carbon (a-C) from constant-volume quenching from the liquid with subsequent relaxation of internal stresses in molecular dynamics simulations using empirical and machine-learning interatomic potentials. By varying volume and quench rate we generate structures with a range of density and amorphous morphologies. We find that all a-C samples show a universal relationship between hybridization, bulk modulus and density despite having distinct cohesive energies. Differences in cohesive energy are traced back to slight changes in the distribution of bond-angles that will likely affect thermal stability of these structures., Comment: 26 pages, 7 figures

Interatomic potential models based on machine learning (ML) are rapidly developing as tools for materials simulations. However, because of their flexibility, they require large fitting databases that are normally created with substantial manual selection and tuning of reference configurations. Here, we show that ML potentials can be built in a largely automated fashion, exploring and fitting potential-energy surfaces from the beginning (de novo) within one and the same protocol. The key enabling step is the use of a configuration-averaged kernel metric that allows one to select the few most relevant structures at each step. The resulting potentials are accurate and robust for the wide range of configurations that occur during structure searching, despite only requiring a relatively small number of single-point DFT calculations on small unit cells. We apply the method to materials with diverse chemical nature and coordination environments, marking a milestone toward the more routine application of ML potentials in physics, chemistry, and materials science.

Amorphous materials are coming within reach of realistic computer simulations, but new approaches are needed to fully understand their intricate atomic structures. Here, we show how machine-learning (ML)-based techniques can give new, quantitative chemical insight into the atomic-scale structure of amorphous silicon (a-Si). Based on a similarity function ("kernel"), we define a structural metric that unifies the description of nearest- and next-nearest-neighbor environments in the amorphous state. We apply this to an ensemble of a-Si networks, generated in melt-quench simulations with an ML-based interatomic potential, in which we tailor the degree of ordering by varying the quench rates down to $10^{10}$ K/s (leading to a structural model that is lower in energy than the established WWW network). We then show how "machine-learned" atomic energies permit a chemical interpretation, associating coordination defects in a-Si with distinct energetic stability regions. The approach is straightforward and inexpensive to apply to arbitrary structural models, and it is therefore expected to have more general significance for developing a quantitative understanding of the amorphous state.

We study the deposition of tetrahedral amorphous carbon (ta-C) films from molecular dynamics simulations based on a machine-learned interatomic potential trained from density-functional theory data. For the first time, the high $sp^3$ fractions in excess of 85% observed experimentally are reproduced by means of computational simulation, and the deposition energy dependence of the film's characteristics is also accurately described. High confidence in the potential and direct access to the atomic interactions allow us to infer the microscopic growth mechanism in this material. While the widespread view is that ta-C grows by "subplantation," we show that the so-called "peening" model is actually the dominant mechanism responsible for the high $sp^3$ content. We show that pressure waves lead to bond rearrangement away from the impact site of the incident ion, and high $sp^3$ fractions arise from a delicate balance of transitions between three- and fourfold coordinated carbon atoms. These results open the door for a microscopic understanding of carbon nanostructure formation with an unprecedented level of predictive power.

Amorphous silicon (a-Si) is a widely studied non-crystalline material, and yet the subtle details of its atomistic structure are still unclear. Here, we show that accurate structural models of a-Si can be obtained by harnessing the power of machine-learning algorithms to create interatomic potentials. Our best a-Si network is obtained by cooling from the melt in molecular-dynamics simulations, at a rate of 10$^{11}$ K/s (that is, on the 10 ns timescale). This structure shows a defect concentration of below 2% and agrees with experiments regarding excess energies, diffraction data, as well as $^{29}$Si solid-state NMR chemical shifts. We show that this level of quality is impossible to achieve with faster quench simulations. We then generate a 4,096-atom system which correctly reproduces the magnitude of the first sharp diffraction peak (FSDP) in the structure factor, achieving the closest agreement with experiments to date. Our study demonstrates the broader impact of machine-learning interatomic potentials for elucidating accurate structures and properties of amorphous functional materials.

We demonstrate how machine-learning based interatomic potentials can be used to model guest atoms in host structures. Specifically, we generate Gaussian approximation potential (GAP) models for the interaction of lithium atoms with graphene, graphite, and disordered carbon nanostructures, based on reference density-functional theory (DFT) data. Rather than treating the full Li--C system, we demonstrate how the energy and force differences arising from Li intercalation can be modeled and then added to a (prexisting and unmodified) GAP model of pure elemental carbon. Furthermore, we show the benefit of using an explicit pair potential fit to capture "effective" Li--Li interactions, to improve the performance of the GAP model. This provides proof-of-concept for modeling guest atoms in host frameworks with machine-learning based potentials, and in the longer run is promising for carrying out detailed atomistic studies of battery materials., Comment: improved discussion, in particular in Section IV.B

While solid-state materials are commonly classified as covalent, ionic, or metallic, there are cases that defy these iconic bonding mechanisms. A prominent example is given by phase-change materials (PCMs) for data storage or photonics, which have recently been argued to show 'resonant' bonding; a clear definition of this mechanism, however, has been lacking until the present day. Here we show that these solids are clearly different from resonant bonding in the pi-orbital systems of benzene and graphene. Instead, they exhibit a unique mechanism between covalent and metallic bonding, which we call 'metavalent' bonding. The materials are on the verge of electron delocalization, which explains their exceptional property portfolio, and we therefore argue that they represent 'incipient metals'. This yields deeper, fundamental insight into the bonding nature of solid-state materials, and is expected to accelerate the discovery and design of new functional materials including PCMs and thermoelectrics.

The allotropes of boron continue to challenge structural elucidation and solid-state theory. Here we use machine learning combined with random structure searching (RSS) algorithms to systematically construct an interatomic potential for boron. Starting from ensembles of randomized atomic configurations, we use alternating single-point quantum-mechanical energy and force computations, Gaussian approximation potential (GAP) fitting, and GAP-driven RSS to iteratively generate a representation of the element's potential-energy surface. Beyond the total energies of the very different boron allotropes, our model readily provides atom-resolved, local energies and thus deepened insight into the frustrated $\beta$-rhombohedral boron structure. Our results open the door for the efficient and automated generation of GAPs and other machine-learning-based interatomic potentials, and suggest their usefulness as a tool for materials discovery.

Phase change alloys are used for non-volatile random access memories exploiting the conductivity contrast between amorphous and metastable, crystalline phase. However, this contrast has never been directly related to the electronic band structure. Here, we employ photoelectron spectroscopy to map the relevant bands for metastable, epitaxial GeSbTe films. The constant energy surfaces of the valence band close to the Fermi level are hexagonal tubes with little dispersion perpendicular to the (111) surface. The electron density responsible for transport belongs to the tails of this bulk valence band, which is broadened by disorder, i.e., the Fermi level is 100 meV above the valence band maximum. This result is consistent with transport data of such films in terms of charge carrier density and scattering time. In addition, we find a state in the bulk band gap with linear dispersion, which might be of topological origin., Comment: 14 pages, 6 figures, 5 tables

We introduce a Gaussian approximation potential (GAP) for atomistic simulations of liquid and amorphous elemental carbon. Based on a machine-learning representation of the density-functional theory (DFT) potential-energy surface, such interatomic potentials enable materials simulations with close-to DFT accuracy but at much lower computational cost. We first determine the maximum accuracy that any finite-range potential can achieve in carbon structures; then, using a novel hierarchical set of two-, three-, and many-body structural descriptors, we construct a GAP model that can indeed reach the target accuracy. The potential yields accurate energetic and structural properties over a wide range of densities; it also correctly captures the structure of the liquid phases, at variance with state-of-the-art empirical potentials. Exemplary applications of the GAP model to surfaces of "diamond-like" tetrahedral amorphous carbon (ta-C) are presented, including an estimate of the amorphous material's surface energy, and simulations of high-temperature surface reconstructions ("graphitization"). The new interatomic potential appears to be promising for realistic and accurate simulations of nanoscale amorphous carbon structures., Comment: 16 pages, 16 figures (+ supplement)

Thermal properties of solid-state materials are a fundamental topic of study with important practical implications. For example, anisotropic displacement parameters (ADPs) are routinely used in physics, chemistry, and crystallography to quantify the thermal motion of atoms in crystals. ADPs are commonly derived from diffraction experiments, but recent developments have also enabled their first-principles prediction using periodic density functional theory (DFT). Here, we combine experiments and dispersion-corrected DFT to quantify lattice thermal expansion and ADPs in crystalline {\alpha}-sulfur (S8), a prototypical elemental solid that is controlled by the interplay of covalent and van der Waals interactions. We first report on single-crystal and powder X-ray diffraction (XRD) measurements that provide new and improved reference data from 10 K up to room temperature. We then use several popular dispersion-corrected DFT methods to predict vibrational and thermal properties of {\alpha}-sulfur, including the anisotropic lattice thermal expansion. Hereafter, ADPs are derived in the commonly used harmonic approximation (in the computed zero-Kelvin structure) and also in the quasi-harmonic approximation (QHA) which takes the predicted lattice thermal expansion into account. At the PBE+D3(BJ) level, the latter leads to excellent agreement with experiments. Finally, more general implications of this study for realistic materials modeling at finite temperature are discussed.