The success of first-principles electronic-structure calculation for predictive modeling in chemistry, solid-state physics, and materials science is constrained by the limitations on simulated length ...scales and timescales due to the computational cost and its scaling. Techniques based on machine-learning ideas for interpolating the Born-Oppenheimer potential energy surface without explicitly describing electrons have recently shown great promise, but accurately and efficiently fitting the physically relevant space of configurations remains a challenging goal. Here, we present a Gaussian approximation potential for silicon that achieves this milestone, accurately reproducing density-functional-theory reference results for a wide range of observable properties, including crystal, liquid, and amorphous bulk phases, as well as point, line, and plane defects. We demonstrate that this new potential enables calculations such as finite-temperature phase-boundary lines, self-diffusivity in the liquid, formation of the amorphous by slow quench, and dynamic brittle fracture, all of which are very expensive with a first-principles method. We show that the uncertainty quantification inherent to the Gaussian process regression framework gives a qualitative estimate of the potential’s accuracy for a given atomic configuration. The success of this model shows that it is indeed possible to create a useful machine-learning-based interatomic potential that comprehensively describes a material on the atomic scale and serves as a template for the development of such models in the future.
Structurally disordered materials pose fundamental questions
, including how different disordered phases ('polyamorphs') can coexist and transform from one phase to another
. Amorphous silicon has ...been extensively studied; it forms a fourfold-coordinated, covalent network at ambient conditions and much-higher-coordinated, metallic phases under pressure
. However, a detailed mechanistic understanding of the structural transitions in disordered silicon has been lacking, owing to the intrinsic limitations of even the most advanced experimental and computational techniques, for example, in terms of the system sizes accessible via simulation. Here we show how atomistic machine learning models trained on accurate quantum mechanical computations can help to describe liquid-amorphous and amorphous-amorphous transitions for a system of 100,000 atoms (ten-nanometre length scale), predicting structure, stability and electronic properties. Our simulations reveal a three-step transformation sequence for amorphous silicon under increasing external pressure. First, polyamorphic low- and high-density amorphous regions are found to coexist, rather than appearing sequentially. Then, we observe a structural collapse into a distinct very-high-density amorphous (VHDA) phase. Finally, our simulations indicate the transient nature of this VHDA phase: it rapidly nucleates crystallites, ultimately leading to the formation of a polycrystalline structure, consistent with experiments
but not seen in earlier simulations
. A machine learning model for the electronic density of states confirms the onset of metallicity during VHDA formation and the subsequent crystallization. These results shed light on the liquid and amorphous states of silicon, and, in a wider context, they exemplify a machine learning-driven approach to predictive materials modelling.
Abstract
Interatomic potential models based on machine learning (ML) are rapidly developing as tools for material 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 and diverse 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 an important step toward the more routine application of ML potentials in physics, chemistry, and materials science.
Nanostructured semiconductors emit light from electronic states known as excitons. For organic materials, Hund's rules state that the lowest-energy exciton is a poorly emitting triplet state. For ...inorganic semiconductors, similar rules predict an analogue of this triplet state known as the 'dark exciton'. Because dark excitons release photons slowly, hindering emission from inorganic nanostructures, materials that disobey these rules have been sought. However, despite considerable experimental and theoretical efforts, no inorganic semiconductors have been identified in which the lowest exciton is bright. Here we show that the lowest exciton in caesium lead halide perovskites (CsPbX
, with X = Cl, Br or I) involves a highly emissive triplet state. We first use an effective-mass model and group theory to demonstrate the possibility of such a state existing, which can occur when the strong spin-orbit coupling in the conduction band of a perovskite is combined with the Rashba effect. We then apply our model to CsPbX
nanocrystals, and measure size- and composition-dependent fluorescence at the single-nanocrystal level. The bright triplet character of the lowest exciton explains the anomalous photon-emission rates of these materials, which emit about 20 and 1,000 times faster than any other semiconductor nanocrystal at room and cryogenic temperatures, respectively. The existence of this bright triplet exciton is further confirmed by analysis of the fine structure in low-temperature fluorescence spectra. For semiconductor nanocrystals, which are already used in lighting, lasers and displays, these excitons could lead to materials with brighter emission. More generally, our results provide criteria for identifying other semiconductors that exhibit bright excitons, with potential implications for optoelectronic devices.
Amorphous silicon (a-Si) is a widely studied noncrystalline 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 using a machine-learning-based interatomic potential. Our best a-Si network is obtained by simulated cooling from the melt at a rate of 1011 K/s (that is, on the 10 ns time scale), contains less than 2% defects, and agrees with experiments regarding excess energies, diffraction data, and 29Si NMR chemical shifts. We show that this level of quality is impossible to achieve with faster quench simulations. We then generate a 4096-atom system that 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 potentials for elucidating structures and properties of technologically important amorphous materials.
Determining the stability of molecules and condensed phases is the cornerstone of atomistic modeling, underpinning our understanding of chemical and materials properties and transformations. We show ...that a machine-learning model, based on a local description of chemical environments and Bayesian statistical learning, provides a unified framework to predict atomic-scale properties. It captures the quantum mechanical effects governing the complex surface reconstructions of silicon, predicts the stability of different classes of molecules with chemical accuracy, and distinguishes active and inactive protein ligands with more than 99% reliability. The universality and the systematic nature of our framework provide new insight into the potential energy surface of materials and molecules.
Amorphous materials are being described by increasingly powerful computer simulations, but new approaches are still needed to fully understand their intricate atomic structures. Here, we show how ...machine‐learning‐based techniques can give new, quantitative chemical insight into the atomic‐scale structure of amorphous silicon (a‐Si). We combine a quantitative description of the nearest‐ and next‐nearest‐neighbor structure with a quantitative description of local stability. The analysis is applied to an ensemble of a‐Si networks in which we tailor the degree of ordering by varying the quench rates down to 1010 K s−1. Our approach associates coordination defects in a‐Si with distinct stability regions and it has also been applied to liquid Si, where it traces a clear‐cut transition in local energies during vitrification. The method is straightforward and inexpensive to apply, and therefore expected to have more general significance for developing a quantitative understanding of liquid and amorphous states of matter.
In silico(n): Machine learning makes it possible to quantify the local structure in amorphous solids and the local atomically resolved energy at the same time, as demonstrated here for an ensemble of amorphous and liquid Si structures.
We demonstrate how the Gaussian process regression approach can be used to efficiently reconstruct free energy surfaces from umbrella sampling simulations. By making a prior assumption of smoothness ...and taking account of the sampling noise in a consistent fashion, we achieve a significant improvement in accuracy over the state of the art in two or more dimensions or, equivalently, a significant cost reduction to obtain the free energy surface within a prescribed tolerance in both regimes of spatially sparse data and short sampling trajectories. Stemming from its Bayesian interpretation the method provides meaningful error bars without significant additional computation. A software implementation is made available on www.libatoms.org.
PDF
