An accurate and transferable machine learning potential for carbon

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 optimization of the many-body smooth overlap of atomic positions 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 [V. L. Deringer and G. Csányi, Phys. Rev. B 95, 094203 (2017)] with the high numerical accuracy necessary for crystalline graphene [Rowe et al., 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

A general-purpose machine-learning force field for bulk and nanostructured phosphorus

Elemental phosphorus is attracting growing interest across fundamental and applied fields of research. However, atomistic simulations of phosphorus have remained an out- standing challenge. Here we show that a universally applicable force field for phosphorus can be created by machine learning (ML) from a suitably chosen ensemble of quantum- mechanical results. Our model is fitted to density-functional theory plus many-body dis- persion (DFT+MBD) data; its accuracy is demonstrated for the exfoliation of black and violet phosphorus (yielding monolayers of “phosphorene” and “hittorfene”); its transfer- ability is shown for the transition between the molecular and network liquid phases. An application to a phosphorene nanoribbon on an experimentally relevant length scale ex- emplifies the power of accurate and flexible ML-driven force fields for next-generation materials modelling. The methodology promises new insights into phosphorus as well as other structurally complex, e.g., layered solids that are relevant in diverse areas of chem- istry, physics, and materials science

Machine learning based modeling of disordered elemental semiconductors: understanding the atomic structure of a-Si and a-C

Disordered elemental semiconductors, most notably a-C and a-Si, are ubiquitous in a myriad of different applications. These exploit their unique mechanical and electronic properties. In the past couple of decades, density functional theory (DFT) and other quantum mechanics-based computational simulation techniques have been successful at delivering a detailed understanding of the atomic and electronic structure of crystalline semiconductors. Unfortunately, the complex structure of disordered semiconductors sets the time and length scales required for DFT simulation of these materials out of reach. In recent years, machine learning (ML) approaches to atomistic modeling have been developed that provide an accurate approximation of the DFT potential energy surface for a small fraction of the computational time. These ML approaches have now reached maturity and are starting to deliver the first conclusive insights into some of the missing details surrounding the intricate atomic structure of disordered semiconductors. In this Topical Review we give a brief introduction to ML atomistic modeling and its application to amorphous semiconductors. We then take a look at how ML simulations have been used to improve our current understanding of the atomic structure of a-C and a-Si

Accuracy and Transferability in Machine Learned Potentials for Carbon

In this thesis, we discuss the approach taken to construct an accurate machine learning (ML) model for atomistic simulations of carbon, constructed using the Gaussian approximation potential (GAP) methodology. We begin by discussing the process for constructing a potential for a single phase, graphene. We then extend this to produce a general-purpose potential, named GAP-20, which describes the properties of the bulk crystalline and amorphous phases, crystal surfaces, and defect structures with a high degree of accuracy. 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 optimization of the manybody smooth overlap of atomic positions 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 with the high accuracy necessary for crystalline graphene which we introduce in this thesis, thereby providing an interatomic potential that will be applicable to a wide range of applications concerning diverse forms of bulk and nanostructured carbon

Structure, Bonding, and Mineralogy of Carbon at Extreme Conditions

The nature and extent of Earth’s deep carbon cycle remains uncertain. This chapter considers high-pressure carbon-bearing minerals, including those of Earth’s mantle and core, as well as phases that might be found in the interiors of larger planets outside our solar system. These phases include both experimentally produced and theoretically predicted polymorphs of carbon dioxide, carbonates, carbides, silicate-carbonates, as well as very high-pressure phases of pure carbon. One theme in the search for possible high P-T, deep-Earth phases is the likely shift from sp2 bonding (trigonal coordination) to sp3 bonding (tetrahedral coordination) in carbon-bearing phases of the lower mantle and core, as exemplified by the graphite-to-diamond transition (Bundy et al. 1961; Davies 1984). A similar phenomenon has been documented in the preferred coordination spheres of many elements at high pressure. For example, silicon is ubiquitously found in tetrahedral coordination in crustal and upper mantle minerals, but adopts octahedral coordination in many high-pressure phases. Indeed, the boundary between Earth’s transition zone and lower mantle may be described as a crystal chemical shift from 4-coordinated to 6-coordinated silicon (Hazen and Finger 1978; Finger and Hazen 1991). Similarly, magnesium and calcium commonly occur in octahedral 6-coordination in minerals at ambient conditions, but transform to 8- or greater coordination in high-pressure phases, as exemplified by the calcite-to-aragonite transformation of CaCO3 and the pyroxene-to-perovskite and post-perovskite transformations of MgSiO3 (Murakami et al. 2004; Oganov and Ono 2004). Consequently, a principal focus in any consideration of deep-Earth carbon minerals must include carbon in higher coordination, and even more complex bonding at more extreme conditions that characterize the interiors of larger planets

Hydrogen Isotope Transport and Separation via Layered and Two-Dimensional Materials

The enrichment of heavy hydrogen isotopes (deuterium, tritium) is required to fulfill their increasing application demands, e.g., in isotope related tracing, cancer therapy and nuclear reaction plants. However, their exceedingly low natural abundance and the close resemblance of physiochemical properties to protium render them extremely difficult to be separated. In this thesis, we investigate hydrogen isotope transport and separation via layered and two-dimensional materials. Three different theoretical challenges are undertaken in this work: (1) identification of the transported hydrogen species (proton H+ or protium H atom) inside interstitial space of layered materials (hexagonal boron nitride, molybdenum disulfide and graphite) and elucidation of their transport mechanism; (2) separation of hydron (proton H+, deuteron D+, and triton T+) isotopes through vacancy-free graphene and hexagonal boron nitride monolayers; (3) capture of the extremely rare light helium isotope (3He) with atomically thin two-dimensional materials. In the case of hydrogen transport, the essential challenges are investigation of its mechanism as well as the identification of transported particles. Regarding the case of hydron isotope separation, the essential questions are whether or not pristine graphene is permeable to the isotopes, and how quantum tunneling and topological Stone-Wales 55-77 defects affect their permeation and separation through graphene. In the last case, to capture the light helium isotope, quantum tunneling, which favors the lighter particles, is utilized to harvest 3He using graphdiyne monolayer. Our results provide novel theoretical insights into hydrogen particle transport inside the interstitial space of van der Waals materials; they uncover the mechanism of hydron isotope separation through 2D graphene and hexagonal boron nitride monolayers; and they predict the influence of pure quantum tunneling on the enrichment of 3He through graphdiyne membrane

Flame-Formed Carbon Nanoparticles: Synthesis and characterization

Nanoparticles and nanostructured materials characterize an increasing research area, gaining strong attention from the scientific community in several fields. During the last decades, many and extraordinary technological advances have been obtained by nano-materials due to their physicochemical properties. In nature, at micro- and nano-scale, materials have existed for a long time before, but it is only through the advent of the technological era, and consequently, the development of nanotechnology, that they have come to the fore. There are several forms of nanoparticles: metal-based, organic-based or organic/inorganic combination and carbon-based ones. Carbon nanoparticles are the most widely studied as carbon is suitable and available raw material. Except for hydrogen, carbon has the most significant number of known compounds and is present on the planet in various forms: from carbon to light and heavy hydrocarbons. Carbon-based nanoparticles have shown a wide variety of structural arrangements that make them a great advantage as they are suitable for various purposes. Several techniques exist to cope with the production of the nano-size materials in both liquid and gas phase; examples are arc-discharge, laser ablation, chemical vapour deposition. The more the process allows to have a production (functional to specific final characteristics of the material) on a large scale and in an economical way, the more it is taken into consideration and studied. Among the various techniques, the use of flame and, therefore, combustion technology is increasingly taken into consideration. Traditionally, combustion is associated with the study of particulate matter and undesired products released into the atmosphere daily to understand the onset of their formation and reduce, if not abate, their emissions. Nevertheless, on the other hand, flame-formed carbon nanoparticles have been the subject of increasing interest in recent decades as a new procedure for synthesizing engineered nanoparticles. In order to obtain flame nanoparticles with desired characteristics and with the highest yield, it is necessary to have an in-depth knowledge of their formation process through the reaction system, the flame. It is necessary to delve into the chemical and physical details of the various steps of the mechanism that lead to the final product; pay attention to the inherent characteristics of the particles, such as size distribution, chemical composition, and physical characteristics. Moreover, depending on the final product to be obtained, flames can be modulated and varied in parameters such as temperature, residence time, mixing effect, and the fuel or additive structure. This PhD thesis focuses on studying and characterizing the carbon nanoparticles synthesized in the well-controlled combustion conditions of premixed fuel-rich flame, using a lab-scale reactor constituted by flat laminar ethylene/air premixed flame. The primary purpose of this activity has been to perform an experimental study on flame-formed carbon nanoparticles, with great attention on the still too unclear step of particle formation in flame, i.e. the nucleation. The first year of the PhD was primarily centred on the study and preliminary characterization of physicochemical evolution of flame-formed carbon nanoparticles. In order to produce different sizes of particles, carbon nanoparticles were collected at different distances from the flame front, i.e., the residence time in the flame was changed. Then, various techniques were used to characterize the produced particles. One of the first investigations was performed in the flame by the on-line differential mobility analyzer to study the particle size distribution. Subsequently, the analytical tools continued with ex-situ techniques such as Raman spectroscopy and Electron Paramagnetic Resonance, the former for chemical and structural information on particles modification and the latter to reveal and confirm the presence of radicals and to identify them. In this thesis, great attention was laid on the presence and role of radical species, above all, in the determining step of nucleation. For this reason, the research continued in the second year with a more detailed analysis of radical formation in the flame products mechanism and a more specific structural characterization of carbon nanoparticles. Indeed, a density functional theory study investigated some aspects related to the behaviour of radical molecules in flame in terms of dimerization and formation of cluster structures. Notably, the study was helpful in the differentiation between - and -radicals. Following the theoretical evaluation of the radical molecules, the question was raised about how such radicals could form, i.e., whether specific structural elements could facilitate their formation and, consequently, direct carbon particles' formation through a specific mechanism. This type of structural investigation was performed through the Proton Nuclear Resonance Spectroscopy ,1H-NMR; for the first time used in a system such as the one studied in this thesis work. Then, in the third and final year of this PhD research work, a comparative physicochemical evolution study in an aromatic fuel environment has been performed. The addition of an aromatic dopant, such as benzene, leads to some change in the flame and the particle formation in terms of particles size distribution, Raman features, and especially radical production, allowing to face up the same questions in such environment and to investigate the effect of aromatic fuel on the nature and the role of radicals in particle nucleation and growth

Improving the efficiency of computation of free energy differences

There has been a recent focus on investigating the properties of semi-conductors at the nanoscale as it is well known that the band-gap of semi-conducting materials is altered due to quantum confinement effects. The potential to fine-tune a material's properties based solely on particle size has raised significant interest both in experimental and computational studies. Zinc sulfide is one of the most studied metal sulfide semi-conductor minerals, due to its potential technological applications.Computational studies of the structural and thermodynamic properties of zinc sulfide nanoparticles and bulk structures have been performed throughout this work. A variety of computational methods have been employed, including molecular dynamics, lattice dynamics, first principles calculations, and free energy techniques, such as metadynamics and free energy perturbation. The thermodynamic stability of zinc sulfide nanoparticles as a function of size and shape has been studied. Investigation of the phase space of these systems required the use of enhanced sampling methods. The metadynamics method was specifically utilised to explore as many structures as possible in combination with extensive simulations. The use of first principles methods for these exploratory simulations was found to be prohibitively expensive, and so force field methods were primarily utilised. Throughout this investigation several force fields were used to compare and contrast their accuracy, while first principles calculations were performed, where possible, to assist in the interpretation and validation of the results.In the present study, two different collective variables, the trace of the inertia tensor and the Steinhardt bond order parameters, have been implemented and their performance in metadynamics compared. The trace of the inertia tensor was found to be useful for exploring clusters of small sizes, while the Q4 Steinhardt parameter, which describes the crystalline order of a solid, is more applicable to larger clusters. Both of these metadynamics studies resulted in clusters displaying zeolite structural motifs, including the zeolite framework `BCT'. This led us to investigate more thoroughly the stability of different zinc sulfide zeolite analogues, thereby highlighting the strengths and weaknesses of all the force fields employed. Many force fields are found to be unable to accurately represent the order of stability for bulk polymorphs.First principles calculations also highlighted that the BCT phase is less stable than either of the bulk polymorphs of zinc sulfide, in contrast to the order of stability obtained by force fields lacking a torsional term, both from literature and the rigid ion model developed during the current study. The larger nanoparticles cleaved from wurtzite exhibited internal strain upon relaxation. A new hypothetical zeolite framework was constructed from the distorted core of these clusters, and was found to possess structural similarities with the `APC' framework. The APC framework is composed of double crankshaft-chains with ”ABCABC…” stacking, while the hypothetical framework identified is formed by the same composite building unit with `ABAB: : : ' type stacking. For all the force fields used the new hypothetical framework was lower in energy than the APC framework, but higher in energy than sphalerite, wurtzite or the BCT phase.Free energy differences between small ZnS clusters in vacuum were calculated using the path variable technique, and also using static methods within the quasi-harmonic approximation. Similar values were obtained using both of these methods, validating the path collective variables used with metadynamics as an effective means of obtaining free energy differences for clusters in vacuum.In addition to clusters in vacuum, a number of studies of ZnS clusters in water were also performed. Both force field and first principles studies were employed to validate the ZnS-water interactions used for the binding energies of water to small clusters. As a further validation, the free energies of solvation of Zn2+ and S2?? in aqueous solution were calculated. The free energy of solvation for the sulfide anion was found to be close to the experimental value, while the parameters for Zn2+-water were found to require substantial modification as the solvation free energy was in error by 500 kJ/mol. While newly derived ZnS-water parameters may prove to be superior for describing ZnS clusters in bulk water, a repetition of the binding energy calculations for individual water molecules bound to ZnS clusters gave energies 2-3 times greater than those obtained via first principles methods and using the five other force fields investigated. These results highlight the issues present when attempting to transfer a model fitted in a certain way to a different application. In particular, the many-body and polarisation effects present when modelling water need to be considered when parameterising ZnS-water interactions

Advanced opto-electronics materials by fullerene and acetylene scaffolding

Functional π-systems with unusual opto-electronic properties are intensively investigated from both fundamental research and technological application viewpoints. This article reports on novel π-conjugated systems obtained by acetylenic and fullerene scaffolding. Linearly conjugated acetylenic nanorods, consisting of monodisperse poly(triacetylene) (PTA) oligomers and extending up to 18 nm length, were prepared to investigate the limits of effective conjugation and to explore at which length a monodisperse oligomer reaches the properties of an infinite polydisperse polymer. With the cyanoethynylethenes (CEEs), a powerful new class of electron acceptors is introduced that undergo intense intramolecular charge-transfer (CT) interactions with appended donors. Macrocyclic scaffolds with unusual opto-electronic properties are perethynylated dehydroannulenes, expanded radialenes, and radiaannulenes bearing peripheral dialkylanilino donor groups. Extended porphyrin-fullerene conjugates are investigated for their novel photophysical and efficient multicharge storage properties. Self-assembly of fullerenes and porphyrins, governed by weak interactions between the two components, leads to unprecedented nanopatterned surfaces that are investigated by scanning tunneling microscopy (STM