General principles to high-throughput constructing two-dimensional carbon allotropes

We propose general principles to construct two-dimensional(2D)single-atom-thick carbon allotropes.They can be viewed as the generalization of patterning Stone–Walse defects(SWDs)by manipulating bond rotation and of patterning inverse SWDs by adding(or removing)carbon pairs on the pristine graphene,respectively.With these principles,numerous 2D allotropes of carbon can be systematically constructed.Using 20 constructed 2D allotropes as prototypical and benchmark examples,besides nicely reproducing all well-known ones,such as pentaheptites,T-graphene,OPGs,etc,we still discover 13 new allotropes.Their structural,thermodynamic,dynamical,and electronic properties are calculated by means of first-principles calculations.All these allotropes are metastable in energy compared with that of graphene and,except for OPG-A and C3-10-H allotropes,the other phonon spectra of 18 selected allotropes are dynamically stable.In particular,the proposed C3-11 allotrope is energetically favorable than graphene when the temperature is increased up to 1043 K according to the derived free energies.The electronic band structures demonstrate that(i)the C3-8 allotrope is a semiconductor with an indirect DFT band gap of 1.04 e V,(ii)another unusual allotrope is C3-12 which exhibits a highly flat band just crossing the Fermi level,(iii)four allotropes are Dirac semimetals with the appearance of Dirac cones at the Fermi level in the lattices without hexagonal symmetry,and(vi)without the spin–orbit coupling(SOC)effect,the hexagonal C3-11 allotrope exhibits two Dirac cones at K and K points in its Brillouin zone in similarity with graphene.

Theoretical Study of Carrier Mobility in Two-Dimensional Tetragonal Carbon Allotrope from Porous Graphene

The carrier mobility of two-dimensional tetragonal carbon allotrope （T-CA） from porous graphene is investigated by first-principles calculations. T-CA can be constructed from divacancy and Stone-Thrower--Wales defects from graphene. T-CA is a direct semiconductor with a band gap of 0.4 eV at F point. T-CA possesses a high carrier mobility of the order of 104 cm2V-ls-1. As our study demonstrates, T-CA has potential applications for next-generation electronic materials.

C2-Si:a Novel Silicon Allotrope in Monoclinic Phase

Based on density functional theory(DFT),a new silicon allotrope C2-Si is proposed in this work.The mechanical stability and dynamic stability of C2-Si are examined based on the elastic constants and phonon spectrum.According to the ratio of bulk modulus and shear modulus,C2-Si has ductility under ambient pressure;compared with Si_(64),Si_(96),I4/mmm and h-Si6,C2-Si is less brittle.Within the Heyd-Scuseria-Ernzerhof(HSE06)hybrid functional,C2-Si is an indirect narrow band gap semiconductor,and the band gap of C2-Si is only 0.716 eV,which is approximately two-thirds of c-Si.The ratios of the maximum and minimum values of the Young’s modulus,shear modulus and Poisson’s ratio in their 3D spatial distributions for C2-Si are determined to characterize the anisotropy.In addition,the anisotropy in different crystal planes is also investigated via 2D representations of the Young’s modulus,shear modulus,and Poisson’s ratio.Among more than ten silicon allotropes,C2-Si has the strongest absorption ability for visible light.

tP40 carbon: A novel superhard carbon allotrope

In this work, a novel carbon allotrope tP40 carbon with space group P4/mmm is proposed. The structural stability, mechanical properties, elastic anisotropy, and electronic properties of tP40 carbon are investigated systematically by using density functional theory (DFT). The calculated elastic constants and phonon dispersion spectra indicate that the tP40 phase is a metastable carbon phase with mechanical stability and dynamic stability. The B/G ratio indicates that tP40 carbon is brittle from 0 GPa to 60 GPa, while tP40 carbon is ductile from 70 GPa to 100 GPa. Additionally, the anisotropic factors and the directional dependence of the Poisson's ratio, shear modulus, and Young's modulus of tP40 carbon at different pressures are estimated and plotted, suggesting that the tP40 carbon is elastically anisotropic. The calculated hardness values of tP40 carbon are 44.0 GPa and 40.2 GPa obtained by using Lyakhov–Oganov's model and Chen's model, respectively, which means that the tP40 carbon can be considered as a superhard material. The electronic band gap within Heyd–Scuseria–Ernzerhof hybrid functional (HSE06) is 4.130 eV, and it is found that the tP40 carbon is an indirect and wider band gap semiconductor material.

Raman and infrared spectra of complex low energy tetrahedral carbon allotropes from first-principles calculations

Up to now,at least 806 carbon allotropes have been proposed theoretically.Three interesting carbon allotropes(named Pbam-32,P6/mmm,and I43d)were recently uncovered based on a random sampling strategy combined with space group and graph theory.The calculation results show that they are superhard and remarkably stable compared with previously proposed metastable phases.This indicates that they are likely to be synthesized in experiment.We use the factor group analysis method to analyze theirΓ-point vibrational modes.Owing to their large number of atoms in primitive unit cells(32 atoms in Pbam-32,36 atoms in P6/mmm,and 94 atoms in I43d),they have many Raman-and infrared-active modes.There are 48 Raman-active modes and 37 infrared-active modes in Pbam-32,24 Raman-active modes and 14 infrared-active modes in P6/mmm,and 34 Raman-active modes and 35 Raman-and infrared-active modes in I43d.Their calculated Raman spectra can be divided into middle frequency range from 600 cm-1 to 1150 cm-1 and high frequency range above 1150 cm-1.Their largest infrared intensities are 0.82,0.77,and 0.70(D/Å)2/amu for Pbam,P6/mmm,and I43d,respectively.Our calculated results provide an insight into the lattice vibrational spectra of these sp3 carbon allotropes and suggest that the middle frequency Raman shift and infrared spectrum may play a key role in identifying newly proposed carbon allotropes.

A NEW CHIRAL ALLOTROPE C_(80)

The theoretical prophecy is given on a new chiral allotrope of Fullerene-C80.C80 molecuule should have 3 C2 symmetric axes, which should be vertical each other.C80 should have two chiral allotropes. 13C-NMR spectra of C80 should consist of 20lines of equal intensity.

The art of designing carbon allotropes

Stimulated by the success of graphene and diamond, a variety of carbon allotropes have been discovered in recent years in either two-dimensional or three-dimensional configurations. Although these emerging carbon allotropes share some common features, they have certain different and novel mechanical or physical properties. In this review, we present a comparative survey of some of the major properties of fifteen newly discovered carbon allotropes. By comparing their structural topology, we propose a general route for designing most carbon allotropes from two mother structures, namely, graphene and diamond. Furthermore, we discuss several future prospects as well as current challenges in designing new carbon allotropes.

A novel hybrid 8p-sp2 metallic carbon allotrope

In this paper, we propose a novel hybrid sp-sp2 monoclinic carbon allotrope mC12. This allotrope is a promising light metallic material, the mechanical and electronic properties of which are studied based on first-principles calculations. The structure of this new mC12 is mechanically and dynamically stable at ambient pressure and has a low equilibrium density due to its large cell volume. Furthermore, calculations of the elastic constants and moduli reveal that mC12 has a rigid mechanical property. Finally, it exhibits metallic characteristics, owing to the mixture of sp-sp2 hybrid carbon atoms.

HSH-C_(10):A new quasi-2D carbon allotrope with a honeycomb-star-honeycomb lattice

Two-dimensional(2 D)materials with honeycomb,kagome or star lattice have been intensively studied because electrons in such lattices could give rise to exotic quantum effects.In order to improve structural diversity of 2 D materials to achieve unique properties,here we propose a new quasi-2 D honeycombstar-honeycomb(HSH)lattice based on first-principles calculations.A carbon allotrope named HSH-C_(10) is designed with the HSH lattice,and its mechanical properties have been intensively investigated through total energy,phonon dispersion,ab initio molecular dynamic simulations,as well as elastic constants calculations.Besides the classical covalent bonds,there is an interesting charge-shift bond in this material from the chemical bonding analysis.Additionally,through the analysis of electronic structure,HSH-C_(10) is predicted to be a semiconductor with a direct band gap of 2.89 e V,which could combine the desirable characteristics of honeycomb and star lattice.Importantly,by modulating coupling strength,a flat band near the Fermi level can be obtained in compounds HSH-C_(6)Si_(4) and HSH-C_(6)Ge_(4),which have potential applications in superconductivity.Insight into such mixed lattice would inspire new materials with properties we have yet to imagine.

P2_(1)2_(1)2_(1)-C16: An ultrawide bandgap and ultrahard carbon allotrope with the bandgap larger than diamond

Ultrawide bandgap semiconductor,e.g.,diamond,is considered as the next generation of semiconductor.Here,a new orthorhombic carbon allotrope(P2_(1)2_(1)2_(1)-C16)with ultrawide bandgap and ultra-large hardness is identified.The stability of the newly designed carbon is confirmed by the energy,phonon spectrum,ab-initio molecular dynamics and elastic constants.The hardness ranges from 88 GPa to 93 GPa according to different models,which is comparable to diamond.The indirect bandgap reaches 6.23 eV,which is obviously larger than that of diamond,and makes it a promising ultra-wide bandgap semiconductor.Importantly,the experimental possibility is confirmed by comparing the simulated X-ray diffraction with experimental results,and two hypothetical transformation paths to synthesize it from graphite are proposed.

HSH-carbon: A novel sp^(2)–sp^(3) carbon allotrope with an ultrawide energy gap

An sp^(2)-sp^(3) hybrid carbon allotrope named HSH-carbon is proposed by the first-principles calculations.The structure of HSH-carbon can be regarded as a template polymerization of[1.1.1]propellane molecules in a hexagonal lattice,as well as,an AA stacking of recently reported HSH-C10 consisting of carbon trigonal bipyramids.Based on calculations,the stability of this structure is demonstrated in terms of the cohesive energy,phonon dispersion,Born–Huang stability criteria,and ab initio molecular dynamics.HSHcarbon is predicted to be a semiconductor with an indirect energy gap of 3.56 eV at the PBE level or 4.80 eV at the HSE06 level.It is larger than the gap of Si and close to the gap of c-diamond,which indicates HSH-carbon is potentially an ultrawide bandgap semiconductor.The effective masses of carriers in the VB and CB edge are comparable with wide bandgap semiconductors such as GaN and ZnO.The elastic behavior of HSH-carbon such as bulk modulus,Young’s modulus and shear modulus is comparable with that of T-carbon and much smaller than that of c-diamond,which suggests that HSH-carbon would be much easier to be processed than c-diamond in practice.

Demanding energy from carbon

Carbon is the central element driving the evolution of our human society towards prosperity over several historical stages.As for now,we are in a stage of blossoming sciences and technologies related to carbon materials,as a result of which our evergrowing energy demand has been largely satisfied.Yet,the expected rise of carbon energy consumption and the emerging environmental concerns have prevented us from being optimistic.To build a sufficiently powered future,we have been revolutionizing our ways of carbon energy utilization by discovering and designing new carbon structures,exploring and enhancing their unique physicochemical properties,and pursuing environmentally friendly strategies.Emerging structures such as graphene and sp-bonded C18 have allowed us to discover carbon’s promising properties such as energy storage and superconductivity,while green energy solutions such as fuel cells and CO2 reduction are working synergistically to purify the ecospheric carbon cycle.Therefore,this essay timely discusses related carbon sciences and technologies that have been the milestones shaping our energy consumption,based on which our energy future can be envisioned to be green and prosperous.

Phase Field Modelling Allotropic Transformation of Solid Solution

Based on multiphase field conception and integrated with the idea of vector-valued phase field,a phase field model for typical allotropic transformation of solid solution is proposed.The model takes the non-uniform distribution of grain boundaries of parent phase and crystal orientation into account in proper way,as being illustrated by the simulation of austenite to ferrite transformation in low carbon steel.It is found that the misorientation dependent grain boundary mobility shows strong influence on the formation of ferrite morphology comparing with the weak effect exerted by misorientation dependent grain boundary energy.The evolution of various types of grain boundaries are quantitatively characterized in terms of its respective grain boundary energy dissipation.The simulated ferrite fraction agrees well with the expectation from phase diagram,which verifies this model.

High-performance violet phosphorus photodetectors with van der Waals-assisted contacts

Black phosphorus(BP) as a narrow-bandgap two-dimensional semiconductor material has been extensively studied. And the allotrope violet phosphorus(VP) exhibits wide bandgap properties extending the application in the visible light band. However,due to the Schottky barrier of metal/semiconductor contacts(M/S), further device application of VP is limited. Here, VP-based photodetectors with van der Waals-assisted contact were demonstrated, achieving quasi-Ohmic M/S contacts. The output characteristics in dark conditions show ultralow current at the pA level. And the device exhibits a high current on-off ratio of 10~5and a fast response speed of 8.4 ms. Furthermore, we constructed the first allotropic photodetector based on BP and VP heterojunction. The device maintains ultralow dark current(~ pA) while exhibiting faster carrier transport, with 945 μs response time and polarization detection capability. These results offer an effective way to study the optoelectronic properties of VP and promote the study of allotropic heterojunction devices.

Mechanical Anisotropic and Electronic Properties of Amm2-carbon under Pressure

Structural, electronic properties and mechanical anisotropy of Amm2-carbon are investigated utilizing tlrst-principles calculations by Oambridge Serial Total Energy Package （CASTEP） code. The work is performed with the generalized gradient approximation in the form of Perdew Burke-Ernzerhof （PBE）, PBEsol, Wu and Cohen （WC） and local density approximation in the form of Ceperley and Alder data as parameterized by Perdew and Zunger （CA-PZ）. The mechanical anisotropy eMculations show that Amm2-carbon exhibit large anisotropy in elastic moduli, such as Poisson＇s ratio, shear modulus and Young＇s modulus, and other anisotropy factors, such as the shear anisotropic factor and the universal anisotropic index AU. It is interestingly that the anisotropy in shear modulus and Young＇s modulus, universal anisotropic index and the shear anisotropie factor all increases with increasing pressure, but the anisotropy in Poisson＇s ratio decreases. The band structure calculations reveal that Amm2-carbon is a direct-band-gap semiconductor at ambient pressure, but with the pressure increasing, it becomes an indirect-band-gap semiconductor.

Physical Properties of Group 14 in P6222 Phase: First-Principles Calculations

Two new Group Ⅳ element allotropes Si3 and Ge3 in P6222 phase are predicted in this work and their physical properties are investigated using the density functional theory.Each of the newly predicted allotropes has a superdense structure, which is mechanically, dynamically, and thermodynamically stable, as verified by elastic constants,phonon dispersion spectra and relative enthalpies, respectively.The mechanical anisotropy properties are studied in detail by illustrating the directional dependence of Young’s modulus, discussing the universal anisotropic index, and calculating shear anisotropy factors together with bulk moduli.It shows that P6222–Si3 exhibits the greater anisotropy than P6222–Ge3, and interestingly both of the newly predicted crystals appear to be isotropic in the(001) plane.Additionally, the Debye temperature, sound velocities, and the minimum thermal conductivity are examined to evaluate the thermodynamic properties of C3, Si3, and Ge3 in P6222 phase, and the electronic band structures are achieved by HSE06 hybrid functional, which indicate that P6222–C3 and –Si3 are indirect band gap semiconductors and P6222–Ge3 exhibits the metallic feature.

A ketone-functionalized aromatic saddle as a potential building block for negatively curved carbon nanobelts

A novel ketone-functionalized aromatic saddle consisting of 72 sp^2 carbon atoms is successfully synthesized and unambiguously identified with X-ray crystallography.It can,in principle,be used as a building block for synthesis of negatively curved carbon nanobelts and for a bottom-up approach to negatively curved carbon allotropes.

Scanning probe microscopy in probing low-dimensional carbon-based nanostructures and nanomaterials

Carbon,as an indispensable chemical element on Earth,has diverse covalent bonding ability,which enables construction of extensive pivotal carbon-based structures in multiple scientific fields.The extraordinary physicochemical properties presented by pioneering synthetic carbon allotropes,typically including fullerenes,carbon nanotubes,and graphene,have stimulated broad interest in fabrication of carbon-based nanostructures and nanomaterials.Accurate regulation of topology,size,and shape,as well as controllably embedding target sp^(n)-hybridized carbons in molecular skeletons,is significant for tailoring their structures and consequent properties and requires atomic precision in their preparation.Scanning probe microscopy(SPM),combined with on-surface synthesis strategy,has demonstrated its capabilities in fabrication of various carbon-based nanostructures and nanomaterials with atomic precision,which has long been elusive for conventional solution-phase synthesis due to realistic obstacles in solubility,isolation,purification,etc.More intriguingly,atom manipulation via an SPM tip allows unique access to local production of highly reactive carbon-based nanostructures.In addition,SPM provides topographic information of carbon-based nanostructures as well as their characteristic electronic structures with unprecedented submolecular resolution in real space.In this review,we overview recent exciting progress in the delicate application of SPM in probing low-dimensional carbon-based nanostructures and nanomaterials,which will open an avenue for the exploration and development of elusive and undiscovered carbon-based nanomaterials.