The discovery of novel carbon allotropes with tailored thermal and mechanical properties is critical for advanced thermal management. However, exploring the vast configurational space of carbon using \textit{ab initio} calculations remains computationally prohibitive. Driven by the rich topological landscape of carbon, where the competition between $sp, sp^2,$ and $sp^3$ hybridization states dictates material performance, we establish a closed-loop AI framework to explore this complex configurational space. We introduce a hybridization entropy descriptor to guide the search beyond conventional forms. Here, we establish a closed-loop AI framework that synergizes a Large Language Model (LLM) for structural generation with a Machine Learning Potential (MLP) for accelerated evaluation. Leveraging CrystaLLM to generate candidates and an iteratively refined MLP for high-fidelity validation, we screened thousands of structures to identify several stable allotropes with exotic properties. Specifically, we report ``yne-diamond C$_{12}$'' and ``yne-hex-diamond C$_{8}$'', which exhibit extreme thermal anisotropy and ultralow in-plane shear stiffness arising from their mixed $sp$-$sp^3$ hybridization. Furthermore, we discovered a complex $sp$-$sp^2$-$sp^3$ hybridized C$_{12}$ phase that combines metallic conductivity with an anomalous negative Poisson's ratio. Notably, we identified a superhard phase (C16_3) possessing a calculated Vickers hardness (103.3 GPa) exceeding that of diamond 96 GPa). Microscopic analysis reveals that thermal transport in these materials is governed by the interplay between rigid frameworks and flexible linkers. This work expands the known carbon phase space and demonstrates the efficacy of coupling generative AI with machine learning potentials for the accelerated inverse design of functional materials.
Monolithic structures can be built into graphene by the addition and subsequent re-arrangement of carbon atoms. To this end, ad-dimers of carbon are a particularly attractive building block because a number of emerging technologies offer the promise of precisely placing them on carbon surfaces. In concert with the more common Stone-Wales defect, repeating patterns can be introduced to create as yet unrealized materials. The idea of building such allotropes out of defects is new, and we demonstrate the technique by constructing two-dimensional carbon allotropes known as haeckelite. We then exte…
In this work, we propose a new methodology for obtaining 3D carbon allotrope structures from 2D ones through topological mapping. The idea is to select a 3D target structure and 'slice' it along different structural directions, creating a series of 2D structures. As a proof of concept, we chose the Tubulane structure 12-hexa(3,3) as a target. Tubulanes are 3D carbon allotropes based on cross-linked carbon nanotubes. One of obtained 2D 'sliced' structures was mapped into the biphenylene carbon (BPC). We showed that compressing BPC along different directions can generate not only the target Tubu…
A structurally stable crystalline carbon allotrope is predicted by means of the first-principles calculations. This allotrope can be derived by substituting each atom in diamond with a carbon tetrahedron, and possesses the same space group Fd^1 3m as diamond, which is thus coined as T- carbon. The calculations on geometrical, vibrational and electronic properties reveal that T-carbon, with a considerable structural stability and a much lower density 1.50 g/cm3, is a semiconductor with a direct band gap about 3.0 eV, and has a Vickers hardness 61.1 GPa lower than diamond but comparable with cub…
Based on structure prediction method, the machine learning method is used instead of the density function theory (DFT) method to predict the material properties, thereby accelerating the material search process. In this paper, we established a data set of carbon materials by high-throughput calculation with available carbon structures obtained from the Samara Carbon Allotrope Database. We then trained an ML model that specifically predicts the elastic modulus (bulk modulus, shear modulus, and the Young's modulus) and confirmed that the accuracy is better than that of AFLOW-ML in predicting the…
Using systematic evolutionary structure searching we propose a new carbon allotrope, phagraphene, standing for penta-hexa-hepta-graphene, because the structure is composed of 5-6-7 carbon rings. This two-dimensional (2D) carbon structure is lower in energy than most of the predicted 2D carbon allotropes due to its sp2-hybridization and density of atomic packing comparable to graphene. More interestingly, the electronic structure of phagraphene has distorted Dirac cones. The direction-dependent cones are further proved to be robust against external strain with tunable Fermi velocities.
A novel stable carbon allotrope is predicted by using first-principles calculations. This allotrope is obtained by replacing one of the two atoms in the primitive cell of diamond with a carbon tetrahedron, thus it contains five atoms in one primitive cell, termed T5-carbon. The stabilities of T5-carbon are checked in structural, thermal, vibrational and energy calculations. The calculations on electronic, thermal, and mechanical properties reveal that T5-carbon is a semiconductor with an indirect band gap of 3.18 eV, and has a lattice thermal conductivity of 409 W/mK. More importantly, the Vic…
Using a generalized genetic algorithm, we propose four new sp3 carbon allotropes with 5-6-7 (5-6-7-type Z-ACA and Z-CACB) or 4-6-8(4-6-8-type Z4-A3B1 and A4-A2B2) carbon rings. Their stability, mechanical and electronic properties are systematically studied using first-principles method. We find that all these four carbon allotropes show amazing stability in comparison with recently proposed carbon phases. Both ZACA and Z-CACB are direct-band-gap semiconductors with band gaps of 2.261 eV and 4.196 eV, respectively. Whereas Z4-A3B1 and A4-A2B2 are indirect-band-gap semiconductors with band gaps…
We report a general scheme to systematically construct two classes of structural families of superhard sp3 carbon allotropes of cold compressed graphite through the topological analysis of odd 5+7 or even 4+8 membered carbon rings stemmed from the stacking of zigzag and armchair chains. Our results show that the previously proposed M, bct-C4, W and Z allotropes belong to our currently proposed families and that depending on the topological arrangement of the native carbon rings numerous other members are found that can help us understand the structural phase transformation of cold-compressed g…
Two novel two-dimensional carbon allotropes comprised of octagons and pentagons are proposed based on the first-principles calculations. The two carbon allotropes, named OPG-L and OPG-Z, are found to have distinct properties. OPG-L is metallic, while OPG-Z is a gapless semimetal. Remarkably, OPG-Z exhibits pronounced electronic anisotropy with highly anisotropic Dirac points at the Fermi level. A tight-binding model is suggested to describe the low-energy quasiparticles, which clarifies the origin of the anisotropic Dirac points. Such an anisotropic electronic characteristic of OPG-Z is expect…
From crystal chemistry rationale and density functional DFT calculations, novel tetragonal carbon C5 is proposed as simplest ultrahard allotrope with mixed hybrid carbon hybridizations (sp2 - sp3). Novel pentacarbon is identified as cohesive and stable both dynamically and mechanically. Whereas charge density is localized about tetrahedral C-sp3, it is found delocalized around trigonal C-sp2 resulting in metallic behavior. The anisotropic structure characteristics caused by the aligned trigonal carbon along the tetragonal c-axis provide high Vickers hardness with a magnitude close to diamond
Four sp3 carbon allotropes with six, eight, and 16 atoms per primitive cell have been derived using a combination of metadynamics simulations and topological scan. A chiral orthorhombic phase oC16 (C2221) was found to be harder than monoclinic M-carbon and shows excellent stability in the high-pressure range. A second orthorhombic phase of Cmmm symmetry, by \sim 0.028 eV/atom energetically lower than W-carbon, can be formed from graphite at \sim 9 GPa. In general, the mechanical response under pressure was found to depend on the structure topology, which reflects the way rings are formed from …
We identify by ab initio calculations a new type of three-dimensional carbon allotropes constructed by inserting acetylenic or diacetylenic bonds into a body-centered cubic C$_8$ lattice. The resulting $sp+sp^3$-hybridized cubane-yne and cubane-diyne structures consisting of C$_8$ cubes can be characterized as a cubic crystalline modification of linear carbon chains, but energetically more favorable than the simplest linear carbyne chain and the cubic tetrahedral diamond and yne-diamond consisting of C$_4$ tetrahedrons. Electronic band calculations indicate that these new carbon allotropes are…
In a recent Letter [1] Y. Fujii et al. proposed a new carbon allotrope and claimed its extremely high Young's and shear moduli of 1691 and 1113 GPa, respectively, surpassing those of diamond by 1.5 and 2 times! The authors also claimed unique negative averaged Poisson's ratio of -0.24, bulk modulus of 381 GPa and record value of the sound speed 28.7 km/s for this carbon modification. Here we show by two independent computations that these values were obtained as a result of errors. The new hypothetical allotrope has in fact quite moderate elastic moduli, unremarkable for a carbon structure wit…
We study the optical properties of lowest-energy carbon allotropes in the infrared, visible and ultra-violet ranges of light in the general gradient approximation of the density functional theory. In our calculations we used the all-electron approach as well as the pseudo-potential approximation. In the infrared range, the complex dielectric functions, infrared and Raman spectra have been calculated using CRYSTAL14 program. The electronic properties and energy-dependent dielectric functions in the visible and ultraviolet ranges have been calculated using VASP program. We have described with a …
Using first-principles method, we investigate the energetic stability, dynamic stability and electronic properties of two three-dimensional (3D) all-sp2 carbon allotropes, sp2-diamond and cubic-graphite. The cubic-graphite was predicted by Michael O'Keeffe in 1992 (Phys. Rev. Lett., 68, 15, 1992.) possessing space group of Pn-3m (224), whereas the sp2-diamond with the space group Fd-3m (227) same as that of diamond has not been reported before. Our results indicate that sp2-diamond is more stable than previously proposed K4-carbon and T-carbon, and cubic-graphite is even more stable than super…
The phonon properties, electronic structures and optical properties of novel carbon allotropes, such as monolayer penta-graphene (PG), double-layer PG and T12-carbon, were explored by means of first-principles calculations. Results of phonon calculations demonstrate that these exotic carbon allotropes are dynamically stable. In addition, the bulk T12 phase is an indirect-gap semiconductor having a bandgap of ~4.89 eV. Whereas the bulk material transforms to a 2D phase, the monolayer and double-layer PG become quasi-direct gap semiconductors with smaller band gaps of ~2.64 eV and ~3.27eV, respe…
A metallic covalently bonded carbon allotrope is predicted via first principles calculations. It is composed of an $sp^3$ carbon framework that acts as a diamond anvil cell by constraining the distance between parallel cis-polyacetylene chains. The distance between these $sp^2$ carbon atoms renders the phase metallic, and yields two well-nested nearly parallel bands that span the Fermi level. Calculations show that this phase is a conventional superconductor, with the motions of the $sp^2$ carbons being key contributors to the electron phonon coupling. The $sp^3$ carbon atoms impart superior m…
We present a systematic search for low-energy metastable superhard carbon allotropes by using the recently developed evolutionary metadynamics technique. It is known that cold compression of graphite produces an allotrope at 15-20 GPa. Here we look for all low-enthalpy structures accessible from graphite. Starting from 2H- or 3R-graphite and applying the pressure of 20 GPa, a large variety of intermediate $sp^3$ carbon allotropes were observed in evolutionary metadynamics simulation. Our calculation not only found all the previous proposed candidates for `superhard graphite', but also predicte…
A Concise Review of Recently Synthesized 2D Carbon Allotropes: Amorphous Carbon, Graphynes, Biphenylene and Fullerene Networks
São Paulo State University (UNESP)（圣保罗州立大学）；Universidade Estadual de Campinas (UNICAMP)（坎皮纳斯州立大学）；Federal University of Rio Grande do Norte (UFRN)（北里奥格兰德联邦大学）；University of Brasília (UnB)（巴西利亚大学）；Rice University（莱斯大学）
A sp2-sp3 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. HSH-carbon is predicted to be a semiconductor with an indirect energy gap of 3.56 eV …
Electronic and structural properties of a 3D carbon allotrope made of Hopf-linked graphenes, which we call a Hopfene - a type of topological crystal, are examined by semi-empirical molecular-orbital and density-functional-theoretical methods, where band-structure analyses reveal very different properties from those of 2D graphenes. Furthermore, the analyses give an interesting finding that, depending on graphene-sheet spacings, Hopfenes exhibit different band features between primary-type Hopfene with a finite minimum sheet spacing and secondary type with its double-sized spacing. The primary …
Novel extended networks of C8, Si8 and silicon carbide Si4C4 are proposed based on crystal chemistry rationale and optimized structures to ground state energies and derived physical properties within the density functional theory (DFT). The two carbon and silicon allotropes and the silicon carbide belong to primitive tetragonal space group P-4m2 Number 115. C8 allotrope structure made of corner sharing C4 and Si4 tetrahedra is illustrated by charge density projections exhibiting sp3 like carbon hybridization. From careful symmetry analysis, Symmetry analysis of C8 indicated that it is another …
We have investigated the structural, mechanical and electronic properties of D-carbon by ab initio calculations, a new phase of crystalline sp3 carbon (pace group D2h5, Pmma-orthorhombic). Total-energy calculations demonstrate that D-carbon is energetically more favorable than previously proposed T6 structure. State-of-the-art theoretical calculations show that this new phase is dynamic, mechanical, and thermal stable at zero pressure, and more stable than graphite beyond 63.7 GPa. Importantly, the calculations reveal that D-carbon possesses high Vickers hardness (86.58 GPa) and bulk modulus (…
Superstructures of cubic and hexagonal diamonds (h- and c-diamond) comprising a family of stable diamond-like $sp^3$ hybridized novel carbon allotropes are proposed, which are referred to as U$_n$-carbon where $n \geq 2$ denotes the number of structural layers in a unit cell. The conventional h- and c-diamond are included in this family as members with $n=2$ and 3, respectively. U$_n$-carbon ($n=4-6$), which are unveiled energetically and thermodynamically more stable than h-diamond and possess remarkable kinetic stabilities, are shown to be insulators with indirect gaps of $5.6 \sim 5.8$ eV, …
We have performed quantum Monte Carlo calculations to study the cohesion energetics of carbon allotropes, including $sp^3$-bonded diamond, $sp^2$-bonded graphene, $sp$-$sp^2$ hybridized graphynes, and $sp$-bonded carbyne. The computed cohesive energies of diamond and graphene are found to be in excellent agreement with the corresponding values determined experimentally for diamond and graphite, respectively, when the zero-point energies, along with the interlayer binding in the case of graphite, are included. We have also found that the cohesive energy of graphyne decreases systematically as t…
A body-centered tetragonal carbon (bct-Carbon) allotrope has been predicted to be a transparent carbon polymorph obtained under pressure. The structural transition pathways from graphite to diamond, M-Carbon, and bct-Carbon are simulated and the lowest activation barrier is found for the graphite-bct transition. Furthermore, bct-Carbon has higher shear strength than diamond due to its perpendicular graphene-like structure. Our results provide a possible explanation for the formation of a transparent carbon allotrope via the cold compression of graphite. We also verify that this allotrope is ha…
This article continues our recent publication [I.A. Baburin and D.M. Proserpio and V.A. Saleev and A.V. Shipilova, Phys. Chem. Chem. Phys.17, 1332 (2015)] where we have presented a comprehensive computational study of sp3 carbon allotropes based on the topologies proposed for zeolites. Here we predict six new silicon and six new germanium allotropes which have the same space group symmetries and topologies as those predicted earlier for the carbon allotropes, and study their structural, elastic, vibrational, electronic and optical properties.
Based on crystal chemistry considerations and quantum density functional theory ground state calculations, rhombohedral rh-C3 and hexagonal h-C6 carbon allotropes are proposed and energetically calculated as new stable ultra-hard phases likewise lonsdaleite. Along the two kinds of carbon in linear C2-C1-C2 lattice, distorted tetrahedra C2(sp3) with an angle of 106.17° (smaller than ideal 109.4°) and C1(sp)-like hybridizations are inferred from charge density projections. The calculated elastic constants point to a strong anisotropy of mechanical properties of rh-C3 and h-C6 with an exceptional…
We present an ab-initio study of boron nitride as well as carbon allotropes. Their relative thermodynamic stabilities and structural phase transitions from low- to high-density phases are investigated. Pressure-temperature phase diagrams are calculated and compared to experimental findings. The calculations are performed using quantum chemical wavefunction based as well as density functional theories. Our findings reveal that predicted energy differences often depend significantly on the choice of the employed method. Comparison between calculated and experimental results allows for benchmarki…
Elemental phosphorus nanostructures are notorious for a large number of allotropes, which limits their usefulness as semiconductors. To limit this structural diversity, we synthesize selectively quasi-1D phosphorus nanostructures inside carbon nanotubes (CNTs) that act both as stable templates and nanoreactors. Whereas zigzag phosphorus nanoribbons form preferably in CNTs with an inner diameter exceeding 1.4 nm, a previously unknown square columnar structure of phosphorus is observed to form inside narrower nanotubes. Our findings are supported by electron microscopy and Raman spectroscopy obs…
The covalent functionalization of carbon allotropes represents a main topic in the growing field of nano materials. However, the development of functional architectures is impeded by the intrinsic polydispersibility of the respective starting material, the unequivocal characterization of the introduced functional moieties and the exact determination of the degree of functionalization. Based on a novel carbon allotrope functionalization reaction, utilizing λ^3-iodanes as radical precursor systems, we were able to demonstrate the feasibility to separate and to quantify thermally detached functio…
In a recent Letter, Fujii et. al. [Phys. Rev. Lett. 125, 016001] predicted a new carbon allotrope, pentadiamond, with remarkable mechanical properties: elastic moduli comparable or larger than diamond, and negative Poisson's ratio $μ$ = -0.241. The estimated Vicker's hardness is 422 GPa, $\sim$4.6 times higher than in diamond($\sim$92 GPa), the hardest material known to date. Pentadiamond, however was not investigated. Motivated by this, we used different approaches to estimate the elastic properties of pentadiamond with different approximations based on Density Functional Theory. The tests we…
A novel allotrope of carbon with $P2/m$ symmetry was identified during an \emph{ab-initio} minima-hopping structural search which we call $M10$-carbon. This structure is predicted to be more stable than graphite at pressures above 14.4 GPa and consists purely of $sp^3$ bonds. It has a high bulk modulus and is almost as hard as diamond. A comparison of the simulated X-ray diffraction pattern shows a good agreement with experimental results from cold compressed graphite.
3D carbon allotropes: Topological quantum materials with obstructed atomic insulating phases, multiple bulk-boundary correspondences, and real topology
Graphite may be viewed as a low-surface-energy carbon allotrope with little layer-layer interaction. Other low-surface-energy allotropes but with much stronger layer-layer interaction may also exist. Here, we report a first-principles prediction for one of the known carbon allotropes, bcc-C6 (a body centered carbon allotrope with six atoms per primitive unit) that should have exceptionally low-surface energy and little size dependence down to only a couple layer thickness. This unique property may explain the existence of the relatively-high-energy bcc-C6 during growth. The electronic properti…
Cyclo-Graphyne: A Highly Porous and Semimetallic 2D Carbon Allotrope with Dirac Cones
Federal University of Parana（巴拉那联邦大学）；Interdisciplinary Center for Science, Technology, and Innovation (CICTI), Federal University of Parana（巴拉那联邦大学跨学科科学与技术创新中心）
From layered 2D carbon to 3D tetrahedral original allotropes C12 and C18 with physical properties related to diamond: Crystal chemistry and DFT investigations
The interplay between light and matter attracts tremendous interest for exploring novel topological quantum states and their phase transitions. Here we show by first-principles calculations and the Floquet theorem that a carbon allotrope bct-C$_{16}$, a typical nodal-line semimetal, exhibits exotic photoinduced Floquet mixed-Weyl semimetallic features. Under the irradiation of a linearly polarized light, bct-C$_{16}$ undergos a topological phase transition from a Driac nodal-line semimetal to a Weyl semimetal with two pairs of tunable Weyl points. With increasing the light intensity, left-hand…
A series of carbon allotropes with novel optoelectronic and rich topological properties is predicted by systematic first-principles calculations. These fascinating carbon allotropes can be derived by inserting acetylenic linkages (-C$\equiv$C-) into graphite, hence they are termed as grapheaynes. Grapheaynes possess two different space groups, $P$2/$m$ or $C$2/$m$, and contain simultaneously the $sp$, $sp^2$, and $sp^3$ chemical bonds. They have formation energies lower than the already experimentally synthesized graphdiyne and other theoretically predicted carbon allotropes with acetylenic li…
We have investigated through fully atomistic reactive molecular dynamics and DFT simulations, the mechanical properties and fracture dynamics of novamene, a new 3D carbon allotrope structure recently proposed. Our results showed that novamene is an anisotropic structure with relation to tensile deformation. Although novamente shares some mechanical features with other carbon allotropes, it also exhibits distinct ones, such as, extensive structural reconstructions (self-healing effect). Novamene presents ultimate strength (~ 100 GPa) values lower than other carbon allotropes, but it has the hig…
Original orthorhombic tetrahedral and trigonal hybrid allotropes Cn with n= 8, 10, 12, 14 possessing ethene -like and propadiene -like units: Crystal chemistry and first principles
All carbon materials, e.g., amorphous carbon (a-C) coatings and C60 fullerene thin films, play an important role in short-wavelength free-electron laser (FEL) research motivated by FEL optics development and prospective nanotechnology applications. Responses of a-C and C60 layers to the extreme ultraviolet (SPring-8 Compact SASE Source in Japan) and soft x-ray (free-electron laser in Hamburg) free-electron laser radiation are investigated by Raman spectroscopy, differential interference contrast, and atomic force microscopy. A remarkable difference in the behavior of covalent (a-C) and molecul…
Flat bands form in a 3D Hopf-linked graphene crystal or a 3D carbon allotrope named Hopfene, which qualitatively differ from bands of only graphenes. This paper discusses carbon-hexagon deformation on the level shift of a flat band via density-functional-theoretical (DFT) analysis to set the flat-band level to the Fermi level, viz., to utilize its large density of states for magnetic- and electronic-property researches. Tight-binding (TB) analysis is also performed for a comparison with the DFT analysis; here, a qualitative agreement between TB and DFT bands is obtained. The DFT analysis shows…
Finding appropriate interatomic potentials which can accurately describe the crystal structure of material is one of important topics in material science. In this paper, several interatomic potentials which comprise of Lennard-Jones (LJ) potentials have been proposed for describing both the crystal structures and the evolution of microstructure of the allotropes of carbon such as diamond and graphite. The validity of these LJ potentials can be checked by molecular dynamics (MD) simulation. For the lattice identification of simulated systems, we have calculated the distribution functions of the…
The exploration of topological phases in carbon allotropes offers a fascinating avenue to realize topological devices based on carbon materials. Here, using first-principles calculations, we propose a novel metastable carbon allotrope, which possesses exotically helical carbon chains bridged by quadrangle-rings. This unique structure with sp2-sp3 bonding networks crystallizes in a noncentrosymmetric face-centered orthogonal (fco) lattice with six atoms in a unit cell, thus named fco-C6. The considerable stability of fco-C6 is confirmed by phonon spectra, elastic constants, and ab initio molecu…
On the Thermomechanical Properties and Fracture Patterns of the Novel Nonbenzenoid Carbon Allotrope (Biphenylene Network): A Reactive Molecular Dynamics Study
Graphene is considered one of the most promising materials for future electronic. However, in its pristine form graphene is a gapless material, which imposes limitations to its use in some electronic applications. In order to solve this problem many approaches have been tried, such as, physical and chemical functionalizations. These processes compromise some of the desirable graphene properties. In this work, based on ab initio quantum molecular dynamics, we showed that a two-dimensional carbon allotrope, named biphenylene carbon (BPC) can be obtained from selective dehydrogenation of porous g…
