A 2D metastable carbon allotrope, penta-graphene, composed entirely of carbon pentagons and resembling the Cairo pentagonal tiling, is proposed. State-of-the-art theoretical calculations confirm that the new carbon polymorph is not only dynamically and mechanically stable, but also can withstand temperatures as high as 1000 K. Due to its unique atomic configuration, penta-graphene has an unusual negative Poisson’s ratio and ultrahigh ideal strength that can even outperform graphene. Furthermore, unlike graphene that needs to be functionalized for opening a band gap, penta-graphene possesses an intrinsic quasi-direct band gap as large as 3.25 eV, close to that of ZnO and GaN. Equally important, penta-graphene can be exfoliated from T12-carbon. When rolled up, it can form pentagon-based nanotubes which are semiconducting, regardless of their chirality. When stacked in different patterns, stable 3D twin structures of T12-carbon are generated with band gaps even larger than that of T12-carbon. The versatility of penta-graphene and its derivatives are expected to have broad applications in nanoelectronics and nanomechanics.

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Penta-graphene: A new carbon allotrope

Flat carbon (sp(2) and sp) networks endow the graphdiyne and graphyne families with high degrees of π-conjunction, uniformly distributed pores, and tunable electronic properties; therefore, these materials are attracting much attention from structural, theoretical, and synthetic scientists wishing to take advantage of their promising electronic, optical, and mechanical properties. In this Review, we summarize a state-of-the-art research into graphdiynes and graphynes, with a focus on the latest theoretical and experimental results. In addition to the many theoretical predictions of the potential properties of graphdiynes and graphynes, we also discuss experimental attempts to synthesize and apply graphdiynes in the areas of electronics, photovoltaics, and catalysis.

Graphdiyne and graphyne: from theoretical predictions to practical construction

Using density functional theory coupled with Boltzmann transport equation with relaxation time approximation, we investigate the electronic structure and predict the charge mobility for a new carbon allotrope, the graphdiyne for both the sheet and nanoribbons. It is shown that the graphdiyne sheet is a semiconductor with a band gap of 0.46 eV. The calculated in-plane intrinsic electron mobility can reach the order of 10(5) cm(2)/(V s) at room temperature, while the hole mobility is about an order of magnitude lower.

Electronic structure and carrier mobility in graphdiyne sheet and nanoribbons: theoretical predictions

Graphynes (GYs) are carbon allotropes with single-atom thickness that feature layered 2D structure assembled by carbon atoms with sp- and sp2- hybridization form. Various functional theories have predicted GYs to have natural band gap with Dirac cones structure, presumably originating from inhomogeneous π-bonding between those carbon atoms with different hybridization and overlap of the carbon 2pz orbitals. Among all the GYs, graphdiyne (GDY) was the first reported to be prepared practically and, hence, attracted the attention of many researchers toward this new planar, layered material, as well as other GYs. Several approaches have been reported to be able to modify the band gap of GDY, containing invoking strain, boron/nitrogen doping, nanoribbon architectures, hydrogenation, and so on. GDY has been well-prepared in many different morphologies, like nanowires, nanotube arrays, nanowalls, nanosheets, ordered stripe arrays, and 3D framwork. The fascinating structure and electronic properties of GDY make i...

Progress in Research into 2D Graphdiyne-Based Materials

In light of the considerable impact synthetic 2D polymers are expected to have on many fundamental and applied aspects of the natural and engineering sciences, it is surprising that little research has been carried out on these intriguing macromolecules. Although numerous approaches have been reported over the last several decades, the synthesis of a one monomer unit thick, covalently bonded molecular sheet with a long-range ordered (periodic) internal structure has yet to be achieved. This Review provides an overview of these approaches and an analysis of how to synthesize 2D polymers. This analysis compares polymerizations in (initially) a homogeneous phase with those at interfaces and considers structural aspects of monomers as well as possibly preferred connection modes. It also addresses issues such as shrinkage as well as domain and crack formation, and briefly touches upon how the chances for a successful structural analysis of the final product can possibly be increased.

Two‐Dimensional Polymers: Just a Dream of Synthetic Chemists?

The optimized geometries of carbon allotropes related to graphite, called graphyne, graphdiyne, graphyne-3, and graphyne-4, as well as their electronic band structures were calculated using a full-potential linear combination of atomic orbitals method in the local-density approximation. These carbon allotropes consist of hexagons connected by linear carbon chains. The bond length of a hexagon is a little longer than that of the bond that links a hexagon to the outside carbon. Furthermore, part of the linear carbon chain is composed of acetylenic linkages (---C\ensuremath{\equiv}C---) rather than cumulative linkages (=C=C=). The binding energies are 7.95 eV/atom for graphyne and 7.78 eV/atom for graphdiyne, and the optimized lattice lengths are 6.86 \AA{} for graphyne and 9.44 \AA{} for graphdiyne. These materials are semiconductors with moderate band gaps. The band gap occurs at the M point or \ensuremath{\Gamma} point depending on the number of acetylenic linkages that are contained between the nearest-neighboring hexagons. The effective masses are very small for both conduction and valence bands.

Optimized geometries and electronic structures of graphyne and its family

Graphyne is a hypothetical carbon allotrope with a layered structure. We calculated the optimized geometries and electronic structures of three-dimensional graphyne in some possible stacking arrangements from symmetry considerations. The optimized lattice constants and the binding energy of graphyne are given in comparison with graphite. The binding energy of graphyne is about 90% of that of graphite, and graphyne will be stable when it is synthesized. The electronic structures are classified into two types, metallic and semiconducting, according to the stacking arrangements. The most stable graphyne is expected to be a semiconductor with a moderate band gap.

Electronic structure of three-dimensional graphyne

The Madelung energy in the (Y, Ca)(Ba, La) 2 Cu 3 O 6+δ system has been calculated in order to find the distribution of hole carriers among sites. We regard the compoundas a superconductor, when the lowest-energy distribution is such that holes enter sites in CuO 2 sheets, whereas we regard it as a semiconductor, when no holes enter sites in the CuO 2 sheets. Based on this criterion, we find a phase diagram, where the superconducting region is separated from the semi-conducting region by a boundary. A good agreement with the experimental finding by Tokura et al . is obtained, when account is taken of the ordering of exygen vacancies in the basal plane of Fig. 1 in the text. It is found that for some compounds with small δ(∼0.25), holes are spontaneously produced in CuO 2 sheets, so that the compounds may be a superconductor although their nominal hole content is zero.

The Madelung Energy in Copper-Oxide-Based Ceramics

Graphyne intercalation compounds are expected to function as layered organic conductors and as storage of atoms and molecules, because graphyne as a host material is highly stable and has large voids. We have performed optimization of the geometry and calculation of the electronic structures for five hypothetical stacking arrangements of the stage-1 potassium-intercalated graphyne by use of the first-principles method. The results are compared with the values of the typical graphite-intercalation compound, C 8 K. The stability of potassium-intercalated graphyne is strongly dependent on the position of intercalated atoms relative to the characteristic voids in the pristine graphyne. It is found that some stacking arrangements are stable, and are expected to intercalate potassium easily since the estimated values of the heat of reaction are larger than that of C 8 K. For the optimized crystal structures the electronic structures show that these materials are metallic. Further, we show the relationship between the amount of charge transfer and each bond length in graphyne.

Potassium intercalated graphyne

The one-dimensional Schrodinger equation with the Kroning-Penny potential plus the electric-field potential eFx has been solved numerically. All the interband effects are included in the exact numerical calculation. Although an infinite crystal was considered, localized wave functions have been obtaind at energies which make a Stark ladder. One Stark ladder is associated with one band. When the probability of the Zener tunneling to the next band is appreciable for given values of parameters, the wave function necessarily penetrates into the region of the next band and is not localized.

Sumiaki Nagai

Papers

Optimized geometries and electronic structures of graphyne and its family

Electronic structure of three-dimensional graphyne

The Madelung Energy in Copper-Oxide-Based Ceramics

Potassium intercalated graphyne

Electrons in Infinite One-Dimensional Crystals in a Uniform Electric Field