Graphene Allotropes Research Articles

Prediction of an ultrasoft graphene allotrope with Dirac cones

Searching for the Dirac materials with ultrasoftness is crucial for flexible electronics applications. Based on first-principles calculations, we propose a new carbon allotrope (named as ph-graphene) with a penta-hexagonal framework, which is energetically more favorable than the penta-graphene composing surely of pentagons and some of already-synthesized carbon allotropes. Ph-graphene has an in-plane stiffness of 27.75 GPa·nm, smaller than those of graphene and penta-graphene by one order. The famous isotropic Dirac cones are well preserved in the ultrasoft ph-graphene, exhibiting delocalized feature of pz orbits with the Fermi velocity of 2.8 × 105 m/s. Additionally, surface hydrogenation alters drastically the electronic and mechanical properties of ph-graphene, resulting in electronic spin-polarization and anisotropic negative Poisson’s ratios sequentially with the increase of hydrogenation concentrations.

Possible nonplanar structure of phagraphene and its thermal stability

It is shown that phagraphene, a recently predicted planar allotrope of graphene with Dirac fermions, is unstable or, at least, almost unstable with respect to transverse atomic displacements. This result is obtained by numerical calculations in the framework of both the tight-binding model and the density functional theory. A nonplanar atomic configuration of phagraphene has a wavy shape and is almost degenerate in energy with the planar configuration. The main types of possible structural defects in phagraphene are determined. The temperature dependence of characteristic times of their formation is found.

Mechanical properties of monolayer penta-graphene and phagraphene: a first-principles study.

Two new graphene allotropes, penta-graphene and phagraphene, have been proposed recently with unique electronic properties, e.g. quasi-direct band gap, direction-dependent Dirac cones and tunable Fermi velocities. However, their mechanical properties have not been fully studied yet. In this work, we have performed extensive density functional theory calculations to evaluate the mechanical properties of these two materials and compared with graphene, graphane, and pentaheptite. Our simulations show that the ultimate tensile strength (UTS) and the strain corresponding to UTS in both penta-graphene and phagraphene are smaller than that of graphene. A complete set of nonlinear anisotropic elastic constants up to the fourth order have been determined for these two allotropes using the tenets of continuum mechanics by fitting the stress-strain responses under uniaxial and biaxial tension until the point of fracture. We propose a new physical explanation for penta-graphene's negative Poisson's ratio based on the atomic de-wrinkling mechanism, driven by the local Hellman-Feynman force on each atom. Additionally, we used charge density plot and virtual Scanning Tunneling Microscopy images to analyze the initiation of fracture under uniaxial and biaxial tensile loading in these two materials. The charge density plots reveal that the charge density in sp3 bonds is lower than that in the sp2 bonds. In phagraphene, all the broken bonds were found to belong to the largest carbon ring in the structure.

When is 6 less than 5? Penta- to hexa-graphene transition

Penta-graphene is a recently proposed graphene allotrope consisting of repeating pentagons. Here, we characterize the small-strain mechanical properties of finite penta-graphene using full atomistic molecular dynamics (MD). Using tensile tests, the uniaxial yield strength (12.7 N/m) and stiffness (approximately 378.3 N/m) are characterized. Extreme strain is observed at ultimate failure (> 50%), with an associated elastic toughness on the order of 5.4 J/m2. In addition, the bond structure of penta-graphene enables a structural transition from a repeating penta- to hexa-form, e.g., the common hexagonal-based sp2-bonding structure of graphene. We show that penta-graphene can be transitioned to a hexagonal energy-reducing graphene form, via applied strain or temperature. The pentagon-based structure begins to degenerate to a graphene-like hexagonal structure at a critical strain of 5.1%, as the system transitions to a lower energy structure. Beyond this critical strain, the system behaves plastically, and does not revert to initial conditions upon stress removal. The hexagonal form (6-ring) represents a lower energy state than the pentagonal form (5-ring). We further observe conformational changes occur due to thermal energy, leading to a transition at T > 600 K. Post-transition, the system behavior reflects that of graphene with lattice defects. This represents a new paradigm of nanomaterials, whereby one material (graphene) can emerge from another metastable form (penta-graphene).

Two-dimensional graphene heterojunctions: The tunable mechanical properties

We report the mechanical properties of different two-dimensional carbon heterojunctions (HJs) made from graphene and various stable graphene allotropes, including α-, β-, γ- and 6612-graphyne (GY), and graphdiyne (GDY). It is found that all HJs exhibit a brittle behaviour except the one with α-GY, which however shows a hardening process due to the formation of triple carbon rings. Such hardening process has greatly deferred the failure of the structure. The yielding of the HJs is usually initiated at the interface between graphene and graphene allotropes, and monoatomic carbon rings are normally formed after yielding. By varying the locations of graphene (either in the middle or at the two ends of the HJs), similar mechanical properties have been obtained, suggesting insignificant impacts from location of graphene allotropes. Whereas, changing the types and percentages of the graphene allotropes, the HJs exhibit vastly different mechanical properties. In general, with the increasing graphene percentage, the yield strain decreases and the effective Young's modulus increases. Meanwhile, the yield stress appears irrelevant with the graphene percentage. This study provides a fundamental understanding of the tensile properties of the heterojunctions that are crucial for the design and engineering of their mechanical properties, in order to facilitate their emerging future applications in nanoscale devices, such as flexible/stretchable electronics.

First principles Raman study of boron and nitrogen doped planar T-graphene clusters

Tetragonal graphene (TG) is one of the theoretically proposed dynamically stable graphene allotropes. In this study, the Raman spectra, IR spectra and some electronic properties of pristine and doped (single boron (B) and nitrogen (N)) TG have been investigated by first-principles based density functional theory (DFT) at the B3LYP/6-31G(d) level. Formation energy computation indicates that for the pristine structures, stability increases with increasing cluster size. In addition, for a particular cluster size, single B doping introduces some distortion in the system while single N doping increases the stability of it. The Raman spectrum of the N doped system is dominated by a single peak but for the B doped system several intense lines are found. For all the structures low intensity similar breathing-like modes have been observed. Besides, relatively low (high) intensity Raman lines are found for single B (N) doping compared to those of the pristine one. The vibrational study also reveals the existence of a prominent phonon Raman line for pristine clusters which hardly changes its position and nature of vibration with varying cluster size. So this mode can be used for identification of pristine TG structures. Unlike pristine TG, the doped structures possess non-zero finite dipole moments due to asymmetry in charge distribution. Large values of the HOMO–LUMO gap as well as the absence of DOS at the Fermi level lead to the semiconducting nature of all the structures. All these theoretical predictions from DFT calculations may shed light on experimental observations involving TG systems.

Phagraphene: A Low-Energy Graphene Allotrope Composed of 5-6-7 Carbon Rings with Distorted Dirac Cones.

Using systematic evolutionary structure searching we propose a new carbon allotrope, phagraphene [fæ'græfi:n], 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 sp(2)-binding features 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.

Nano level optimization of graphene allotropes by means of a hybrid parallel evolutionary algorithm

The article describes the application of a Hybrid Parallel Evolutionary Algorithm (HPEA) to optimal searching for new, stable atomic arrangements of two-dimensional graphene-like carbon lattices. The proposed approach combines the parallel evolutionary algorithm and the conjugated-gradient optimization technique. The main goal of the optimization is to find stable arrangements of carbon atoms under certain imposed conditions (e.g. density, shape and size of the unit cell). The fitness function is formulated as the total potential energy of an atomic system. The optimized structure is considered as a discrete atomic model and interactions between atoms are modeled using the AIREBO potential, especially developed for carbon and hydrocarbon materials. The parallel approach used in computations allows significant reduction of computation time. Validation of the obtained results and examples of the models of the new 2D materials obtained using the described algorithm are presented, along with their mechanical properties.

A novel two-dimensional material B2S3and its structural implication to new carbon and boron nitride allotropes

We propose a single layer of B2S3as a new potential 2D material, conceived directly from its existing layered 3D crystal. New 2D BN and graphene allotropes are constructed from B2S3.

Graphene allotropes under extreme uniaxial strain: an ab initio theoretical study.

Using density functional theory calculations, we study the response of three representative graphene allotropes (two pentaheptites and octagraphene) as well as graphene, to uniaxial strain up to their fracture limit. Those allotropes can be seen as distorted graphene structures formed upon periodically arranged Stone-Walles transformations. We calculate their mechanical properties (Young's modulus, Poisson's ratio, speed of sound, ultimate tensile strength and the corresponding strain), and we describe the pathways of their fracture. Finally, we study strain as a factor for the conversion of graphene into those allotropes upon Stone-Walles transformations. For specific sets of Stone-Walles transformations leading to an allotrope, we determine the strain directions and the corresponding minimum strain value, for which the allotrope is more favorable energetically than graphene. We find that the minimum strain values which favor those conversions are of the order of 9-13%. Moreover, we find that the energy barriers for the Stone-Walles transformations decrease dramatically under strain, however, they remain prohibitive for structural transitions. Thus, strain alone cannot provide a synthetic route to these allotropes, but could be a part of composite procedures for this purpose.

Formation of carbon nanoscrolls from graphene nanoribbons: A molecular dynamics study

Carbon nanoscrolls (CNSs) are one of the carbon-based nanomaterials similar to carbon nanotubes (CNTs) but are not widely studied in spite of their great potential applications. Their practical applications are hindered by the challenging fabrication of the CNSs. A physical approach has been proposed recently to fabricate the CNS by rolling up a monolayer graphene nanoribbon (GNR) around a CNT driven by the interaction energy between them. In this study, we perform extensive molecular dynamics (MD) simulations to investigate the various factors that impact the formation of the CNS from GNR. Our simulation results show that the formation of the CNS is sensitive to the length of the CNT and temperature. When the GNR is functionalized with hydrogen, the formation of the CNS is determined by the density and distribution of the hydrogen atoms. Graphyne, the allotrope of graphene, is inferior to graphene in the formation of the CNS due to the weaker bonds and the associated smaller atom density. The mechanism behind the rolling of GNR into CNS lies in the balance between the GNR–CNT van der Waals (vdW) interactions and the strain energy of GNR. The present work reveals new important insights and provides useful guidelines for the fabrication of the CNS.

Temperature and strain-rate dependent fracture strength of graphynes

Graphyne is an allotrope of graphene. The mechanical properties of graphynes (α-, β-, γ- and 6,6,12-graphynes) under uniaxial tension deformation at different temperatures and strain rates are studied using molecular dynamics simulations. It is found that graphynes are more sensitive to temperature changes than graphene in terms of fracture strength and Young's modulus. The temperature sensitivity of the different graphynes is proportionally related to the percentage of acetylenic linkages in their structures, with the α-graphyne (having 100% of acetylenic linkages) being most sensitive to temperature. For the same graphyne, temperature exerts a more pronounced effect on the Young's modulus than fracture strength, which is different from that of graphene. The mechanical properties of graphynes are also sensitive to strain rate, in particular at higher temperatures.

DFT characterization of a new possible graphene allotrope

In the present work we have studied the electronic and magnetic properties of the new one- and two-dimensional π-conjugated materials containing biphenylene (Bp)-monomer on the basis of DFT calculations including the periodic boundary condition for the infinite structures. Thus, we have predicted a new planar and stable graphene allotrope composed of a combination of the four-, six- and eight-membered rings of the (4, 6, 6, 8) topology, which resembles the classical graphene. These novel materials are predicted to demonstrate the promising hole/electron mobility values which are typical for the ambipolar organic semiconductors. Furthermore, the growth of π-conjugated Bp-based 2D sheets leads to the material with the band-gap being significantly smaller than that for the 1D polymer ribbons containing the same number of the Bp-units. The Bp-based nanotubes are also designed and are predicted to be promising candidates for miniaturizing electronics.

Structure-mediated thermal transport of monolayer graphene allotropes nanoribbons

We report the study of the thermal transport management of monolayer graphene allotrope nanoribbons (size ∼20×4nm2) by the modulation of their structures via molecular dynamics simulations. The thermal conductivity of graphyne (GY)-like geometries is observed to decrease monotonously with increasing number of acetylenic linkages between adjacent hexagons. Strikingly, by incorporating those GY or GY-like structures, the thermal performance of graphene can be effectively engineered. The resulting hetero-junctions possess a sharp local temperature jump at the interface, and show a much lower effective thermal conductivity due to the enhanced phonon–phonon scattering. More importantly, by controlling the percentage, type and distribution pattern of the GY or GY-like structures, the hetero-junctions are found to exhibit tunable thermal transport properties (including the effective thermal conductivity, interfacial thermal resistance and rectification). This study provides a heuristic guideline to manipulate the thermal properties of 2D carbon networks, ideal for application in thermoelectric devices with strongly suppressed thermal conductivity.

Thermal transport and thermoelectric properties of beta-graphyne nanostructures

Graphyne, an allotrope of graphene, is currently a hot topic in the carbon-based nanomaterials research community. Taking beta-graphyne as an example, we performed a comprehensive study of thermal transport and related thermoelectric properties by means of nonequilibrium Green’s function (NEGF). Our simulation demonstrated that thermal conductance of beta-graphyne is only approximately 26% of that of the graphene counterpart and also shows evident anisotropy. Meanwhile, thermal conductance of armchair beta-graphyne nanoribbons (A-BGYNRs) presents abnormal stepwise width dependence. As for the thermoelectric property, we found that zigzag beta-graphyne nanoribbons (Z-BGYNRs) possess superior thermoelectric performance with figure of merit value achieving 0.5 at room temperature, as compared with graphene nanoribbons (∼0.05). Aiming at obtaining a better thermoelectric coefficient, we also investigated Z-BGYNRs with geometric modulations. The results show that the thermoelectric performance can be enhanced dramatically (figure of merit exceeding 1.5 at room temperature), and such enhancement strongly depends on the width of the nanoribbons and location and quantity of geometric modulation. Our findings shed light on transport properties of beta-graphyne as high efficiency thermoelectrics. We anticipate that our simulation results could offer useful guidance for the design and fabrication of future thermoelectric devices.

Electronic Structures of Carbon-Based Kagomé Lattices

A structurally stable two-dimensional carbon allotrope of graphene is studied theoretically based on the first-principles calculations. This allotrope can be formed by inserting acetylene and diacetylene fragments into β-graphyne. The calculations on structure and electronic energy spectra show that the carbon Kagomé lattice is a structurally stable semimetal with the Dirac cones below the Fermi surface, in contrast to the Dirac points at the Fermi surface in intrinsic graphene.

Mechanical properties of hydrogen functionalized graphene allotropes

Molecular dynamics (MD) simulations have been performed to investigate the mechanical properties of hydrogen functionalized graphene allotropes (GAs) for H-coverage spanning the entire range (0–100%). Four allotropes (graphyne, cyclic graphene, octagonal graphene, and biphenylene) with larger unit lattice size than graphene are considered. The effect of the degree of functionalization and molecular structure on the Young’s modulus and strength are investigated, and the failure processes of some new GAs are reported for the first time. We show that the mechanical properties of the hydrogenated GAs deteriorate drastically with increasing H-coverage within the sensitive threshold, beyond which the mechanical properties remain insensitive to the increase in H-coverage. This drastic deterioration arises both from the conversion of sp2 to sp3 bonding and easy rotation of unsupported sp3 bonds. Allotropes with different lattice structures correspond to different sensitive thresholds. The Young’s moduli deterioration of fully hydrogenated allotropes can be up to 70% smaller than that of the corresponding pristine structure. Moreover the tensile strength shows an even larger drop of about 90% and higher sensitivity to H-coverage even if it is small. Our results suggest that the unique coverage-dependent deterioration of the mechanical properties must be taken into account when analyzing the performance characteristics of nanodevices fabricated from functionalized GAs.

Exciton spectra in two-dimensional graphene derivatives

The energy spectra and wave functions of bound excitons in important two-dimensional (2D) graphene derivatives, i.e., graphyne and graphane, are found to be strongly modified by quantum confinement, making them qualitatively different from the usual Rydberg series. However, their parity and optical selection rules are preserved. Thus a one-parameter modified hydrogenic model is applied to quantitatively explain the ab initio exciton spectra, and allows one to extrapolate the electron-hole binding energy from optical spectroscopies of 2D semiconductors without costly simulations. Meanwhile, our calculated optical absorption spectrum and enhanced spin singlet-triplet splitting project graphyne, an allotrope of graphene, as a candidate for intriguing energy and biomedical applications.

Theoretical Raman fingerprints ofα-,β-, andγ-graphyne

The novel graphene allotropes $\alpha$-, $\beta$-, and $\gamma$-graphyne derive from graphene by insertion of acetylenic groups. The three graphynes are the only members of the graphyne family with the same hexagonal symmetry as graphene itself, which has as a consequence similarity in their electronic and vibrational properties. Here, we study the electronic band structure, phonon dispersion, and Raman spectra of these graphynes within an \textit{ab-initio}-based non-orthogonal tight-binding model. In particular, the predicted Raman spectra exhibit a few intense resonant Raman lines, which can be used for identification of the three graphynes by their Raman spectra for future applications in nanoelectronics.

Graphenylene: a promising anode material for lithium-ion batteries with high mobility and storage

It is known that low-dimensional carbon allotropes can be used as a new class of anode materials for lithium-ion batteries. However, the existing carbon allotropes cannot meet the increasing energy and power demand, and thus there is still a need for further development of new materials for lithium-ion batteries. In the present work, a new graphene allotrope, known as graphenylene, is found to be capable of storing lithium with greater density of energy. Ab initio density functional theory calculations indicate that the unique dodecagonal holes in graphenylene enable lithium ions to diffuse both on and through graphenylene layers with energy barriers no higher than 0.99 eV. Adsorption of a lithium atom on graphenylene is stronger than that on pristine graphene. The highest lithium storage capacities for monolayer and bilayer graphenylene compounds are Li3C6 and Li2.5C6, respectively, which correspond to specific capacities of 1116 and 930 mA h g−1. Both specific and volumetric capacities of lithium-intercalated graphenylene compounds are significantly larger than those for graphene. The high lithium mobility and large lithium storage capacity demonstrate that graphenylene is a promising anode material for modern lithium-ion batteries.