Origin of anisotropic negative Poisson's ratio in graphene

Alloying enhanced negative Poisson's ratio in two-dimensional aluminum gallium nitride (AlxGa1-xN)

The negative Poisson's ratio (NPR) effect usually endows materials with promising ductility and shear resistance, facilitating a wider range of applications. It has been generally acknowledged that alloys show strong advantages in manipulating material properties. Thus, a thought-provoking question arises: how does alloying affect the NPR? In this paper, based on first-principles calculations, we systematically study the NPR in two-dimensional (2D) GaN and AlN, and their alloy of AlxGa1-xN. It is intriguing to find that the NPR in AlxGa1-xN is significantly enhanced compared to the parent materials of GaN and AlN. The underlying mechanism mainly originates from a counter-intuitive increase of the bond angle θ. We further study the microscopic origin of the anomalies by electron orbital analysis as well as electron localization functions. It is revealed that the distribution and movement of electrons change with the applied strain, providing a fundamental view on the effect of strain on lattice parameters and the NPR. The physical origin as revealed in this study deepens the understanding of the NPR and shed light on the future design of modern nanoscale electromechanical devices with fantastic functions based on the auxetic nanomaterials and nanostructures.

Nonlinearity induced negative Poisson's ratio of two-dimensional nanomaterials

Materials exhibiting a negative Poisson's ratio have garnered considerable attention due to the improved toughness, shear resistance, and vibration absorption properties commonly found in auxetic materials. In this work, the nonlinear effect on the Poisson's ratio was derived theoretically and verified by first-principle calculations and molecular dynamics simulations of two-dimensional nanomaterials including graphene and hexagonal boron nitride. The analytic formula explicitly shows that the Poisson's ratio depends on the applied strain and can be negative for large applied strains, owing to the nonlinear interaction. Both first-principle calculations and molecular dynamics simulations show that the nonlinear effect is highly anisotropic for graphene, where the nonlinearity-induced negative Poisson's ratio is much stronger for the strain applied along the armchair direction. These findings provide valuable insights into the behavior of materials with negative Poisson's ratios and emphasize the importance of considering nonlinear effects in the study of the Poisson's ratio of two-dimensional materials.

A Novel Quasi-Planar Two-dimensional Carbon Sulfide with Negative Poisson's Ratio and Dirac Fermions

In the present study, a novel and unconventional two-dimensional (2D) material with Dirac electronic features has been designed using sulflower with the help of density functional theory methods and first principles calculations. This 2D material comprises of hetero atoms (C, S) and belongs to the tetragonal lattice with P4 /nmm space group. Scrutiny of the results show that the 2D nanosheet exhibits a nanoporous wave-like geometrical structure. Quantum molecular dynamics simulations and phonon mode analysis emphasize the dynamical and thermal stability. The novel 2D nanosheet is an auxetic material with an anisotropy in the in-plane mechanical properties. Both composition and geometrical features are completely different from the conditions necessary for the formation of Dirac cones in graphene. However, the presence of semi-metallic nature, linear band dispersion relation, massive fermions and massless Dirac fermions are observed in the novel 2D nanosheet. The massless Dirac fermions exhibit highly isotropic Fermi velocities (vf =0.68×106  m/s) along all crystallographic directions. The zero-band gap semi metallic features of the novel 2D nanosheet are perturbative to the electric field and external strain.

Auxetic ographene: a new 2D Dirac nodal-ring semimetal carbon-based material with a high negative Poisson's ratio

Auxetic and semimetallic materials possess many advanced applications due to the negative Poisson's ratio (NPR) effect and unique electronic properties. However, candidates with the above properties are rather scarce, especially in the 2D carbon materials. Here, a new 2D NPR material with a Dirac nodal ring, named ographene, is identified using first-principles calculations. Ographene possesses anisotropic Young's modulus and unusual in-plane NPR (-0.11), which mainly originated from its puckered tetrahedron structure. In addition, the electronic band structure calculations show that ographene is a topological node-ring semimetal with high Fermi velocity. Moreover, the electronic band structure is robust against external strain. The intrinsic NPR coupled with robust electronic properties renders auxetic ographene promising for applications in electronics and mechanics areas.

Accessing negative Poisson's ratio of graphene by machine learning interatomic potentials

The negative Poisson's ratio (NPR) is a novel property of materials, which enhances the mechanical feature and creates a wide range of application prospects in lots of fields, such as aerospace, electronics, medicine, etc. Fundamental understanding on the mechanism underlying NPR plays an important role in designing advanced mechanical functional materials. However, with different methods used, the origin of NPR is found different and conflicting with each other, for instance, in the representative graphene. In this study, based on machine learning technique, we constructed a moment tensor potential for molecular dynamics (MD) simulations of graphene. By analyzing the evolution of key geometries, the increase of bond angle is found to be responsible for the NPR of graphene instead of bond length. The results on the origin of NPR are well consistent with the start-of-art first-principles, which amend the results from MD simulations using classic empirical potentials. Our study facilitates the understanding on the origin of NPR of graphene and paves the way to improve the accuracy of MD simulations being comparable to first-principle calculations. Our study would also promote the applications of machine learning interatomic potentials in multiscale simulations of functional materials.

Toward Planar Iodine 2D Crystal Materials

Usually, the octet rule determines whether an elemental 2D material can only be set by one of the elements in groups IIIA-VA, whose outmost electrons can form hybridized orbits from an s-wave and a p-wave. The hybridized orbits can accommodate all of the outermost electrons and form robust σ bonds. As for the elements in VIA-VIIA, the outermost electrons seem too abundant to be accommodated in hybridized orbits. Here, we show a spd² hybridization rule, accommodating all of the outermost electrons of halogen elements. Each atom can be connected to a contiguous atom by a robust σ bond and carries one dangling unpaired electron, implying that the formation of a π bond is possible. One iodine atomic layer can be robustly locked by the σ bond, forming an iodiene sheet by spd² hybridized orbits. With application of compression strain, the π bond forms, and further compression drives the band inversion successively at the valence band and the conduction band. The appearance of Dirac points (arc or hoop) suggests that the transformation of a normal semimetal into a Dirac semimetal occurs.

Reconfiguring graphene to achieve intrinsic negative Poisson's ratio and strain-tunable bandgap

A new two-dimensional carbon-based material consisting of pentagonal and hexagonal elements is identified by numerical experiments, which is called phgraphene and possesses not only a tunable semimetallic feature but also a direction-dependent even sign-changed Poisson's ratio. The structural stability of such a new material is first checked systematically. It is found that phgraphene has a similar energy as theγ-graphyne, a thermally stable structure from the room temperature to 1500 K, and elastic constants satisfying the Born-Huang criterion. Both the band structure and density of states are further verified with different techniques, which demonstrate a Dirac semimetallic characteristic of phgraphene. A more interesting finding is that the band structure can be easily tuned by an external loading, resulting in the transition from semimetal to semiconductor or from type I to type III. As a new material that may be applied in the future, the mechanical property of phgraphene is further evaluated. It shows that phgraphene is a typically anisotropic material, which has not only direction-dependent Young's moduli but also direction-dependent even sign-changed Poisson's ratios. The microscopic mechanisms of both the electrical and mechanical properties are revealed. Such a versatile material with tunable band structure and auxetic effect should have promising applications in the advanced nano-electronic field in the future.

Large piezoelectric and thermal expansion coefficients with negative Poisson's ratio in strain-modulated tellurene

Two dimensional (2D) chalcogenide monolayers have diversified applications in optoelectronics, piezotronics, sensors and energy harvesting. The group-IV tellurene monolayer is one such emerging material in the 2D family owing to its piezoelectric, thermoelectric and optoelectronic properties. In this paper, the mechanical and piezoelectric properties of 2D tellurene in centrosymmetric β and non-centrosymmetric β' phases are investigated using density functional theory. β'-Te has shown a negative Poisson's ratio of -0.024 along the zigzag direction. Giant in-plane piezoelectric coefficients of -83.89 × 10-10 C m-1 and -42.58 × 10-10 C m-1 are observed for β'-Te under biaxial and uniaxial strains, respectively. The predicted values are remarkably higher, that is 23 and 12 times the piezoelectric coefficient of a MoS2 monolayer with biaxial and uniaxial strain in the zigzag direction, respectively. A large thermal expansion coefficient of tellurene is also estimated using quasi harmonic approximation. High piezoelectricity combined with exotic mechanical and thermal properties makes tellurene a very promising candidate in nanoelectronics.

Consistent evaluation of continuum scale properties of two-dimensional materials: a case study on graphene

We handshake statistical mechanics with continuum mechanics to develop a methodology for consistent evaluation of the continuum scale properties of two-dimensional materials. The methodology is tested on pristine graphene. Our scope is kept limited to elastic modulus, E, which has been reported to vary between 0.912 TPa and 7 TPa, Poisson's ratio, ν, which has been reported to vary from being negative to a value as large as 0.46, and effective thickness, q, whose value varies between 0.75 Å and 3.41 Å. Such a large scatter arises due to inconsistent evaluation of these properties and making assumptions that may not be valid at atomistic scales. Our methodology combines three separate methods: uniaxial tension, equibiaxial tension, and flexural out-of-plane free vibrations of simply supported sheets, which, when used in tandem in molecular dynamics, can provide consistent values of E, ν and q. The only assumption made in the present study is the validity of the continuum scale thin plate vibration equation to represent the free vibrations of a graphene sheet. Our results suggest that-(i) graphene is auxetic in nature, (ii) E decreases with increasing size and temperature, and (iii) the effective thickness q increases with increasing size and temperature. Further, a robustness study of the computed mechanical properties shows consistent results, with differences varying between 1.4% and 6%.

Graphene-Based One-Dimensional Terahertz Phononic Crystal: Band Structures and Surface Modes

In this paper, we provide a theoretical and numerical study of the acoustic properties of infinite and semi-infinite superlattices made out of graphene-semiconductor bilayers. In addition to the band structure, we emphasize the existence and behavior of localized and resonant acoustic modes associated with the free surface of such structures. These modes are polarized in the sagittal plane, defined by the incident wavevector and the normal to the layers. The surface modes are obtained from the peaks of the density of states, either inside the bulk bands or inside the minigaps of the superlattice. In these structures, the two directions of vibrations (longitudinal and transverse) are coupled giving rise to two bulk bands associated with the two polarizations of the waves. The creation of the free surface of the superlattice induces true surface localized modes inside the terahertz acoustic forbidden gaps, but also pseudo-surface modes which appear as well-defined resonances inside the allowed bands of the superlattice. Despite the low thickness of the graphene layer, and though graphene is a gapless material, when it is inserted periodically in a semiconductor, it allows the opening of wide gaps for all values of the wave vector k// (parallel to the interfaces). Numerical illustrations of the band structures and surface modes are given for graphene-Si superlattices, and the surface layer can be either Si or graphene. These surface acoustic modes can be used to realize liquid or bio-sensors graphene-based phononic crystal operating in the THz frequency domain.

Me-graphene: a graphene allotrope with near zero Poisson's ratio, sizeable band gap, and high carrier mobility

The exploration of new two-dimensional (2D) allotropes of carbon has attracted great research attention after graphene, but experiment-feasible graphene allotropes with novel properties are still rare. Here, we predict a new allotrope of graphene, named Me-graphene, composed of both sp2- and sp3-hybridized carbon by topological assembly of C-(C3H2)4 molecules. With a transitional ratio of sp2- and sp3-hybridized carbon atoms (12 : 1) between those of graphene (1 : 0) and penta-graphene (2 : 1), Me-graphene has transition properties between those of graphene and penta-graphene, such as energy, band gap, and Poisson's ratio. Unusually, Me-graphene exhibits a near zero Poisson's ratio of from -0.002 to 0.009 in the xy-plane (or called "anepirretic"), different from that of graphene (0.169) and penta-graphene (-0.068). More importantly, the near zero Poisson's ratio behavior remains in a large strain range, being less than ±0.02 for strain from -15% to +3%. Me-graphene possesses an indirect band gap of 2.04 eV, as a transition of graphene (semimetal) and penta-graphene (wide band gap), and turns into a direct-bandgap semiconductor with an enlarged band gap of 2.62 eV under compressive strain. It possesses high hole mobility of 1.60 × 105 cm2 V-1 s-1 at 300 K. Me-Graphene has potential applications in electronic, photoelectric and high-speed mechatronic devices. The transitional properties related to the ratio of sp2- and sp3-hybridized carbon atoms are inspiring for searching for new graphene allotropes with combinational properties.

Flexible C6BN Monolayers As Promising Anode Materials for High-Performance K-Ion Batteries

K-ion batteries attract extensive attention and research efforts because of the high energy density, low cost, and high abundance of K. Although they are considered suitable alternatives to Li-ion batteries, the absence of high-performance electrode materials is a major obstacle to implementation. On the basis of density functional theory, we systematically study the feasibility of a recently synthesized C₆BN monolayer as anode material for K-ion batteries. The specific capacity is calculated to be 553 mAh/g (K₂C₆BN), i.e., about twice that of graphite. The C₆BN monolayer is characterized by high strength (in-plane stiffness of 309 N/m), excellent flexibility (bending strength of 1.30 eV), low output voltage (average open circuit voltage of 0.16 V), and excellent rate performance (diffusion barrier of 0.09 eV). We also propose two new C₆BN monolayers. One has a slightly higher total energy (0.10 eV) than the synthesized C₆BN monolayer, exhibiting enhanced electronic properties and affinity to K. The other is even energetically favorable due to B-N bonding. All three C₆BN monolayers show good dynamical, thermal, and mechanical stabilities. We demonstrate excellent cyclability and improved conductivity by K adsorption, suggesting great potential in flexible energy-storage devices.

Temperature-Dependent Mechanical Properties of Graphene/Cu Nanocomposites with In-Plane Negative Poisson's Ratios

Negative Poisson's ratio (NPR), also known as "auxetic", is a highly desired property in a wide range of future industry applications. By employing molecular dynamics (MD) simulation, metal matrix nanocomposites reinforced by graphene sheets are studied in this paper. In the simulation, single crystal copper with crystal orientation [1 1 0] is selected as the matrix and an embedded-atom method (EAM) potential is used to describe the interaction of copper atoms. An aligned graphene sheet is selected as reinforcement, and a hybrid potential, namely, the Erhart-Albe potential, is used for the interaction between a pair of carbon atoms. The interaction between the carbon atom and copper atom is approximated by the Lennard-Jones (L-J) potential. The simulation results showed that both graphene and copper matrix possess in-plane NPRs. The temperature-dependent mechanical properties of graphene/copper nanocomposites with in-plane NPRs are obtained for the first time.

Chemically Tuning Quantized Acoustic Phonons in 2D Layered MoO3 Nanoribbons

Molybdenum trioxide (α-MoO₃) is a 2D layered metal oxide that can be altered in color from transparent white to dark blue with reversible intercalation of zerovalent metals, and whose mechanical properties can be controlled through intercalation. Here, we use Brillouin laser light spectroscopy to map the entire angular dispersion curves of multiple acoustic phonon branches of 2D layered MoO₃, directly probing the effects of phonon quantum confinement when the phonon wavelength is comparable to the material thickness. Since acoustic phonons dictate elasticity, we thereby determine the full elastic stiffness tensor and the thickness of each nanoribbon to a statistical precision (derived from standard error propagation) corresponding to less than a monolayer. We show how intercalation of metallic Sn, Co, and Cu can chemically tune the quantized acoustic phonons and elasticity of MoO₃ nanoribbons. This work provides the methodology to extract precise elastic constants from complex Brillouin scattering of 2D materials, taking advantage of phonon confinement to capture the complete elastic response with a single scattering geometry.

Two-Dimensional Carbon-Based Auxetic Materials for Broad-Spectrum Metal-Ion Battery Anodes

Auxetic materials possess special applications due to their unique negative Poisson's ratios (NPRs). As a classic 2D carbon material, the NPR of graphene is still deliberated. Introducing the NPR in graphene would increase its extraordinary properties, and the NPR together with other properties would bring more significant applications for graphene. In this Letter, on the basis of first-principles calculations, we reconfigure the structure of graphene, and, as an example, we propose a new 2D planar carbon allotrope, xgraphene, which is constructed by 5-6-7 carbon rings. Our theoretical calculations indicate that xgraphene has an NPR and constitutes a broad spectrum of metal ion battery anodes with high performance. Its maximum storage capacities are 930/1302/744/1488 mAh/g for Li/Na/K/Ca-ion batteries. It has low metal-ion diffusion energy barriers (≤0.49 eV) and low average open-circuit voltages (≤0.53 V). Our density functional theory results also showed that it is intrinsically metallic and possesses dynamic, thermal, and mechanical stabilities. Its intrinsic NPR, which stems from the weakness of coupling of carbon-carbon bonds, is found upon loading the uniaxial strain along the armchair direction. This work not only opens up a new direction for the design of the next-generation broad-spectrum energy-storage materials with low cost and high performance but also offers a class application for auxetic materials.