Superior mechanical flexibility of phosphorene and few-layer black phosphorus

Recent reports on the fabrication of phosphorene, that is, mono- or few-layer black phosphorus, have raised exciting prospects of an outstanding two-dimensional (2D) material that exhibits excellent properties for nanodevice applications. Here, we study by first-principles calculations the adsorption of CO, CO2, NH3, NO, and NO2 gas molecules on a monolayer phosphorene. Our results predict superior sensing performance of phosphorene that rivals or even surpasses that of other 2D materials such as graphene and MoS2. We determine the optimal adsorption positions of these molecules on the phosphorene and identify molecular doping, that is, charge transfer between the molecules and phosphorene, as the driving mechanism for the high adsorption strength. We further calculated the current-voltage (I-V) relation using the nonequilibrium Green's function (NEGF) formalism. The transport features show large (1-2 orders of magnitude) anisotropy along different (armchair or zigzag) directions, which is consistent with the anisotropic electronic band structure of phosphorene. Remarkably, the I-V relation exhibits distinct responses with a marked change of the I-V relation along either the armchair or the zigzag directions depending on the type of molecules. Such selectivity and sensitivity to adsorption makes phosphorene a superior gas sensor that promises wide-ranging applications.

First principles study of the electronic properties and band gap modulation of two-dimensional phosphorene monolayer: Effect of strain engineering

Small strain induced large piezoelectric coefficient in α-AsP monolayer

Recently fabricated two dimensional (2D) phosphorene crystal structures have demonstrated great potential in applications of electronics. In this work, strain effect on the electronic band structure of phosphorene was studied using first principles methods. It was found that phosphorene can withstand a surface tension and tensile strain up to 10 N/m and 30%, respectively. The band gap of phosphorene experiences a direct-indirect-direct transition when axial strain is applied. A moderate -2% compression in the zigzag direction can trigger this gap transition. With sufficient expansion (+11.3%) or compression (-10.2% strains), the gap can be tuned from indirect to direct again. Five strain zones with distinct electronic band structure were identified and the critical strains for the zone boundaries were determined. The origin of the gap transition was revealed and a general mechanism was developed to explain energy shifts with strain according to the bond nature of near-band-edge electronic orbitals. Effective masses of carriers in the armchair direction are an order of magnitude smaller than that of the zigzag axis indicating the armchair direction is favored for carrier transport. In addition, the effective masses can be dramatically tuned by strain, in which its sharp jump/drop occurs at the zone boundaries of the direct-indirect gap transition.

Two-dimensional monolayer Tellurium, termed as Tellurene (Te), has recently been fabricated in the experiment. In this work, under uniaxial strain applied along either the armchair or zigzag direction with strain strength varying from 0 to 40%, we have investigated the mechanical property of Te including three allotropes (α-Te, β-Te, and γ-Te). Our results show that the β-Te exhibits the most obvious anisotropy in the stress-strain curve, Young's modulus, and Poisson's ratio, which is thought to originate from its inherent structure characteristic. The stress-strain curve demonstrates that the β-Te can withstand relatively high critical strain up to 36% in the armchair direction and 35% in the zigzag direction. The calculated Young's modulus E(θ) of the β-Te is 55 GPa in the zigzag direction and that is 27 GPa in the armchair direction. The comparative high critical strain and small Young's modulus mean that β-Te has good flexibility. Moreover, under the strain range within 15%, the direction being easy to be stretched has a reversion, which is thought to be decided by the competition between the puckered structure and the transfer charge resistant to deformation. Furthermore, when the strain is applied along the direction parallel to the pucker of β-Te, it is interesting to find that Poisson's ratio is negative in the out-of-plane direction. The hinged structure of the β-Te contributes to the negative Poisson's ratio, which can be comprehended by the hypothetical step-by-step evolution process.

The thermoelectric power factor of bilayer phosphorene is investigated by performing first‐principle calculations based on density functional theory combined with semiclassical Boltzmann transport theory. Our simulations show that the thermoelectric performance of phosphorene strongly depends on the interlayer coupling, the direction of the temperature gradient, and the direction of strain. We find that the interlayer coupling oppositely affects the power factor induced by the temperature gradient along either the zigzag direction or the armchair direction; the power factor under the effect of the temperature gradient is larger for monolayer (bilayer) phosphorene along the armchair (zigzag) direction. We also show that the power factor for bilayer phosphorene monotonically increases as a function of tensile strain up to 6%, despite the direction of strain. Above a strain of 6%, the power factor continues to increase with increasing strain along the armchair direction, while it decreases with increasing strain in the zigzag direction. Copyright © 2016 John Wiley & Sons, Ltd.

Recently, the effect of temperature on the mechanical property (the Young's modulus) of the single-layer molybdenum disulfide (SLMoS2) is shown to be insignificant, which is obviously incompatible with the previously published result, i. e. the Young's modulus of SLMOS2 decreases monotonically as temperature increases. Aiming at clarifying the relationships between the mechanical properties of the single-layer molybdenum disulfide (SLMoS2) along the armchair (AC) and zigzag (ZZ) directions and the temperature, classical molecular dynamics (MD) simulations are performed to stretch the SLMoS2 along the AC and ZZ directions at the temperatures ranging from 1 K to 800 K by using the Stillinger-Weber (SW) interatomic potentials in this paper. The mechanical properties of SLMoS2 at the temperatures ranging from 1 K to 800 K, including ultimate strength, ultimate strain, and Young's Modulus, are calculated based on the stress-strain results obtained from the simulations. Results are obtained and given as follows. (1) The mechanical properties of the SLMoS2, including the ultimate strength and Young's modulus, are found to monotonically decrease as temperature increases. Increasing the temperature, the ultimate strength of SLMoS2 in the AC direction drops faster than in the ZZ direction, whereas the Young's modulus of SLMoS2 in the ZZ direction decreases quicker than in the AC direction, which means that the chirality effect on the ultimate strength is remarkably different from the Young's modulus of SLMoS2. However, the ultimate strain in the ZZ direction at the temperatures in a range from 1 K to 800 K is close to that in the AC direction, which means that the effect of chirality on the ultimate strain is insignificant. (2) Unlike the published results in the literature, the phase transition of SLMoS2 is found to only occur at a temperature of 1 K and at the moment of initial crack formation as tensiled along the ZZ direction, and the new phase of quadrilateral structure keeps stable after unloading. (3) The linear thermal expansion coefficients along the ZZ and AC directions are also measured, the magnitudes of which are found to be consistent with the published experimental results. Our simulation results support the viewpoint that the effect of the temperature on the mechanical property of SLMoS2 is significant, and the SLMoS2 can be regarded as an anisotropic material as the chirality effect cannot be ignored. The linear thermal expansion coefficients obtained with MD simulation are all in good agreement with the experimental data.

This paper investigates the mechanical behaviors of few-layer black phosphorus (FLBP) by using molecular dynamics simulations. Results show that both tensile and compressive behaviors are strongly anisotropic in the armchair and zigzag directions due to the unidirectional puckers in each atomic layer, and that the compressive behavior is dependent on the number of atomic layers. In particular, the compressive and buckling strengths of FLBP can be significantly enhanced by stacking more atomic layers together, while this has little influence on both Young’s modulus and tensile strength. It is interesting to found that increasing the number of atomic layers in FLBP or the dimension ratio can lead to a drastically reduced flexibility in armchair direction, showing that both compressive and buckling strengths become higher than those in zigzag direction. It is also demonstrated that the reorientation of FLBP’s atomic configuration occurs under certain conditions. The mechanism of deformation underlying the mechanical behaviors of FLBP is also discussed, suggesting that changing the number of atomic layers is an effective way to engineer two-dimensional materials for desired material properties.

Strain engineered structural, mechanical and electronic properties of monolayer phosphorene: A DFT study

Two-dimensional (2D) carbon allotropes beyond graphene, particularly graphynes, offer versatile platforms for tuning structure-property relationships in mixed sp-sp2 hybridized lattices. Here, we introduce pyrene-based α-graphyne, a novel derivative constructed via selective linker removal and hydrogen passivation, embedding extended aromatic domains while preserving the α-topology. Density functional theory calculations (PBE-GGA) confirm dynamic and thermal stability up to 2000 K, supported by phonon dispersion and ab initio molecular dynamics simulations. Mechanical analysis reveals high stiffness (Young's modulus ∼174 N m-1; shear modulus ∼71 N m-1) and a nearly isotropic elastic response. The pristine lattice exhibits Dirac-like semimetallicity. The hexagonal lattice was transformed into an equivalent orthorhombic supercell, allowing uniaxial compressive and tensile strains along armchair and zigzag directions. Under ±3% strain, a finite band gap emerges symmetrically in the meV regime. Along the zigzag direction, the gap reaches 18.6 meV (-3%) and 11.2 meV (+3%), while along the armchair direction it increases to 20.0 and 14.3 meV, respectively. For equal strain magnitudes, the larger response under armchair deformation reflects stronger modulation of pz-pz orbital overlap and strain-induced lifting of Dirac-point degeneracy. Chemical functionalization provides an additional degree of control: selective hydrogenation and fluorination at sp2 sites stabilize wide band gaps of 3.93 eV and 3.21 eV, respectively, while complete chlorination destabilizes the lattice due to steric crowding and out-of-plane distortions. Gas adsorption analysis further reveals strong, site-dependent binding for small molecules (Cl2, F2, NO, O2, and CO2), highlighting chemically active acetylenic regions. Together, these results establish pyrene-based α-graphyne as a mechanically robust, strain-tunable, and chemically responsive 2D carbon framework.

HOP-graphene is a graphene structural derivative consisting of 5-, 6-, and 8-membered carbon rings with distinctive electrical properties. This paper presents a systematic investigation of the effects of varying sizes, strain rates, temperatures, and defects on the mechanical properties of HOP-graphene, utilizing molecular dynamics simulations. The results revealed that Young's modulus of HOP-graphene in the armchair direction is 21.5% higher than that in the zigzag direction, indicating that it exhibits greater rigidity in the former direction. The reliability of the tensile simulations was contingent upon the size and strain rate. An increase in temperature from 100 K to 900 K resulted in a decrease in Young's modulus by 7.8% and 2.9% for stretching along the armchair and zigzag directions, respectively. An increase in the concentration of introduced void defects from 0% to 3% resulted in a decrease in Young's modulus by 24.7% and 23.1% for stretching along the armchair and zigzag directions, respectively. An increase in the length of rectangular crack defects from 0 nm to 4 nm resulted in a decrease in Young's modulus for stretching along the armchair and zigzag directions by 6.7% and 5.7%, respectively. Similarly, an increase in the diameter of the circular hole defect from 0 nm to 4 nm resulted in a decrease in Young's modulus along both the armchair and zigzag directions, with a corresponding reduction of 11.0% and 10.4%, respectively. At the late stage of tensile fracture along the zigzag direction, HOP-graphene undergoes a transformation to an amorphous state under tensile stress. Our results might contribute to a more comprehensive understanding of the mechanical properties of HOP-graphene under different test conditions, helping to land it in potential practical applications.

Molecular dynamic (MD) simulation was employed to take the molecular fingerprint of mechanical properties of beryllium-oxide nanotubes (BeONTs). In this regard, the effect of the radius, the number of walls (single-, double-, and triple-walled), and the interlayer distance, as well as the temperature on the Young's modulus, failure stress, and failure strain, are visualized and discussed. It was unveiled that larger single-walled BeONTs have lower Young's modulus in zigzag and armchair direction, and the highest Young's modulus was obtained for the (8,0) zigzag and (4,4) armchair SWBeONTs as of 645.71 GPa and 624.81 GPa, respectively. Unlike Young's modulus, however, the failure properties of the armchair structures were higher than those of zigzag ones. Furthermore, similar to SWBEONTs, an increase in the interlayer distance of double-walled BeONTs (DWBeONTs) led to a slight reduction in Young's modulus value, while no meaningful trend was found among failure behavior. For double-walled BeONTs (TWBeONTs), the elastic modulus was obviously higher in both armchair and zigzag directions compared to DWBeONTs.

Electronic structure and optic absorption of phosphorene under strain

Strain effects on monolayer MoSi2N4: Ideal strength and failure mechanism

Molecular dynamics simulations for mechanical properties of the monolayer PtS2 with line defect