Comment on "Two-dimensional penta-like PdPSe with a puckered pentagonal structure: a first-principles study" by A. Bafekry, M. M. Fadlallah, M. Faraji, A. Shafique, H. R. Jappor, I. Abdolhoseini Sarsari, Y. S. Ang and M. Ghergherehchii, Phys. Chem. Chem. Phys., 2022, 24, 9990.

Recently, Bafekry et al. [Phys. Chem. Chem. Phys., 2022, 24, 9990-9997] presented their density functional theory (DFT) results on the electronic, thermal and dynamical stability, and the elastic, optical and thermoelectric properties of the PdPSe monolayer. The aforementioned theoretical work however includes inaccuracies in the analysis of the electronic band structure, bonding mechanism, thermal stability and phonon dispersion relation of the PdPSe monolayer. We also found noticeable errors in the evaluation of Young's modulus and thermoelectric properties. In contrast with their findings, we show that the PdPSe monolayer shows a rather high Young's modulus and because of its moderate lattice thermal conductivity it cannot be a promising thermoelectric material.

Comment on 'Two-dimensional carbon nitride C6N nanosheet with egg-comb-like structure and electronic properties of a semimetal [2021,Nanotechnology32, 215702]'.

Recently, Bafekryet al(2021Nanotechnology32215702) predicted a novel two-dimensional carbon nitride with an egg-comb-like structure and a C6N stoichiometry. Their density functional theory results reveal the thermal stability of this structure at 300 K. They also examined the thermoelectric properties of this monolayer up to 500 K. By adopting the same methodology employed in the original work by Bafekryet al(2021Nanotechnology32215702), we show that this monolayer is thermally unstable and cannot be employed for practical applications. Aforementioned theoretical work also includes inaccuracies in the evaluation of thermoelectric properties of the C6N monolayer, as they did not consider the contribution of the lattice thermal conductivity.

Highly anisotropic mechanical and optical properties of 2D NbOX2 (X = Cl, Br, I) revealed by first-principle.

In the latest experimental success, NbOI2two-dimensional (2D) crystals with anisotropic electronic and optical properties have been fabricated (Adv. Mater.33 (2021), 2101505). In this work inspired by the aforementioned accomplishment, we conduct first-principles calculations to explore the mechanical, electronic, and optical properties of NbOX2(X = Cl, Br, I) nanosheets. We show that individual layers in these systems are weakly bonded, with exfoliation energies of 0.22, 0.23, and 0.24 J m-2, for the isolation of the NbOCl2, NbOBr2,and NbOI2monolayers, respectively, distinctly lower than those of the graphene. The optoelectronic properties of the single-layer, bilayer, and bulk NbOCl2, NbOBr2,and NbOI2crystals are investigated via density functional theory calculations with the HSE06 approach. Our results indicate that the layered bulk NbOCl2, NbOBr2,and NbOI2crystals are indirect gap semiconductors, with band gaps of 1.79, 1.69, and 1.60 eV, respectively. We found a slight increase in the electronic gap for the monolayer and bilayer systems due to electron confinement at the nanoscale. Our results show that the monolayer and bilayer of these novel 2D compounds show suitable valence and conduction band edge positions for visible-light-driven water splitting reactions. The first absorption peaks of these novel monolayers along the in-plane polarization are located in the visible range of light which can be a promising feature to design advanced nanoelectronics. We found that the studied 2D systems exhibit highly anisotropic mechanical and optical properties. The presented first-principles results provide a comprehensive vision about direction-dependent mechanical and optical properties of NbOX2(X = Cl, Br, I) nanosheets.

First-principles investigation of electronic, mechanical and thermoelectric properties of graphene-like XBi (X = Si, Ge, Sn) monolayers.

Research progress on single layer group III monochalcogenides has been increasing rapidly owing to their interesting physics. Herein, we investigate the dynamically stable single layer forms of XBi (X = Ge, Si or Sn) using density functional theory calculations. Phonon band dispersion calculations and ab initio molecular dynamics simulations reveal the dynamical and thermal stability of the considered monolayers. Raman spectra calculations indicate the existence of 5 Raman active phonon modes, 3 of which are prominent and can be observed in possible Raman measurements. The electronic band structures of the XBi single layers were investigated with and without the effects of spin-orbit coupling (SOC). Our results show that XBi single layers show semiconducting properties with narrow band gap values without SOC. However, only single layer SiBi is an indirect band gap semiconductor, while GeBi and SnBi exhibit metallic behaviors when adding spin-orbit coupling effects. In addition, the calculated linear elastic parameters indicate the soft nature of the predicted monolayers. Moreover, our predictions for the thermoelectric properties of single layer XBi reveal that SiBi is a good thermoelectric material with increasing temperature. Overall, it is proposed that single layer XBi structures can be alternative, stable 2D single layers with varying electronic and thermoelectric properties.

Tunable electronic properties of the dynamically stable layered mineral Pt2HgSe3 (Jacutingaite).

Density functional theory calculations are performed in order to study the structural and electronic properties of monolayer Pt2HgSe3. Our results show that the dynamically stable monolayer Pt2HgSe3 is a topological insulator with a band gap of 160 meV. In addition, the effect of layer thickness, strain and electric field on the electronic properties are systematically investigated using fully relativistic calculations. We find that the electronic properties are sensitive to the applied electric field. With increasing electric field strength up to 0.5 V Å-1, the band gap decreases from 160 to 10 meV at 0.5 V Å-1. Interestingly, upon further increasing the electric field up to 1.0 V Å-1, the band gap opens again and reaches its bare value (160 meV) at 1.0 V Å-1, which indicates that the band gap is reversibly controllable via the applied external electric field. Moreover, the electronic properties are also examined under uniaxial and biaxial strain. Our results reveal that the band gap value can be tuned to 150 meV (at 1%) and to 92 meV (at 6%) under uniaxial strain, while under biaxial tensile strain, it increases to 170 meV at 5% and fluctuates between 150 and 100 meV in the range of 5-10%. In contrast, the biaxial-compressive strain is found to drive the semiconducting-to-metallic transition for sufficiently large compressions (over 8%). On the other hand, we find that increasing the thickness of Pt2HgSe3 modifies the band gap to 150 meV (for the bilayer) and 140 meV (for the trilayer). In the bilayer Pt2HgSe3 structure, we further investigated the effect of out-of-plane pressure, both compressive and tensile, and our results show that the electronic structure of bilayer Pt2HgSe3 is largely preserved. Our study provides new insight into the modification of the electronic structure of monolayer Pt2HgSe3 upon application of external fields and variation in the layer thickness.

Embedding of atoms into the nanopore sites of the C6N6 and C6N8 porous carbon nitride monolayers with tunable electronic properties.

Using first-principles calculations, we study the effect of embedding various atoms into the nanopore sites of both C6N6 and C6N8 monolayers. Our results indicate that the embedded atoms significantly affect the electronic and magnetic properties of C6N6 and C6N8 monolayers and lead to extraordinary and multifarious electronic properties, such as metallic, half-metallic, spin-glass semiconductor and dilute-magnetic semiconductor behaviour. Our results reveal that the H atom concentration dramatically affects the C6N6 monolayer. On increasing the H coverage, the impurity states also increase due to H atoms around the Fermi-level. C6N6 shows metallic character when the H atom concentration reaches 6.25%. Moreover, the effect of charge on the electronic properties of both Cr@C6N6 and C@C6N8 is also studied. Cr@C6N6 is a ferromagnetic metal with a magnetic moment of 2.40 µB, and when 0.2 electrons are added and removed, it remains a ferromagnetic metal with a magnetic moment of 2.57 and 2.77 µB, respectively. Interestingly, one can observe a semi-metal, in which the VBM and CBM in both spin channels touch each other near the Fermi-level. C@C6N8 is a semiconductor with a nontrivial band gap. When 0.2 electrons are removed, it remains metallic, and under excess electronic charge, it exhibits half-metallic behaviour.

Electronic, optical and thermoelectric properties of boron-doped nitrogenated holey graphene.

We employ first principles calculations to investigate the electronic, optical, and thermoelectric properties of ten boron-doped nitrogenated holey graphene (NHG) monolayers. We find that most of the proposed structures remain stable during ab initio molecular dynamics simulations, in spite of their increased formation energies. Density functional theory calculations employing a hybrid functional predict band gaps ranging from 0.73 eV to 2.30 eV. In general, we find that boron doping shifts optical absorption towards the visible spectrum, and also reduces light reflection in this region. On the other hand, the magnitude of optical absorption coefficients are reduced. Regarding the thermoelectric properties, we predict that boron doping can enhance the figure of merit ZT of NHG by up to 55%. Our results indicate that boron-doped NHG monolayers may find application in solar cells and thermoelectric devices.

Electrical and Thermal Transport in Coplanar Polycrystalline Graphene-hBN Heterostructures.

We present a theoretical study of electronic and thermal transport in polycrystalline heterostructures combining graphene (G) and hexagonal boron nitride (hBN) grains of varying size and distribution. By increasing the hBN grain density from a few percent to 100%, the system evolves from a good conductor to an insulator, with the mobility dropping by orders of magnitude and the sheet resistance reaching the MΩ regime. The Seebeck coefficient is suppressed above 40% mixing, while the thermal conductivity of polycrystalline hBN is found to be on the order of 30-120 Wm-1 K-1. These results, agreeing with available experimental data, provide guidelines for tuning G-hBN properties in the context of two-dimensional materials engineering. In particular, while we proved that both electrical and thermal properties are largely affected by morphological features (e.g., by the grain size and composition), we find in all cases that nanometer-sized polycrystalline G-hBN heterostructures are not good thermoelectric materials.

Anisotropic mechanical and optical response and negative Poisson's ratio in Mo2C nanomembranes revealed by first-principles simulations.

Transition metal carbides include a wide variety of materials with attractive properties that are suitable for numerous and diverse applications. A most recent experimental advance could provide a path toward the successful synthesis of large-area and high-quality ultrathin Mo2C membranes with superconducting properties. In the present study, we used first-principles density functional theory calculations to explore the mechanical and optical response of single-layer and free-standing Mo2C. Uniaxial tensile simulations along the armchair and zigzag directions were conducted and we found that while the elastic properties are close along various loading directions, the nonlinear regimes in stress-strain curves are considerably different. We found that Mo2C sheets present negative Poisson's ratio and thus can be categorized as an auxetic material. Our simulations also reveal that Mo2C films retain their metallic electronic characteristic upon uniaxial loading. We found that for Mo2C nanomembranes the dielectric function becomes anisotropic along in-plane and out-of-plane directions. Our findings can be useful for the practical application of Mo2C sheets in nanodevices.

A structural insight into mechanical strength of graphene-like carbon and carbon nitride networks.

Graphene, one of the strongest materials ever discovered, triggered the exploration of many 2D materials in the last decade. However, the successful synthesis of a stable nanomaterial requires a rudimentary understanding of the relationship between its structure and strength. In the present study, we investigate the mechanical properties of eight different carbon-based 2D nanomaterials by performing extensive density functional theory calculations. The considered structures were just recently either experimentally synthesized or theoretically predicted. The corresponding stress-strain curves and elastic moduli are reported. They can be useful in training force field parameters for large scale simulations. A comparative analysis of these results revealed a direct relationship between atomic density per area and elastic modulus. Furthermore, for the networks that have an armchair and a zigzag orientation, we observed that they were more stretchable in the zigzag direction than the armchair direction. A critical analysis of the angular distributions and radial distribution functions suggested that it could be due to the higher ability of the networks to suppress the elongations of the bonds in the zigzag direction by deforming the bond angles. The structural interpretations provided in this work not only improve the general understanding of a 2D material's strength but also enables us to rationally design them for higher qualities.

Mechanical properties of borophene films: a reactive molecular dynamics investigation.

The most recent experimental advances could provide ways for the fabrication of several atomic thick and planar forms of boron atoms. For the first time, we explore the mechanical properties of five types of boron films with various vacancy ratios ranging from 0.1-0.15, using molecular dynamics simulations with ReaxFF force field. It is found that the Young's modulus and tensile strength decrease with increasing the temperature. We found that boron sheets exhibit an anisotropic mechanical response due to the different arrangement of atoms along the armchair and zigzag directions. At room temperature, 2D Young's modulus and fracture stress of these five sheets appear in the range 63-136 N m(-1) and 12-19 N m(-1), respectively. In addition, the strains at tensile strength are in the ranges of 9%-14%, 11%-19%, and 10%-16% at 1, 300, and 600 K, respectively. This investigation not only reveals the remarkable stiffness of 2D boron, but establishes relations between the mechanical properties of the boron sheets to the loading direction, temperature and atomic structures.

Mechanical responses of borophene sheets: a first-principles study.

Recent experimental advances for the fabrication of various borophene sheets introduced new structures with a wide range of applications. Borophene is the boron atom analogue of graphene. Borophene exhibits various structural polymorphs all of which are metallic. In this work, we employed first-principles density functional theory calculations to investigate the mechanical properties of five different single-layer borophene sheets. In particular, we analyzed the effect of the loading direction and point vacancy on the mechanical response of borophene. Moreover, we compared the thermal stabilities of the considered borophene systems. Based on the results of our modelling, borophene films depending on the atomic configurations and the loading direction can yield a remarkable elastic modulus in the range of 163-382 GPa nm and a high ultimate tensile strength from 13.5 GPa nm to around 22.8 GPa nm at the corresponding strain from 0.1 to 0.21. Our study reveals the remarkable mechanical characteristics of borophene films.

Mechanical response of all-MoS2 single-layer heterostructures: a ReaxFF investigation.

Molybdenum disulfide (MoS2) is a highly attractive 2D material due to its interesting electronic properties. Recent experimental advances confirm the possibility of further tuning the electronic properties of MoS2 through the fabrication of single-layer heterostructures consisting of semiconducting (2H) and metallic (1T) MoS2 phases. Nonetheless, despite significant technological and scientific interest, there is currently limited information concerning the mechanical properties of these heterostructure systems. This investigation aims at extending our understanding of the mechanical properties of all-MoS2 single-layer structures at room temperature. This goal was achieved by performing extensive classical molecular dynamics simulations using a recently developed ReaxFF force field. We first studied the direction dependent mechanical properties of defect-free 2H and 1T phases. Our modelling results for pristine 2H MoS2 were found to be in good agreement with the experimental tests and first-principles theoretical predictions. We also discuss the mechanical response of 2H/1T single layer heterostructures. Our reactive molecular dynamics results suggest all-MoS2 heterostructures as suitable candidates for providing a strong and flexible material with tuneable electronic properties.

Atomistic modeling of mechanical properties of polycrystalline graphene.

We performed molecular dynamics (MD) simulations to investigate the mechanical properties of polycrystalline graphene. By constructing molecular models of ultra-fine-grained graphene structures, we studied the effect of different grain sizes of 1-10 nm on the mechanical response of graphene. We found that the elastic modulus and tensile strength of polycrystalline graphene decrease with decreasing grain size. The calculated mechanical proprieties for pristine and polycrystalline graphene sheets are found to be in agreement with experimental results in the literature. Our MD results suggest that the ultra-fine-grained graphene structures can show ultrahigh tensile strength and elastic modulus values that are very close to those of pristine graphene sheets.

Goldene: An Anisotropic Metallic Monolayer with Remarkable Stability and Rigidity and Low Lattice Thermal Conductivity.

In a recent breakthrough in the field of two-dimensional (2D) nanomaterials, the first synthesis of a single-atom-thick gold lattice of goldene has been reported through an innovative wet chemical removal of Ti3C2 from the layered Ti3AuC2. Inspired by this advancement, in this communication and for the first time, a comprehensive first-principles investigation using a combination of density functional theory (DFT) and machine learning interatomic potential (MLIP) calculations has been conducted to delve into the stability, electronic, mechanical and thermal properties of the single-layer and free-standing goldene. The presented results confirm thermal stability at 700 K as well as remarkable dynamical stability of the stress-free and strained goldene monolayer. At the ground state, the elastic modulus and tensile strength of the goldene monolayer are predicted to be over 226 and 12 GPa, respectively. Through validated MLIP-based molecular dynamics calculations, it is found that at room temperature, the goldene nanosheet can exhibit anisotropic tensile strength over 9 GPa and a low lattice thermal conductivity around 10 ± 2 W/(m.K), respectively. We finally show that the native metallic nature of the goldene monolayer stays intact under large tensile strains. The combined insights from DFT and MLIP-based results provide a comprehensive understanding of the stability, mechanical, thermal and electronic properties of goldene nanosheets.

Remarkably high tensile strength and lattice thermal conductivity in wide band gap oxidized holey graphene C2O nanosheet.

Recently, the synthesis of oxidized holey graphene with the chemical formula C2O has been reported (J. Am. Chem. Soc. 2024, 146, 4532). We herein employed a combination of density functional theory (DFT) and machine learning interatomic potential (MLIP) calculations to investigate the electronic, optical, mechanical and thermal properties of the C2O monolayer, and compared our findings with those of its C2N counterpart. Our analysis shows that while the C2N monolayer exhibits delocalized π-conjugation and shows a 2.47 eV direct-gap semiconducting behavior, the C2O counterpart exhibits an indirect gap of 3.47 eV. We found that while the C2N monolayer exhibits strong absorption in the visible spectrum, the initial absorption peaks in the C2O lattice occur at around 5 eV, falling within the UV spectrum. Notably, we found that the C2O nanosheet presents significantly higher tensile strength compared to its C2N counterpart. MLIP-based calculations show that at room temperature, the C2O nanosheet can exhibit remarkably high tensile strength and lattice thermal conductivity of 42 GPa and 129 W/mK, respectively. The combined insights from DFT and MLIP-based results provide a comprehensive understanding of the electronic and optical properties of C2O nanosheets, suggesting them as mechanically robust and highly thermally conductive wide bandgap semiconductors.

Electronic, Thermal and Mechanical Properties of Carbon and Boron Nitride Holey Graphyne Monolayers.

In a recent experimental accomplishment, a two-dimensional holey graphyne semiconducting nanosheet with unusual annulative π-extension has been fabricated. Motivated by the aforementioned advance, herein we theoretically explore the electronic, dynamical stability, thermal and mechanical properties of carbon (C) and boron nitride (BN) holey graphyne (HGY) monolayers. Density functional theory (DFT) results reveal that while the C-HGY monolayer shows an appealing direct gap of 1.00 (0.50) eV according to the HSE06(PBE) functional, the BNHGY monolayer is an indirect insulator with large band gaps of 5.58 (4.20) eV. Furthermore, the elastic modulus (ultimate tensile strength) values of the single-layer C- and BN-HGY are predicted to be 127(41) and 105(29) GPa, respectively. The phononic and thermal properties are further investigated using machine learning interatomic potentials (MLIPs). The predicted phonon spectra confirm the dynamical stability of these novel nanoporous lattices. The room temperature lattice thermal conductivity of the considered monolayers is estimated to be very close, around 14.0 ± 1.5 W/mK. At room temperature, the C-HGY and BN-HGY monolayers are predicted to yield an ultrahigh negative thermal expansion coefficient, by more than one order of magnitude larger than that of the graphene. The presented results reveal decent stability, anomalously low elastic modulus to tensile strength ratio, ultrahigh negative thermal expansion coefficients and moderate lattice thermal conductivity of the semiconducting C-HGY and insulating BN-HGY monolayers.

Atomistic modeling of the mechanical properties: the rise of machine learning interatomic potentials.

Since the birth of the concept of machine learning interatomic potentials (MLIPs) in 2007, a growing interest has been developed in the replacement of empirical interatomic potentials (EIPs) with MLIPs, in order to conduct more accurate and reliable molecular dynamics calculations. As an exciting novel progress, in the last couple of years the applications of MLIPs have been extended towards the analysis of mechanical and failure responses, providing novel opportunities not heretofore efficiently achievable, neither by EIPs nor by density functional theory (DFT) calculations. In this minireview, we first briefly discuss the basic concepts of MLIPs and outline popular strategies for developing a MLIP. Next, by considering several examples of recent studies, the robustness of MLIPs in the analysis of the mechanical properties will be highlighted, and their advantages over EIP and DFT methods will be emphasized. MLIPs furthermore offer astonishing capabilities to combine the robustness of the DFT method with continuum mechanics, enabling the first-principles multiscale modeling of mechanical properties of nanostructures at the continuum level. Last but not least, the common challenges of MLIP-based molecular dynamics simulations of mechanical properties are outlined and suggestions for future investigations are proposed.

A first-principles and machine-learning investigation on the electronic, photocatalytic, mechanical and heat conduction properties of nanoporous C5N monolayers.

Carbon nitride nanomembranes are currently among the most appealing two-dimensional (2D) materials. As a nonstop endeavor in this field, a novel 2D fused aromatic nanoporous network with a C5N stoichiometry has been most recently synthesized. Inspired by this experimental advance and exciting physics of nanoporous carbon nitrides, herein we conduct extensive density functional theory calculations to explore the electronic, optical and photocatalytic properties of the C5N monolayer. In order to examine the dynamic stability and evaluate the mechanical and heat transport properties under ambient conditions, we employ state of the art methods on the basis of machine-learning interatomic potentials. The C5N monolayer is found to be a direct band gap semiconductor, with a band-gap of 2.63 eV according to the HSE06 method. The obtained results confirm the dynamic stability, remarkable tensile strengths over 10 GPa and a low lattice thermal conductivity of ∼9.5 W m-1 K-1 for the C5N monolayer at room temperature. The first absorption peak of the single-layer C5N along the in-plane polarization is predicted to appear in the visible range of light. With a combination of high carrier mobility, appropriate band edge positions and strong absorption of visible light, the C5N monolayer might be an appealing candidate for photocatalytic water splitting reactions. The presented results provide an extensive understanding concerning the critical physical properties of the C5N nanosheets and also highlight the robustness of machine-learning interatomic potentials in the exploration of complex physical behaviors.

Molecular Junctions Enhancing Thermal Transport within Graphene Polymer Nanocomposite: A Molecular Dynamics Study.

Thermal conductivity of polymer-based (nano)composites is typically limited by thermal resistances occurring at the interfaces between the polymer matrix and the conductive particles as well as between particles themselves. In this work, the adoption of molecular junctions between thermally conductive graphene foils is addressed, aiming at the reduction of the thermal boundary resistance and eventually lead to an efficient percolation network within the polymer nanocomposite. This system was computationally investigated at the atomistic scale, using classical Molecular Dynamics, applied the first time to the investigation of heat transfer trough molecular junctions within a realistic environment for a polymer nanocomposite. A series of Molecular Dynamics simulations were conducted to investigate the thermal transport efficiency of molecular junctions in polymer tight contact, to quantify the contribution of molecular junctions when graphene and the molecular junctions are surrounded by polydimethylsiloxane (PDMS) molecules. A strong dependence of the thermal conductance was found in PDMS/graphene model, with best performances obtained with short and conformationally rigid molecular junctions. Furthermore, the adoption of the molecular linkers was found to contribute additionally to the thermal transport provided by the surrounding polymer matrix, demonstrating the possibility of exploiting molecular junctions in composite materials.