Tersoff Potential Research Articles

Description of Short-Range Interactions of Carbon-Based Materials with a Combined AIREBO and ZBL Potential.

An accurate description of short-range interactions among atoms is crucial for simulating irradiation effects in applications related to ion modification techniques. A smooth integration of the Ziegler-Biersack-Littmark (ZBL) potential with the adaptive intermolecular reactive empirical bond-order (AIREBO) potential was achieved to accurately describe the short-range interactions for carbon-based materials. The influence of the ZBL connection on potential energy, force, and various AIREBO components, including reactive empirical bond-order (REBO), Lennard-Jones (LJ), and the torsional component, was examined with configurations of the dimer structure, tetrahedron structure, and monolayer graphene. The REBO component is primarily responsible for the repulsive force, while the LJ component is mainly active in long-range interactions. It is shown that under certain conditions, the torsional energy can lead to a strong repulsive force at short range. Molecular dynamics simulations were performed to study the collision process in configurations of the C-C dimer and bulk graphite. Cascade collisions in graphite with kinetic energies of 1 keV and 10 keV for primary knock-on atoms showed that the short-range description can greatly impact the number of generated defects and their morphology.

Enhancing the thermal conductivity and viscosity of ethylene glycol-based single-walled carbon nanotube (SWCNT) nanofluid: An investigation utilizing equilibrium molecular dynamics simulation

In this work, thermal conductivity (TC), viscosity, and rheological properties of an ethylene glycol (EG) based single-walled carbon nanotube (SWCNT) nanofluid (NF) have been computed using equilibrium molecular dynamics (EMD) simulation. In SWCNT, for the interaction between carbon atoms, Tersoff potential is used. Results indicate that TC and viscosity increase in nonlinear fashion with volume fraction. However, with temperature, TC increases but viscosity decreases. Increased interaction between CNT and liquid atoms of EG, and the high heat conductance ability of SWCNT nanoparticles enhance the effective conductivity and viscosity of NFs. Longer CNTs provide more efficient heat transfer pathways and more interactions between CNT & base fluid molecules, which contribute to enhanced TC and viscosity of NFs. Weakening of intermolecular forces within the NF with increasing temperature decreases viscosity. To validate the results, radial distribution function (RDF) and stress autocorrelation function (SACF) have been estimated. Mean square displacement (MSD) investigation demonstrates that the diffusion of liquid atoms (or molecules) serves as the fundamental mechanism for heat conduction in nanofluid. The results have been compared with experimental findings for analogous dispersive medium. Broadly, an attempt has been made to explore how interactions between the base fluid and nanoparticles (NPs) can enhance the thermal and rheological efficiencies of nanofluids.

Triple junction excess energy in polycrystalline metals

The energetics of triple lines are often negligible in polycrystalline systems, but may play a significant role in the finest nanocrystals, and in fact lower the excess defect energies of those polycrystals. This paper develops a methodology to assess polycrystalline average grain boundary and triple junction excess energies for pure fcc metals Ni, Cu, Al, Pd, Pt, Ag and Au using embedded atom method potentials. It is found that there are correlations between the triple line energy and physical quantities such as grain boundary and dislocation line energy, but with a negative sign indicating that triple junctions reduce intergranular excess energy per area on average. The relationship with grain boundary energy is of order ∼−4.5 × 10−10 m, and the triple junction energy is about −1/12 of the dislocation line energy. Despite their low energy, triple junctions can significantly affect total system energy due to their high density in the finest nanocrystals; for example, 6-nm Pd nanocrystals have an effective intergranular energy of ∼0.83 J/m2 (compared with the large grain size limit of 0.93 J/m2), translating to a measurable bulk excess enthalpy of ∼6 kJ/mol. Such excess enthalpy is experimentally assessable, and the present framework can be used to measure triple junction energies. For instance, re-analyzing data of Lu and Sun (Phil. Mag., 1997) we obtain grain boundary and triple junction energies of 0.33 J/m2 and −3.0 × 10−10 J/m respectively for Selenium nanocrystals, which can be compared with modeled values of 0.76 J/m2 and −1.02 × 10−10 J/m by using our method with a published bond-order potential for Se.

Mechanical properties of Si(1−x)–C(x): strength and stiffness of materials using LAMMPS molecular dynamics simulation

This study investigated the mechanical properties (elastic modulus, tensile strength, yield strength, and toughness) of different percent C of silicon carbide (SiC) using molecular dynamics simulations via the large-scale atomic/molecular massively parallel simulator (LAMMPS) with the uniaxial tensile test at four strain rates: 0.1, 0.5, 1.0, and 5.0 m s−1, using the Tersoff potential. The simulation uses 20 × 20 × 20 atoms (108.6 Å × 108.6 Å × 108.6 Å) of the diamond cubic structure of Si, then carbon atoms were placed randomly at 5% intervals from 0–50 percent C. Results show improved mechanical properties when increasing percent C until peaking at 25%, before decreasing. This is caused by the shortest bond length at 25 percent C from the increase of Si=C using the radial distribution function analysis. Increasing the strain rate generally improves the mechanical properties of the material. The deformation mechanism shows that increasing (decreasing) strain rate generally results in multiple (lesser) failure points with a ductile (brittle) fracture mode.

Molecular Dynamics Simulations of Effects of Geometric Parameters and Temperature on Mechanical Properties of Single-Walled Carbon Nanotubes

Carbon nanotubes (CNTs) are considered an advanced form of carbon. They have superior characteristics in terms of mechanical and thermal properties compared to other available fibers and can be used in various applications, such as supercapacitors, sensors, and artificial muscles. The properties of single-walled carbon nanotubes (SWNTs) are significantly affected by geometric parameters such as chirality and aspect ratio, and testing conditions such as temperature and strain rate. In this study, the effects of geometric parameters and temperature on the mechanical properties of SWNTs were studied by molecular dynamics (MD) simulations using the Large-scaled Atomic/Molecular Massively Parallel Simulator (LAMMPS). Based on the second-generation reactive empirical bond order (REBO) potential, SWNTs of different diameters were tested in tension and compression under different strain rates and temperatures to understand their effects on the mechanical behavior of SWNTs. It was observed that the Young’s modulus and the tensile strength decreases with increasing SWNT tube diameter. As the chiral angle increases, the tensile strength increases, while the Young’s modulus decreases. The simulations were repeated at different temperatures of 300 K, 900 K, 1500 K, 2100 K and different strain rates of 1 × 10−3/ps, 0.75 × 10−3/ps, 0.5 × 10−3/ps, and 0.25 × 10−3/ps to investigate the effects of temperature and strain rate, respectively. The results show that the ultimate tensile strength of SWNTs increases with increasing strain rate. It is also seen that when SWNTs were stretched at higher temperatures, they failed at lower stresses and strains. The compressive behavior results indicate that SWNTs tend to buckle under lower stresses and strains than those under tensile stress. The simulation results were validated by and consistent with previous studies. The presented approach can be applied to investigate the properties of other advanced materials.

Ab Initio-Based Bond Order Potential for Arsenene Polymorphs Developed via Hierarchical Reinforcement Learning.

Arsenene, a less-explored two-dimensional material, holds the potential for applications in wearable electronics, memory devices, and quantum systems. This study introduces a bond-order potential model with Tersoff formalism, the ML-Tersoff, which leverages multireward hierarchical reinforcement learning (RL), trained on an ab initio data set. This data set covers a spectrum of properties for arsenene polymorphs, enhancing our understanding of its mechanical and thermal behaviors without the complexities of traditional models requiring multiple parameter sets. Our RL strategy utilizes decision trees coupled with a hierarchical reward strategy to accelerate convergence in high-dimensional continuous search spaces. Unlike the Stillinger-Weber approach, which demands separate formalisms for buckled and puckered forms, the ML-Tersoff model concurrently captures multiple properties of the two polymorphs by effectively representing the local environment, thereby avoiding the need for different atomic types. We apply the ML model to understand the mechanical and thermal properties of the arsenene polymorphs and nanostructures. We observe an inverse relationship between the critical strain and temperature in arsenene. Thermal conductivity calculations in nanosheets show good agreement with ab initio data, reflecting a decrease in thermal conductivity attributable to increased anharmonic effects at higher temperatures. We also apply the model to predict the thermal behavior of arsenene nanotubes.

Size dependence of melting process of armchair hexagonal boron nitride nanoribbon

The dependence on the initial configuration size of armchair hexagonal boron nitride nanoribbon (h-BNNR) is investigated by molecular dynamics simulation. The initial configuration size of armchair h-BNNR containing 10000, 20000, and 30000 identical atoms of B and N is heated from 50 K to 6000 K via Tersoff potentials to study the dependence on the initial configuration size of the phase transition from crystal to liquid of armchair h-BNNR. Some results can be listed: the phase transition exhibits a first-order type; the phase transition from crystal to liquid states depends on the initial configuration size; the melting points of 10000, 20000, and 30000 atoms are 3640 K, 4000 K, and 4400 K, respectively; the dependence on the heating rate of the armchair h-BNNR is considered for the case of 20000 atoms; in this study range, the melting point decreases as the heating rate decreases; the atomic mechanism of melting process is studied by analyzing the parameter and the appearance of the liquid-like atoms based on the critical value ; the critical value is used to classify solid-like and liquid-like atoms; the appearance of liquid-like atoms upon heating starts from the edges and grow inward; at the phase transition temperature, almost the entire crystal structure of the armchair h-BNNR configuration collapses.

Thermal conductivity of irregularly shaped nanoparticles from equilibrium molecular dynamics

The computation of thermal conductivity for finite nanoparticulate systems, particularly those of irregular shapes, poses significant challenges. The nonequilibrium molecular dynamics (NEMD) methods has been extensively utilized in numerous prior studies for the computation of thermal conductivity of nanoparticles. One of our recent works (Dong et al 2021 Phys. Rev. B 103 035417) proposed that equilibrium molecular dynamics (EMD) methods can be used for the simulation of thermal conductivity of finite-scale systems and demonstrated their equivalence to NEMD methods. In this study, we investigated the application of the (EMD) approach for the computation of thermal conductivity in zero-dimensional nanoparticles. In our initial step, we merged both methodologies to substantiate the equivalence in thermal conductivity calculation for cube and cylinder nanoparticles. After filtering the data, we confirmed the usefulness of EMD for evaluating the thermal conductivity of zero-dimensional materials. The NEMD method faces challenges in accurately predicting thermal conductivity in nanoparticle systems with a varying cross-sectional area along the transport direction, whereas EMD methods can be utilized to estimate thermal conductivity when the volume is known. In a subsequent study, we used the state-of-the-art machine learning potential to calculate the thermal conductivity of spherical nanoparticles and compared the results with those obtained using the classical Tersoff potential. Ultimately, we predicted the thermal conductivity of nanoparticles with various geometries in all directions. Our findings collectively demonstrate the simplicity and effectiveness of employing EMD methods for calculating thermal conductivity in nanoparticle systems, thereby opening up new avenues for investigating thermal transport properties in particle systems as well as nanopders.

Interatomic potentials for graphene reinforced metal composites: Optimal choice

Graphene reinforced metal matrix composites represent a promising class of materials for high-strength surface coatings because of their high strength and ductility. This study reports the application of different interatomic potentials to correctly describe the interaction between graphene and metals (Al, Cu, Ni, and Ti) by molecular dynamics. Both simple pair potentials, such as Lennard-Jones and Morse, and many-body potentials, such as bond order potential are applied for the simulation of a graphene/metal system at room temperature. Three different structures are considered: (i) graphene interacting with one metal atom; (ii) graphene interacting with a metal nanoparticle, and (iii) three-dimensional graphene network filled with metal nanoparticles. We first determine the potential energy that any graphene/metal system can reach during exposure at 300 K; then, we analyze the interaction dynamics for all considered systems and all potentials. A considerable difference in the interaction between metal nanoparticles with planar and folded graphene was found. For graphene/Ni, graphene/Cu, and graphene/Ti, the Lennard-Jones and Morse potentials provide accurate energetic and structural properties of the studied structures; they also describe interaction in the graphene/metal system in a similar way, at variance with bond-order potential. For graphene/Al, the Tersoff and Morse potentials describe the interaction better than Lennard-Jones. For the simulation of graphene/Me system, the optimal choice of the potential for different structures is of crucial importance. The presented analysis of the interatomic potentials appears to be promising for realistic and accurate simulations of graphene reinforced metal composites.

Liquid–liquid transition and ice crystallization in a machine-learned coarse-grained water model

Mounting experimental evidence supports the existence of a liquid-liquid transition (LLT) in high-pressure supercooled water. However, fast crystallization of supercooled water has impeded identification of the LLT line TLL(p) in experiments. While the most accurate all-atom (AA) water models display a LLT, their computational cost limits investigations of its interplay with ice formation. Coarse-grained (CG) models provide over 100-fold computational efficiency gain over AA models, enabling the study of water crystallization, but have not yet shown to have a LLT. Here, we demonstrate that the CG machine-learned water model Machine-Learned Bond-Order Potential (ML-BOP) has a LLT that ends in a critical point at pc = 170 ± 10 MPa and Tc = 181 ± 3 K. The TLL(p) of ML-BOP is almost identical to the one of TIP4P/2005, adding to the similarity in the equation of state of liquid water in both models. Cooling simulations reveal that ice crystallization is fastest at the LLT and its supercritical continuation of maximum heat capacity, supporting a mechanistic relationship between the structural transformation of water to a low-density liquid (LDL) and ice formation. We find no signature of liquid-liquid criticality in the ice crystallization temperatures. ML-BOP replicates the competition between formation of LDL and ice observed in ultrafast experiments of decompression of the high-density liquid (HDL) into the region of stability of LDL. The simulations reveal that crystallization occurs prior to the coarsening of the HDL and LDL domains, obscuring the distinction between the highly metastable first-order LLT and pronounced structural fluctuations along its supercritical continuation.

Enhancing piezoelectric performance of CNTs through B and N substitution under combined mechanical loads: insights from MD simulations

The piezoelectric properties of carbon nanotubes (CNTs) doped with boron (B) and nitrogen (N) were studied using the classical molecular dynamics (MD) simulation software package large scale atomic/molecular massively parallel simulator. The interactions among the nanotube atoms C, N, and B were calculated using the Tersoff potential. MD simulations were performed to observe the changes in the piezoelectric coefficient of the doped CNTs under loading conditions like tension, torsion, and a combination of both. We considered a wide range of chirality to determine the influence of structural variation on the piezoelectric effect. The study revealed that B-CNTs exhibit superior piezoelectric coefficients compared to N-CNTs, indicating the significant role of dopant type. Moreover, under tensile loading, zigzag-oriented B-CNTs showed higher piezoelectric coefficients with a maximum e33 = 0.2441 C m−2, whereas under torsional loading, armchair-oriented B-CNTs showed enhanced response with a maximum e36 = 0.0564 C m−2. A notable observation was that under combined loading conditions (tensile and torsional), the piezoelectric behavior of the B-CNTs was dependent on the nanotube’s chirality and did not yield a linear additive response. The polarization induced under combined loading in most of the doped CNTs is significantly higher than the sum of polarization generated under tensile and torsional loading conditions. This behavior suggests that the overall piezoelectric effect under combined loading can be enhanced, which emphasizes the need for an approach to optimize the mechanical loading condition. The results showcase the potential of B-/N-CNTs to be engineered for efficient performance by demonstrating that tailored mechanical loading can enhance the piezoelectric responses in doped CNTs, opening a pathway for highly functional and efficient nanoscale piezoelectric devices.

Comparison of Interatomic Potentials for Modeling Defects in Graphene Using Molecular Dynamics

In this work, we tested the ability of classical interatomic potentials to describe the energy characteristics of defects of various dimensionality in graphene crystals. Brenner's Reactive Empirical Bond Order potentials (second generation REBO, AIREBO, AIREBO-M), Tersoff potentials, as well as BOP and LCBOP potentials were considered. The data obtained in this work using the molecular dynamics method was compared with literature data obtained using the density functional theory. It is noted that when modeling point and linear defects, the potentials of the REBO family and the LCBOP potential demonstrate the best agreement with the literature data. For modeling pseudo-graphene crystals, the best fit is demonstrated by the Tersoff B-N-C potential, which shows slightly overestimated energy values for linear and point defects, but most accurately describes the geometry of the crystal lattice. The potential of BOP demonstrates its inability to correctly model defect configurations with high densities of eight-member defect rings. When simulating four-member carbon defect rings, most potentials exhibit distortions in the crystal lattice that are not observed in the density functional theory calculations.

Molecular dynamics to model carbon infiltration into a porous silicon matrix: An experimental and computational approach

In this work, a porous silicon matrix (PSm) and its functionalization with carbon atoms are modeled by molecular dynamics (MD); the simulation is correlated experimentally to analyze the model results. Computationally, the Tersoff potential for the silicon carbon system is used to build a model by MD using Large-scale Atomic/Molecular Massively Parallel Simulator free-source code (LAMMPS). First, a model of a PSm with an aleatory distributed macroporous was built; then, C atoms were injected into the PSm model to functionalize the matrix; finally, the model shows the functionalization of the PSm, forming carbon-silicon composites, which are Si clusters surrounded by C atoms. Experimentally, PSm was fabricated using samples of a p-type crystalline silicon wafer by electrochemical etching. A colloidal suspension of graphene oxide (GOs) was used as a source of carbon atoms: the GOs was added to the electrolyte, during the etching process, to functionalize the PSm with C atoms. AFM images show that the PSm pores are not obstructed after functionalization. Carbon-silicon composites were formed into the PSm samples according to X-ray diffraction and EDS characterizations. The results of the modeling agree with the results of the experiments.

Investigation of the mechanical characteristics and thermal behavior of a polymer matrix by addition of different graphene oxide nanosheets: A molecular dynamics simulation

Molecular dynamics simulation (MDS) was applied to examine the effect of graphene oxide nanosheets (GONs) with different edges (armchair and zig-zag edges) on the mechanical behavior (MB) and thermal behavior (TB) of the base polymer matrix (PM). The physical quantities, such as the maximum stress on the samples, stress–strain diagram, ultimate strength (US), Young's modulus (YM), the order parameter (OP), and length changes (LC) were measured for 10 ns. Lennard-Jones (LJ), Tersoff, and Coulomb potentials were used. The PM's maximum stress, US, and YM values were 0.26, 0.22, and 2.23 GPa, respectively. After 10 ns, the OP of PM decreased from 0.79 to 0.52. In studying the PM, the LC was 17 Å when increasing structure temperature to 350 K. The TB and MB of zig-zag nanosheet were higher than for the armchair type. By adding GONs with an atomic ratio of 1% to PM, maximum stress, US, and YM values in structures with armchair nanosheets were 0.34, 0.28, and 2.78 GPa, respectively, and for samples with zig-zag nanosheets were 0.35, 0.30, and 2.96 GPa. After 10 ns, LC increased from 10 to 11 Å for the sample with a zig-zag edge, and from 10 to 12 Å for an armchair edge. This atomic behavior indicated that the atomic structure of Detda and Dgeba matrixes with GONs with a zig-zag edge had higher thermal stability.

The deposition properties of tetrahedral amorphous carbon coatings deposited on piston ring: Molecular dynamics simulation

The tetrahedral amorphous carbon (ta-C) coatings are deposited on piston rings to improve the tribological property of the piston ring-cylinder liner system of the internal combustion engines. The deposition parameters are optimized by molecular dynamics simulation to reduce the cost of coatings’ fabrication. The ta-C coatings with higher sp3 fraction, lower friction coefficient, and superior anti-wear properties are achieved by optimizing the incident energy and substrate temperature of carbon atoms. The second nearest-neighbor modified embedded-atom method potential and Tersoff potential are used to describe the interatomic interactions. The effects of the incident energy of the carbon atoms and substrate temperature on the deposition properties of the ta-C coatings are discussed. The numerical results show that the ta-C coatings with high sp3 fraction, high density, and good interface mixing are obtained, and the deposition properties of the ta-C coatings are improved.

Atomistic simulation of the mechanical behaviors of the pristine and vacancy-induced Ti2C MXene: Effect of temperature, strain rate, and chirality

In context with growing concerns regarding mechanical damage in nanoelectromechanical systems (NEMS) and energy devices, this study implemented atomistic molecular dynamics simulation to examine the mechanical performance of Ti2C MXene, a high prospectus material in the field of NEMS and energy technologies. Bond-order Tersoff potential was employed to assess the distinction in the mechanical performance of pristine and vacancy-induced Ti2C depending on different physiological conditions, including temperature, loading rate, and chirality. A competitive elastic modulus of 130.72 GPa and 129.12 GPa has been determined along the armchair and zigzag chirality. However, tensile strength along armchair chirality was found to be 30.52 GPa, 21.4% greater than its contrary direction, whereas zigzag chirality withstands 13.55% greater strain at failure than the armchair chirality, measuring 0.273. Superior tensile strength is observed in armchair chirality, whereas zigzag chirality withstands more significant strain at failure. Mechanical attributes show declining trends as the temperature rises; however, the trend is upward while loading happens rapidly. Both carbon and titanium point vacancies degrade mechanical characteristics individually, but the conjugal influence of temperature and point vacancy makes the deterioration more severe. Carbon, the central constituent element, was found to be more significant in the functionality of Ti2C MXene. Therefore, carbon vacancy shows higher formation energy and more significant deterioration in mechanical performance than titanium vacancy. This exhaustive investigation will significantly aid in the safe design of MXene-based nanoelectromechanical devices and catalyze further experimental research on the same layered materials.

Mechanical behavior of alpha quartz with void defects under tension: a molecular dynamics study using different interatomic potentials

This study employs a series of molecular dynamics (MD) simulations, utilizing three commonly used interatomic potentials, i.e. van Beest, Kramer, and van Santen (BKS), Vashishta, and Tersoff to analyze the structural and mechanical characteristics within both void-free and single-void α-quartz configurations. Two distinct ensembles, NVT and NPT, were separately applied to investigate the tensile response. The validation of MD results included a comparative study of the three potentials as well as a comparison with experimental microstructural and tension studies. While BKS and Vashishta potentials accurately calculated the bond lengths, density and lattice parameters compared to the experimental values for void-free α-quartz, the results obtained with Tersoff potential exhibited relatively large deviations. The BKS potential offered an accurate description of the mechanical response of α-quartz by successfully predicting stress–strain curves. The Vashishta potential overpredicted Young’s modulus as compared to BKS. The Tersoff potential could capture the elastic deformation but was unable to predict the fracture behavior. The presence of a spherical void significantly reduced mechanical behavior of α-quartz, and the extent of this reduction was highly related to void size. When applying the BKS potential with an NVT ensemble, the ultimate tensile strengths decreased by 19% and 72% with void sizes of 2.5 and 15 Å, respectively. Equivalent stress analysis reveals that the BKS potential can effectively capture greater stress concentration around the void compared to other two potentials. Based on the comparison study, the BKS potential seems to be the most suitable one to describe α-quartz under tension in a realistic manner.

Parametrization protocol and refinement strategies for accurate and transferable analytic bond-order potentials: Application to Re

Parametrization protocol and refinement strategies for accurate and transferable analytic bond-order potentials: Application to Re

Atomistic modelling of the Pb-Bi system from a constructed bond order potential

Lead-bismuth eutectic (LBE) alloys are currently considered one of the most promising liquid metal coolants for fast reactors, and especially accelerator-driven systems (ADS). An analytical bond-order potential (BOP) of Pb-Bi has been constructed to account for the electronic interactions and angular contribution of Pb-Bi system. The newly developed BOP has been validated to show a better performance than the Pb-Bi potentials already published in the literature. Molecular dynamics simulations based on current BOP has been adopted to investigate various properties of Pb-Bi binary system. It accurately predict the heats of formation, density, and thermal expansion coefficient of liquid LBE at 700 K. The diffusion coefficient and viscosity of liquid Pb44.5Bi55.5 are calculated, which are in good agreement with experimental observations in the literature. These findings provide a foundation for future design of Pb-Bi eutectic alloys for use in ADS and heavy-metal-cooled fast nuclear reactors.

Effects of sp3 bond ratio and modulation ratios on nanotribology behaviors of diamond-like carbon coatings investigated using atomistic nanoscratching simulations.

Diamond-like carbon (DLC) films are amorphous solids in which carbon atoms are linked by hybridized sp3, sp2, and sp bonds. The mechanical and tribological properties of DLC films can be adjusted by tuning the sp2/sp3 bond ratio. These films are typically used as protective coatings for components such as dies, automotive engines, mechanical seals, hard disk drives, biological engineering devices, and micro/nano-electromechanical systems. Further exploration of the mechanical and tribological behavior of DLC films is important for enhancing functional design for the above applications. The simulation results show that single-layer DLC with a higher sp3 ratio has better resistance to indentation. Single-layer DLC with a lower initial sp3 ratio has lower friction and a shorter repeated cycle in the friction force curve due to an increase in the graphitization of the friction interface. Single-layer DLC with a higher sp3 ratio has a higher coefficient of friction because compared with the normal force, the friction force is much more sensitive to an increase in the sp3 ratio. Molecular dynamics simulations based on the Tersoff potential were performed using the open-source code LAMMPS (Large-scale Atomic/Molecular Massively Parallel Simulator).