Tersoff Interatomic Potential Research Articles

Effects of Topological Parameters on Thermal Properties of Carbon Nanotubes via Molecular Dynamics Simulation

Due to their unique properties, carbon nanotubes (CNTs) are finding a growing number of applications across multiple industrial sectors. These properties of CNTs are subject to influence by numerous factors, including the specific chiral structure, length, type of CNTs used, diameter, and temperature. In this topic, the effects of chirality, diameter, and length of single-walled carbon nanotubes (SWNTs) on the thermal properties were studied using the reverse non-equilibrium molecular dynamics (RNEMD) method and the Tersoff interatomic potential of carbon–carbon based on the Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS). For the shorter SWNTs, the effect of chirality on the thermal conductivity is more obvious than for longer SWNTs. Thermal conductivity increases with increasing chiral angle, and armchair SWNTs have higher thermal conductivity than that of zigzag SWNTs. As the tube length becomes longer, the thermal conductivity increases while the effect of chirality on the thermal conductivity decreases. Furthermore, for SWNTs with longer lengths, the thermal conductivity of zigzag SWNTs is higher than that of the armchair SWNTs. Thermal resistance at the nanotube–nanotube interfaces, particularly the effect of CNT overlap length on thermal resistance, was studied. The simulation results were compared with and in agreement with the experimental and simulation results from the literature. The presented approach could be applied to investigate the properties of other advanced materials.

Investigating the atomic behavior of carbon nanotubes as nanopumps

In this study, we utilized molecular dynamics (MD) simulations to investigate the nano pumping process of Carbon Nanotube (CNT) in an aqueous environment. In this research, an attempt has been made to investigate and analyze the pumping process of fullerene C20 and water molecules through a carbon nanotube that is externally stimulated by two oscillators. It should be noted that this nano pump is completely immersed in an aqueous environment and the inside and outside of the carbon nanotube is filled with water molecules. To simulate the aqueous environment with NaCl impurities and carbon structures, we employed the Universal Force Field and Tersoff interatomic potentials, respectively. The stability of the simulated structures was demonstrated through an equilibrium process, which was a result of the appropriate settings in our MD simulations. To describe the CNT nano pumping process, we analyzed the velocity and translational/rotational components of C20 kinetic energy over time steps. By decreasing the water impurity concentration from 0.50 to 0.075 mol/l, the nano pumping time varied from 10.98 to 10.11 ps, respectively. Additionally, optimization of the atomic wave producing in the nano pumping process led to a further decrease in pumping time to 10.01 ps. Finally, a 2.86% variation in calculated results was observed by changing the water MD simulation model from SPC to TIP4P.

Atomistic model of an oxide film in contact with a liquid metal coolant: Defects concentrations and chemical potentials of dissolved Fe–O

The paper considers a prototype atomistic model of an oxide film with a wüstite structure in contact with a liquid metal coolant containing dissolved iron and oxygen. On the basis of direct molecular dynamics modeling with the Tersoff interatomic potential for Fe–O, we check the correspondence between the formation free energies of defects, determined from the temperature dependencies of their equilibrium concentrations, and the formation free energies determined from the calculation of the chemical potentials of dissolved iron and oxygen, the static calculations for defect energies and thermodynamic integration for defect entropies in the oxide lattice. The influence of liquid metal coolant on the chemical potentials of solvated Fe–O is highlighted. These results pave a way for bridging the gap between multiscale models of oxide film formation and ab initio first principles calculations of atomistic models.

FAD Technique and Differentiation of a Composite Function

Different approaches to the calculation of the gradient of a composite function of several variables are compared, namely, exact analytically derived formulas, formulas based on the fast automatic differentiation (FAD) technique, and standard software packages implementing the ideas of the FAD technique. The approaches are compared as applied to a composite function representing the energy of a system of atoms with the Tersoff interatomic potential. The comparison criterion is the computer time required for computing the gradient of the function. The results show that the FAD technique is superior to the analytical formulas. The standard packages take nearly the same time to compute the function gradient as the FAD technique formulas.

Nonlinear thermal transport in graphene nanoribbon: A molecular dynamics study

Effects of different factors on the thermal conductivity of graphene nanoribbons (GNRs) is investigated using nonequilibrium molecular dynamics (NEMD) simulations with LAMMPS code, taking advantage of the optimized Tersoff interatomic potential. The influences of temperature, size, and layer number on thermal transport are considered for both zigzag and armchair GNRs. It is found that increasing the size (length⩽40 nm and width⩽10 nm) enhances the thermal conductivity of both GNR types by a power-law relationship at room temperature. In contrast, the thermal conductivity of GNRs drastically drops as the temperature rises in the range of 50–500 K. The power-law reduction of conductivity, owing to the temperature increase, is faster in zigzag GNR than in armchair one. In addition, in the range of 1–10 layers, the thermal conductivity experiences a power-law decrease with increasing number of GNRs layers because of the out-of-plane scattering of phonons. Our results reveal how boundary scattering, growing phonon number and Umklapp scattering govern nonlinear thermal transport mechanism. This study also demonstrates a dramatic influence of the edge structure of GNR on thermal conduction.

Stability of Strained Stanene Compared to That of Graphene.

Stanene, composed of tin atoms, is a member of 2D-Xenes, two-dimensional single element materials. The properties of the stanene can be changed and improved by applying deformation, and it is important to know the range of in-plane deformation that the stanene can withstand. Using the Tersoff interatomic potential for calculation of phonon frequencies, the range of stability of planar stanene under uniform in-plane deformation is analyzed and compared with the known data for graphene. Unlike atomically flat graphene, stanene has a certain thickness (buckling height). It is shown that as the tensile strain increases, the thickness of the buckled stanene decreases, and when a certain tensile strain is reached, the stanene becomes absolutely flat, like graphene. Postcritical behaviour of stanene depends on the type of applied strain: critical tensile strain leads to breaking of interatomic bonds and critical in-plane compressive strain leads to rippling of stanene. It is demonstrated that application of shear strain reduces the range of stability of stanene. The existence of two energetically equivalent states of stanene is shown, and consequently, the possibility of the formation of domains separated by domain walls in the stanene is predicted.

Effects of transverse geometry on the thermal conductivity of Si and Ge nanowires

We explore the effects of geometry on the thermal conductivity (κ) of silicon and germanium nanowires, with lengths between 10–120 nm and diameters up to 5–6 nm. To this end we perform molecular dynamics simulations with the LAMMPS software, using Tersoff interatomic potentials. We consider nanowires with polygonal cross section and we discuss the effect of the transverse geometry on the thermal conductivity. We also consider tubular (hollow) nanowires and core/shell combinations of Si/Ge and Ge/Si, and we compare the heat transport of the core/shell structure with that of the separated core and shell components.

Study on shock compression phase transition of single crystal siliconbased on molecular dynamics simulation

Crystalline silicon has a complicated phase transition mechanism, which has received extensive attention in the research field of phase diagram, and the deformation mechanism of silicon crystals under dynamic loading is the current research hotspot. In order to reveal its deformation and phase transition behaviors under intensive dynamic loading, molecular dynamics method was used to simulate the shock compression behavior of single crystal silicon along the crystal directions [001], [110] and [111] at an initial ambient temperature of 300 K, respectively. All simulations were carried out basing on the classical open-source codes LAMMPS and a Tersoff interatomic potential was adopted to describe the material responses of silicon under dynamic compression. Before shock loading, periodic boundary conditions were applied along the three independent directions, and an NPT ensemble was used to equilibrate the systems; then shock compression was applied by using the piston method, where a virtual piston wall impinges the sample such that the particle velocity in the sample is the same as the piston speed after the shock reaches a steady state. The shock particle velocities varied from 0.3 km/s to 3.2 km/s, and a timestep of 0.001 ps was adopted. During the stress wave formation and propagation, the simulation system was in the NVE ensemble with the absence of temperature control. The loading method and effect are similar to typical plane impact experiments. The results show that with the increase of shock particle velocity, the shear stress of single crystal silicon increases gradually and then decreases sharply due to the structural phase change. Both the phase transition threshold and the phase transition mechanism are anisotropic. Among them, a variety of solid-solid phase transitions and solid-liquid phase transitions are observed under shock compression along the [001] crystal direction. The phenomenon of solid-liquid coexistence is highly consistent with the recent international experiments. The research results provides new nano-scale results to support the study of phase transition of crystalline silicon under dynamic loading.

Instability analysis of silicon cylindrical nanoshells under axial compressive load using molecular dynamics simulations

Molecular dynamics (MD) simulation has provided researchers with a simple as well as accurate technique to investigate atomic and molecular systems. In the current investigation, the nonlinear axial buckling characteristics of cylindrical nanoshells made of silicon are studied based on MD simulations with Tersoff interatomic potential. Nanoshells with radius to thickness ratio of 10 are considered. The simulations are performed for different thermal environments and shell lengths to demonstrate the influences of them on the critical axial buckling loads of cylindrical nanoshells. It is found that through increase of length to radius ratio, the critical axial buckling load of silicon nanoshell decreases, but its critical end-shortening increases. Furthermore, it is revealed that by increasing the value of temperature, the both critical buckling load and critical end-shortening of silicon nanoshell under axial compressive load decreases. The given MD results can be useful to develop more computationally efficient and accurate continuum descriptions of silicon micro/nano-structures.

Toughness and strength anisotropy among high-symmetry directions in 3C-SiC

This paper presents a quantitative understanding of toughness and strength anisotropy in 3C-SiC under uniaxial deformation. We consider four high-symmetry crystallographic directions including [100], [110], [111], and [112¯] for loading, and find that both toughness and strength are the maximum along the [100] direction and the minimum along the [111] direction. The maximum anisotropy in crack nucleation-toughness is 145% and in fracture toughness 126%, relative to the [111] direction. The corresponding anisotropies in fracture strain and fracture strength are found to be 62% and 36%, respectively. An atomistic analysis shows that bonds deform uniformly for loading along the [100] direction, whereas for loading along the [110], [111], or [112¯] directions, bonds deform nonuniformly and it breaks the symmetry of the local atomic structure. The nonuniform bond deformation creates different sets of bond lengths and forms the atomistic basis for the direction-dependent mechanical behavior. The simulations are conducted with four different interatomic potentials including the Stillinger-Weber, Tersoff, Vashishta, and Environment Dependent Interatomic Potentials. It is found that only the Stillinger-Weber potential exhibits first-principles accurate strength and toughness as well as brittlelike fracture. Also, there is a sizeable difference among the potentials in terms of the crack nucleation toughness and strength. We find the difference to originate from the dissimilarity in the forcing function and its derivative in the nonlinear regime of mechanical deformation. A mathematical analysis suggests that it is essential for the forcing function to accurately represent the first-principles accurate forcing function, at least up to the maximum bond force, to produce accurate fracture properties and patterns.

Application of the Tersoff interatomic potential to pressure-induced polyamorphism of silicon

Molecular-dynamics simulations of the pressure-induced structural changes of amorphous Si have been performed using the Tersoff interatomic potential to examine the validity of this potential. Amorphous Si with a tetrahedral network was prepared by melt-quenching methods, and it was then compressed under isothermal–isobaric conditions. The changes of the atomic pair-distribution functions and static structure factors with increasing pressure were in agreement with those observed experimentally. The pressure-induced amorphous structures contained a short-range order similar to the β-tin and Imma structures. These results suggest that the Tersoff potential is suitable for describing the structural changes of amorphous Si under high pressure.

A molecular dynamics study of the mechanical properties of h-BCN monolayer using a modified Tersoff interatomic potential

Using molecular dynamics (MD) simulations, we investigate the mechanical properties of hexagonal BCN monolayer, a newly synthesized two-dimensional material with an atom ratio of B/C/N = 1:1:1. The Tersoff potential is modified to get good agreement between predicted and measured fracture strengths of graphene. With this modified Tersoff potential, we perform extensive MD simulations to study the effect of temperature, strain rate and vacancy defect on the mechanical properties of h-BCN. It is found that h-BCN is a strong material with fracture strength of 81.4–93.5 GPa, albeit ∼35% lower than that of graphene. Similar to graphene, temperature has strong effect on the mechanical properties of h-BCN. As the temperature increases from 10 K to 1300 K, the fracture strength and strain of h-BCN drops by 55% and 62%, respectively. The strain rate is found to have a moderate effect. When the strain rate increases from 0.00002 to 0.0125 ps−1, the fracture strength and strain of h-BCN increases 6.1% and 12%, respectively. As for the atomic defect, a very small concentration (0.028%) of vacancy in h-BCN is able to cause a 28% reduction in fracture strength and a 35.5% reduction in fracture strain. These findings have significance for its future applications in nanodevices.

Thermal transport across grain boundaries in polycrystalline silicene: A multiscale modeling

During the fabrication process of large scale silicene, through common chemical vapor deposition (CVD) technique, polycrystalline films are quite likely to be produced, and the existence of Kapitza thermal resistance along grain boundaries could result in substantial changes of their thermal properties. In the present study, the thermal transport along polycrystalline silicene was evaluated by performing a multiscale method. Non-equilibrium molecular dynamics simulations (NEMD) was carried out to assess the interfacial thermal resistance of various constructed grain boundaries in silicene. The effects of tensile strain and the mean temperature on the interfacial thermal resistance were also examined. In the following stage, the effective thermal conductivity of polycrystalline silicene was investigated considering the effects of grain size and tensile strain. Our results indicate that the average values of Kapitza conductance at grain boundaries at room temperature were estimated to be nearly 2.56 × 109 W/m2 K and 2.46 × 109 W/m2 K through utilizing Tersoff and Stillinger-Weber interatomic potentials respectively. Also, in spite of the mean temperature, whose increment does not change Kapitza resistance, the interfacial thermal resistance could be controlled by applying strain. Furthermore, it was found that by tuning the grain size of polycrystalline silicene, its thermal conductivity could be modulated up to one order of magnitude.

БЛИЖНИЙ ПОРЯДОК В СПЛАВАХ Fe–Cr: МОДЕЛИРОВАНИЕ

Short-range order in Fe–Cr alloys was studied by the Monte Carlo method. The simulation was carried out in the framework of the Metropolis algorithm in LAMMPS software package. Simulation data analysis was carried out using Ovito data visualization and analysis software. The alloy model assumes that the lattice structure is fixed and that interactions exist between the first neighbors and the second neighbors. The FeCr interaction was determined using the Abell–Brenner–Tersoff interatomic interaction potential (ABOP). Various admixture concentrations of chromium interstitial in iron have been studied, namely, 5–50 at. %. The mixing energy of the Fe–Cr system was calculated for various concentrations of interstitial impurities. Calculations showed that the chosen interaction potential correctly simulates changes in the sign of the mixing energy as a function of Cr concentration. When used in Monte Carlo kinetic modeling, the potential correctly predicts decomposition of initially random Fe–Cr alloys, depending on Cr concentration. The Cowley short-range order parameter, which is used for quantitative assessment of the degree of order, has been determined. According to experiments, there is a strong tendency of ordering in distribution of Cr at low concentrations, which becomes evident in negative values of the short-range order parameters.

An atomistic study of phase transition in cubic diamond Si single crystal subjected to static compression

It is been widely experimentally reported that Si under static compression (typically in a Diamond Anvil Setup-DAC) undergoes different phase transitions. Even though numerous interatomic potentials are used for numerical studies of Si under different loading conditions, the efficacy of different available interatomic potentials in determining the phase transition behavior in a simulation environment similar to that of DAC has not been probed in literature which this manuscript addresses. Hydrostatic compression of Silicon using seven different interatomic potentials demonstrates that Tersoff(T0) performed better as compared to other potentials with regards to demonstration of phase transition. Using this Tersoff(T0) interatomic potential, molecular dynamics simulation of cubic diamond single crystal silicon has been carried out along different directions under uniaxial stress condition to determine anisotropy of the samples, if any. β-tin phase could be observed for the [001] direction loading whereas Imma along with β-tin phase could be observed for [011] and [111] direction loading. Amorphization is also observed for [011] direction. The results obtained in the study are based on rigorous X-ray diffraction analysis. No strain rate effects could be observed for the uniaxial loading conditions.

Molecular-dynamics simulations of solid phase epitaxy in silicon: Effects of system size, simulation time, and ensemble

Solid phase epitaxial (SPE) recrystallization of amorphous Si on a Si(001) substrate was examined by large-scale (6144–129024 Si atoms), long-time (up to 2000 ns) molecular-dynamics (MD) simulations using the empirical Tersoff interatomic potential. We particularly focused on the effects of the MD cell size, simulation time, and ensemble on the SPE growth rate. We found that the simulations under the isothermal–isochoric conditions (NVT ensemble) show a higher crystallization rate than those under the isothermal–isobaric conditions (NPT ensemble). The system size dealt with in the present MD simulation, i.e., >6144 Si atoms, was enough to estimate the SPE growth rate. The Arrhenius plot of the growth rate between 1300 and 1600 K exhibited a single activation energy, ∼2.4 eV, which is in agreement with the experimental value (∼2.7 eV). However, the growth rate at temperatures below 1300 K deviated from the extrapolated ones from 1300 to 1600 K, which is because recrystallization does not reach a steady state: long-time MD simulations are required to estimate the growth rate at low temperature. The structure analysis of amorphous/crystalline interfaces suggested that the braking of atomic bonds parallel to the interface becomes a rate-limiting step of the SPE growth.

Dislocation mobility and Peierls stress of c-type screw dislocations in GaN from molecular dynamics

Motion of a single c-type screw dislocation, with [0001] Burgers vector, in single crystal GaN is explored using classical molecular dynamics (MD) simulations with both Tersoff and Stillinger-Weber (SW) interatomic potentials. Three different dislocation core structures (full, small void, and open) along two distinct glide planes ((11¯00) and (1¯1¯20)) are studied. The system is sheared by applying opposing forces to atoms near the surface, with interior atoms maintained at a temperature of 1300 K. This results in glide for screw dislocations with a full core structure, with velocities dependent on the choice of interatomic potential. Full core dislocation glide also results in the nucleation of void defects for both potentials. Small void dislocations glide cleanly with no debris using the SW potential, but glide is not observed for the Tersoff potential. The difference between the potentials is most fully demonstrated from the response of open core dislocations in the (1¯1¯20) slip system. For the Tersoff potential, full core screw dislocations are nucleated from the surface of the open core dislocations, while dislocation glide loops are nucleated for the SW potential. The discrepancy in results using the different potentials is discussed, and attributed to the short cut off distance of the Tersoff potential. Finally, a dislocation dipole system is used to calculate the Peierls stress of the {11¯00}〈0001〉 full core screw dislocation, and compared to experimental results.

Gap discrete breathers in strained boron nitride

Linear and nonlinear dynamics of hexagonal boron nitride (h-BN) lattice is studied by means of molecular dynamics simulations with the use of the Tersoff interatomic potentials. It is found that sufficiently large homogeneous elastic strain along zigzag direction opens a wide gap in the phonon spectrum. Extended vibrational mode with boron and nitrogen sublattices vibrating in-plane as a whole in strained h-BN has frequency within the phonon gap. This fact suggests that a nonlinear spatially localized vibrational mode with frequencies in the phonon gap, called discrete breather (also often termed as intrinsic localized mode), can be excited. Properties of the gap discrete breathers in strained h-BN are contrasted with that for analogous vibrational mode found earlier in strained graphene. It is found that h-BN modeled with the Tersoff potentials does not support transverse discrete breathers.

Shear response of β-SiC bulk dependent on temperature and strain rate

The shear responses of β-SiC are investigated using molecular dynamics simulation with the Tersoff interatomic potential. Results show a clear decreasing trend in critical stress, fracture strain and shear modulus as temperature increases. Above a critical temperature, β-SiC bulk just fractures after the elastic deformation. However, below the critical temperature, an interesting pattern in β-SiC bulk emerges due to the elongation of Si-C bonds before fracture. Additionally, the shear deformation of β-SiC at room temperature is found to be dependent on the strain rate. This study may shed light on the deformation mechanism dependent on temperature and strain rate.

Nanoindentation of ultra-hard cBN films: A molecular dynamics study

Cubic Boron nitride (cBN) exhibits excellent mechanical properties including high strength, hardness and thermal resistance, etc. We optimized the parameters in the Tersoff interatomic potential for cBN based on its cohesive energy, lattice parameter, elastic constants, surface energy and stacking fault energy. We performed with molecular dynamics (MD) simulations the nanoindentation on the (001) and (111) surface of monocrystalline cBN thin films to study the deformation mechanisms and the effects of temperature and substrate orientation. It was found that during the indentation plastic deformation is mainly stress-induced slips of dislocations along {111}<110> orientations. It was also found that the hardness of cBN depends strongly on temperature, and the capability of plastic deformation is enhanced with the increase of temperature.