Modified Morse Potential Function Research Articles

Accuracy of the New Modified Morse Potential Energy Function for Ground and Excited States of Diatomic Molecules

Accuracy of the New Modified Morse Potential Energy Function for Ground and Excited States of Diatomic Molecules

On the derivation of coefficient of Morse potential function for the silicene: a DFT investigation.

In this paper, the structural and mechanical properties of silicene are investigated by the density functional theory calculations. To calculate Young's, bulk, and shear moduli and Poisson's ratio of the silicene, the optimized unit cells containing two atoms are proposed and the effect of chirality on the elastic properties of silicene is examined. It is shown that the silicene has an isotropic behavior, while graphene has an anisotropic behavior. The results showed that calculated moduli for the silicene are significantly lower than those of graphene in zigzag and armchair directions, while Poisson's ratio of silicene is higher than that of graphene. The paper describes one common type of inharmonic interatomic potentials used for constructing nonlinear models of the material using the modified Morse potential function. Using this concept, the effects of chirality on dissociation energy, inflection point, and coefficients of the modified Morse potential function are studied. Comparison of the cutoff distance value in the modified Morse potential showed that inflection point values for the armchair and zigzag graphene are highly direction-dependent, whereas these values have negligible difference for silicene.

An atomistic-based finite element progressive fracture model for silicene nanosheets

A progressive finite element method is proposed herein to investigate the fracture of silicene nanosheets. By treating a silicene nanosheet as a buckled frame structure, its mechanical behavior is simulated using the modified Morse potential function. The interatomic force per atom is calculated for all atoms as a set of inharmonic oscillator networks, which are described by the modified Morse potential function, while the nonlinear behavior is defined by these interatomic forces with an iterative solution procedure as strain increases. The nonlinear stress–strain relationships of the armchair and zigzag silicene nanosheets are also obtained for pristine and defective cases including the tensile strength and ultimate strain. For the silicene with both configurations, i.e., armchair and zigzag, a sudden drop is seen in the stress–strain diagram, showing that both of them represent the brittle behavior. Moreover, it is concluded that the tensile strength and ultimate strain of the armchair silicenes are slightly larger than those of the zigzag one. It is also seen that the mechanical properties of the silicene are significantly affected by the single-vacancy and Stone–Wales defects. The computed results reveal that single-vacancy defects can reduce the ultimate strain of silicene by approximately 7.3% with respect to that of pristine silicene, whereas the effect of Stone–Wales defects is less significant.

A new modified Morse potential energy function for diatomic molecules

A new modified Morse potential is introduced to describe the vibrational motion of diatomic molecules. The vibrational energy eigenvalues for the ground state of the H2 and N2 molecules are obtained by numerically solving the time-independent Schrödinger equation using a Python program and the Matrix Numerov method for the case of the Morse potential, Hulbert-Hirschfelder potential, and the modified Morse potential functions. The comparison of the vibrational energy eigenvalues and the anharmonicity constant obtained for the modified Morse potential function reveals better agreement with the experimental data than the other potential functions. Also, the proposed modified Morse potential function fits the RKR potential energy curve more closely than the Morse potential function and Hulbert-Hirschfelder potential function, especially in the region where the potential extends to near the dissociation limit.

Evaluation of the Morse potential function coefficients for germanene by the first principles approach

In this paper, first principles calculations are used to investigate atomic structure and mechanical properties of germanene nanosheet. By applying uniaxial and biaxial tensile strains as well as shear strain, the tensile and shear properties of the germanene nanosheet, including Young’s and bulk moduli, Poisson’s ratio, and shear moduli are computed. Furthermore, the parameters of the modified Morse potential function are calculated for Ge–Ge interaction in the germanene nanosheet. Also, the mechanical behavior of germanene nanosheet is studied under tensile loading at large strains extended to the plastic range. Based on the simulations, Young’s modulus of the armchair and zigzag germanene nanosheet are computed as 52.8 and 49.9N/m, respectively. Besides, the values of Poisson’s ratio of the armchair and zigzag germanene nanosheet are obtained as 0.35 and 0.29, respectively.

A modified molecular-continuum model for estimating the strength and fracture toughness of graphene and carbon nanotube

A molecular-continuum model proposed previously for the estimation of elastic stiffness of nanomaterials is modified to estimate ultimate tensile strength and mode I/mode II fracture toughness of graphene and carbon nanotubes. By taking the modified Morse potential function and applying uniform strain field for a perfect specimen, a nonlinear stress-strain diagram can be plotted to estimate tensile strength. To estimate fracture toughness, a parameter called the strain intensity factor is introduced, and the near tip solution of linear elastic fracture mechanics rewritten in terms of strain intensity factor is used to locate the atoms of the cracked specimen. With the changes of bond distance and bond angle between atoms set in the deformed state, the potential energy within the region of representative volume is evaluated and treated as the strain energy in the cracked specimen. Using the well-known relation between strain energy release rate and stress intensity factor, a nonlinear generalized stress-strain diagram which showing the relation between stress intensity factor and strain intensity factor can be plotted. The estimated fracture toughness is then obtained from the maximum point of this diagram. To know whether our estimation is stable with respect to the crack size and tube radius, estimation based upon different parameters are presented for graphene and carbon nanotubes. By integrated symbolic and numerical computation, the results estimated by this model are shown to fall in the reasonable range predicted by the other experimental or numerical methods.

A new force field for the adsorption of H2, O2, N2, CO, H2O, and H2S gases on alkali doped carbon nanotubes

ABSTRACTThe main goal of this work is the generation of a new force field data set to the interaction of several gases such as H2, O2, N2, CO, H2O, and H2S with alkali cation-doped carbon nanotubes (CNTs) using ab initio calculations at the MP2(full)/6-311++G(d,p) level of theory. Different alkali cations including Li+, Na+, K+ and Cs+ were used to dope in the CNT. The calculated potential energy curve for the interaction of each gas molecule with each alkali cation-doped CNTs was fitted to an analytical potential function to obtain the parameters of the potential function. A modified Morse potential function was selected for the fitting in which the electrostatic interactions has been accounted by adding the β/r term to the Morse potential. The accuracy of the calculated force field was checked via Grand Canonical Monte Carlo (GCMC) simulation of the H2 adsorption on Li-doped graphite and Li-doped CNT. The results of these simulations were compared with the experimental measurements and the closeness of the simulation results with the experimental data indicated the accuracy of the proposed force field. The main merit of this work is the derivation of a specific force field for interaction of each of six gases with four alkali cation-doped CNT, which can be used in molecular simulation of these 24 of systems. The simulation results showed the increase of the H2 adsorption capacity of nanotube and graphite up to 50% and 10%, respectively, due to the insertion of Li ions.

Prediction of fracture toughness for carbon nanotubes

A modified molecular-continuum model is employed to predict fracture toughness of carbon nanotubes. In this model, the modified Morse potential function is used to evaluate the potential energy, and the near tip solution of linear elastic fracture mechanics is used to locate the atoms of the cracked specimen under tensile or shear loads. The representative volume is selected to be a circular region with center at the crack tip and radius determined from the equivalence of strain energy and virtual work for crack advancement. Using the relation between strain energy release rate and stress intensity factor, a nonlinear generalized stress-strain diagram is generated and the fracture toughness is then estimated to be the maximum point of this diagram. Through proper choice of representative volume and crack simulation, a vast of computational time can be saved and the results predicted by this model are shown to be consistent with those predicted by the other experimental or numerical methods.

The Dynamics Behavior of Rh Nanoclusters on Boron Nitride Sheet

The configurations and corresponding adsorption energies of Rh(n) (n = 4-13) nanoclusters on the boron nitride sheet are investigated by density functional theory (DFT). We use the force-matching method (FMM) to modify parameters of Morse and Tersoff potential functions. To elucidate the dynamical behaviors of Rh nanoclusters on the boron nitride sheet, molecular dynamics (MD) is applied with modified Morse potential function parameter. Finally, the square displacement (SD) is utilized the dynamics behavior of different size Rh nanoclusters at different temperatures.

Relationship between the Stress Intensity Factors and Bond σ in Graphene Sheet

Relationship between the stress intensity factors and the bond σ in the plane of interatomic hexagonal structures within graphite is given numerically. Under the consideration in this plane, the bond π and van der Waals force are ignored, and the plane strain of macroscopical elasticity is considered. The molecular mechanics is used to describe the displacements of atoms in the area near the tip of a crack, and the linear elastic fracture mechanics is used outside this area. Connection between these two theories is based on an assumption that the displacements of atoms along the boundary described by the molecular mechanics are equal to those described by the fracture mechanics. The nonlinear equations of molecular mechanics derived by the modified Morse potential function are solved by using Matlab software. When choosing the maximum stretching force of atomic bond as a failure criterion, the fracture toughness is obtained for Mode I and Mode II problems.

Studies of Size Effects on Carbon Nanotubes' Mechanical Properties by Using Different Potential Functions

We use molecular mechanics calculations to study size effects on mechanical properties of carbon nanotubes. Both single‐walled nanotubes (SWNTs) and multi‐walled nanotubes (MWNTs) are considered. The size‐dependent Young's modulus decreases with the increasing tube diameter for a reactive empirical bond order (REBO) potential function. However, we observe a contrary trend if we use other potential functions such as the modified Morse potential function and the universal force field (UFF). Such confliction is only obtained for small tubes within cutoff diameters (3 nm for REBO and 1.5 nm for others). In light of these predictions, Young's moduli of large nanotubes concur with experimental results for all the potential functions. No matter which potential function is used, the Poisson's ratio decreases with the increasing tube diameter. We also study the chirality effects on mechanical properties of SWNTs. We find that the Young's moduli are insensitive to the chirality of nanotubes. The chirality effect on the Poisson's ratio is significant for the UFF but not the REBO or modified Morse potential functions.

Analysis of fracture nucleation in carbon nanotubes through atomistic-based continuum theory

The elastic modulus and fracturing of single-wall carbon nanotubes are studied through an atomistic-based continuum theory. The interatomic potential used is a modified Morse potential function. The Young's modulus that is predicted agrees well with prior experimental results and the results of atomistic studies. The fracture strain that is predicted also agrees well with the results of prior atomistic studies, but is a little higher than the experimental results. The results show that the fracture strain and fracture strength are moderate, dependent on the chirality of the carbon nanotubes.

Prediction of stiffness and strength of single-walled carbon nanotubes by molecular-mechanics based finite element approach

Molecular-mechanics based finite element approach was used to predict the tensile stiffness and strength of single-walled carbon nanotubes. Different types of nanotubes, such as Arm-Chair, Zig-Zag, and chiral type, were discussed in detail. Nanotube stiffness was predicted to be independent of both the nanotube diameter and the nanotube helicity, but Poisson ratio was dependent of the nanotube diameter. In addition to the stiffness, nanotube strength was also analyzed by molecular-mechanics based finite element approach. Modified Morse potential function was selected to model the breakage of CC chemical bond with the separation energy of 7.7 eV. Nanotube strength was predicted at 77–101 GPa with the fracture strain around 0.3. The nanotube strength was found to be moderately dependent of the nanotube helicity, but independent of the nanotube diameter.

High resolution Fourier transform infrared emission spectra of lithium iodide

The high resolution infrared emission spectrum of lithium iodide has been recorded with a Fourier transform spectrometer. A total of 1024 transmissions with Δ v = 1 for 7 LiI (from v = 1 → 0 to v = 8 → 7), 387 transitions with Δ v = 2(v = 2 → 0 to v = 6 → 4) and 504 transitions with Δ v = 1 for 6 LiI (v = 1 → 0 to v = 5 → 4) have been assigned. The infrared data have been used to determine improved mass-dependent Dunham Y lm coefficients for the ground X1 Σ+ electronic state. The mass-independent Dunham U lm coefficients were obtained along with Born-Oppenheimer breakdown constants. Finally, all of the data were fitted to the eigenvalues of the radial Schrodinger equation containing a modified Morse potential function to determine the parameters of an effective ground state potential.)

High resolution Fourier transform infrared emission spectra of lithium iodide

The high resolution infrared emission spectrum of lithium iodide has been recorded with a Fourier transform spectrometer. A total of 1024 transmissions with Δ v = 1 for 7 LiI (from v = 1 → 0 to v = 8 → 7), 387 transitions with Δ v = 2(v = 2 → 0 to v = 6 → 4) and 504 transitions with Δ v = 1 for 6 LiI (v = 1 → 0 to v = 5 → 4) have been assigned. The infrared data have been used to determine improved mass-dependent Dunham Y lm coefficients for the ground X1 Σ+ electronic state. The mass-independent Dunham U lm coefficients were obtained along with Born-Oppenheimer breakdown constants. Finally, all of the data were fitted to the eigenvalues of the radial Schrödinger equation containing a modified Morse potential function to determine the parameters of an effective ground state potential.)

Modified Morse potential function for heavy rare gas solids: I-argon

The well-known Morse potential function has been modified to suit the solidified heavy rare gas solids (Ar, Kr and Xe) by changing the numerical coefficient of its attractive ‘exponential’ term from 2 to 2.25. The dispersion curves for argon calculated with the modified potential function in the principal symmetry directions give excellent fit to the inelastic neutron scattering data.

On the Hulburt-Hirschfelder potential function for the Ar 2 molecule

The modified Morse potential function known as the Hulburt-Hirschfelder function has been used for the Ar 2 molecule using experimental values for the spectroscopic constants. The consistency of this potential is checked by recalculating the vibrational levels using Cashion's method. The results are satisfactory. The potential may be useful for calculating the anharmonic properties of crystalline argon.

Diffusion in ordered DO 3 structures

A model for diffusion in ordered DO 3 type of structure is presented. The model is based on the six-jump vacancy cycle suggested by Huntington for b.c.c. ordered structures. A modified Morse potential function was employed to calculate activation energies of migration and formation of various types of vacancies and their variation with the degree of long range order. The activation energies of migration and formation of vacancies strongly depend upon the degree of long range order. Calculated activation energies for diffusion for different kinds of vacancies at S 31 = 0.5 compare well with the experimental values.