Morse Potential Function Research Articles

Density functional theory guided Monte Carlo simulations: Application to melting of Na13

We present a density functional theory (DFT) based Monte Carlo simulation method in which a simple energy function gets fitted on-the-fly to DFT energies and gradients. The fitness of the energy function gets tested periodically using the classical importance function technique [R. Iftimie, D. Salahub, D. Wei, and J. Schofield, J. Chem. Phys. 113, 4852 (2000)]. The function is updated to fit the DFT energies and gradients of the most recent structures visited whenever it fails to achieve a preset accuracy. In this way, we effectively break down the problem of fitting the entire potential energy surface (PES) into many easier problems, which are to fit small local regions of the PES. We used the scaled Morse potential empirical function to guide a DFT Monte Carlo simulation of Na(13) at various temperatures. The use of empirical function guide produced a computational speed-up of about 7 in our test system without affecting the quality of the results.

Cross sections for the electron impact non-dissociative ion of hydrogen and its isotopic molecule

In the edge plasma, hydrogen and its isotopic molecule will be ionized via collisions with the energetic electrons in the plasmas. The cross section data for the electron impact non-dissociative ion of the hydrogen and its isotopic molecule, which are unavailable from the literature are calculated on the basis of Morse potential function, Franck-Condon theory and semi-classical Gryzinski method. The change of cross section with electron energy and the effect of vibrational level of ground state on the cross section are presented in the paper. The results show that the vibrational excitation plays an important role in the process of ion.

Study on Nanometric Machining Mechanism of Monocrystalline Silicon by Molecular Dynamics

A three-dimensional model of molecular dynamics (MD) was employed to study the nanometric cutting mechanism of monocrystalline silicon. The model included the utilization of the Morse potential function to simulate the interatomic force between the workpiece and the tool, and the Tersoff potential function between silicon atoms. Amorphous phase transformation and chip volume change are observed by analyses of the snapshots of the MD simulation of the nanometric cutting process, energy and cutting forces. Dislocations and elastic recovery in the deformed region around the tool do not appear. Cutting forces initiate the amorphous phase transformation, and thrust forces play an important role in driving the further transformation development. Nanometric cutting mechanism of monocrystalline silicon is not the plastic deformation involving the generation and propagation of dislocations, but deformation via amorphous phase transformation.

Investigation of Interatomic Potential on Chip Formation Mechanism in Nanometric Cutting Using MD Simulation

Nowadays, the nano-machining process is used to produce high quality finished surfaces with precise form accuracy. To understand and analyze the chip formation mechanism of nano-machining process on an atomistic scale, since the experimentation is not an easy task, numerical simulation such as molecular dynamic (MD) simulation is a very useful method. In this paper, MD simulation of the nano-metric cutting of single-crystal copper was performed with a single crystal diamond tool. The model was solved with both pair wise Morse potential function and embedded atom method (EAM) potential to simulate the inter-atomic force between the work-piece and a rigid tool. The chip formation mechanism, dislocation generation, tool forces and generated temperature were investigated. Results show that the Morse potential cannot perform an appropriate defect formation and plastic deformation in nano-metric cutting of metals. Also, tool forces in Morse potential are more than the forces in EAM potential. Furthermore, the fluctuations of resultant forces in Morse potential are greater than that of EAM. In addition, using many-body interaction potentials like EAM can lead to substantial changes in surface energies, elastic-plastic properties and atomic displacement, compared with the pair-wise potentials like Morse. Finally, the atomic displacement investigation shows that in EAM potential study, only the atoms in a local region near the cutting process are displaced, but in Morse potential a large portion of atoms has affected during cutting process. Subsequently, the chip temperature in EAM potential is more than that of Morse potential.

Preliminary assessment of a multifunctional potential energy function

A potential energy function that is reducible to the Lennard–Jones, Morse, Buckingham and Linnett potential functions by prescribing 0 and 1 to its two type-parameters is herein centralized at 0.5 for both the type-parameters. Assessment on the potential's suitability is made herein by parameterization of its shape parameters for a sampling of noble gases, small molecules (including diatoms), Buckminsterfullerene, polymers and metals for both bonded and non-bonded interactions. Comparison between the parameterized potential with other sources exhibit good agreement. A preliminary map of shape parameter product versus the shape parameter ratio was plotted to observe the distribution of bonded and non-bonded interactions within the framework of the multi-functional potential. Due to the wide ranging applicability of this new potential function for quantifying covalent and metallic bonds as well as intermolecular interactions for small and large molecules, it is herein proposed that extensive parameterization to be performed for this potential function. The use of a single potential function across various types of bonding and molecular sizes will aid the development of multi-scale analysis due to the smooth transition of energy quantification from one scale to another.

Generation Mechanism of Micro/Nano Machined Surfaces Based on Molecular Dynamics

A three-dimensional model of molecular dynamics (MD) was employed to study the nanometric cutting mechanism of monocrystalline copper. The model included the utilization of the Morse potential function to simulate the interatomic force. By analyses of the snapshots of the various stages of the nanometric cutting process, the generation and propagation of the dislocations around the tool are observed. Some of these dislocations are observed to travel through the entire depth of the workpiece. Those that could most escape completely through the machined surface due to elastic recovery were found to introduce atom step on the machined surface. By analyses of the cutting forces during the entire nanometric cutting process, significant fluctuations are observed in the cutting force curves. The stress distribution plots of the various stages of the nanometric cutting process show that the mechanism of chip formation is significantly different from the conventional shear ahead of the tool in the case of a polycrystalline material. Most atoms ahead of tool are compressed, but forces of one or two layers atoms contact the cutting tool are tensile. With the chip formation, a small tensile zone ahead of tool generates in the compression zone and moves with the tool.

Computer Simulation on TiO2 Nanostructure Films and Experimental Study Using Sol–Gel Method

Molecular dynamics simulation with an experimental work was performed on the TiO2 nanostructure film. The Morse potential function was used for the interatomic interactions. Then, the equations of motion for molecules and atoms are solved by Verlet algorithm. The effects of deposition rate and the number of TiO2 molecules were studied for morphology characterization of film surface. In addition, TiO2 nanostructure film was prepared experimentally with the sol–gel dip-coating method. The results of MD simulations provide a reasonable compatibility with Dektak surface profiler, atomic force microscopy (AFM) and scanning electron microscopy (SEM) images due to the morphology and surface structure of films.

Modification of Morse potential in conventional force fields for applying FPDP parameters

Although the Morse potential function is widely used in molecular modeling software, newer potential functions that possess more parameters provide greater accuracy. Against this backdrop, the Four-Parameter-Diatomic-Potential (FPDP) was selected for converting its parameter into those of the Morse potential due to the former’s resemblance to the latter. A pair of modified Morse indices was extracted by imposing equal force constant for infinitesimal bond stretching and equal energy integral for complete interatomic separation. Results reveal very good agreement for both bond compression and bond stretching. The developed parameter conversion would enable all FPDP parameters to be converted into the modified Morse parameters. Only minor algorithm alterations are required for incorporating the modified Morse function into molecular modeling packages that adopt the conventional Morse potential for describing 2-body bonded interaction.

The Linear Thermal Expansion of Bulk Nanocrystalline Ingot Iron from Liquid Nitrogen to 300 K

The linear thermal expansions (LTE) of bulk nanocrystalline ingot iron (BNII) at six directions on rolling plane and conventional polycrystalline ingot iron (CPII) at one direction were measured from liquid nitrogen temperature to 300 K. Although the volume fraction of grain boundary and residual strain of BNII are larger than those of CPII, LTE of BNII at the six measurement directions were less than those of CPII. This phenomenon could be explained with Morse potential function and the crystalline structure of metals. Our LTE results ruled out that the grain boundary and residual strain of BNII did much contribution to its thermal expansion. The higher interaction potential energy of atoms, the less partial derivative of interaction potential energy with respect to temperature T and the porosity free at the grain boundary of BNII resulted in less LTE in comparison with CPII from liquid nitrogen temperature to 300 K. The higher LTE of many bulk nanocrystalline materials resulted from the porosity at their grain boundaries. However, many authors attributed the higher LTE of many nanocrystalline metal materials to their higher volume fraction of grain boundaries.

Size- and Temperature-Dependent Thermal Expansion Coefficient of a Nanofilm

The thermal expansion coefficient (TEC) of an ideal crystal is derived by using a method of Boltzmann statistics. The Morse potential energy function is adopted to show the dependence of the TEC on the temperature. By taking the effects of the surface relaxation and the surface energy into consideration, the dimensionless TEC of a nanofilm is derived. It is shown that with decreasing thickness, the TEC can increase or decrease, depending on the surface relaxation of the nanofilm.

Relations between Varshni and Morse potential energy parameters

Abstract A set of relationships between the Morse and Varshni potential functions for describing covalent bondstretching energy has been developed by imposing equal force constant and equal energy integral. In view of the extensive adoption of Morse function in molecular force fields, this paper suggests two sets of parameter conversions from Varshni to Morse. The parameter conversion based on equal force constant is applicable for small change in bond length, while the parameter conversion based on equal energy integral is more applicable for significant bond-stretching. Plotted results reveal that the Varshni potential function is more suitable for describing hard bonds rather than soft bonds.

Temperature effects on formation of metallic patterns in direct nanoimprint technique—Molecular dynamics simulation and experiment

Temperature effects on the formation of metallic nano-scale patterns that are fabricated by direct nanoimprint technique were investigated both theoretically and experimentally in this paper. For the theoretical study, a three-dimensional molecular dynamics model that applied the Morse potential function was employed to simulate the relationship between the interatomic force between the Ni-mold and gold thin film during nanoimprint process under the variation of temperature. The simulation was used for examining the mechanics in the pattern-forming process and the results were used as a reference for preparing nanoimprint experiment. The direct nanoimprint experiment was operated at different temperatures, i.e. 298 K, 323 K, 373 K, 423 K, and 493 K, for the purpose of assessing the effects of temperature on the formation of nano-scale patterns. From the results of the molecular dynamics simulation and direct nanoimprint experiment, it was concluded that the higher the temperature is, the deeper and wider the patterns are produced. The results showed that the temperature of thin film and mold may be assigned to be 373–423 K in order to obtain good quality of pattern transfer of the mold.

Modeling of skutterudite CoSb3 with molecular dynamics method

Abstract Skutterudite materials have generated considerable interest as new thermoelectric materials over the past few years. For binary skutterudite compound CoSb3 with complicated cubic crystal structure, Morse potential energy function is employed to describe atomic interactions to lay special emphasis on its mechanical properties. The parameters of Morse potential function between different species of atom pairs (Co–Co, Sb–Sb and Co–Sb) are individually determined based on known crystal structures and elastic properties from experiment or first principle calculation results. To test the accuracy of the obtained potential parameters, molecular dynamics simulation was first performed to inverse deduce and compare with preceding used values, and the results show excellent agreement. Moreover, the practicability and feasibility of the potential was verified. In terms of the obtained potential parameters, the virtual uniaxial tensile simulation was performed for single crystal CoSb3 with bulk model using the conventional molecular dynamics algorithm. The mechanical response and deformation behavior are carefully analyzed. In contrast to conventional bulk CoSb3, single crystal bulk CoSb3 exhibits much better mechanical performances. It undergoes elastic deformation before 10% strain, and achieves ultimate stress 13.3 GPa at the strain of 10.2%, subsequently sudden fracture occurs near the middle of the model, demonstrating typical brittleness.

Virtual Internal Pair-Bond Model for Quasi-Brittle Materials

The present multiscale investigation employs the initial and total fracture energy through a virtual internal pair-bond (VIPB) model. The proposed VIPB model is an extension of the traditional virtual internal bond (VIB) model. Two different types of potentials, a steep short-range potential and a shallow long-range potential, are employed to describe the initial and the total fracture energies, respectively. The Morse potential function is modified for the virtual bond potential so that it is independent of specific length scales associated with the lattice geometry. This feature is incorporated in the VIPB model, which uses both fracture energies and cohesive strength. With respect to the discretization by finite elements, we address the element size dependence in conjunction with the J integral. Parameters in the VIPB model are evaluated by numerical simulations of a pure tension test in conjunction with measured fracture parameters. We also validate the VIPB model by predicting load versus crack mouth opening displacement curves for geometrically similar specimens, and the measured size effect. Finally, we provide an example involving fiber-reinforced concrete, which demonstrates the advantage of the VIPB model over the usual VIB model.

UTILIZATION OF GENERALIZED MORSE PARAMETERS FOR CONVENTIONAL MORSE FUNCTIONS USED IN MOLECULAR MECHANICS

The greater number of parameters in the generalized Morse (GM) potential energy function, as compared with the conventional Morse (CM) potential, allows the former to be more flexible for curve fitting of experimental data. Owing to its simplicity, the CM function has been more widely adopted in molecular modeling softwares. Hence the conversion of the more accurate GM parameters into the commonly used CM parameter is useful for enhancing the latter. This paper proposes three methods for extracting the CM parameter from the GM parameters. The short-range relation was obtained by equating curvatures at the minimum well-depth, whereas the mid-range relation was obtained by equating equal energy integral from equilibrium to dissociation. The long-range relation was obtained by equating the CM parameter with the attractive index of the GM parameter.

Modeling of hydrogen-assisted cracking in iron crystal using a quasi-Newton method

A Quasi-Newton method was applied in the context of a molecular statics approach to simulate the phenomenon of hydrogen embrittlement of an iron lattice. The atomic system is treated as a truss-type structure. The interatomic forces between the hydrogen-iron and the iron-iron atoms are defined by Morse and modified Morse potential functions, respectively. Two-dimensional hexagonal and 3D bcc crystal structures were subjected to tensile numerical tests. It was shown that the Inverse Broyden's Algorithm-a quasi-Newton method-provides a computationally efficient technique for modeling of the hydrogen-assisted cracking in iron crystal. Simulation results demonstrate that atoms of hydrogen placed near the crack tip produce a strong deformation and crack propagation effect in iron lattice, leading to a decrease in the residual strength of numerically tested samples.

Potential energy surface of S 8 dimer

Intermolecular interaction energies of 20 orientations of crown-shaped S 8 dimers were calculated at the MP2/aug(df)-6-311G* level with ab initio calculations. The strongest attraction of the dimers studied was 9.924 kcal mol −1, for the face to face orientation. The potential energy surface was represented as a parameterised sum of atomic pair potentials. The sulphur atomic pair parameters of the Morse potential function were ε = 0.398 kcal mol −1, A = 1.294 Å −1 and R ∗ = 4.007 Å. A comparison to the solid state structures of S 8 showed that the best gas phase dimer orientation is close to the closest packing of S 8 dimers in crystalline state.

Effect of temperature on nano-scale adhesion for MEMS

Molecular dynamics simulation of adhesion behaviour during sliding friction between different materials is proposed. The Newton's equations of motion are established by using Morse potential function. The improved Verlet algorithm is employed to solve atom trajectories. Simulation show that adhesion tends to occur when the system's temperature increases sharply. There are few direct experimental measurements of the adhesion between surfaces of metals because it is very costly. The effects of such variables as block temperature, material properties are very hard to measure experimentally. The model is meaningful to delay or to prevent adhesion in MEMS by selecting the proper parameters.

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.

Molecular Dynamics Simulation of Adhesion Effect on Material Removal and Tool Wear in Diamond Grinding of Silicon Wafer

This study aims to clarify the interaction between a silicon wafer and individual diamond abrasives in grinding to support the estimation of optimal grinding conditions for minimizing the subsurface damages and maximizing the removal rate. In this paper, the effects of adhesion (or lubrication) between a Si wafer and a diamond abrasive on the material removal and tool wear were analyzed by means of the molecular dynamics simulation. A few simulations were performed with changing the dissociation (cohesion) energy of a Morse potential function between a pair of Si and C atoms to evaluate the influence of adhesion on the material removal process. As a result, a trend similar to the actual diamond grinding process of silicon wafer was confirmed, which suggested that the reduction in adhesion (or proper lubrication) is effective for the reduction in subsurface damages, grinding forces, grinding temperature and tool wear, but may lead to reduction in the material removal rate as well.