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Introduction to Nanosensors
Published in Vinod Kumar Khanna, Nanosensors, 2021
A prototype of the chemical bond is treated in many textbooks on quantum mechanics: the H2+ ion is a model for the covalent bond. This quantum-mechanical problem can be solved analytically and gives interesting insights into the character of chemical bonds. The Morse potential (Israelachvili 1991), a convenient model for the potential energy of a diatomic molecule, describes a chemical bond with bonding energy Ebond, equilibrium distance a, and a decay length κ. Although the Morse potential can be used for a qualitative description of chemical forces, it lacks an important property of chemical bonds: anisotropy. Chemical bonds, especially covalent bonds, show an inherent angular dependence on the bonding strength. Using the Stillinger–Weber potential (one of the first attempts to model a semiconductor with a classical model, it is based on a two-body term and a three-body term), one can explain subatomic features in Si images. With increasing computer power, it becomes more and more feasible to perform ab initio calculations for tip–sample forces.
Qualitative Theory of Differential Equations
Published in Vladimir A. Dobrushkin, Applied Differential Equations with Boundary Value Problems, 2017
21. The Morse potential, named after American physicist Philip M. Morse (19031985), is a convenient model for the potential energy of a diatomic molecule. The corresponding model reads y=De(e-2a(y-re)-e-a(y-re)) $ {y} = D_{e} (e^{{ - 2a(y - r_{e} )}} - e^{{ - a(y - r_{e} )}} ) $ , where De is the dissociation energy, re is the equilibrium bond distance, y is the distance between the atoms, and the parameter a controls the “width” of the potential. By plotting a phase portrait, show that the equation has periodic solutions.
Numerical Methods in Microscale Heat Transfer: Modeling of Phasechange and Laser Interactions with Materials
Published in W.J. Minkowycz, E.M. Sparrow, Advances in Numerical Heat Transfer, 2018
In several molecular dynamics simulations (e.g. [72,73]), the transport of laser energy was effected via “energy carriers.” A Monte Carlo/molecular dynamics simulation method was developed for laser melting and evaporation of materials [72]. The Morse potential function was used for the two-body interatomic potential for simulation of atomic motion. The incident laser energy was transferred by massless energy carriers, the trajectories of which were tracked by the test particle Monte Carlo method. Figure 9 shows the so-called “vapor shielding effect,” which reduces the laser energy absorbed by the solid due to energy absorption by vapor.
Scratching a soft layer above a hard substrate
Published in Philosophical Magazine, 2023
Iyad Alabd Alhafez, Michael Kopnarski, Herbert M. Urbassek
Atoms in the material interact via the Morse potential, If the three Morse parameters D, and α are adjusted such that the lattice constant a = 3.615 Å, the cohesive energy eV and the bulk modulus B = 134.4 GPa correspond to the values of Cu [36], the values for the ‘soft’ material are obtained. A series of Morse potentials was published [37], in which the lattice constant and cohesive energy were kept fixed, but the elastic (and plastic) properties were changed in a wide range. From this series, we chose a model with an approximately 3.4 times larger bulk modulus as the ‘hard’ material. The shear modulus G and the hardness H vary approximately in proportion with the change of the bulk modulus. All these properties are contained in Table 1.
Ro-vibrational energies of caesium molecules with the Tietz-Hua oscillator
Published in Molecular Physics, 2021
Ridha Horchani, Noor Al-Kindi, Haikel Jelassi
The choice of the appropriate potential energy form depends on the considered molecule. In the last decades, several multi-parameter potential energy functions have been applied to diatomic molecules and have shown a good agreement with the experimental data [5,12–19]. It is worth noting that those potentials cannot be applied successfully to all diatomic molecules. The ideal potential is chosen to satisfy the conditions at its limits of coordinates (V(0) = ∞ and V(∞) is constant). The first most widely used potential energy function for diatomic molecules was the Morse potential [3], V(r) = De(1–exp(α(r–re)))2, where De is the dissociation energy, re is the equilibrium bond length, and α denotes the range of the potential. The Morse potential allows for dissociation, but when the bond length approaches 0, it gives a large value instead of infinity which leads to a small wave function (not equal to 0) for bound vibrational states.
Mechanical properties of thermoelectric Mg2Si using molecular dynamics simulations
Published in Mechanics of Advanced Materials and Structures, 2019
Ying Zhang, Yuchuan Chu, Wei Xing, Liang Zheng, Yong Cao
A suitable potential function needs to be selected to present the macroscopic properties of the thermoelectric Mg2Si during the MD simulations. In this research, the Morse potential function is chosen to describe the interaction between two atoms in the modeling system. The specific form of the Morse potential function is as follows: where D, α, rij, and r0 are the binding energy, elastic modulus, distance between atoms, and equilibrium distance, respectively. The fitted values of these parameters, listed in Table 1 [14], are obtained by optimizing the solved equation set including the stress balance equation, the energy balance equation, and the elastic constant equilibrium equation.