The integral-differential and integral approach for the estimation of the classical Lennard-Jones and Biswas-Hamann potentials

Surulere, Samuel A.; Shatalov, M. Y.; Mkolesia, A.C.; Ehigie, J. O.

doi:10.1504/ijmmno.2020.108612

Cited by 2 publications

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“…It should be noted that this form of the Biswas -Hamann potential is quite similar to the Kaxiras -Pandey potential, see [11,12]. The parameters β 1 , β 2 , A and B were obtained as [10]. The classical Morse potential is one of the hybrid forms of the Morse potential (proposed by [13]), after expansion of its empirical formula.…”

Section: Methodsmentioning

confidence: 96%

“…It is known that numerical integration is relatively more accurate, compared with numerical differentiation. The least squares method with the integral approach was used to estimate the modified Lennard -Jones and Biswas -Hamann potential parameters in [10]. The mathematical representation of the Biswas -Hamann potential considered in [9] and [10] is…”

Section: Methodsmentioning

confidence: 99%

“…were estimated in [14] using the least squares method with the integral-differential approach as β = 1.735 Å −1 , A CM = 4152 eV, B CM = 44.679 eV. In the literature, the coefficients A BH , A CM in Eqs.…”

Section: Methodsmentioning

confidence: 99%

“…(2.1) and (2.2) are known as the attractive terms, while the coefficients B BH , B CM are known as the repulsive terms. The mathematical representation of the classical Lennard -Jones potential considered in [9] and [10] is In what follows, we will consider the transformation of the interaction potentials by shifting the potential variables U (r) and r, in the horizontal and vertical direction. For the classical Morse potential in Eq.…”

Section: Methodsmentioning

confidence: 99%

“…Another quantitative metric used to validate our estimates are the values of the goal function. A detailed discussion of the formulation of the least squares method with differential, integral-differential or integral approaches is presented in [9,10,14]. The PECs presented in Figs.…”

Section: 6)mentioning

confidence: 99%

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Nonlinear Interactions in Nanolattices Described by the Classical Morse, Biswas – Hamann and Modified Lennard – Jones Potentials

Adeniji¹,

Fedotov²,

Ehigie³

et al. 2022

Nelin. Dinam.

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The oscillatory motion in nonlinear nanolattices having different interatomic potential energy functions is investigated. Potential energies such as the classical Morse, Biswas – Hamann and modified Lennard – Jones potentials are considered as interaction potentials between atoms in one-dimensional nanolattices. Noteworthy phenomena are obtained with a nonlinear chain, for each of the potential functions considered. The generalized governing system of equations for the interaction potentials are formulated using the well-known Euler – Lagrange equation with Rayleigh’s modification. Linearized damping terms are introduced into the nonlinear chain. The nanochain has statistical attachments of $40$ atoms, which are perturbed to analyze the resulting nonlinearities in the nanolattices. The range of initial points for the initial value problem (presented as second-order ordinary differential equations) largely varies, depending on the interaction potential. The nanolattices are broken at some initial point(s), with one atom falling off the slender chain or more than one atom falling off. The broken nanochain is characterized by an amplitude of vibration growing to infinity. In general, it is observed that the nonlinear effects in the interaction potentials cause growing amplitudes of vibration, accompanied by disruptions of the nanolattice or by the translation of chaotic motion into regular motion (after the introduction of linear damping). This study provides a computationally efficient approach for understanding atomic interactions in long nanostructural components from a theoretical perspective.

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Section: Methodsmentioning

confidence: 96%

Section: Methodsmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

Section: 6)mentioning

confidence: 99%

See 3 more Smart Citations

Nonlinear Interactions in Nanolattices Described by the Classical Morse, Biswas – Hamann and Modified Lennard – Jones Potentials

Adeniji¹,

Fedotov²,

Ehigie³

et al. 2022

Nelin. Dinam.

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Optimal interatomic potentials using modified method of least squares: Optimal form of interatomic potentials

Surulere,

Shatalov,

Olayiwola

2023

Open Physics

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The problem of optimization of interatomic potentials is formulated and solved by means of generalization of the Morse, Kaxiras–Pandey, and Rydberg potentials. The interatomic potentials are treated as solutions of some second-order ordinary differential equations which will be classified and analyzed. The most appropriate analytic form of the understudied potentials will be proposed based on a one-dimensional search for the parameter, γ \gamma , which is the power of the interatomic distance, r r . The optimal analytic form will also be proposed for metals such as gold, copper, aluminium, titanium, and the silver–copper alloy. The method of least squares will be used to estimate the potential parameters. Phenomenological potentials such as the classical Rydberg, classical Morse, generalized Morse, Kaxiras–Pandey, and classical Lennard–Jones will be studied, and new potentials based on the combination of some of the aforementioned potentials will also be proposed. Metrics such as the goal function values, will be used to identify which optimal value of the parameter, γ \gamma , is most appropriate to introduce into the preferred interatomic potential for interaction between atoms.

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The integral-differential and integral approach for the estimation of the classical Lennard-Jones and Biswas-Hamann potentials

Cited by 2 publications

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Nonlinear Interactions in Nanolattices Described by the Classical Morse, Biswas – Hamann and Modified Lennard – Jones Potentials

Nonlinear Interactions in Nanolattices Described by the Classical Morse, Biswas – Hamann and Modified Lennard – Jones Potentials

Optimal interatomic potentials using modified method of least squares: Optimal form of interatomic potentials

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