Open Access

ARTICLE

Delocalized Nonlinear Vibrational Modes in Bcc Lattice for Testing and Improving Interatomic Potentials

Denis S. Ryabov¹, Igor V. Kosarev^2,3, Daxing Xiong⁴, Aleksey A. Kudreyko⁵, Sergey V. Dmitriev^2,6,*

1 Institute of Physics, Southern Federal University, 194 Stachki Ave., Rostov-on-Don, 344090, Russia
2 Institute of Molecule and Crystal Physics, UFRC of Russian Academy of Sciences, 151 Oktyabrya Ave., Ufa, 450075, Russia
3 Research Laboratory for Metals and Alloys Under Extreme Impacts, Ufa University of Science and Technology, 32 Zaki Validi Str., Ufa, 450076, Russia
4 MinJiang Collaborative Center for Theoretical Physics, College of Physics and Electronic Information Engineering, Minjiang University, Fuzhou, 350108, China
5 Bashkir State Medical University, 3 Lenin Str., Ufa, 450008, Russia
6 Ufa State Petroleum Technological University, 1 Kosmonavtov Str., Ufa, 450062, Russia

* Corresponding Author: Sergey V. Dmitriev. Email:

Computers, Materials & Continua 2025, 82(3), 3797-3820. https://doi.org/10.32604/cmc.2025.062079

Received 09 December 2024; Accepted 01 February 2025; Issue published 06 March 2025

Abstract

Molecular dynamics (MD) is a powerful method widely used in materials science and solid-state physics. The accuracy of MD simulations depends on the quality of the interatomic potentials. In this work, a special class of exact solutions to the equations of motion of atoms in a body-centered cubic (bcc) lattice is analyzed. These solutions take the form of delocalized nonlinear vibrational modes (DNVMs) and can serve as an excellent test of the accuracy of the interatomic potentials used in MD modeling for bcc crystals. The accuracy of the potentials can be checked by comparing the frequency response of DNVMs calculated using this or that interatomic potential with that calculated using the more accurate ab initio approach. DNVMs can also be used to train new, more accurate machine learning potentials for bcc metals. To address the above issues, it is important to analyze the properties of DNVMs, which is the main goal of this work. Considering only the point symmetry groups of the bcc lattice, 34 DNVMs are found. Since interatomic potentials are not used in finding DNVMs, they are exact solutions for any type of potential. Here, the simplest interatomic potentials with cubic anharmonicity are used to simplify the analysis and to obtain some analytical results. For example, the dispersion relations for small-amplitude phonon modes are derived, taking into account interactions between up to the fourth nearest neighbor. The frequency response of the DNVMs is calculated numerically, and for some DNVMs examples of analytical analysis are given. The energy stored by the interatomic bonds of different lengths is calculated, which is important for testing interatomic potentials. The pros and cons of using DNVMs to test and improve interatomic potentials for metals are discussed. Since DNVMs are the natural vibrational modes of bcc crystals, any reliable interatomic potential must reproduce their properties with reasonable accuracy.

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Keywords

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