PSI - Issue 65

I.V. Kosarev et al. / Procedia Structural Integrity 65 (2024) 127–132 I.V. Kosarev, E.A. Korznikova, S.V. Dmitriev / Structural Integrity Procedia 00 (2024) 000–000

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1. Introduction

Molecular dynamics is an important modern technique for the study of materials. This method allows the study of systems containing millions of atoms at times on the order of a nanosecond. However, there is a well-known problem with the accuracy of the interatomic potentials used, many of which provide qualitative or quantitative descriptions for only a limited number of properties of the material or process under study Kawecka et al. (2024), Babicheva (2019), Shepelev (2020). In recent years, machine-learning potentials, which provide more accurate results, have begun to occupy a significant place in the field of molecular dynamics (Ghosh et al., 2022; Mortazavi et al., 2023). However, for both classical and machine-learning potentials, the problem of checking their accuracy remains important, since the quality of the interatomic potentials used completely determines the results obtained by the molecular dynamics method. To test the potentials, the use of delocalized nonlinear vibrational modes (DNVMs) is proposed. DNVMs are exact solutions of the equations of motion obtained using the bush theory developed by Chechin and Sakhnenko (Chechin and Sakhnenko 1998). This theory is based solely on the symmetry of molecules (Chechin et al., 2015) and crystals (Chechin and Ryabov 2023; Shcherbinin et al., 2022; Ryabov et al., 2023). According to DNVM, the oscillations of atoms with small amplitudes are phonons, but such oscillations persist even with large amplitudes. This fact allows one to take into account the nonlinear range of vibrations when testing or developing potentials, which is a key issue in many molecular dynamics problems. Since DNVMs are derived considering only the lattice symmetry, they are a universal tool for whole classes of materials belonging to the same crystallographic group. It has already been shown that a phase transition can be associated with certain high symmetry points of the first Brillouin zone (Evarestov and Kitaev 2016). Since phase transitions are driven by high-amplitude vibrations, DNVMs are candidates for analyzing and generating interatomic potentials that more accurately reproduce phase transitions. In this work, 14 single-component DNVMs (Rosenberg modes), Rosenberg (1960), previously studied for bcc tungsten, Kosarev et al. (2024), Dmitriev et al, (2024), are used to analyze bcc vanadium. Using them via the Large scale Atomic/Molecular Massively Parallel Simulator (LAMMPS), Plimpton (1995), three classical and one machine-learned interatomic potential are analyzed. The lack of agreement of the obtained results is demonstrated and the problem of the quality of interatomic potentials in describing large amplitude oscillations is raised. As follows from the symmetry rules, a supercell of size 2x2x2 primitive cells is sufficient to analyze all studied DNVMs of the bcc lattice. However, to simplify the work, a cubic computational cell of 16 atoms is used, with an edge of 2a, where a is the lattice parameter. The DNVMs are excited by specifying certain initial displacements of the atoms from the equilibrium positions, where the length of the displacement vector is equal to the amplitude of the oscillation, since the initial velocities of all atoms are zero. The displacement vectors for the 14 DNVMs considered are shown in Fig. 1. The magnitude of the initial displacement is given as a function of the number of non-zero components of the displacement vector, i.e., A, A/√2, and A/√3 for one-, two-, and three-component displacement vectors, respectively, where A is the oscillation amplitude. The amplitude-frequency characteristics were obtained in the amplitude range from 0.005 to 0.25 Å with a step of 0.005 Å. Three classical potentials, two of which are EAM (embedded atom method) and one MEAM (modified embedded atom method) potentials, were chosen for the calculations using the LAMMPS software package. The potentials were denoted as A2003_EAM, Han et al. (2003); O2009_EAM, Olsson (2009); and L2001_MEAM, Lee et al. (2001), respectively. Machine-learned Gaussian approximation potential (GAP), which we denote as B2020_GAP, Byggmästar et al. (2020), is also analyzed. As shown previously, Kosarev et al. (2024), the 14 DNVMs considered can be divided into 4 groups, such that DNVMs in the same group have the same frequency at small oscillation amplitudes. DNVMs 1 through 4 belong to the first group (G1), 5 through 7 to the second group (G2), 8 through 10 to the third group (G3), and 11 through 14 to the fourth group (G4). At small amplitudes, groups G1, G2, and G4 represent N-point phonons of the first Brillouin zone, so that groups G1, G2, and G4 represent transverse T1, transverse T2, and longitudinal phonons, 2. Methodology