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Collective Motions of Atoms in Crystals

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Abstract

The collective motions of atoms in the molecular dynamics model of a classical Lennard-Jones monocrystal are studied in the process of heating up to a spinodal decomposition and subsequent cooling of the melt until spontaneous crystallization. A hysteresis in the degree of collectivity of atomic motions is found. A new numerical method based on the use of a four-point correlator is used to study the collectivity in the motion of atoms in crystals. This correlator represents the mean cosine of the angle between the displacement vectors of two atoms over time τ, which were initially close to each other. Two features are found: (a) the correlator increases with the temperature in the monocrystal; (b) the correlator in the polycrystal, which was formed during crystallization, appears to be higher than in the initial monocrystal. The distributions of the correlator’s values over the angles between displacements are computed. Two contributions to the atoms’ motions are distinguished: an anisotropic motion, which does not depend on temperature, and an almost isotropic motion, whose angular distribution has the form of a Boltzmann distribution. The excitation energies, which corresponds to the second contribution, are calculated.

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ACKNOWLEDGMENTS

We thank V.V. Pisarev for his interest in the study and his discussion of the study. The calculations were carried out on the Desmos and Fisher computing clusters of the Joint Institute for High Temperatures of the Russian Academy of Sciences.

Funding

This study was supported by the Russian Science Foundation (grant no. 18-19-00734) and the Russian Ministry of Science and Higher Education under state assignment no. 075-00460-21-00.

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Authors and Affiliations

  1. Moscow Institute of Physics and Technology (National Research University), Moscow, Russia

    V. D. Negodin

  2. Joint Institute for High Temperatures, Russian Academy of Sciences, Moscow, Russia

    V. D. Negodin, D. Iu. Fleita & G. E. Norman

  3. National Research University Higher School of Economics, Moscow, Russia

    D. Iu. Fleita & G. E. Norman

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  1. V. D. Negodin
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  2. D. Iu. Fleita
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  3. G. E. Norman
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Correspondence to V. D. Negodin.

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Negodin, V.D., Fleita, D.I. & Norman, G.E. Collective Motions of Atoms in Crystals. Math Models Comput Simul 15, 1075–1083 (2023). https://doi.org/10.1134/S2070048223060157

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