Collective Motions of Atoms in Crystals

• Published in: Mathematical models and computer simulations 2023-12, Vol.15 (6), p.1075-1083
• Main Authors: Negodin, V. D., Fleita, D. Iu, Norman, G. E.
• Format: Article
• Language: English
• Subjects: Angular distribution; Boltzmann distribution; Correlation; Crystallization; Mathematical Modeling and Industrial Mathematics; Mathematics; Mathematics and Statistics; Molecular dynamics; Numerical methods; Polycrystals; Simulation and Modeling; Single crystals; Spinodal decomposition; Trigonometric functions
• ISSN: 2070-0482; 2070-0490
• DOI: 10.1134/S2070048223060157

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.