Collective motions of atoms in crystals

Collective motions of atoms in molecular dynamics model of classical Lennard-Jones crystal are under consideration in process of heating up to spinodal decomposition and subsequent cooling of the melt to spontaneous crystallization. Collective motions magnitude hysteresis was found. A new numerical method based on four-point correlator usage was used for studying collectivity in the motion of atoms in crystals. This correlator represents the mean cosine of angle between replacement vectors of two atoms over time $\tau$, which were initially close to each other. Two features were found: (a) correlator increases with temperature in monocrystal; (b) correlator in polycrystal, which was formed during crystallization, appeared to be higher than in initial monocrystal. Distributions of correlator's values over the angles between displacements were computed. Two contributions in atoms’ motions were distinguished: first is anisotropic, temperature independent and second is almost isotropic, which angular distribution has the form of the Boltzmann distribution. Excitation energies, which corresponds to second contribution, were calculated.