Discrete breathers in a triangular β-Fermi-Pasta-Ulam-Tsingou lattice

Delocalized nonlinear vibrational modes and discrete breathers in β-FPUT simple cubic lattice

The problem of finding various discrete breathers (DBs) in the β-Fermi-Pasta-Ulam-Tsingou simple cubic lattice is addressed. DBs are obtained by imposing localizing functions on delocalized nonlinear vibrational modes (DNVMs) having frequencies above the phonon spectrum of the lattice. Among 27 DNVMs with the wave vector at the boundary of the first Brillouin zone there are three satisfying this condition. Seven robust DBs of different symmetries are found using this approach.

Discrete breathers in square lattices from delocalized nonlinear vibrational modes

Standing and moving discrete breathers (or equally, intrinsic localized modes) in a square β-Fermi-Pasta-Ulam-Tsingou lattice are obtained by applying localizing functions to the delocalized nonlinear vibrational modes (DNVMs) found earlier by Ryabov and Chechin. The initial conditions used in our study do not correspond to exact spatially localized solutions, but make it possible to obtain long-lived quasibreathers. The approach employed in this work can easily be used to search for quasibreathers in three-dimensional crystal lattices, for which DNVMs with frequencies outside the phonon spectrum are known.

Supersonic Motion of Atoms in an Octahedral Channel of fcc Copper

In this work, the mass transfer along an octahedral channel in an fcc copper single crystal is studied for the first time using the method of molecular dynamics. It is found that the initial position of the bombarding atom, outside or inside the crystal, does not noticeably affect the dynamics of its motion. The higher the initial velocity of the bombarding atom, the deeper its penetration into the material. It is found out how the place of entry of the bombarding atom into the channel affects its further dynamics. The greatest penetration depth and the smallest dissipation of kinetic energy occurs when the atom moves exactly in the center of the octahedral channel. The deviation of the bombarding atom from the center of the channel leads to the appearance of other velocity components perpendicular to the initial velocity vector and to an increase in its energy dissipation. Nevertheless, the motion of an atom along the channel is observed even when the entry point deviates from the center of the channel by up to 0.5 Å. The dissipated kinetic energy spent on the excitation of the atoms forming the octahedral channel is nearly proportional to the deviation from the center of the channel. At sufficiently high initial velocities of the bombarding atom, supersonic crowdions are formed, moving along the close-packed direction ⟨1¯10⟩, which is perpendicular to the direction of the channel. The results obtained are useful for understanding the mechanism of mass transfer during ion implantation and similar experimental techniques.

Modulational Instability of Delocalized Modes in fcc Copper

Delocalized nonlinear vibrational modes (DNVMs) are exact solutions of the equations of motion, and therefore, DNVMs exist at any vibration amplitude and do not depend on interaction potentials. For the first time, modulation instability of four one-component three-dimensional DNVMs is studied in a single crystal of fcc copper with the use of methods of molecular dynamics. DNVMs frequencies, evolution of stresses, kinetic and potential energies, and heat capacity depending on the oscillation amplitudes are analyzed. It is found that all four DNVMs are characterized by a hard-type anharmonicity. Modulation instability of DNVMs results in a formation of chaotic discrete breathers (DBs) with frequency above the upper edge of the phonon spectrum of the crystal. The lifetime of chaotic DBs is found to be in the range of 30-100 ps. At low-oscillation frequencies, longer-lived DBs are formed. The growth of modulation instability leads to an increase in mechanical stresses and a decrease in the heat capacity of the crystal. The results obtained in this work enrich our understanding of the influence of the modulation instability of DNVMs on the properties of metals.

Effect of the stiffness of interparticle bonds on properties of delocalized nonlinear vibrational modes in an fcc lattice

Delocalized nonlinear vibrational modes (DNVMs) supported in crystal lattices are exact solutions to the equations of motion of particles that are determined by the symmetry of the lattices. DNVMs exist for any vibration amplitudes and for any interparticle potentials. It is important to know how the properties of DNVMs depend on the parameters of interparticle potentials. In this work, we analyze the effect of the Morse potential stiffness on the properties of one-component DNVMs in a face-centered cubic (fcc) lattice. In particular, the frequencies, kinetic and potential energy, mechanical stress, and elastic constants of DNVMs in a large range of vibration amplitudes are considered. Frequency-amplitude dependency obtained for the Morse crystal is compared with that obtained earlier for copper by using the potentials of the many-body embedded atom method. The properties of DNVMs are mainly dictated by their symmetry and are less influenced by the interparticle potentials. It is revealed that at low and high stiffness of interparticle bonds, different sets of DNVMs have frequencies above the phonon band. This is important to predict the possible types of discrete breathers supported by the fcc lattice. The results obtained in the work enrich the understanding of the influence of interparticle potentials on the properties of the studied family of exact dynamic solutions.