Stability of Strained Stanene Compared to That of Graphene.

Stanene, composed of tin atoms, is a member of 2D-Xenes, two-dimensional single element materials. The properties of the stanene can be changed and improved by applying deformation, and it is important to know the range of in-plane deformation that the stanene can withstand. Using the Tersoff interatomic potential for calculation of phonon frequencies, the range of stability of planar stanene under uniform in-plane deformation is analyzed and compared with the known data for graphene. Unlike atomically flat graphene, stanene has a certain thickness (buckling height). It is shown that as the tensile strain increases, the thickness of the buckled stanene decreases, and when a certain tensile strain is reached, the stanene becomes absolutely flat, like graphene. Postcritical behaviour of stanene depends on the type of applied strain: critical tensile strain leads to breaking of interatomic bonds and critical in-plane compressive strain leads to rippling of stanene. It is demonstrated that application of shear strain reduces the range of stability of stanene. The existence of two energetically equivalent states of stanene is shown, and consequently, the possibility of the formation of domains separated by domain walls in the stanene is predicted.

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.

Discrete breathers in a triangular ß-Fermi-Pasta-Ulam-Tsingou lattice.

A practical approach to the search for (quasi-) discrete breathers (DBs) in a triangular ß-FPUT lattice (after Fermi, Pasta, Ulam, and Tsingou) is proposed. DBs are obtained by superimposing localizing functions on delocalized nonlinear vibrational modes (DNVMs) having frequencies above the phonon spectrum of the lattice. Zero-dimensional and one-dimensional DBs are obtained. The former ones are localized in both spatial dimensions, and the latter ones are only in one dimension. Among the one-dimensional DBs, two families are considered: the first is based on the DNVMs of a triangular lattice, and the second is based on the DNVMs of a chain. We speculate that our systematic approach on the triangular ß-FPUT lattice reveals all possible types of spatially localized oscillations with frequencies bifurcating from the upper edge of the phonon band as all DNVMs with frequencies above the phonon band are analyzed.