Statistical data quasi-breathers soft type of nonlinearity in crystals stoichiometry A$_3$B

In this paper by method of molecular dynamics study conducted statistical characteristics of quasi-breather in the model crystal stoichiometry A$_3$B, on the example Pt$_3$Al. The simulation was performed using molecular dynamics package LAMMPS Molecular Dynamics Simulator. The model is a volumetric FCC crystal stoichiometry A$_3$B. As a special case considered crystal Pt$_3$Al, containing 50.000 atoms. Alloys stoichiometry A$_3$B with L1$_2$ superstructure are the most numerous, searching the currently known systems with L1$_2$ structure revealed about 190 of these phases in the composition A$_3$B. Also with this structure alloys are the most frequently chosen for the model and the fundamental research to the development of the structural and physical foundations of the creation of new structural and functional materials with a variety of unique properties. Alloys with L1$_2$ structure are the basis for the development of currently existing superalloys. To simulate the use of the potential of interatomic interaction produced by the method embedded atom (EAM). Excitation model quasi-breather observed rejecting Al atoms along the $<100>$ direction. Unlike the exact discrete breathers, quasi-breathers are not strictly periodic in time of dynamic objects, although localized in space. They arise in any sufficiently small deviations from the exact breather solutions in multidimensional space of all possible initial conditions for solving the Cauchy problem for the original differential equations, since in this case there is no complete suppression of the contributions from the peripheral oscillations of the particles with their own frequencies. The weakening influence from the breather nucleus leads to the presence of a small breather solution deposits having different frequencies. These small deposits can detect vibrations in all chains of particles, in particular, and central. Therefore, there are standard deviations $\eta \left( t_k \right)$ oscillation frequency different from the average particle breather frequency $\bar{\omega}$. The larger the value $\eta \left( t_k \right)$, the larger the breather differs quasi-exact solution from the breather solutions for which $\eta \left( t_k \right)$ = 0 at any given time t$_k$. Received model phonon spectrum of the crystal obtained according to the standard deviation, coefficient of variation and the average frequency of the model of quasi-breather from the time of its existence. Statistical data analysis allows us to conclude that in this model using the interatomic potential obtained by submerged atom (EAM), a quasi-breather model solution differs slightly from the corresponding exact breather. This demonstrates the stability of the resulting discrete breathers in model cells and the possibility of bringing in real alloys considered composition.