THE MATHEMATICAL MODEL FOR A NANOCRYSTALLINE MEDIUM WITH DENSE PACKING OF PARTICLES

Abstract

A two-dimensional model for a nanocrystalline medium is considered that represents a hexagonal lattice consisting of elastically interacting round particles possessing translational and rotational degrees of freedom. Linear differential equations are derived in the long-wavelength approximation that describe propagation and interaction of waves of various types in such a medium. The interrelation between the macro-elasticity constants of the medium and the parameters of its microstructure is revealed. The dependence of elastic wave velocities on the sizes of nanoparticles is analyzed. Estimates for the velocity and the critical frequency of the microrotation wave in some hexagonal crystals are obtained. The developed continuum model is compared with the equations of the two-dimensional isotropic Cosserat continuum with centrally symmetric particles.