Acoustic identification of nanocrystalline media

Two-dimensional (2D) models of nanocrystalline media with close proximity (a hexagonal lattice) and with non-dense packing (a square lattice) are considered in this paper. It is supposed that particles have a round shape and possess two translational and one rotational degrees of freedom. The differential equations describing the propagation of acoustic and rotational waves in such media have been derived. Analytical relationships between the macroelasticity constants of the medium and microstructure parameters have been found. These relationships appear to be different for nanocrystalline media with hexagonal and square lattices. It has been shown that identification of macroparameters of a nanocrystalline medium can be obtained by measurement of wave velocities and the form of dispersion dependences of acoustic and rotational waves.