Permittivity of polycrystal: Laminar structure

A simple model of the laminar polycrystal is constructed that can be solved analytically and it also provides various mixing formulas. The polycrystal structure is composed of the layers, which represent rotated anisotropic crystallites. The dielectric response of such structure is much more complex comparing with the response of the layered structure built up of the isotropic materials. The general formal expressions for the effective permittivity were derived. The micro-geometry is determined by the distribution function of the crystal orientations. The effective permittivity can be controlled by variation of the distribution function. By discussing three examples it was shown that the uniform distribution of 2D rotations, as well as uniform 3D rotations, leads to the logarithmic-like mixing law of the effective permittivity.