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.

构建了层状多晶的简单模型，可以对其进行解析求解，并且还提供了各种混合公式。多晶结构由代表旋转的各向异性微晶的层组成。与由各向同性材料构成的分层结构的响应相比，这种结构的介电响应要复杂得多。推导了有效介电常数的一般形式。微观几何形状由晶体取向的分布函数确定。可以通过改变分布函数来控制有效介电常数。通过讨论三个示例，可以看出2D旋转的均匀分布以及3D旋转的均匀分布导致有效介电常数的对数混合律。