can be expressed generally (in SI) as . The polarizability of individual particles is related to the average electric susceptibility of the medium by the Clausius–Mossotti relation: where R = molar refractivity , = Avogadro constant, = electronic polarizability, p = density of molecules, M = molar mass, and is the material's relative permittivity or dielectric constant (or in optics, the square of the refractive index). Polarizability for anisotropic or non-spherical media cannot in general be represented as a scalar quantity. Defining as a scalar implies both that applied electric fields can only induce polarization components parallel to the field and that the and directions respond in the same way to the applied electric field. For example, an electric field in the -direction can only produce an component in and if that same electric field were applied in the -direction the induced polarization would be the same in magnitude but appear in the component of . Many crystalline materials have directions that are easier to polarize than others and some even become polarized in directions perpendicular to the applied electric field, and the same thing happens with non-spherical bodies. Some molecules and materials with this sort of anisotropy are optically active, or exhibit linear birefringence of light. Tensor To describe anisotropic media a polarizability rank two tensor or matrix is defined, so that: The elements describing the response parallel to the applied electric field are those along the diagonal. A large value of here means that an electric-field applied in the -direction would strongly polarize the material in the -direction. Explicit expressions for have been given for homogeneous anisotropic ellipsoidal bodies. Application in crystallography The matrix above can be used with the molar refractivity equation and other data to produce density data for crystallography. Each polarizability measurement along with the refractive index associated with its direction will yield a direction specific density that can be used to develop an accurate three dimensional assessment of molecular stacking in the crystal. This relationship was first observed by Linus Pauling. Tendencies Generally, polarizability increases as the volume occupied by electrons increases. In atoms, this occurs because larger atoms have more loosely held electrons in contrast to smaller atoms with tightly bound electrons. On rows of the periodic table, polarizability therefore decreases from left to right. Polarizability increases down on columns of the periodic table. Likewise, larger molecules are generally more polarizable than smaller