The Electric Field in Crystals: The Refractivity of Rutile

A calculation has been made of the electric fields at the ionic sites in the lattice of rutile (TiO2, tetragonal) due to induced dipoles at all the other sites. Following Lorentz, we divide the field at any site into two parts, one due to the distant dipoles outside a large cavity and the other due to the dipoles inside the cavity. A careful analysis has been made of the influence of the shape of the cavity. For accurate calculations in non-cubic crystals, a sphere (chosen by Lorentz) is not suitable but a rectangular cavity similar to the unit cell offers an excellent means of obtaining the accurate values for the fields. Rutile has a large refractivity and a large positive birefringence, both being dominated by the oxygen ion polarizability. The refractive indices cannot be explained if the oxygen ion polarizability is isotropic, but they can be explained if we introduce an anisotropic polarizability. The anisotropy is linked to the crystal structure.