The static dielectric constant of dipolar solids

A calculation of the static dielectric constant of a crystalline - dipolar material of simple structure is outlined. It is assumed that the dipoles are arranged in a simple cubic structure (NaCl type) and that ordering forces between them depend on the shape of the molecule and are exerted between nearest neighbors only (short range forces). Each dipole is assumed to have two possible positions 180° apart and, in equilibrium at the absolute zero of temperature, nearest neighbors point in opposite directions so that the part of the dielectric constant due to the permanent dipoles is zero. The material is then completely ordered. As the temperature is raised, thermal agitation causes more and more dipoles to turn through 180° and eventually a second order transition temperature T₀ at which long range order disappears, is reached. The variation of static dieleciric constant with temperature can be calculated using Fröhlich´s general formula and taking account of the short range ordering forces by Bethe´s method.