Clausius–Mossotti relation

The Clausius–Mossotti relation expresses the dielectric constant (relative permittivity) ε_r of a material in terms of the atomic polarizibility α of the material's constituent atoms and/or molecules, or a homogeneous mixture thereof. It is named after Ottaviano-Fabrizio Mossotti and Rudolf Clausius. It is equivalent to the Lorentz–Lorenz equation. It may be expressed as:

ϵ r − 1 ϵ r + 2 = N α 3 ϵ 0

where

In the case that the material consists of a mixture of two or more species, the right hand side of the above equation would consist of the sum of the molecular polarizability contribution from each species, indexed by i in the following form:

ϵ r − 1 ϵ r + 2 = ∑ i N i α i 3 ϵ 0

In the CGS system of units the Clausius–Mossotti relation is typically rewritten to show the molecular polarizability volume α ′ = α / ( 4 π ε 0 ) which has units of volume (m³). Confusion may arise from the practice of using the shorter name "molecular polarizability" for both α and α ′ within literature intended for the respective unit system.