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:

${\displaystyle {\frac {\epsilon _{\mathrm {r} }-1}{\epsilon _{\mathrm {r} }+2}}={\frac {N\alpha }{3\epsilon _{0}}}}$

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:

${\displaystyle {\frac {\epsilon _{\mathrm {r} }-1}{\epsilon _{\mathrm {r} }+2}}=\sum _{i}{\frac {N_{i}\alpha _{i}}{3\epsilon _{0}}}}$

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