Clausius-Mosotti-Lorentz equation

The linear and non-linear polarizabilities of organic molecules are usually determined from measurements of macroscopic susceptibilities of liquid solutions. Classical examples are the measurements of the refractive index, n, or the relative permittivity of pure organic liquids and their interpretation by the well-known Lorentz-Lorenz and Clausius-Mosotti equations. These... 

The molar refractivity is the volume of the substance taken up by each mole of that substance. In SI units, MR is expressed as m /mol. MR is a molecular descriptor of a liquid, which contains both information about molecular volume and polarizability, usually defined by the Lorenz-Lorentz equation [Lorentz, 1880a, 1880b] (also known as the Clausius-Mosotti equation) ... 

Starting from the Clausius-Mosotti equation (9.7) and assuming that it can be applied to each principal direction Ox, in an orthorhombic crystal, show that the Lorentz-Lorenz equation can be written in a form that leads to the equation , = (1 + 2x,)/(l — x,), where , is the refractive index for light polarised parallel to Ox,- and X,- = q ,-/(3 oF), with a,- equal to the polarisability per unit cell for light polarised parallel to Ox,- and V the volume of the unit cell. 

The refractive index of a compound oxide or a multi-component glass may be roughly estimated by using the Lorenz-Lorentz formula (Clausius-Mosotti s formula in terms of the dielectric constant and polarizability) which gives the relation between the refractive index and polarizability of materials described as equation (31-1). 

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