Editing Polarizability (section)

===Definition===

Electric polarizability is the relative tendency of a charge distribution, like the [[electron cloud]] of an [[atom]] or [[molecule]], to be distorted from its normal shape by an external [[electric field]].

The polarizability <math>\alpha</math> in [[Isotropy|isotropic]] media is defined as the ratio of the induced [[Electric dipole moment|dipole moment]] <math>\mathbf{p}</math> of an atom to the electric field <math>\mathbf{E}</math> that produces this dipole moment.<ref>Introduction to Electrodynamics (3rd Edition), D.J. Griffiths, Pearson Education, Dorling Kindersley, 2007, {{ISBN|81-7758-293-3}}</ref>

:<math>\alpha = \frac{|\mathbf{p}|}{|\mathbf{E}|}</math>

Polarizability has the [[International System of Units|SI units]] of C·m<sup>2</sup>·V<sup>−1</sup> = A<sup>2</sup>·s<sup>4</sup>·kg<sup>−1</sup> while its cgs unit is cm<sup>3</sup>. Usually it is expressed in cgs units as a so-called polarizability volume, sometimes expressed in [[Angstrom|Å]]<sup>3</sup> = 10<sup>−24</sup> cm<sup>3</sup>. One can convert from SI units (<math>\alpha</math>) to cgs units (<math>\alpha'</math>) as follows:

:<math>\alpha' (\mathrm{cm}^3) =  \frac{10^{6}}{ 4 \pi \varepsilon_0 }\alpha (\mathrm{C{\cdot}m^2{\cdot}V^{-1}}) = \frac{10^{6}}{ 4 \pi \varepsilon_0 }\alpha (\mathrm{F{\cdot}m^2}) </math> ≃ 8.988×10<sup>15</sup> × <math>\alpha  (\mathrm{F{\cdot}m^2}) </math>

where <math>\varepsilon_0 </math>, the [[permittivity|vacuum permittivity]], is ≈8.854 × 10<sup>−12</sup> (F/m). If the polarizability volume in cgs units is denoted <math>\alpha'</math> the relation can be expressed generally<ref name=Atkins>{{cite book|title=Atkins' Physical Chemistry|year=2010|publisher=[[Oxford University Press]]|isbn=978-0-19-954337-3|pages=622–629|last1=Atkins|first1=Peter|last2=de Paula|first2=Julio|chapter=17}}</ref> (in SI) as <math>\alpha = 4\pi\varepsilon_0 \alpha' </math>.

The polarizability of individual particles is related to the average [[electric susceptibility]] of the medium by the [[Clausius–Mossotti relation]]: 
:<math>R={\displaystyle \left({\frac {4\pi}{3}}\right)N_\text{A}\alpha_{c}=\left({\frac {M}{p}}\right)\left({\frac {\varepsilon_\mathrm{r}-1}{\varepsilon_\mathrm{r}+2}}\right)}</math>
where ''R''  is the [[molar refractivity]], <math>N_\text{A}</math> is the [[Avogadro constant]], <math>\alpha_c</math> is the electronic polarizability, ''p'' is the density of molecules, ''M''  is the [[molar mass]], and <math>\varepsilon_{\mathrm r} = \epsilon/\epsilon_0</math> is the material's relative permittivity or [[dielectric constant]] (or in optics, the square of the [[refractive index]]).

Polarizability for anisotropic or non-spherical media cannot in general be represented as a [[scalar (physics)|scalar]] quantity. Defining <math>\alpha</math> as a scalar implies both that applied electric fields can only induce polarization components parallel to the field and that the <math>x, y</math> and <math>z</math> directions respond in the same way to the applied electric field. For example, an electric field in the <math>x</math>-direction can only produce an <math>x</math> component in <math>\mathbf{p}</math> and if that same electric field were applied in the <math>y</math>-direction the induced polarization would be the same in magnitude but appear in the <math>y</math> component of  <math>\mathbf{p}</math>. Many crystalline materials have directions that are easier to polarize than others and some even become polarized in directions perpendicular to the applied electric field{{Citation needed|date=September 2020}}, and the same thing happens with non-spherical bodies. Some molecules and materials with this sort of anisotropy are [[Optical rotation|optically active]], or exhibit linear [[birefringence]] of light.