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⭐ Core Definition: Polarizability

Polarizability usually refers to the tendency of matter, when subjected to an electric field, to acquire an electric dipole moment in proportion to that applied field. It is a property of particles with an electric charge. When subject to an electric field, the negatively charged electrons and positively charged atomic nuclei are subject to opposite forces and undergo charge separation. Polarizability is responsible for a material's dielectric constant and, at high (optical) frequencies, its refractive index.

The polarizability of an atom or molecule is defined as the ratio of its induced dipole moment to the local electric field; in a crystalline solid, one considers the dipole moment per unit cell. Note that the local electric field seen by a molecule is generally different from the macroscopic electric field that would be measured externally. This discrepancy is taken into account by the Clausius–Mossotti relation (below) which connects the bulk behaviour (polarization density due to an external electric field according to the electric susceptibility $\chi =\varepsilon _{\mathrm {r} }-1$ ) with the molecular polarizability $\alpha$ due to the local field.

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⭐ Core Definition: Polarizability
Polarizability in the context of Rayleigh scattering
Polarizability in the context of Permittivity

Polarizability in the context of Rayleigh scattering

Rayleigh scattering (/ˈreɪli/ RAY-lee) is the scattering or deflection of light, or other electromagnetic radiation, by particles with a size much smaller than the wavelength of the radiation. For light frequencies well below the resonance frequency of the scattering medium (normal dispersion regime), the amount of scattering is inversely proportional to the fourth power of the wavelength (e.g., a blue color is scattered much more than a red color as light propagates through air). The phenomenon is named after the 19th-century British physicist Lord Rayleigh (John William Strutt).

Rayleigh scattering results from the electric polarizability of the particles. The oscillating electric field of a light wave acts on the charges within a particle, causing them to move at the same frequency. The particle, therefore, becomes a small radiating dipole whose radiation we see as scattered light. The particles may be individual atoms or molecules; it can occur when light travels through transparent solids and liquids, but is most prominently seen in gases.

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Polarizability in the context of Permittivity

In electromagnetism, the absolute permittivity, often simply called permittivity and denoted by the Greek letter $ε$ (epsilon), is a measure of the electric polarizability of a dielectric material. A material with high permittivity polarizes more in response to an applied electric field than a material with low permittivity, thereby storing more energy in the material. In electrostatics, the permittivity plays an important role in determining the capacitance of a capacitor.

In the simplest case, the electric displacement field $D$ resulting from an applied electric field E is

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Polarizability in the context of "Unit cell"

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⭐ Core Definition: Polarizability

Polarizability in the context of Rayleigh scattering

Polarizability in the context of Permittivity