Lyddane–Sachs–Teller relation
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In condensed matter physics, the Lyddane–Sachs–Teller relation (or LST relation) determines the ratio of the natural frequency of longitudinal optic lattice vibrations (phonons) () of an ionic crystal to the natural frequency of the transverse optical lattice vibration () for long wavelengths (zero wavevector).[1][2][3][4][5] The ratio is that of the static permittivity to the permittivity for frequencies in the visible range .[6]
The relation holds for systems with a single optical branch, such as cubic systems with two different atoms per unit cell. For systems with many phonon branches, the relation does not necessarily hold, as the permittivity for any pair of longitudinal and transverse modes will be altered by the other modes in the system. The Lyddane–Sachs–Teller relation is named after the physicists R. H. Lyddane, Robert G. Sachs, and Edward Teller.