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 acoustic lattice vibrations (phonons) (\omega_L) of an ion crystal to the natural frequency of the transverse optical lattice vibration (\omega_T) for k=0 which equals the ratio of the static permittivity \varepsilon_{st} (Often also \varepsilon(0)) for the permittivity for frequencies in the visible range \varepsilon_{\infty} (often also \varepsilon(\omega_s)).[1]

\frac{\omega_L^2}{\omega_T^2} = \frac{\varepsilon_{st}}{\varepsilon_{\infty}}

The Lyddane-Sachs-Teller relation is named after the physicists R. H. Lydanne, Edward Teller, and R. G. Sachs.