Lyddane–Sachs–Teller relation

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) ( $\omega_L$ ) of an ion crystal to the natural frequency of the transverse optical lattice vibration ( $\omega_T$ ) for k=0.^[1] The ratio is equal to 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 $\varepsilon(\omega_s)$ ).^[2]

\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.

References

↑ Lyddane, R.; Sachs, R.; Teller, E. "On the Polar Vibrations of Alkali Halides". Physical Review 59 (8): 673–676. doi:10.1103/PhysRev.59.673.
↑ Laurence Charles, Robinson: The Lyddane-Sachs-Teller-relationship