Dielectric function and the Lyddane-Sachs-Teller relation for crystals with Debye polarization

A derivation of the Lyddane-Sachs-Teller (LST) relation is presented for a dielectric dispersion having both the low-frequency Debye modes and the optical-frequency damped-oscillator modes. It is shown that the LST relation should be expressed as ε(0)-S′ε=ωl2ωt2 which reduces to the familiar LST relation ε(0)ε=ωl2ωt2 in the absence of a permanent dipole polarization (S′=0), or should be expressed equivalently as ε(0)(ε+S)=ωzωp (S is the oscillator mode strength and ωz and ωp are the zero and pole of the dielectric function in the low-frequency limit) rather than as ε(0)εA=A |ωz1||ωz2||ωz3||ωp1||ωp2||ωp3| for practical use. © 1976 The American Physical Society.