Lyddane-Sachs-Teller relation

The physical significance of t0e and c0u should be clear from Fig. 9.16. If (9.22) and (9.23) are combined we obtain the Lyddane-Sachs-Teller relation ... 

This is the background for the Lyddane-Sachs-Teller relation to be treated below. For transverse optical vibrations the origin of an is field is less obvious, but it is also present and its reaction on the eigenfrequency of the TO phonon later gives rise to the polaritons. 

One can show, that in this case Ic is parallel to P, P, and also to w, i.e. this solution is the dispersion relation of the LO mode. It is remarkable that wL, which now turns out to be the frequency of the LO mode, does not depend on k. cjl has no dispersion in the center of BZ 1 and is always greater than oiT because e0 > e . Eq. (11.20) is called the Lyddane-Sachs-Teller relation. 

A linear relation between and T at the zone center is found (see Figure 1.12) suggesting that the temperature dependence of the optic mode frequency relates to the phase transition. In accordance with the Lyddane-Sachs-Teller relation... 

The static dielectric constants eo, can be determined from the analysis of IR spectra with sufficient spectral data coverage below and above the reststrahlen regions. For photon energies far above the phonon resonances but still sufficiently below the electronic band-to-band transitions, the DFs converge to the high-frequency dielectric constants OCjwhich is related to 0, by the Lyddane-Sachs-Teller relation (3.5). measure the sum of... 

This expression is known as the Lyddane-Sachs-Teller relation [61]. 

Lux (lx) - The SI unit of illuminance, equal to cd sr m [1] Lyddane-Sachs-Teller relation - A relation between the phonon frequencies and dielectric constants of an ionic crystal which states that = e(°°)/e(0), where co., is the angular fre-... 

The general trend that the wavelength of the phonon modes depends approximately on the reduced mass M of the oscillating system like A M " is reasonably fulfilled just as the Lyddane-Sachs-Teller relation, connecting LO and TO frequencies with the optical and static dielectric constants, taken from table 19.6. 

The elastic coefficients Cn and C44 are obtained from velocity of soimd measurements, and the values in Table 16.1 were taken from Kiffel, Introduction to Solid State Physics, 2nd edition. The values for Solid State Physics, 7th edition, were obtained by observing the onset of strong reflectance in the infrared. In Qiapter 24, it is shown that ionic materials reflect strongly as well as absorb at frequencies slightly above their transverse resonant frequency. The values for optical dielectric constants using the Lyddane, Sachs, Teller relation (see Chapter 23) and were also taken from Kittel, Solid State Physics, 7th edition. All frequencies are in units of 10 /s. 

The Dielectric Constant and the Lyddane-Sachs-Teller Relation... 

Generalized Lyddane-Sachs-Teller Relation Consider a dielectric constant of the form... 

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