The IR Vibrational Properties of Composite Solids and Particles: The Lyddane-Sachs-Teller Relation Revisited

Abstract

Hot pressed zinc sulfide, dispersion hardened with diamond particles has turned out to be an ideal material in which to explore the optical complexity introduced by perhaps the simplest optical composite structure. Because the transverse vibrational mode of ZnS is IR active while that of diamond is IR inactive, the vibrational polarization properties of the resulting medium are extremely inhomogeneous at far infrared frequencies. This novel system has turned out to be extremely useful for identifying the important dynamical features underlying the optical properties of all transparent composites and complex dielectrics. One result of far ir measurements of the reststrahlen region of this system is the discovery of a generalized Lyddane-Sachs-Teller (LST) relation for solids and liquids. The characteristic dynamical frequencies are defined in terms of second moments of the relevant response functions, and very general causality arguments are used to obtain the generalized LST relation. The measured electronic excitation properties of silicon have been used to illustrate the generality of the resulting relation, which provides a useful connection between the long-wavelength dynamical behavior of nonmetallic condensed media and their static and high-frequency dielectric properties. When the characteristic vibrational frequencies of small disordered dielectric particles are described in terms of optical moments of the appropriate response functions, a generalized Fröhlich relation follows which connects the second moment of the small particle response function to the dc dielectric properties of the particle. This result is then used to obtain a new representation for the Clausius-Mossotti relation. Finally, the frequency dependent extinction cross section of an ellipsoidal particle of arbitrary size is examined from the same perspective of sum rules and optical moments. A number of general results can be found. It is demonstrated here that an extinction strength sum rule exists which directly relates the effective number of oscillators in the scattering particle to the integral over the extinction cross section spectrum, independent of particle shape. In addition, the characteristic frequency for the extinction cross section spectrum has the interesting property of being independent of particle size. It is also shown that the frequency expression characterizing the extinction properties of an ellipsoid of arbitrary size has the same form as the Fröhlich relation for small single crystal particles. The expression agrees with the generalized Fröhlich relation that relates the squared frequency characterizing the absorption behavior of an ellipsoid in the Rayleigh limit with the small particle dielectric constant. The end result is that there is a much stronger connection between the scattering and absorptive properties of a large disordered particle and the absorptive properties of a small single crystalline particle than previously recognized.