Crystals optical vibrations

In ionic and partially ionic crystals optic vibrations are associated with strong electric moments and hence can interact directly with the transverse electric field of incident infrared electromagnetic radiation. In terms of the phenomenological theory of infrared dispersion, if , and D are the electric field, polarization and displacement vectors respectively, then... 

The general dispersion formula obtained for the coupling of the vibrational equations with the Maxwell field can be brought into the form of Fresnel s wellknown equation for the wave normal from crystal optics. It is usually written in the form... 

The transducers most commonly employed in biosensors are (a) Electrochemical amperometric, potentiometric and impedimetric (b) Optical vibrational (IR, Raman), luminescence (fluorescence, chemiluminescence) (c) Integrated optics (surface plasmon resonance (SPR), interferometery) and (d) Mechanical surface acoustic wave (SAW) and quartz crystal microbalance (QCM) [4,12]. 

Of central importance for understanding the fundamental properties of ferroelec-trics is dynamics of the crystal lattice, which is closely related to the phenomenon of ferroelectricity [1]. The soft-mode theory of displacive ferroelectrics [65] has established the relationship between the polar optical vibrational modes and the spontaneous polarization. The lowest-frequency transverse optical phonon, called the soft mode, involves the same atomic displacements as those responsible for the appearance of spontaneous polarization, and the soft mode instability at Curie temperature causes the ferroelectric phase transition. The soft-mode behavior is also related to such properties of ferroelectric materials as high dielectric constant, large piezoelectric coefficients, and dielectric nonlinearity, which are extremely important for technological applications. The Lyddane-Sachs-Teller (LST) relation connects the macroscopic dielectric constants of a material with its microscopic properties - optical phonon frequencies ... 

Apart from acoustic phonons, which account for heat transport in insulating media, propagation of vibrational energy is usually not considered in crystals, as the dispersion of optical modes is normally very small over the Brillouin zone. However, there is an important class of optical vibrations in crystals for which spatial propagation can be the dominant property at optically accessible wave vectors. This class is identical with that of infrared active modes and its members are known as phonon-polaritons. ... 

Some interesting and important conclusions were drawn by separating the phonon spectrum in accordance with the polarization of the oscillations [15]. The whole spectrum was divided into six branches, each of which has an almost Gaussian form of the distribution curve g( ). For cubic crystals, these six branches consist of three acoustical branches (one branch of longitudinal and two branches of transverse waves) and three optical branches (one longitudinal and two transverse waves). The acoustical vibrations can be compared with the vibrations of atoms in a unit cell, and the optical vibrations with mutual oscillations of the sublattices in relation to one another. The curves of the density distribution of oscillations in each [Pg.180]

The sharp structure observed in the fundamental optical spectra of crystals, both vibrational and electronic, can be classified and interpreted by symmetry arguments based explicitly on the existence of long-range order. Indeed, this is one of the few properties of crystals which cannot be accounted for on the basis of short-range order alone If the long-range order is destroyed, the sharp structural detail, which is typical for crystals, disappears. However, the broad features of the spectra are similar if the short-range order is similar. 

The lattice component was calculated using the harmonic approximation, in which all the acoustic and low-frequency optical vibrations are included with the help of a single Debye fimction, while high-frequency crystal vibrations are taken into accoimt by Einstein s equation. According to Kelley s derivations (Gurvich et al., 1978-1984) based on the Born-von Karman d)mamic crystal lattice theory, we therefore have... 

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