Lattice vibrations electromagnetic field

Now we can consider the electromagnetic field absorption by the lattice mode (the first mode) and the intracellular one (the second mode) when the modes are perturbed by described fluctuations. We suppose that the operator in the Hamiltonian (D19) is a small perturbation that is, the fluctuation energy is smaller than the energy of regular vibrations. 

The translational modes, which are of course the only modes which can exist in simple monatomic crystals, can be treated in more detail. This is appropriate since we saw in the previous section that it is just these vibrations which are responsible for the negative expansion coefficient of ice at low temperatures. We said before that there is no exact correspondence between lattice modes and infrared spectra because of the different coupling of different modes to the electromagnetic field. With translational vibrations of... 

Absorption. Photons interact with electronic and vibrational transitions in the glass in the UV and IR regions, respectively. In the UV, absorption is due to electronic transitions across the band gap. Absorption occurs at shorter wavelengths for a larger band gap. In the IR, absorption is due to a coupling of the electromagnetic field to lattice vibrations. 

Phonons Based on an analogy between crystal lattice vibrations and those of an electromagnetic field, these particles of quantized vibrational energy were used by physicists to facilitate calculations of thermal and electrical conduction in solids. 

Conduction band electrons in metals are able to interact with an optical electric field Their motion is damped by collisions with the vibrating lattice and so some of the light energy is transferred to the lattice. In this manner the material is heated. In semiconductors the motions of both electrons in the conduction band and holes in the valence band must be considered. In dielectrics the electrons are effectively bound to the atoms or molecules that compose the material. The appUed optical field induces a polarization in the material. Upon relaxation some of the energy in the polarization is coupled to the lattice and the material is heated. These processes of absorption of energy from an optical field can be treated by classical electromagnetics. That is. Maxwell s equations, the constitutive equations of matter, and the boundary conditions for each material can be solved in each case. 

An oriented sample, such as a drawn polymer film, exhibits different vibrational spectra when the orientation of the sample relative to the direction of linear polarised electromagnetic radiation is altered. In other words, it should be borne in mind that, in the presence of polarised radiation, the relative intensities of bands may be affected. The interaction between the polarised electric field of the radiation and the dipole moment associated with the vibration becomes a maximum or minimum depending on the angle between these two vectors, 0° or 90°. Hence, in polarised light, the spectra of stretch-oriented polymers exhibit dichroism." Dichroism may also be observed in the stressed areas of a polymeric sample. The dichroic behaviour of a sample can provide information on (a) the direction of the vibrational modes, (b) the orientation of the functional group in the crystalline lattice and (c) the fraction of the perfect orientation in the oriented sample. The monitoring of the dichroism can be used to monitor the production of oriented polymeric films. This is commercially important as the physical properties of drawn samples are related to the degree of orientation. 

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