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As the rules of quantum mechanics apply to all the different vibrational modes in the solid, the lattice pulsates as a complete assembly in discrete energy steps, or thermal phonons. According to the kinetic theory of solids, a phonon is a quantized mode of vibration occurring in a rigid crystal lattice. The study of phonons is an important part of solid state physics, because phonons play a major role in many of the physical properties of solids, including a material's thermal and electrical conductivity.
The phonon is related to both the frequency of vibration and the temperature. If the temperature is raised, the amplitude of vibration increases. The concept of the phonon is therefore considered as the quantum of lattice vibrational energy onto which is superimposed a complex pattern of standing and/or traveling waves that represent changes in temperature. If the solid is at a uniform temperature, the standing wave concept is adequate as the phonon vibrations are uniformly distributed.
Multi-phonon absorption occurs when two or more phonons simultaneously interact to produce electric dipole moments with which the incident radiation may couple. These dipoles can absorb energy from the incident radiation, reaching a maximum coupling with the radiation when the frequency is equal to the vibrational mode of the molecular dipole (e.g. Si-O bond in quartz) in the far-infrared spectral region.
All of the resonant absorption processes involved in an optically transparent material can be explained by the same common principle. At particular frequencies, the incident radiation is allowed to propagate through the lattice producing the observed transparency. Other frequencies however, are forbidden when the incident radiation is at resonance with any of the properties of the lattice material (e.g. molecular vibrational frequencies), and as such are transferred as thermal energy, exciting the atoms or electrons.
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