Thermal disorder frozen

Distortions of the First Kind and Thermal Disorder. In crystallography the best-known example for a lattice distortion of the first kind is the reduction of peak intensity from random temperature movement of the atoms. In materials science a frozen-in thermal disorder of nanostructures25 is observed as well. The result of this kind of disorder is a multiplicative26 attenuation of the scattering intensity by the Debye-Waller factor... 

Thermally-induced network vibrations broaden the absorption edge and shift the band gap of semiconductors. The thermal disorder couples to the optical transition through the deformation potential, which describes how the electronic energy varies with the displacement of the atoms. The bond strain in an amorphous material is also a displacement of atoms from their ideal position, and can be described by a similar approach. The description of static disorder in terms of frozen phonons is a helpful concept which goes back 20 years. Amorphous materials, of course, also have the additional disordering of the real phonon vibrations. 

That the first stage of ordering (resistivity decrease) is correlated with excess vacancies not being in thermal equilibrium can be seen from measurement during isochronally lowering the temperature from the disordered state (0), which shows that atomic mobility is frozen below 280°C. 

According to the theory of the Urbach absorption edge in crystals, the slope E is proportional to the thermal displacement of atoms r(7). The frozen phonon model assumes that an amorphous semiconductor has an additional temperature independent term, r , representing the displacements which originate from the static disorder, so that... 

Colomban, P, Courret, H., Remain, F., Gouadec, G., and Michel, D., Sol-gel prepared pure and Li-doped hexacelsian polymorphs. An infrared, Raman and thermal expansion study of -phase stabilization by frozen short-range disorder, J. Am. Ceram. Soc., 83, 2974, 2000. 

Because the diffraction experiment involves the average of a very large number of unit cells (of the order of 10 in a crystal used for X-ray diffraction analysis), minor static displacements of atoms closely simulate the effects of vibrations on the scattering power of the average atom. In addition, if an atom moves from one disordered position to another, it will be frozen in time during the X-ray diffraction experiment. This means that atomic motion and spatial disorder are difficult to separate from each other by simple experimental measurements of intensity falloff as a function of sm6/X. For this reason, atomic displacement parameter is considered a more suitable term than the terms that have been used historically, such as temperature factor, thermal parameter, or vibration parameter for each of the correction factors included in the structure factor equation. A displacement parameter may be isotropic (with equal displacements in all directions) or anisotropic (with different values in different directions in the crystal). 

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