Limiting-phonon velocity

As the fluid is cooled further towards the glass transition the phonon velocities reach their limiting frequency values (13) ... 

Phonon velocity is constant and is the speed of sound for acoustic phonons. The only temperature dependence comes from the heat capacity. Since at low temperature, photons and phonons behave very similarly, the energy density of phonons follows the Stefan-Boltzmann relation oT lvs, where o is the Stefan-Boltzmann constant for phonons. Hence, the heat capacity follows as C T3 since it is the temperature derivative of the energy density. However, this T3 behavior prevails only below the Debye temperature which is defined as 0B = h( DlkB. The Debye temperature is a fictitious temperature which is characteristic of the material since it involves the upper cutoff frequency ooD which is related to the chemical bond strength and the mass of the atoms. The temperature range below the Debye temperature can be thought as the quantum requirement for phonons, whereas above the Debye temperature the heat capacity follows the classical Dulong-Petit law, C = 3t)/cb [2,4] where T is the number density of atoms. The thermal conductivity well below the Debye temperature shows the T3 behavior and is often called the Casimir limit. 

Phonon transport is the main conduction mechanism below 300°C. Compositional effects are significant because the mean free phonon path is limited by the random glass stmcture. Estimates of the mean free phonon path in vitreous siUca, made using elastic wave velocity, heat capacity, and thermal conductivity data, generate a value of 520 pm, which is on the order of the dimensions of the SiO tetrahedron (151). Radiative conduction mechanisms can be significant at higher temperatures. 

Dislocations move when they are exposed to a stress field. At stresses lower than the critical shear stress, the conservative motion is quasi-viscous and is based on thermal activation that overcomes the obstacles which tend to pin the individual dislocations. At very high stresses, > t7crit, the dislocation velocity is limited by the (transverse) sound velocity. Damping processes are collisions with lattice phonons. 

Here, r = t( f) is the relaxation time of those conduction electrons which have acquired the additional momentum hSkx on the Fermi surface and relax back to thermal equilibrium after the electric field is switched off. This relaxation process is an inelastic scattering process in which the electrons which occupy a state A on the Fermi surface, that is, which have wavevectors kp, are scattered into unoccupied states B on the Fermi surface (Fig. 8.5). This scattering can be with a phonon, with a statistical lattice defect, or with an impurity. In a simple metal, the scattering occurs only for the electrons at the Fermi energy, and thus only those electrons which move with the Fermi velocity determine the mobility, and together with it and the concentration n of all the charge carriers, then limit the specific conductivity. 

The magnetoelastic anomalies in sound velocities as discussed in previous sections are only the long-wavelength limit of 4f electron-phonon coupling effects. Very interesting consequences of this coupling also occur for high-... 

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