Phonons Debye temperature

Finally, it can be shown from dre quantum dreoiy of vibrational energy in dre solid state drat, at temperatures above dre Debye temperature 0d, dre density of phonons, p, is inversely related to 6 according to dre equation... 

The Debye temperatures of stages two and one were determined by inelastic neutron scattering measurements [33], The total entropy variation using equation 8 is in the order of about 2 J/(mol.K). Although smaller in value, such variation accounts for 10-15% of the total entropy and should not be neglected. We are currently carrying on calculations of the vibrational entropy from the phonon density of states in LixC6 phases. 

In the following, we shall describe separately the temperature dependence of the contributions to the thermal conductivity for the two heat carriers . In the case of phonons, the Debye temperature 0D will be taken as a reference in analysing the temperature dependence of the thermal conductivity. 

Low-temperature (T < 1K) heat conduction of a pure metal, like copper of our experiment (Cu Debye temperature 0D 340K), is mostly electronic [27] and the phonon contribution should be negligible. With the latter hypothesis, in the 30-150 mK temperature range ... 

Since in our temperature range, the Debye temperature of Ge is 370K [47], the phonon contribution to the heat capacity can be neglected. Hence, the heat capacity of our samples is expected to follow the equation ... 

When Wqi / Wq2 the magnetization recovery may appear close to singleexponential, but the time constant thereby obtained is misleading [50]. The measurement of 7) of quadrupolar nuclei under MAS conditions presents additional complications that have been discussed by comparison to static results in GaN [50]. The quadrupolar (two phonon Raman) relaxation mechanism is strongly temperature dependent, varying as T1 well below and T2 well above the Debye temperature [ 119]. It is also effective even in cases where the static NQCC is zero, as in an ideal ZB lattice, since displacements from equilibrium positions produce finite EFGs. 

Recoilless Optical Absorption in Alkali Halides. Recently Fitchen et al (JO) have observed zero phonon transitions of color centers in the alkali halides using optical absorption techniques. They have measured the temperature dependence of the intensity of the zero phonon line, and from this have determined the characteristic temperatures for the process. In contrast to the Mossbauer results, they have found characteristic temperatures not too different from the alkali halide Debye temperatures. 

The inelastic collisions can be either with another electron, when TjOcT-2 (cf. Section 10) or with phonons, when above the Debye temperature TjOcT-1. 

At higher temperatures, scattering by phonons, always an inelastic process, will in most cases determine L. For temperatures above the Debye temperature... 

Similar expressions can be generated for holes simply by letting coc - — relaxation time xB needs justification, which will not be attempted here. Suffice it to say that this assumption is not bad for elastic scattering processes, which include most of the important mechanisms. A well-known exception is polar optical-phonon scattering, at temperatures below the Debye temperature (Putley, 1968, p. 138). We have further assumed here that t is independent of energy, although this condition will be relaxed later. 

Zimmermann and Konig211) introduce the phonon contribution of the lattice by a Debye model with an interpolated Debye temperature... 

The experimentally measured specific heat of metal group III nitrides and the phonon determined specific heat for several chosen Debye temperatures are presented in FIGURE 1. 

As a good approximation it is assumed, that the adsorbed species are vibrating in resonance with the lattice phonon vibrations of the solid stationary phase. The phonon frequency can be evaluated from phonon spectra, from the standard entropy of solid metals, from the Debye temperatures or from the Lindemann equation [9]. 

N is Avogadro s number and is the Debye temperature) and whose intercept at T = 0 is y. In the Debye model, the slope has a dependency (actually, r" for an n-dimen-sional solid) owing to the lattice or phonon contribution to the heat capacity. Of course, the heat capacity normally measured is Cp, the heat capacity at constant pressure. However, for solids the difference between Cp and Cy is typically less than 1 percent at low temperatures and thus can be neglected. 

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