Degeneracy temperature

K). T is the measurement temperature and Tq is the "degeneracy temperature," equal to kEo, where k is the Boltzmann constant. According to a two-dimensional electron gas model for graphitic carbons (see ref. 2a), is the energy "shift" from the Fermi level (Ep), to the top of the valence band. Small values of To ( <344 K) and consequently of Eq signify a more perfect graphite... 

The formation of more carriers win involve energies of order zl, so we expect two degeneracy temperatures, 7i and T2, where T2 is given by... 

Some specific heats are shown in Fig. 6.4. They are about three times that for palladium and would imply a bandwidth of 600 K ( 2oeV) if interpreted by a model without correlation. Figure 6.5 (Mott and Jones 1936) shows that Cv should tend to a constant value at about one-third of the degeneracy temperature. 

The T2 term in the resistivity p of metallic V203 above 20kbar, first observed by McWhan and Rice (1969), is shown in Fig. 6.7. It will be noticed that there is some tendency for p to saturate above 300 K as for Landau-Baber scattering with a low degeneracy temperature (Chapter 2). 

Fig. 6.5 Specific heat of a degenerate gas as a function of temperature when the degeneracy temperature is exceeded (Mott and Jones 1936).

We think that all these observations are to be explained by the assumption that metallic V203 is a highly correlated electron gas, as first suggested by Brinkman and Rice (1970b) and described in Chapter 4. The very low degeneracy temperature suggests that there may also be some mass enhancement of the carriers by polaron formation. Two electrons per atom would just half fill an ej band, so that the number of electron-like and hole-like carriers would be... 

Hall effect measurements are reported for three single crystals of the charge transfer salt HMTSF-TCNQ in the temperature range 1.4-200 K at ambient pressure and under hydrostatic pressures of approximately 6 Kbars. There is evidence that the high conductivity of this material at low temperatures arises from a small number of electrons with a high mobility and a low degeneracy temperature as suggested by other experiments and a recent band-structure calculation. 

To summarise, it seems clear that at low T the conductivity of HMTSF TCNQ arises from small pockets of electrons with a degeneracy temperature of about 2CK and there is mounting evidence that these are an intrinsic property of the material. The proposed band structure accounts for many of the experimental observations but a number of problems remain. One interesting experiment is X-ray diffuse scattering at low T. It is known that there is a longitudinally polarised "2kp" soft phonon down to 100, if this condenses to... 

These results do not agree with experimental results. At room temperature, while the translational motion of diatomic molecules may be treated classically, the rotation and vibration have quantum attributes. In addition, quantum mechanically one should also consider the electronic degrees of freedom. However, typical electronic excitation energies are very large compared to k T (they are of the order of a few electronvolts, and 1 eV corresponds to 10 000 K). Such internal degrees of freedom are considered frozen, and an electronic cloud in a diatomic molecule is assumed to be in its ground state f with degeneracy g. The two nuclei A and... 

The arc and spark spectra of the individual lanthanides are exceedingly complex. Thousands of emission lines are observed. For the trivalent rare-earth ions in soUds, the absorption spectra are much better understood. However, the crystal fields of the neighboring atoms remove the degeneracy of some states and several levels exist where only one did before. Many of these crystal field levels exist very close to a base level. As the soUd is heated, a number of the lower levels become occupied. Some physical properties of rare-earth metals are thus very sensitive to temperature (7). 

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