Electronic heat capacity general

Statistical thermodynamics tells us that Cv is made up of four parts, translational, rotational, vibrational, and electronic. Generally, the last part is zero over the range 0 to 298 K and the first two parts sum to 5/2 R, where R is the gas constant. This leaves us only the vibrational part to worry about. The vibrational contr ibution to the heat capacity is... 

The electronic contribution is generally only a relatively small part of the total heat capacity in solids. In a few compounds like PrfOHE with excited electronic states just a few wavenumbers above the ground state, the Schottky anomaly occurs at such a low temperature that other contributions to the total heat capacity are still small, and hence, the Schottky anomaly shows up. Even in compounds like Eu(OH)i where the excited electronic states are only several hundred wavenumbers above the ground state, the Schottky maximum occurs at temperatures where the total heat capacity curve is dominated by the vibrational modes of the solid, and a peak is not apparent in the measured heat capacity. In compounds where the electronic and lattice heat capacity contributions can be separated, calorimetric measurements of the heat capacity can provide a useful check on the accuracy of spectroscopic measurements of electronic energy levels. 

In concluding this introduction we may observe that the majority of the heat capacity results reported in the literature have been analysed on the basis of one or other of the above discussed assumptions. Generally a least squares fit over some specified temperature range has been made within which the relative importance of the various terms has been taken into consideration. For example, for very low temperatures (v.l.t.), below around 0.5 K, say, the nuclear term is clearly dominant when it exists. There is danger, on the other hand, in putting too much stress on graphical analysis, as we have considered in section 1.5 above, for we must be clear as to what part of the linear T and cubic terms are attributable to the unenhanced electronic and lattice terms, respectively, as presented in sections 1.2 and 1.3 above. There have been some theoretical... 

Metals provided additional problems for the classical theory of heat capacity. Metals are generally much better conductors of heat than nonmetals because most of the heat is carried by the free electrons. According to the classical theory, this electron gas should contribute an additional (3/2)R to the heat capacity. But the measured heat capacity of metals approached nearly the same 3R Dulong-Petit limit as the nonmetals. How can the electrons be a major contributor to the thermal conductivity and not provide significant additional heat capacity ... 

Metals generally have higher thermal conductivity than nonmetals because of the presence of free electrons, but the electrons do not contribute to the heat capacity as they would be expected to form classical considerations. The low heat capacity is compensated by the high Fermi velocity, so the conductivity calculated using quantum mechanics is almost the same as the classical result. 

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