Sommerfeld, electronic contribution

Another application of the concept of fractional valence bonds has been made in the field of metals and alloys. In the usual quantum mechanical discussion of metals, initiated by W. Pauli (Z. Physik, 41, 81 (1927)) and Sommerfeld (Naturwiss., 15, 825 (1927)), the assumption was made that only a small number of electrons contribute significantly to the binding together of the metal... 

The free-electron gas was first applied to a metal by A. Sommerfeld (1928) and this application is also known as the Sommerfeld model. Although the model does not give results that are in quantitative agreement with experiments, it does predict the qualitative behavior of the electronic contribution to the heat capacity, electrical and thermal conductivity, and thermionic emission. The reason for the success of this model is that the quantum effects due to the antisymmetric character of the electronic wave function are very large and dominate the effects of the Coulombic interactions. 

Specific heat. In the Fermi liquid theory, the expression for the electronic contribution to the specific heat is linear in temperature CXT) = yT, where the Sommerfeld constant is... 

A more general relation between potential and electronic pressure for a density-functional treatment of a metal-metal interface has been given.74) For two metals, 1 and 2, in contact, equilibrium with respect to electron transfer requires that the electrochemical potential of the electron be the same in each. Ignoring the contribution of chemical or short-range forces, this means that —e + (h2/ m)x (3n/7r)2/3 should be the same for both metals. In the Sommerfeld model for a metal38 (uniformly distributed electrons confined to the interior of the metal by a step-function potential), there is no surface potential, so the difference of outer potentials, which is the contact potential, is given by... 

Fig. 57. Specific heat contribution y(H) of the vortex core electrons in the mixed state (normalized by the Sommerfeld parameter /n) of the Yj[Lu jrNi2B2C samples from fig. 56 as function of the applied magnetic field (normalized by //c2(0)). The straight line y(H)

The 6th Solvay Conference on Magnetism, held in 1930,85 was opened by a contribution by Sommerfeld on Magnetism and Spectroscopy in which he discussed the angular momenta and magnetic moments of the atoms which had been derived from the investigation of their electronic constitution. 

Arnold Johannes Wilhelm Sommerfeld (1868-1951). German physicist. In addition to his pioneering work on the relationship between atomic structure and spectral lines, he made important contributions to understanding the electronic properties of metals. 

This expression will be used later on when we are calculating the contribution of the free electrons to the molar specific heat capacity of the metal at constant volume (see section 1.8.2.1). However, in order to do that, we need to know the term , which is the number of free electrons per atom of the metal. Sommerfeld s model does not provide us with this number, but Brillouin s band theory, or zone theory, can be used to evaluate it. 

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