Sommerfeld theory of metals
In solid-state physics, the Sommerfeld theory (after Arnold Sommerfeld ) is the theory that describes the conduction electrons in a metal as Fermigas . Sommerfeld worked it out in 1933, thereby improving Drude's theory , which had considered conduction electrons to be a classic ideal gas .
In a Fermigas, because of the Pauli principle, the individual particles cannot have the same momentum . At temperatures very close to zero Kelvin , the electrons therefore fill a sphere ( Fermi sphere ) in the momentum space . The radius of this sphere is the momentum associated with the Fermi energy . The influence of the lattice of the atomic cores is taken into account by calculating with the effective mass instead of the true electron mass .
The Sommerfeld theory explains in particular that the contribution of the electrons to the specific heat of a metal can be neglected compared to the contribution of the atomic cores, so that the experimentally found Dulong-Petit law about the specific heat of monoatomic solids applies. On the other hand, the Drude theory is not compatible with this law.
The Sommerfeld theory also explains that the proportion of electrons in the specific heat increases proportionally to the temperature. It also gives the correct value of the constant of proportionality in the Wiedemann-Franz law and the magnitude of the thermal force in the Seebeck effect .
Individual evidence
- ^ Wissenschaft-Online-Lexika: Entry on the Sommerfeld theory of metals in the Lexicon of Physics. Retrieved August 23, 2009
literature
- Neil W. Ashcroft, ND Mermin: Solid State Physics . Saunders College Publishing, New York 1976. Chapter 2
- A. Sommerfeld, H. Bethe: electron theory of metals. In: Handbook of Physics. Vol. 24-2. Springer Verlag, Heidelberg 1933, pp. 333-622.