Sommerfeld’s model

Further development of Sommerfeld s theory of metals would extend well outside the intended scope of this textbook. The interested reader may refer to any of several books for this (e.g. Seitz, 1940). Rather, this book will discuss the band approximation based upon the Bloch scheme. In the Bloch scheme, Sommerfeld s model corresponds to an empty lattice, in which the electronic Hamiltonian contains only the electron kinetic-energy term. The lattice potential is assumed constant, and taken to be zero, without any loss of generality. The solutions of the time-independent Schrodinger equation in this case can be written as simple plane waves, = exp[/A r]. As the wave function does not change if one adds an arbitrary reciprocal-lattice vector, G, to the wave vector, k, BZ symmetry may be superimposed on the plane waves to reduce the number of wave vectors that must be considered ... 

Sommerfeld s model is perfectly well suited for chemical applications - particularly for determining specific heat capacities -but it is totally unsuited for explaining the electrical properties and the experimental fact that not all energy levels are acceptable in the metal. It was the band theory, developed by Brillouin, which was first able to explain these properties and also the nature of the bond between the metal atoms with the introduction of a periodic field. 

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. 

---

See also in sourсe #XX -- [ , ]

---