Free-electron theory of metals

This rule conforms with the principle of equipartition of energy, first enunciated by Maxwell, that the heat capacity of an elementary solid, which reflected the vibrational energy of a three-dimensional solid, should be equal to 3RJK-1 mol-1. The anomaly that the free electron theory of metals described a metal as having a three-dimensional structure of ion-cores with a three-dimensional gas of free electrons required that the electron gas should add another (3/2)R to the heat capacity if the electrons behaved like a normal gas as described in Maxwell s kinetic theory, whereas the quantum theory of free electrons shows that these quantum particles do not contribute to the heat capacity to the classical extent, and only add a very small component to the heat capacity. 

The free-electron theory of metals was developed in three main stages (1) classical free-electron theory, (2) quantum free-electron theory, and (3) band theory. 

The molecular orbital treatment of a crystalline solid considers the outer electrons as belonging to the crystal as a whole (10,11). Sommer-feld s early free electron theory of metals neglected the field resulting... 

ELECTRON GAS. The term electron gas is used to denote a system of mobile electrons, as. for example, the electrons in a metal that are free to move. In the free electron theory of metals, these electrons move through the metal in the region of nearly uniform positive potential created by the ions of the crystal lattice. This theory when modified by the Pauli exclusion principle, serves to explain many properties of metals, especially the alkali metals. For metals with more complex electronic structure, and semiconductors, the band theory of solids gives a better picture. 

The success of the simple free electron theory of metals was so staking that it was natural to ask how the same ideas could be apphed to other types of solids, such as semiconductors and insulators. The basic assumption of the free electron theory is that the atoms may be stopped of their outer electrons, the resulting ions arranged in the crystalline lattice, and the electrons then poured into the space between. 

THE MODERN THEORY OFSOLIDS, Frederick Seitz. First inexpensive edition of classic work on theory of ionic crystals, free-electron theory of metals and semiconductors, molecular binding, much more. 736pp. 55 x 814. 

The electronic structure of metals and metallic surfaces are interpreted by the free-electron theory of metals [1, 2]. 

Let us now introduce the further assumptions valid in the free-electron theory of metals which are due to the translational symmetry ... 

As was indicated earlier in this article, a detailed microscopic understanding of the phenomena underlying electrolysis took a very long time to mature and depended on postulation, proof and acceptance of such concepts as spontaneous ionization in solution, ionic hydration, free ion mobility in solution and the free-electron theory of metals. 

In the free-electron theory of metals, the valence electrons of a nontransition metal are treated as noninteracting particles in a box, the sides of the box being the surfaces of the metal. This approximation, though crude, gives fairly good results for some properties of metals. 

In Eq. 3.4, a relates to the electron structure and scattering in the metal. From the free electron theory of metal, Fermi velocity is defined as the fi ee electron movement velocity at the highest energy (E ), and the relaxation time r is the time between the first and second collisions of the electron. So the electron mean free path Ip nearby the Fermi surface can be expressed as Ip = v t. In addition, o can be also expressed as below " ... 

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