Conduction electrons nearly free electron model

Solid state physicists are familiar with the free- and nearly free-electron models of simple metals [9]. The essence of those models is the fact that the effective potential seen by the conduction electrons in metals like Na, K, etc., is nearly constant through the volume of the metal. This is so because (a) the ion cores occupy only a small fraction of the atomic volume, and (b) the effective ionic potential is weak. Under these circumstances, a constant potential in the interior of the metal is a good approximation—even better if the metal is liquid. However, electrons cannot escape from the metal spontaneously in fact, the energy needed to extract one electron through the surface is called the work function. This means that the potential rises abruptly at the surface of the metal. If the piece of metal has microscopic dimensions and we assume for simplicity its form to be spherical - like a classical liquid drop, then the effective potential confining the valence electrons will be spherically symmetric, with a form intermediate between an isotropic harmonic oscillator and a square well [10]. These simple model potentials can already give an idea of the reason for the magic numbers the formation of electronic shells. 

Y content, if one assumes the relation of 7 h =- INne, which can be derived from the nearly free-electron model, holds. Here, N is the atomic density and n is the number of electrons per atom. The strongly attractive interaction between Al and R atoms suggests that the s- and p-electrons in Al hybridize with s- and d-electrons in R, leading to a decrease of the free electrons which are attributed to electrical conductivity. As a result, the increase of the number of Al-R pairs in Al-R amorphous alloys with increasing... 

Jellium is a good model for sp metals. This group of metals comprises, amongst others, the elements Hg, Cd, Zn, Tl, In, Ga and Pb, all of which are important as electrode materials in aqueous solutions. They possess wide conduction bands with delocalized electrons, which form a quasi-free-electron gas. The jellium model cannot be applied to transition metals, which have narrow d bands with a localized character. The sd metals Cu, Ag and Au are borderline cases. Cu and Ag have been successfully treated by a modified version of jellium [3], because their d orbitals are sufficiently low in energy. This is not possible for gold, whose characteristic color is caused by a d band near the Fermi level. 

Classical Free-Electron Theory, Classical free-electron theory assumes the valence electrons to be virtually free everywhere in the metal. The periodic lattice field of the positively charged ions is evened out into a uniform potential inside the metal. The major assumptions of this model are that (1) an electron can pass from one atom to another, and (2) in the absence of an electric field, electrons move randomly in all directions and their movements obey the laws of classical mechanics and the kinetic theory of gases. In an electric field, electrons drift toward the positive direction of the field, producing an electric current in the metal. The two main successes of classical free-electron theory are that (1) it provides an explanation of the high electronic and thermal conductivities of metals in terms of the ease with which the free electrons could move, and (2) it provides an explanation of the Wiedemann-Franz law, which states that at a given temperature T, the ratio of the electrical (cr) to the thermal (k) conductivities should be the same for all metals, in near agreement with experiment ... 

De Gennes and Saint James (1963) explained the temperature variation of the spin periodicity in the HAFM structure near by the effects of conduction electrons scattering by the 4f spin disorder. EUiott and Wedgewood (1964) considered the influence of superzone boundaries introduced by the helical structure into the energy spectrum of the conduction free electrons. They showed that with an increase of the 4f spin order the value of Q should decrease and the first-order HAFM-FM transition should occur. Miwa (1965) in his model took into account both these factors. On the base of Miwa s model Umebayashi et al. (1968) obtained the following ejqiression for the pressure dependence of (p... 

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