Free or conduction electrons

When applied to the motion of ions in a crystal, the term drift applies to motion of ions under the influence of an electric field. Although movement of electrons in conduction bands determines conductivity in metals, in ionic compounds it is the motion of ions that determines the electrical condu-ctivity. There are no free or mobile electrons in ionic crystals. The mobility of an ion, ji, is defined as the velocity of the ion in an electric field of unit strength. Intuitively, it seems that the mobility of the ion in a crystal should be related to the diffusion coefficient. This is, in fact, the case, and the relationship is... 

There exist no free or Fermi electrons in glass, which is considered to be a semiconductor with a very low specific conductivity (10 to 10 ohm cm. i). The question then arises Where do the secondary electrons originate in ozonizer tubes when the discharge enters the self-maintained region ... 

The electronic absorption spectra of nanocrystals of metals is dominated by the surface plasmon band which arises due to the collective coherent excitation of the free electrons within the conduction band [66-69]. A schematic illustration of the electric field component of an incoming light wave inducing a polarization of the free or itinerant electrons is shown in Fig. 1.15. It corresponds to the dipolar excitation mode which is the most relevant for particles whose diameters are much less than the wavelength of light. However, higher order excitations are possible and come into play for nanocrystals with diameters in the range of tens of nanometers. 

In a real system, the positron exists in different states. It may annihilate either with valence or conduction electrons of the bulk. These processes give rise to a bulk annihilation rate Ab. It may also be trapped in various defect states Dj where the electron density is smaller than in the bulk, i.e. a single vacancy, a cluster of vacancies, dislocations, impurities etc. Each defect state will be characterized by an annihilation rate Dj- In a vacancy-like defect the trapped-positron lifetime is increased compared to free positrons aimihilating in the bulk, as the electron density is locally reduced. Each defect state leads to a different lifetime Tdj = 1/Ap,. 

The ordered moments of all compounds are distinctly below the free-ion value, gj = 3.4. Apparently the 5f electrons are not completely localized and their magnetic moment is washed out by hybridization with valence or conduction electrons. This effect gets more pronounced with decreasing interatomic distances. The chalcogenides show a stronger tendency towards hybridization, probably due to their unbound valence electrons. 

The electric neutrality is ensured by free or trapped electrons and conductivity cr is expressed as (indicating the mobility of the electrons by p)... 

Instead of depending on the thermally generated carriers just described (intrinsic conduction), it is also possible to deUberately incorporate various impurity atoms into the sihcon lattice that ionize at relatively low temperatures and provide either free holes or electrons. In particular. Group 13 (IIIA) elements n-type dopants) supply electrons and Group 15 (VA) elements (p-type dopants) supply holes. Over the normal doping range, one impurity atom supphes one hole or one electron. Of these elements, boron (p-type), and phosphoms, arsenic, and antimony (n-type) are most commonly used. When... 

The third group is the continuum, models, and these are based on simple concepts from classical electromagnetism. It is convenient to divide materials into two classes, electrical conductors and dielectrics. In a conductor such as metallic copper, the conduction electrons are free to move under the influence of an applied electric field. In a dielectric material such as glass, paraffin wax or paper, all the electrons are bound to the molecules as shown schematically in Figure 15.2. The black circles represent nuclei, and the electron clouds are represented as open circles. 

We begin with a presentation of the ideas of the electronic structure of metals. A liquid or solid metal of course consists of positively charged nuclei and electrons. However, since most of the electrons are tightly bound to individual nuclei, one can treat a system of positive ions or ion cores (nuclei plus core electrons) and free electrons, bound to the metal as a whole. In a simple metal, the electrons of the latter type, which are treated explicitly, are the conduction electrons, whose parentage is the valence electrons of the metal atoms all others are considered as part of the cores. In some metals, such as the transition elements, the distinction between core and conduction electrons is not as sharp. 

For the conduction electrons, it is reasonable to consider that the inner-shell electrons are all localized on individual nuclei, in wave functions very much like those they occupy in the free atoms. The potential V should then include the potential due to the positively charged ions, each consisting of a nucleus plus filled inner shells of electrons, and the self-consistent potential (coulomb plus exchange) of the conduction electrons. However, the potential of an ion core must include the effect of exchange or antisymmetry with the inner-shell or core electrons, which means that the conduction-band wave functions must be orthogonal to the core-electron wave functions. This is the basis of the orthogonalized-plane-wave method, which has been successfully used to calculate band structures for many metals.41... 

In addition to the effect of the nonideality of the metal on the electrolyte phase, one must consider the influence of the electrolyte phase on the metal. This requires a model for the interaction between conduction electrons and electrolyte species. Indeed, this interaction is what determines the position of electrolyte species relative to the metal in the interface. Some of the work described below is concerned with investigating models for the electrolyte-electron interaction. Although we shall not discuss it, the penetration of water molecules between the atoms of the metal surface may be related3 to the different values of the free-charge or ionic contribution to the inner-layer capacitance found for different crystal faces of solid metals. Rough calculations have been done to... 

In band theory the electrons responsible for conduction are not linked to any particular atom. They can move easily throughout the crystal and are said to be free or very nearly so. The wave functions of these electrons are considered to extend throughout the whole of the crystal and are delocalized. The outer electrons in a solid, that is, the electrons that are of greatest importance from the point of view of both chemical and electronic properties, occupy bands of allowed energies. Between these bands are regions that cannot be occupied, called band gaps. 

When the size of metals is comparable or smaller than the electron mean free path, for example in metal nanoparticles, then the motion of electrons becomes limited by the size of the nanoparticle and interactions are expected to be mostly with the surface. This gives rise to surface plasmon resonance effects, in which the optical properties are determined by the collective oscillation of conduction electrons resulting from the interaction with light. Plasmonic metal nanoparticles and nanostructures are known to absorb light strongly, but they typically are not or only weakly luminescent [22-24]. 

In metals, valence electrons are conduction electrons, so they are free to move along the solid. On the contrary, valence electrons in insulators are located around fixed sites for instance, in an ionic solid they are bound to specific ions. Semiconductors can be regarded as an intermediate case between metals and insulators valence electrons can be of both types, free or bound. 

This notion of occasional ion hops, apparently at random, forms the basis of random walk theory which is widely used to provide a semi-quantitative analysis or description of ionic conductivity (Goodenough, 1983 see Chapter 3 for a more detailed treatment of conduction). There is very little evidence in most solid electrolytes that the ions are instead able to move around without thermal activation in a true liquid-like motion. Nor is there much evidence of a free-ion state in which a particular ion can be activated to a state in which it is completely free to move, i.e. there appears to be no ionic equivalent of free or nearly free electron motion. 

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