Band theory level

Color from Color Centers. This mechanism is best approached from band theory, although ligand field theory can also be used. Consider a vacancy, for example a missing CF ion in a KCl crystal produced by irradiation, designated an F-center. An electron can become trapped at the vacancy and this forms a trapped energy level system inside the band gap just as in Figure 18. The electron can produce color by being excited into an absorption band such as the E transition, which is 2.2 eV in KCl and leads to a violet color. In the alkaU haUdes E, = 0.257/where E is in and dis the... 

The high electrical conductivity of metals as well as the high electron (and hole) mobility of inorganic covalently bound semiconductors have both been clarified by the band theory [I9, which slates that the discrele energy levels of individual atoms widen in the solid stale into alternatively allowed and forbidden bands. The... 

Therefore, there could exist rich defects in Ba3BP30i2, BaBPOs and Ba3BP07 powders. From the point of energy-band theory, these defects will create defect energy levels in the band gap. It can be suggested that the electrons and holes introduced by X-ray excitation in the host might be mobile and lead to transitions within the conduction band, acceptor levels, donor levels and valence band. Consequently, some X-ray-excited luminescence bands may come into being. 

In order to explain the changing optical properties of AIROFs several models were proposed. The UPS investigations of the valence band of the emersed film support band theory models by Gottesfeld [94] and by Mozota and Conway [79, 88]. The assumption of nonstoichiometry and electron hopping in the model proposed by Burke et al. [87] is not necessary. Recent electroreflectance measurements on anodic iridium oxide films performed by Gutierrez et al. [95] showed a shift of optical absorption bands to lower photon energies with increasing anodic electrode potentials, which is probably due to a shift of the Fermi level with respect to the t2g band [67]. 

According to band theory, the electrons inside a metal populate the valence band up to the highest occupied molecular orbital, which is called the Fermi level. The potential applied to a metallic electrode governs the energy of its electrons according to Figure 5. 

The free-electron model is a simplified representation of metallic bonding. While it is helpful for visualizing metals at the atomic level, this model cannot sufficiently explain the properties of all metals. Quantum mechanics offers a more comprehensive model for metallic bonding. Go to the web site above, and click on Web Links. This will launch you into the world of molecular orbitals and band theory. Use a graphic organizer or write a brief report that compares the free-electron and band-theory models of metallic bonding. 

Chapter 4 discussed semiconductivity in terms of band theory. An intrinsic semiconductor has an empty conduction band lying close above the filled valence band. Electrons can be promoted into this conduction band by heating, leaving positive holes in the valence band the current is carried by both the electrons in the conduction band and by the positive holes in the valence band. Semiconductors, such as silicon, can also be doped with impurities to enhance their conductivity. For instance, if a small amount of phosphorus is incorporated into the lattice the extra electrons form impurity levels near the empty conduction band and are easily excited into it. The current is now carried by the electrons in the conduction band and the semiconductor is known as fl-type n for negative). Correspondingly, doping with Ga increases the conductivity by creating positive holes in the valence band and such semiconductors are called / -type (p for positive). 

The above simple picture of solids is not universally true because we have a class of crystalline solids, known as Mott insulators, whose electronic properties radically contradict the elementary band theory. Typical examples of Mott insulators are MnO, CoO and NiO, possessing the rocksalt structure. Here the only states in the vicinity of the Fermi level would be the 3d states. The cation d orbitals in the rocksalt structure would be split into t g and eg sets by the octahedral crystal field of the anions. In the transition-metal monoxides, TiO-NiO (3d -3d% the d levels would be partly filled and hence the simple band theory predicts them to be metallic. The prediction is true in TiO... 

The energy states of gaseous atoms split because of the overlap between electron clouds. Obviously, therefore, atoms must come much closer before the clouds of the core electrons begin to overlap compared with the distance at which the clouds of outer (or valence) electrons overlap (Fig. 6.119). Hence, at the equilibrium interatomic distances, the energy levels of the core electrons (in contrast to the valence electrons) do not show any band structure and therefore will be neglected in the following discussion. This simplified picture of the band theory of solids will now be used to explain the differences in conductivity of metals, semiconductors, and insulators. 

Many ferromagnets are metals or metallic alloys with delocalized bands and require specialized models that explain the spontaneous magnetization below Tc or the paramagnetic susceptibility for T > Tc. The Stoner-Wohlfarth model,6 for example, explains these observed magnetic parameters of d metals as by a formation of excess spin density as a function of energy reduction due to electron spin correlation and dependent on the density of states at the Fermi level. However, a unified model that combines explanations for both electron spin correlations and electron transport properties as predicted by band theory is still lacking today. 

Molecular orbital (MO) theory has been used to explain the bonding in metallic crystals, such as pure sodium or pure aluminum. Each MO, instead of dealing with a few atoms in a typical molecule, must cover the entire crystal (might be 1020 or more atoms ). Following the rule that the number of MOs must equal the number of atomic orbitals (AOs) combined, this many MOs must be so close on an energy level diagram that they form a continuous band of energies. Because of this factor, the theory is known as band theory. 

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