Origin of the insulating state

While the classical models can reproduce and sometimes predict some structural properties, they are unable to inform about the electronic characteristics of insulators, because they assume that the electrons are frozen around the ionic cores. The next step consists in finding the microscopic origin of the forbidden gap present in the electronic excitation spectrum, which is the defining property of the insulating state. 

The gap width is fixed by the electronic excitation of lowest energy. Starting from a classical model with localized electrons, two types of excitations may be considered. 

Charge-transfer excitation When an electron is transferred from an anion to a cation, a charge-transfer excitation is produced  

The charge-transfer energy A is related to the cation th ionization potential / and to the oxygen second electronic affinity A2. To a first 

Cation charge fluctuation A second type of excitation may occur when two cations exchange an electron. Its energy U is associated with the reaction  

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The origin of the short lifetime on glass is not as clear. We attributed to injection and suggested that surface states, or some other localized states near the surface, serve as electron acceptors on insulators as well as on semiconductors (18,27). Kemnitz et al. (12,25) proposed instead that "irregular" surface sites enhance internal conversion and lead to t-, while "ideal" sites hinder internal conversion and lead to These authors... 

Statement of the problem. Let us consider the problem of a steady-state thermocapillary motion in a liquid layer of thickness h. The motion is assumed to be two-dimensional. The dependence of the surface tension on temperature is assumed to be quadratic according to (5.9.19). The thermogravitational effect is not taken into account. It is assumed that the linear temperature distribution is maintained on the hard lower surface, and the plane surface of the layer is thermally insulated. The origin of the Cartesian coordinates X, Y is placed on the solid surface at the point with temperature To. The velocity and temperature fields are described by Eqs. (5.9.1)-(5.9.4) with jg = 0. 

Recent studies by Zaanen, Sawatzky, and Allen have made it clear that the origin of the metal-insulator transition in transition-metal compounds, discussed in Section 19-B, is not associated with the s- to f-state promotion to which we attributed it and nothing from that section should be used without considering these more recent and complete studies. 

Since bulk CdS shows free-exciton emission at low temperatures [34], it is interesting to compare these results on CdS with the discussion in Sect. 3.3.9b on the transition from semiconductors to insulators. There it was shown that narrow-line free-exciton emission transforms into broad-band localized emission, if the amount of delocalization of the excited state decreases. Since the valence band to conduction band transition of CdS is in principle a - Cd " " charge-transfer transition, this would bring the discussion on CdS in line with results from a different origin (see Sect. 3.3.9b). By all means the case of Cd32S 4(SC(,Hs)35.DMF4 is a nice example of luminescence research on a well-defined cluster showing the quantum-size effect. 

Another example is insulators for cable connectors which have been previously injection moulded from LR or HTV. Then, they are expanded and held in that state by a plastic spiral which is removed when it is applied onto the cable (thus retaining the original shape of the insulator). A large number of similar applications can be found in the automotive, medical fields, etc. 

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