Energy gaps dielectric models

Table 5.5 shows experimental values of E, E and the cohesive energies (from Table 5.3) for a number of AB compounds. The average energy gap results are those calculated from experimental data on high-frequency dielectric constants for the crystals. Later we will compare these values of E with those calculated from our earlier bonding models. 

From the simple band model of luminescence, it follows that fading is small if the electron traps, which produce luminescence excitation centers, have a sufficiently large energy depth. The temperature of glow peak maximum (180-260 °C) corresponds to the relatively deep centers Ea = 0.8-1.2 eV). So, the requirement of small fading leads to TL dosimetric materials being wide band gap dielectrics (Kortov 2007). 

Several conclusions can be drawn from Table 3. First, in accordance with the two-state model, /So and jSj all increase with decreasing HOMO-LUMO gap. Second, the intrinsic second-order polarizability of p-nitroaniline is increased by two-thirds when the solvent is changed from p-dioxane to methanol or A-methylpyrrolidone, even when the values are corrected for the differences in (A ). As we have adopted the value for p-nitroaniline in dioxane as a standard, it should therefore be noted that molecules that truly surpass the best performance of p-nitroaniline should have a second-order polarizability of l. p-nitroaniline (dioxane). As a third conclusion, there is a poor correlation between and the static reaction field as predicted by (91). This is in part due to the fact that the bulk static dielectric constant, E° in (89), differs from the microscopic dielectric constant. For example, p-dioxane has long been known for its anomalous solvent shift properties (Ledger and Suppan, 1967). Empirical microscopic dielectric constants can be derived from solvatochromism experiments, e.g. e = 6.0 for p-dioxane, and have been suggested to improve the estimation of the reaction field (Baumann, 1987). However, continuum models can only provide a crude estimate of the solute-solvent interactions. As an illustration we try to correlate in Fig. 7 the transition energies of p-nitroaniline with those of a popular solvent polarity indicator with negative solvatochromism. 

Fig. 6.2 Bandwidth models of solids. Electrons of atoms in solids inUxact and, when located in the same space, cannot have four identical quantum numbers (Pauli exelusion principle). Therefore, their energy splits into very elose lying levels and energy bands are created. In the diagram, only the band formed by valenee electrons (valence band) and the iimnediately higher band (conductivity band) are shown. In ceramic dielectrics and semiconductors these bands are separated by a band gap. Eg an inadmissible energy range ftn the eleetrons. Note the occupation of bands by electrons is indicated by shadowing. iEp denotes the Fermi level which equals the chemical potential of an electrons and, in a different approach, stands ftn the energy level at whieh the probability of electron occupation equals 50 %...

The apparent band gap is thus increased for small R. Tlie predicted approach of E to Eg is shown in Fig. 7. The source of such a anall approach to bulk properties seems to be caused by a strong chemical bonding. The related question is the dependence of ionization potential on size. This can be modeled by a combination of size dependence of the HOMO (as previously described) with size dependent electrostatic energy of a charged dielectric sphere. The decrease of ionization potential, which could be derived from Eq. (12), opens the possibility of controlling photochemical processes via particles (see below). 

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