Simple trapping model

In practical situations any intermediate case is possible. In the case of the transition-limited regime, the link between positron states in the specimen and the experimental positron lifetime spectrum is provided by the simple trapping model (STM) [103]. Let m t) denote the probability that positron will be present in the specimen at time t. In the case of an ideal crystal i.e., if no defect is present in the specimen), positrons will be delocalised in the material. The time when positron thermalisa-tion is accomplished is chosen as t = 0, so m t = 0) = 1. The probability m t) decreases exponentially with time ... 

The simple trapping model (STM) can be used to interpret the results from PL measurements [129], According to this model, for positrons implanted into a homogeneous solid with a bulk lifetime z, = 1/Ab and with N different kinds of homogeneously distributed microscopic defects with lifetimes Xi = jA and trapping rates ki, the annihilation spectrum will consist of A +1 exponentials. Through defect trapping, the bulk lifetime will be reduced to tq = l/(Ab -I- k), where... 

The ability to detect discrete rovibronic spectral features attributed to transitions of two distinct conformers of the ground-state Rg XY complexes and to monitor changing populations as the expansion conditions are manipulated offered an opportunity to evaluate the concept of a thermodynamic equilibrium between the conformers within a supersonic expansion. Since continued changes in the relative intensities of the T-shaped and linear features was observed up to at least Z = 41 [41], the populations of the conformers of the He - lCl and He Br2 complexes are not kinetically trapped within a narrow region close to the nozzle orifice. We implemented a simple thermodynamic model that uses the ratios of the peak intensities of the conformer bands with changing temperature in the expansion to obtain experimental estimates of the relative binding energies of these complexes [39, 41]. 

All attempts (74,89) to find a sensible, quantitative relation between the wavelength of maximum absorption ( max) and typical macroscopic properties of the solvent (i.e., dielectric constant) have so far failed (146). However, the size of the solvent cavity in which the electron is trapped also plays a decisive role (101) in determining the transition energy [Eqs. (2), (3)], and the solvent dependence of A.max might well indicate a variation in cavity size from solvent to solvent. In this spirit, Dorfman and Jou (48) have evaluated cavity radii on the basis of the simple Jortner model for the solvated electron. The values are shown in Fig. 3, which shows a plot of the optical transition energy max versus... 

However, there is no molecular trapping in this system, so the Arrhenius behaviour does not come from full or partial thermalization prior to dissociation. A simple analytic model provides an explanation for this behaviour. We assume that the main effect of increasing the energy in the surface oscillator is to downshift the threshold for the rotational or vibrational transition. If we make a linear approximation... 

In this chapter, several simple flow models will be considered for different structures of the easily penetrable roughness. Generally, two EPR structures will be investigated. In Section 3.1, it will be taken for simplicity that the EPR consists of small spheres trapped in the volume. Therefore, no equations will be required for characterizing the medium of obstruction . This structure is called the EPR made up of immobile elements . In contrast, the obsUuctions in Section 3.2 will be allowed to move along the wind ( EPR made up of mobile elements , or Droplet EPR ). Analytical solutions will be derived whenever it is possible. 

As shown in Fig. 7.26, when the sensor is exposed to vapor, individual molecules can diffuse into the semiconductor thin film and be adsorbed mostly at the grain boundaries [13], If the adsorbed analytes have large dipole moment, such as H2O ( 2 debye) and DMMP ( 3 debye), the adsorption of those analyte molecules at the grain boundaries close to or at the semiconductor-dielectric interface can locally perturb the electrical profile around the conduction channel, and hence change the trap density in the active layer. We can interpret the trapping effects by a simple electrostatic model discussed briefly in Sect. 7.2. The electric field induced by a dipole with dipole moment of p (magnitude qL in Fig. 7.4) is ... 

The Prigogine simple cell model (P) considers each monomer in the system to be trapped in the cell created by its surroundings. The general cell potential, generated by the surroundings, is simplified to be athermal (cf. free volume theory), whereas the mean potential between the centers of different cells are described by the Leimard-Jones 6-12 potential. The P model EoS can be summarized as... 

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). 

Simple DFT Model of Clusters Embedded in Rare Gas Matrix Trapping Sites and Spectroscopic Properties of Na Embedded in Ar. 

If simple band models are assumed for an-T and the contacts, materials like the noble metals with a workfunction of 5.3eV (Au) or 5.6 eV (Pt) lead to ohmic contacts whereas materials with low workfunctions as A1 (4.28 eV), Mg (3.66 eV), or Ca (2.87 eV) form Schottky barriers. The rectification ratio I(- -U)/I(-U) was determined for endcapped a-6T in a LED device to be 240 for Ca, 7 for Mg, and 40 for A1 [330]. This shows that the work function is not the only factor influencing the Schottky barrier height, but that also trap states or an interfacial layer due to reactions between metal and thiophene may play a role. The influence of interface layers on Schottky barriers is also shown for In [331] and eutectic Ga,In [332] on p-doped dodecathiophene. For other Schottky diodes, compare [250] and references therein. 

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