Positional disordering

Figure Al.3.28. Examples of disorder (a) perfeet erystal, (b) eompositional disorder, (e) positional disorder whieh retains the short-range order and (d) no long-range or short-range order.

Figure 6 shows the field dependence of hole mobiUty for TAPC-doped bisphenol A polycarbonate at various temperatures (37). The mobilities decrease with increasing field at low fields. At high fields, a log oc relationship is observed. The experimental results can be reproduced by Monte Carlo simulation, shown by soHd lines in Figure 6. The model predicts that the high field mobiUty follows the following equation (37) where d = a/kT (p is the width of the Gaussian distribution density of states), Z is a parameter that characterizes the degree of positional disorder, E is the electric field, is a prefactor mobihty, and Cis an empirical constant given as 2.9 X lO " (cm/V). ...

Based on the Monte Carlo simulations, it is seen that the presence of positional disorder causes the mobiUty to decrease with increasing field at low fields (37). This is the case because the introduction of positional disorder into the system provides the carrier with energetically more favorable routes, which occasionally are against the field direction. These detour routes are most efficient at low fields, but are eliminated at high fields. This rationalizes the decrease of hole mobilities with increasing field. 

The tetrahedrally bonded materials, such as Si and Ge, possess only positional disorder however, materials of this type exhibit high density of defect states (DOS). It is only with the addition of elements such as hydrogen and/or a halogen, typically fluorine, that the DOS is reduced to a point such that electronic device appHcations emerge. These materials contain up to - 10 atomic % hydrogen, commonly called hydrogenated amorphous siHcon (i -Si H). 

In order to address the possible influence of positional disorder, we have chosen to analyze the way basic operations such as translations and rotations affect the properties calculated for highly symmetric configurations. This approach could provide guidelines to prevent the loss of significant optical coupling between the ground state and the lowest excited state, and hence the quenching of luminescence in the solid state. 

Figure 4-10. Sketch of Hie operations applied ui a colacial dimer formed by two slilbene molecules separated by 4 A when investigating the role of positional disorder. The modilicalions are induced by (I) the translation of one molecule along the chain-axis direction (II) the translation of one molecule along the in-planc transverse axis (III) the rotation of one slilbene unit around its long axis and (IV) the rotation of one slilbene molecule around the slacking axis while keeping the parallelism between the molecular planes.

These modifications constitute important sub-cases of the case of positional disorder for which only some characterizing points of the structure maintain long-range three-dimensional periodicity (indicated as case i in Sect. 2.1). 

We can expect disorder to increase when a system is heated because the supply of energy increases the thermal motion of the molecules. Heating increases the thermal disorder, the disorder arising from the thermal motion of the molecules. We can also expect the entropy to increase when a given amount of matter spreads into a greater volume or is mixed with another substance. These processes disperse the molecules of the substance over a greater volume and increase the positional disorder, the disorder related to the locations of the molecules. 

Some changes are accompanied by a change in volume. Because a larger volume provides a greater range of locations for the molecules, we can expect the positional disorder of a gas and therefore its entropy to increase as the volume it occupies is increased. Once again, we can use Eq. 1 to rum this intuitive idea into a quantitative expression of the entropy change for the isothermal expansion of an ideal gas. 

Table 7.1 lists the standard entropies of vaporization of a number of liquids. These and other data show a striking pattern many values are close to 85 J-K 1-mol h This observation is called Trouton s rule. The explanation of Trouton s rule is that approximately the same increase in positional disorder occurs when any liquid is converted into vapor, and so we can expect the... 

That is, S —> 0 as T - 0. The perfect crystal part of this statement of the third law refers to a substance in which all the atoms are in a perfectly orderly array, and so there is no positional disorder. The T— 0 part of the statement implies the absence of thermal motion-—thermal disorder vanishes as the temperature approaches zero. As the temperature of a substance is raised from zero, more orientations become available to the molecules and their thermal disorder increases. Thus we can expect the entropy of any substance to he greater than zero above T = 0. 

Potassium nitrate dissolves readily in water, and its enthalpy of solution is +34.9 kj-niol. (a) Does the enthalpy of solution favor the dissolving process (b) Is the entropy change of the system likely to be positive or negative when the salt dissolves (c) Is the entropy change of the system primarily a result of changes in positional disorder or thermal disorder ... 

The defects of the matrix play an important role on luminescent performances in these materials. Taking into consideration the preparation process of these compounds with the solid-state reaction of mixtures of BaC03, H3BO3, and NH4H2PO4 at different molar ratio, non-equal evaporation during the sintering process of these powders is inevitable and thus results in the formation of intrinsic defects, such as cation and oxygen vacancies. Positional disorder of B and Vacant B (Vb)" have been reported in SrBPOs crystals on the basis of... 

Examples of Positional Disorder with Long-Range Three-Dimensional Periodicity Maintained Only for Some Characterizing Points of Structure... 

Figure 2. (a) Crystal structure ofCClfSb(OTeFs)f (b) A view of the CClf cation, with key bond lengths and bond angles, showing the two-fold positional disorder around the crystallographic inversion center.82... 

Some of the differences in solubilities are also related to different disordering of the crystal surface. As shown by Bishop et al. (1987) with Raman investigations, the biogenic phases are characterized by greater positional disorder than synthetic minerals of the same composition. 

To analyze the negative field dependence of the mobihty in EHO-OPPE within the Gaussian disorder transport formahsm and to determine the diagonal (energetic) disorder parameter a and the off-diagonal (positional) disorder parameter d, the following relation between the charge mobihty p and the disorder parameters was employed [75] ... 

Off-diagonal (positional) disorder parameter. Diagonal (energetic) disorder parameter at 20 °G. 

Mesomorphic state having long-range orientational order and either partial positional order or complete positional disorder. 

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