Degree of disorder

Materials that contain defects and impurities can exhibit some of the most scientifically interesting and economically important phenomena known. The nature of disorder in solids is a vast subject and so our discussion will necessarily be limited. The smallest degree of disorder that can be introduced into a perfect crystal is a point defect. Three common types of point defect are vacancies, interstitials and substitutionals. Vacancies form when an atom is missing from its expected lattice site. A common example is the Schottky defect, which is typically formed when one cation and one anion are removed from fhe bulk and placed on the surface. Schottky defects are common in the alkali halides. Interstitials are due to the presence of an atom in a location that is usually unoccupied. A... 

A quantitative way of dealing with the degree of disorder in a system is to define something called the thermodynamic probability Q. which counts the number of ways in which a particular state can come about. Thus situations we characterize as relatively disordered can come about in more ways than a relatively ordered state, just as an unordered deck of cards compared to a deck arranged by suits. 

At first sight, self-organization appears to violate the Second Law of Thermodynamics, which asserts that the entropy S of an isolated system never decreases (or, more formally, > 0) see figure 11.2-a. Since entropy is essentially a measure of the degree of disorder in a system, the Second Law is usually interpreted to mean that an isolated system will become increasingly more disordered with time. How, then, can structure emerge after a system has had a chance to evolve ... 

Fig. 12.2. A schematic representation of the intuitive relationship between complexity and the degree of disorder in a system.

Another way of looking at it is that Shannon information is a formal equivalent of thermodynamic entroi)y, or the degree of disorder in a physical system. As such it essentially measures how much information is missing about the individual constituents of a system. In contrast, a measure of complexity ought to (1) refer to individual states and not ensembles, and (2) reflect how mnc h is known about a system vice what is not. One approach that satisfies both of these requirements is algorithmic complexity theory. 

With rise of temperature, the polarization produced by given electrostatic charges decreases, because the thermal agitation maintains, in opposition to the field, a higher degree of disorder. At a higher temperature the loss of free energy by the dielectric is smaller that is to say,... 

That this should be so is a corollary of the Second Law of Thermodynamics which is concerned essentially with probabilities, and with the tendency for ordered systems to become disordered a measure of the degree of disorder of a system being provided by its entropy, S. In seeking their most stable condition, systems tend towards minimum energy (actually enthalpy, H) and maximum entropy (disorder or randomness), a measure of their relative stability must thus embrace a compromise between H and S, and is provided by the Gibb s free energy, G, which is defined by,... 

From these it will be seen that a more negative value of or a more positive value of will in each case lead to an increase in Ke. Furthermore, there is a hypothesis that if the degree of disorder in a system increases it will almost certainly be accompanied by an increase in entropy... 

If heat is applied to an endothermic reactionwill increase and, conversely, heat applied to an exothermic reaction will result in a decrease in K.. At the same time heat will tend to increase the disorder of the system and favour the side of the reaction with the greatest potential disorder. However the degree of disorder can rarely be assessed easily and the magnitude of the latter effect is difficult to determine. Overall the variation of Ke is unlikely to exceed a few per cent per kelvin. 

Figure 9.11 (a) Configurational entropy of a spinel AB2O4 as a function of the composition parameter, x. (b) Degree of disorder, x, as a function of temperature for selected values of AdisH. 

The Gibbs energy of this defect reaction defines the degree of disorder through the equilibrium constant. 

It is probable that varying degrees of ordering of chains exist in a cellulosic material and that a sharp differentiation of crystalline and non-crystalline celluloses may not be feasible or even possible. Theoretically, the lateral surfaces of crystallites are amorphous but may have far less importance in determining such properties as strength, flexibility and extensibility than the non-crystalline cellulose which supplies continuity of structure in the direction of crystallite orientation. Yet properties like moisture absorption and swelling may be more dependent upon the amount of cellulose which exceeds a certain degree of disorder (permeability) than upon location. The definition of crystallinity may, therefore, be made ultimately in terms of practical objectives. 

Concentrated (isotropic) solution p3. Once the concentration exceeds p2 the polymers have a tendency to align with each other. They still show a degree of disorder but over a limited concentration range both the dynamics and distribution of particles in space are substantially modified. This isotropic state is maintained up to a concentration pT which is of the same order as (bL2) l ... 

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