Composition, local

The local-composition models have hmited flexibility in the fitting of data, but they are adequate for most engineering purposes. Moreover, they are implicitly generalizable to multicomponent systems without the introduction of any parameters beyond those required to describe the constituent binaiy systems. For example, the Wilson equation for multicomponent systems is written ... 

Equation-of-State Approach Although the gamma/phi approach to X- E is in principle generally applicable to systems comprised of subcritical species, in practice it has found use primarily where pressures are no more than a few bars. Moreover, it is most satisfactoiy for correlation of constant-temperature data. A temperature dependence for the parameters in expressions for is included only for the local-composition equations, and it is at best only approximate. 

At any plane in a Raoultian alloy system parallel to die original interface, the so-called chemical diffusion coefficient Dchem. which determines the flux of atoms at any given point, and is usually a function of the local composition so that according to Darken (1948), Dchem is given by... 

Figure 9.3. Computer simulation of dendrites growing into a Ni Cu alloy with 41 at.% ofCii. The tints show local composition (courtesy W.J. Boettinger and J.A. Warren).

Thus the result is the formation of a single-phase solid solution. The insertion of additional guest species involves only a change in the overall (and thus also the local) composition of the solid solution, rather than the formation of additional phases. 

At a given ideal composition, two or more types of defects are always present in every compound. The dominant combinations of defects depend on the type of material. The most prominent examples are named after Frenkel and Schottky. Ions or atoms leave their regular lattice sites and are displaced to an interstitial site or move to the surface simultaneously with other ions or atoms, respectively, in order to balance the charge and local composition. Silver halides show dominant Frenkel disorder, whereas alkali halides show mostly Schottky defects. 

Renon used the concept of local composition to develop a non-random, two-liquid (NRTL) three parameter (al2, tp, ti() equations given below (Prausnitz et al., 1986). 

FIGURE 39 Corrosion. Corrosion is the process of gradual deterioration of metals and alloys as a result of their interaction with the environment. The corrosion process is a reversal of metallurgical processes, whereby metals are recovered from the minerals in which they occur in nature (a). It is an electrolytic process, brought about by the passage of electric currents. Any metal or alloy contains sites in which there are slight local compositional differences. When such compositional differences are exposed to a humid or wet environment, extremely small electrolytic cells as the one shown in (b) are created in each cell, an electric current drives the otherwise nonspontaneous corrosion reactions. In a surface undergoing corrosion there are millions of electrolytic cells. 

When examining the initial stages of copolymerization in the framework of the traditional approach, the local composition x is taken to be equal to its global value throughout the whole reaction system. Such an assumption is certain to hold, provided the growing macroradical is in a coil conformational state. 

Thus, X-ray fluorescence offers the possibility of determining the composition of a sample. In an SEM, where the beam can be directed at desired positions of the sample, one can obtain the local composition on a scale of about 5-10 nm. 

Chen, C.-C.., 1993, A Segment Based Local Composition Model for the Gibbs Energy of Polymer solutions. Fluid Phase Equilibria, 83, 301. 

Renon, H., Prauznits, J.M., 1968, Local Compositions in Thermodynamic Excess Functions for Liquid Mixtures, AIChE Journal, 14, 135. 

The second is based on the local composition concept and represents work in progress. 

The local compostion model is developed as a symmetric model, based on pure solvent and hypothetical pure completely-dissociated liquid electrolyte. This model is then normalized by infinite dilution activity coefficients in order to obtain an unsymmetric local composition model. Finally the unsymmetric Debye-Huckel and local composition expressions are added to yield the excess Gibbs energy expression proposed in this study. 

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