Multicomponent systems, solid

The exponents apply not only to solid systems (e.g. order-disorder phenomena and simple magnetic systems), but also to fluid systems, regardless of the number of components. (As we have seen in section A2.5.6.4 it is necessary in multicomponent systems to choose carefully the variable to which the exponent is appropriate.)... 

There are many types of phase diagrams in addition to the two cases presented here these are summarized in detail by Zief and Wilcox (op. cit., p. 21). Solid-liquid phase equilibria must be determined experimentally for most binaiy and multicomponent systems. Predictive methods are based mostly on ideal phase behavior and have limited accuracy near eutectics. A predic tive technique based on extracting liquid-phase activity coefficients from vapor-liquid equilib-... 

Tersoff, J., Modeling Solid-State Chemistry Interatomic Potentials for Multicomponent Systems," Phys. Rev. B, Vol. 39, No. 8,1989, pp. 5566-5568. 

The most widely studied deformable systems are emulsions. These can come in many forms, with oil in water (O/W) and water in oil (W/O) the most commonly encountered. However, there are multiple emulsions where oil or water droplets become trapped inside another drop such that they are W/O/W or O/W/O. Silicone oils can become incompatible at certain molecular weights and with different chemical substitutions and this can lead to oil in oil emulsions O/O. At high concentrations, typical of some pharmaceutical creams, cosmetics and foodstuffs the droplets are in contact and deform. Volume fractions in excess of 0.90 can be achieved. The drops are separated by thin surfactant films. Selfbodied systems are multicomponent systems in which the dispersion is a mixture of droplets and precipitated organic species such as a long chain alcohol. The solids can form part of the stabilising layer - these are called Pickering emulsions. 

In developing the thermodynamic framework for ECES, we attempted to synthesize computer software that would correctly predict the vapor-liquid-solid equilibria over a wide range of conditions for multicomponent systems. To do this we needed a good basis which would make evident to the user the chemical and ionic equilibria present in aqueous systems. We chose as our cornerstone the law of mass action which simply stated says "The product of the activities of the reaction products, each raised to the power indicated by its numerical coefficient, divided by the product of the activities of the reactants, each raised to a corresponding power, is a constant at a given temperature. ... 

Pharmaceutical solids can generally be described as crystalline or amorphous (or glassy). In fact, the actual solid phase composition of a pharmaceutical formulation is usually characterized by an intermediate composition, both crystalline and amorphous in character. In a multicomponent system, such as a solid formulation comprising drug and excipient(s), certain components or even a single component may be... 

Wood B. I (1987). Thermodynamics of multicomponent systems containing several solid solutions. In Reviews in Mineralogy, vol. 17, P. H. Ribbe (series ed.), Mineralogical Society of America. 

To a certain extent the expression multicomponent catalysts is an arbitrary one. There is no doubt that the pure chemical elements and pure chemical compounds have to be called single component catalysts. It is, however, questionable whether a material such as steel should be classified as a single component system or as a multicomponent system. Some of the multicomponent catalysts, for instance, the iron-alumina catalyst consist of two separate solid phases but it would be misleading to accept the presence of more than one phase as the decisive criterion for multicomponent catalysts. The more than additive catalytic action of Cu-ions and Fe-ions in an homogeneous aqueous medium represents obviously a case of multicomponent catalysis, although it occurs in a single-phase system. As to solid multicomponent catalysts, they usually consist of more than one single phase, but there are exceptions to this rule, such as in cases in which mixed crystals or solid solutions are formed from the components. 

Structure parameters. For a single compound, the structure parameters include the proportion of atoms and their connectivity, the geometric and energetic parameters of bonds, angles, and conformation, and the electronic parameters of electron distribution and polarization. For multicomponent systems of solutions, microstmctural material, and composite material, the additional structure parameters include the proportion of the various components, and the relations of their phases as solutions, colloids, or composite solids. 

Some transition metal complexes are excellent conductors. Thin films of cyto-chrome-C3, which contains four heme moieties coordinated by protein, exhibited a high conductivity with mixed valence state (Fe /Fe ) and showed an increase in conductivity as the temperature was decreased (2 x 10 S cm at 268 K) [68-70]. The temperature dependence of conductivity in the highly conductive region is the opposite of that of semiconductors and may preclude the ionic conduction as a dominant contribution. However, since the high conductivity is realized in the presence of hydrogenase and hydrogen, the system is not strictly a single but rather a multicomponent molecular solid. 

The unary phase diagram is seldom used in solid state syntheses. However, the unary diagram forms the basis for the phase diagrams of multicomponent systems. Since there are no composition variables, the only externally controllable variables in a unary system are simply the temperature and pressure. For this... 

In many studies the chemisorption and the surface reaction is just the first step in a series of solid state reactions that take place as atoms from the surface move into the bulk. Corrosion, oxide, carbide and other compound formations are generally initiated at the surface and then propagate into the bulk. There may be a concentration gradient of certain constituents at the surface in a multicomponent system that would influence the mechanical or chemical properties of the system. Hardening of materials and other forms of passivation treatment frequently involve introduction of certain substances only in the near surface region. For the investigation of these problems RHEED is a powerful technique. 

Let us now consider the equalization of the component concentrations in an inhomogeneous multicomponent system. We may start with Eqn. (4.33) which relates the component fluxes, jk, to the (n-1) independent forces, Vyq, of the n-compo-nent solid solution. In local equilibrium, the chemical potentials are functions of state. Hence, at any given P and T... 

When all the SE s of a solid with non-hydrostatic (deviatoric) stresses are immobile, no chemical potential of the solid exists, although transport between differently stressed surfaces takes place provided external transport paths are available. Attention should be given to crystals with immobile SE s which contain an (equilibrium) network of mobile dislocations. In these crystals, no bulk diffusion takes place although there may be gradients of the chemical free energy density and, in multicomponent systems, composition gradients (e.g., Cottrell atmospheres [A.H. Cottrell (1953)]). 

Since linear variation of hardness is not always the case, equation (5.7) is approximate. But Glazov and Vigdorovich consider that the production of many very complex solid solution systems does require some method if only rough, for hardness analysis of such systems. They formulate the additivity principle for multicomponent systems as follows the numerical increase in hardness of multi-component solid solutions equals the sum of hardness increments in bi-component solutions... 

Solute-solute Interactions may affect the diffusion rates In the fluid phase, the solid phase, or both. Toor (26) has used the Stefan-Maxwell equations for steady state mass transfer In multicomponent systems to show that, in the extreme, four different types of diffusion may occur (1) diffusion barrier, where the rate of diffusion of a component Is zero even though Its gradient Is not zero (2) osmotic diffusion, where the diffusion rate of a component Is not zero even though the gradient Is zero (3) reverse diffusion, where diffusion occurs against the concentration gradient and, (4) normal diffusion, where diffusion occurs In the direction of the gradient. While such extreme effects are not apparent in this system, it is evident that the adsorption rate of phenol is decreased by dodecyl benzene sulfonate, and that of dodecyl benzene sulfonate increased by phenol. 

The thermodynamic equations for the Gibbs energy, enthalpy, entropy, and chemical potential of pure liquids and solids, and for liquid and solid solutions, are developed in this chapter. The methods used and the equations developed are identical for both pure liquids and solids, and for liquid and solid solutions therefore, no distinction between these two states of aggregation is made. The basic concepts are the same as those for gases, but somewhat different methods are used between no single or common equation of state that is applicable to most liquids and solids has so far been developed. The thermodynamic relations for both single-component and multicomponent systems are developed. 

About 800 000 tons of solid catalysts are prepared and used every year worldwide, but this does not mean that we understand how they work. Catalyst synthesis and treatment recipes are often based on empirical studies, handed down the generations like ancient medicines. Since chemists dislike ignorance even more than nature abhors a vacuum, much research is done to find out how solid catalysts work. And, since the real industrial catalysts are usually multicomponent, nonuniform solids, much of this research is done on simplified model systems [28],... 

Here, we only present the simplest thermodynamic expressions used in the CALPHAD method for the major phase classes observed in multicomponent systems namely, disordered miscible and immiscible phases and ordered sublattice phases. The reader is referred to specialized textbooks for further discussion. The Gibbs energies for disordered two-component solid and liquid solution phases are most easily represented by the regular solution model (Eq. 2.10) or one of its variants ... 

Soils are multicomponent systems consisting of solid, liquid, and gaseous phases. These three phases are constantly in a dynamic state, trying to maintain equilibrium. Any type of perturbation in one phase influences the other two phases so that a new equilibrium state is approached. An equilibrium process that has been extensively investigated in soil systems employing the Freundlich equation involves sorption. Consider the reaction... 

As a molecule approaches the solid surface, a balance is established between the intermolecular attractive and repulsive forces. If other molecules are already adsorbed, both adsorbent-adsorbate and adsorbate-adsorbate interactions come into play. It is at once evident that assessment of the adsorption energy is likely to become exceedingly complicated in the case of a multicomponent system - especially if the adsorption is taking place from solution at a liquid-solid interface. For this reason, in the numerous attempts made to calculate energies of adsorption, most attention has been given to the adsorption of a single component at the gas-solid interface. 

Adsorption Chromatography. The principle of gas-solid or liquid-solid chromatography may be easily understood from equation 35. In a linear multicomponent system (several sorbates at low concentration in an inert carrier) the wave velocity for each component depends on its adsoiption equilibrium constant. Thus, if a pulse of the mixed sorbate is injected at the column inlet, the different species separate into bands wliich travel through the column at their characteristic velocities, and at the outlet of the column a sequence of peaks corresponding to the different species is detected. Measurement of the retention time (tl) under known flow conditions thus provides a simple means of determining the equilibrium constant (Henry constant) ... 

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