Stability. .127 ternary systems

It was shown some time ago that one can also use a similar thermodynamic approach to explain and/or predict the composition dependence of the potential of electrodes in ternary systems [22-25], This followed from the development of the analysis methodology for the determination of the stability windows of electrolyte phases in ternary systems [26]. In these cases, one uses isothermal sections of ternary phase diagrams, the so-called Gibbs triangles, upon which to plot compositions. In ternary systems, the Gibbs Phase Rule tells us... 

This concept has also been demonstrated at ambient temperature in the case of the Li-Sn-Cd system [47,48]. The composition-de-pendences of the potentials in the two binary systems at ambient temperatures are shown in Fig. 15, and the calculated phase stability diagram for this ternary system is shown in Fig. 16. It was shown that the phase Li4 4Sn, which has fast chemical diffusion for lithium, is stable at the potentials of two of the Li-Cd reconstitution reaction plateaus, and therefore can be used as a matrix phase. 

A high-T modification of Nb5Si3 crystallizes with the Cf5B3 type. Si—B substitution stabilizes the high-T form to lower T reaching far into the ternary system. The stabilization of the homologous Ta5(Si, 8)3, however, is far less pronounced. 

Organic matter is also the essential component of natural soils and its association with microorganisms may influence the behavior and fate of toxic metals. A variety of batch complexation experiments were performed by Borrok et al. (2007) in single, binary and ternary systems for the three components natural organic matter (NOM), bacterium (B. subtilis) and metals (Pb, Cu, Cd, and Ni) to determine the significance of ternary complexation. They found that the formation of bacteria-metal-NOM complex is a rapid, fully-reversible chemical process. The stability of bacteria-metal-NOM complexes increases with the decrease of pH. All NOM fractions form ternary complexes to similar extents at circumneutral pH, but humic acid becomes the dominant NOM fraction in ternary complexes at low pH. The abundance of humic acid in ternary form is greatest with Ni or Cd systems and less with Pb and Cu systems. Their results suggest that... 

It is sometimes convenient to fix the pressure and decrease the degrees of freedom by one in dealing with condensed phases such as substances with low vapour pressure. The Gibbs phase rule for a ternary system at isobaric conditions is Ph + F = C + 1=4, and there are four phases present in an invariant equilibrium, three in univariant equilibria and two in divariant phase fields. Finally, three dimensions are needed to describe the stability field for the single phases e.g. temperature and two compositional terms. It is most convenient to measure composition in terms of mole fractions also for ternary systems. The sum of the mole fractions is unity thus, in a ternary system A-B-C ... 

Figure 7.10 Phase stability relations in a ternary system in which components are totally immiscible at solid state, and relationships with three binary joins.

Figure 7.12 Phase stability relations in a ternary system with complete solid state miscibility of components 1-2 and complete immiscibility at solid state for components 1-3 and 2-3.

The behaviour of ternary systems consisting of two polymers and a solvent depends largely on the nature of interactions between components (1-4). Two types of limiting behaviour can be observed. The first one occurs in non-polar systems, where polymer-polymer interactions are very low. In such systems a liquid-liquid phase separation is usually observed each liquid phase contains almost the total quantity of one polymer species. The second type of behaviour often occurs in aqueous polymer solutions. The polar or ionic water-soluble polymers can interact to form macromolecular aggregates, occasionally insoluble, called "polymer complexes". Examples are polyanion-polycation couples stabilized through electrostatic interactions, or polyacid-polybase couples stabilized through hydrogen bonds. 

The effect of adding a surfactant, (NaDDS), was also investigated. One such case only is shown in Fig. 6 where BE is replaced by a 5 1 mixture of BE-NaDDS. The main effect of NaDDS is to increase the miscibility range of the oil in water. Various ratios of BE-NaDDS were used and, as a first approximation, the change in the phase diagram is directly proportional to the concentration of NaDDS. The addition of a surfactant probably stabilizes the microstructures which were already present in the ternary system BE-DEC-H O and decreases the quantity of BE needed to solubilize DEC. Therefore the presence of a surfactant is useful but not essential to the stability of microemulsions. 

There are other factors to be considered. In a number of systems ternary phases exist whose stability indicates that there are additional, and as yet unknown, factors at work. For example, in the Ni-Al-Ta system r, which has the NisTi structure, only exists as a stable phase in ternary alloys, although it can only be fully ordered in the binary system where it is metastable. However, the phase competes successfully with equilibrium binary phases that have a substantial extension into the ternary system. The existence of the ly-phase, therefore, is almost certainly due to... 

There is, however, another statement of the necessary and sufficient condition of thermodynamic stability of the multicomponent system in relation to mutual diffusion and phase separation that is less stringent than equation (3.20) because it may be fulfilled not for every component of the multicomponent system. For example, in the case of the ternary system biopolymeri + biopolymer2 + solvent, it appears enough to fulfil only two of the inequalities (Prigogine and Defay, 1954)... 

Fig. 45.—Regions of Stability of the Solid Phases in the Ternary System, H2S04 —Na2S04—HaO (P. Pascal and M. Ero).

The isothermal solubility curve of mixtures of potassium sulphate and sulphuric acid expresses the composition of the soln. at 25° in equilibrium with the solid phase or phases, when the mol. ratio of K2SO4 and SO3 per 1000 grms. of soln. are plotted as co-ordinates. The ranges of stability in the ternary system K20—S03—H20, are diagrammed in Fig. 51, where the conditions have been studied in the vicinity of the SOs-apex, as far as the formation of KHS207, hut not as far as the well-known potassium pyrosulphate. The meaning of the diagram... 

Stability Considerations of AB5 Hydrides in Chemical Heat Pump Applications with Reference to the New LaNi5 xAlx Ternary System... 

Finally, let us briefly point out some essential features of the stability analysis for a more general transport problem. It can be exemplified by the moving a//9 phase boundary in the ternary system of Figure 11-12. Referring to Figure 11-7 and Eqn. (11.10), it was a single independent (vacancy) flux that caused the motion of the boundary. In the case of two or more independent components, we have to formulate the transport equation (Fick s second law) for each component, both in the a- and /9-phase. Each of the fluxes jf couples at the boundary b with jf, i = A,B,... (see, for example, Eqn. (11.2)). Furthermore, in the bulk, the fluxes are also coupled (e.g., by electroneutrality or site conservation). 

Normally, it is not possible to obtain analytical solutions for this transport problem and so we cannot a priori calculate the reaction path. Kirkaldy [J. S. Kirkaldy, D. J. Young (1985)] did pioneering work on metal systems, based on investigations by C. Wagner and the later work of Mullins and Sekerka. They used the diffusion path concept to formulate a number of stability rules. These rules can explain the facts and are predictive within certain limits if applied properly. One of Kirkaldy s results is this. The moving interface in a ternary system is morphologically stable if... 

It is convenient to use phase diagrams [46] to represent the thermodynamic properties that determine the stability and equilibrium composition of water-containing aerosols. The properties of interest are the temperature, the vapour pressure and composition of the various components in the condensed phases. This is particularly important with respect to the composition and stability of the various hydrates formed at low temperature in the nitric acid-water [47] and sulfuric acid-water binary systems [48], and the ternary systems HjSO/HNOj/HjO and HjSO/HCl/HjO [49],... 

We can now consider the conditions of stability for pure substances, binary systems, and ternary systems based on Equations (5.122), (5.132), and (5.134), respectively. In order to satisfy the conditions, the coefficient of each term (except the last term in each applicable equation, which is zero) must be positive. If any one of the terms is negative for a hypothetical homogenous system, that system is unstable and cannot exist. 

For ternary systems the conditions of stability in addition to those given by Equations (5.135) and (5.136) are... 

Problems concerning the conditions of stability of homogenous systems for critical phases in ternary systems are very similar to those for the gas-liquid phenomena in binary systems, because of two independent variables at constant temperature and pressure. The conditions for stability are (82G/dnl)T P 2 3>0 and (820, given by Equations (5.146) and (5.147), respectively. Inspection of the condition equivalent to Equation (5.148) given by Equation (5.152) shows that (82(j>/dnl)TP> 2i 3 and, therefore, it is the condition expressed by Equation (5.147) or (5.150) that determines the boundary between stable... 

It was discussed that the structure created by the ternary system oil/water/ nanoparticle follows the laws of spreading thermodynamics, as they hold for ternary immiscible emulsions (oil 1 /oil 2/water) [114,116,117]. The only difference is that the interfacial area and the curvature of the solid nanoparticle has to stay constant, i.e., an additional boundary condition is added. When the inorganic nanoparticles possess, beside charges, also a certain hydrophobic character, they become enriched at the oil-water interface, which is the physical base of the stabilizing power of special inorganic nanostructures, the so-called Picker-... 

Has 21% Cr, 13% Mo, 3% W, 3% Fe, 60% Ni and suitable for use in oxidizing environments corrosion resistance better than C-276, C-4 in oxidizing media, better pitting resistance inferior to C-276, C-4 in reducing media and with respect to crevice corrosion Superior to C-22, C-276, super thermal stability attributed to the ternary system, Ni-Cr-Mo devoid of W, Cu, Ti and Ta Similar to C-276 in composition except for Cr level being 16-21% alloy is solution annealed at 1200°C and rapidly cooled to prevent precipitation of intermetallic phases thermal behavior not as good as Alloy 59 and its corrosion resistance was less than 59 1.6% Cu has been added to C59 lower corrosion resistance and thermal stability than Alloy 59... 

Here, the adsorption of valine on different cation-exchanged montmorillonites is described (Nagy and Konya 2004). A discussion of the kinds of interactions that are possible in the ternary system of montmorillonite/valine/metal ions will be presented, and a description how the metal ions can affect these interactions. The interlayer cations (calcium, zinc, copper ions) were chosen on the basis of the stability constants of their complexes with valine. The adsorption of valine on montmorillonite is interpreted using a surface-complexation model. 

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