Reciprocal systems ternary

A ternary reciprocal system is a system containing four components, but where these components are related through a reciprocal reaction. One example is the system LiCl-LiF-KCl-KF. Solid LiCl, LiF, KC1 and KF are highly ionic materials and take the rock salt crystal structure, in which the cations and anions are located on separate sub-lattices. It is therefore convenient to introduce ionic fractions (Xj) for each sub-lattice as discussed briefly in Section 3.1. The ionic fractions of the anions and cations are not independent since electron neutrality must be fulfilled  

For this reason, the system is defined by the four neutral components LiCl, LiF, KC1 and KF, which in addition can be related by the reciprocal reaction 

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Figure 4.21 Calculated phase diagram of the ternary reciprocal system LiCl-LiF-KCl-KF [20], Reprinted with permission 2001 by ASM International and TMS (The Minerals, Metals and Materials Society).

Figure 9.9 Activity of AC in the hypothetical ternary reciprocal system AC-BD for different values of AXGIRT.

Among the possible chemical reactions in the ternary reciprocal system Li+, B + // F , leading to the compound formation, the following four are considered to be probable ... 

The phase equilibrium in the ternary reciprocal system Li+, K+ //F , [TiOs] " was studied by Nikonova and Berul (1967). Also this system was studied up to approximately 40 mole % LiF only, since above this, the LiF content Li2Ti03 precipitates from the melt. It was found that the system KF-Li2Ti03 is the stable diagonal of the above-mentioned reciprocal system. This could also be confirmed by the calculation of the standard Gibbs energy of the metathetical reaction... 

The phase diagram of the ternary reciprocal system Na+, K+ // F , TiO " was studied by Sholokhovich (1955). Two binary compounds, Na2Ti03-K2Ti03 and (Na2Ti03)3-2NaF, are formed in this system. The authors qualify this ternary reciprocal system as irreversible. 

Ternary ionic systems contain four kinds of ions, which can be constituted in three different ways (A+, B+, C+/X ), (A+ZX", Y , Z ), or (A" ", B+/X , Y ). The first two arrangements are additive ternary systems (the former one is a system with a common anion, the latter one is a system with a common cation), while the last one is a ternary reciprocal system. Having in mind the restriction of electro-neutrality, there are only three independent salt components, from which the solution could be built up. 

Let US now pay attention to ternary reciprocal systems. They contain two different cations and two different anions. Due to such a composition, they differ somewhat from the additive ternary systems. There are four constituents, AX, AY, BX, BY, but only three of them are independent components. The solution can be made up in four ways, i.e. AX-AY-BX, AX-AY-BY, AX-BX-BY, and AY-BX-BY. In each of these cases, the composition of the final solution will differ. 

While the composition of an ordinary ternary system is represented by a triangle, the ternary reciprocal system is represented by a square, corners of which represent the pure constituents AX, AY, BX, BY. The final solution that we are considering lies inside the two triangles AX-BX-BY and AY-BX-BY. 

There are two peculiarities of the ternary reciprocal system. The first one concerns the activities and the chemical potentials. Regardless of the way the solution was made up, the activities and chemical potentials of all the four constituents are defined and are the same no matter which of the three components were chosen. In our example for the Temkin s ideal solution a x = x +xx = 0.15, [Pg.132]

Phase diagrams of the ternary reciprocal systems are represented in the vertical projection as rectangles, whereas on the opposite apexes of the diagonals, figurative points of the compounds without the common ion are placed. 

Figure 3.35. Phase diagram of the simple ternary reciprocal system.

Simple ternary reciprocal systems. The phase diagram of a simple ternary reciprocal system is schematically shown in Figure 3.35. In the systems of this type the exchange in the metathetical reaction between components takes place, for example p = q = r = s=l. 

Figure 3.36. Phase diagram of the ternary reciprocal system A" ", B " //...

Quaternary reciprocal systems are composed of six components, which form three ternary reciprocal systems and two ternary systems with a common ion. The concentration diagram of this system can be represented by a three-sided prism, on each side is the vertical... 

For ternary reciprocal systems, a lower minimum melting temperature can be obtained (Table 7.3.3, second paragraph, N02, N03 column). The system with the lowest melting temperature is K, Li//N02, NO3 (94 C), followed by the system Li, Na//N02, NO3 (126 °C). In general, it can be seen that all listed ternary reciprocal systems have low melting temperatures compared to the previously discussed systems. The Hitec system K, Na//N02, NO3 (142 C) is of industrial importance and was discussed in the previous paragraph. 

Binary systems with a common anion and ternary reciprocal systems... 

Grover (in preparation). A third-order Margules model for the solution properties of a ternary reciprocal system is based on a ten-term polynomial expansion for and G x in terns of the compositional parameters X2/(Xi+X2) and X3. This formulation is consistent with classic (additive) ternary solution theory but allows asymmetric mixing behaviour solubility of the four reciprocal components in any appropriate number of coexisting phases. 

Two coexisting, non-colinear binary solutions, a(l-2) and b(l-2), form a ternary reciprocal system at 650°C and 2000 bars. At this temperature and pressure there is not ternary solution away from the binary joins. The following values have been determined for the Margules parameters of solutions a and b ... 

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