Concentration tetrahedron

The binary compound BCX3 divides the AX-BX-CX2 and DX2-BX-CX2 ternary systems into four simple ternary subsystems. The crystallization paths of ternary mixtures end in one of the six ternary eutectic points E , where the ternary mixtures solidify. The crystallization path of any quaternary mixture follows the dotted boundary lines inside the concentration tetrahedron and ends in one of the two quaternary eutectic points Eq,. 

Fig. 1. Scheme of the Si-B-C-N concentration tetrahedron with stable and metastable solid phases indicated... 

The compositions of solid phases appearing in the Si-B-C-N system are indicated in the concentration tetrahedron as shown in Fig. 1. Some of them appear in different modifications. The basic crystallographic data of stable phases are given in Table 1. 

In Fig. 1.9b, azeotrope 13 gives rise to ctis-surface, which crosses edges 1-3 and 3 in a b-points and divides the concentration tetrahedron into two regions... 

In the concentration tetrahedron, all points of a-surfaces are characterized by the property that the liquid-vapor tie-lines in these points are directed along the straight lines passing through that edge of the concentration tetrahedron, which connects the vertexes whose numbers are missing in the index of or-surface. For example, in the points of o 13-surface in Fig. 1.9b, the liquid-vapor tie-lines are directed to edge 2-4. 

In the concentration tetrahedron, the ternary azeotrope gives rise not only to three a-surfaces, but also to one specific a-line in the points of which not two but three components of the phase equilibrium coefficients are equal to each other. We will call the line a three-index a-line. For example, in Fig. 1.10b, the ternary azeotrope 123 gives rise to the o i23-line, which crosses the face 1-3-4 in the i23-point (it isn t shown). 

The quaternary azeotrope gives rise to six a-surfaces in the concentration tetrahedron (the number of combinations is every two from four). Each a-surface gives... 

For a mixture of acetone(l)-methanol(2)-chloroform(3)-ethanol(4), draw the bonds between components and azeotropes in the concentration tetrahedron, as well as the boundaries of each distillation region. 

Let s examine the analysis of structure of reversible distillation trajectory bundles at the concrete example of four-component mixture acetone(l)-benzene(2)-chloroform(3)-toluene(4). At the beginning, the segments of the components order Regff at the edges of the concentration tetrahedron are defined by means of scanning and calculation of the values Ki (Fig. 4.13a). The corresponding regions of components order Reg in the tetrahedron are shown in Fig. 4.13b and in its faces - in Fig. 4.14. The whole face 1-2-3, where the component 4 that is absent... 

Figure 4.14. Component-order Reg. and tear-off RegJ-g and R 8rev,s regions on three-component faces of the concentration tetrahedron (shaded for the overhead product anddarkershaded forthe bottom product) for the acetone l)-benzene(2)-chloroform(3)-toluene(4)...

What minimum information is necessary to define the contour of possible product region Reg, or Regg in face 1-3-4 of concentration tetrahedron 1-2-3-4 ... 

Calculate Q -lines for the faces of the concentration tetrahedron of a mixture of acetone(l)-benzene(2)-chloroform(3)-toluene(4). 

Stationary points 5, 5, and iV+ (5 = A ) move along the edges of concentration tetrahedron. The section trajectory bundle may be presented in the following brief form (the bundle s direction is indicated by the double arrow, its stationary points around it) ... 

Figure 5.25 shows the evolution of top section trajectory bundle at separation of four-component ideal mixture, when the product is ternary mixture 1,23 (i.e., at indirect split) K >K2>Kj,> K, xdi -I-xd2+xd3 = 1). At small values of the parameter L/V, the stable node Ai+ that at the increase of the parameter L/F moves away from the product point along reversible distillation trajectory appears at face 1-2-3 (Fig. 5.25a). After this node reaches reversible distillation trajectory tear-off point from face 1-2-3 inside concentration tetrahedron, it turns into the saddle...

Deviations from the described evolution for nonideal zeotropic and azeotropic mixtures are analogous to those that were discussed before for three-component mixtures. As an example of such deviation, let s examine separation of four-component mixture, the top product of which is component 1 and inside concentration tetrahedron there is a23-surface, that divides it into component-order... 

Location of sections trajectories of such conditional mixture in concentration tetrahedron should follow general described above regularities for usual four-component mixtures. Therefore, such visualization allows us to understand and to foresee the designing peculiarities and difficulties of separation of mixtures with large numbers of component. 

In the concentration tetrahedron and its faces, there is a region of order of components RegJ. Which sharp extractive sphts are feasible for this mixture ... 

Figure 4.13 shows the segments of identical order of the components Regard at the edges of concentration tetrahedron and the regions of identical order of com-... 

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