Triangular diagrams equilateral

Equilateral-triangular diagrams have some practical disadvantages. 

The right triangular diagram (Figure 3.11) is similar to the equilateral triangular diagram each corner represents one of the pure components. 

Figure 3.10a is the most common way that ternary liquid-liquid equilibrium data are displayed in the chemical literature. Such an equilateral triangular diagram has the property that the sum of the lengths of the perpendiculars drawn from any interior point to the sides equals the altitude. Thus, if each of the altitudes is scaled from 0 to 100, the percent of, say, furfural, at any point sucl) as M, is simply the length of the line perpendicular to the base opposite the pure furfural apex, which represents 100% furfural. 

Equation-tearing methods, 562-594 Equilateral triangular diagram, in extraction, 106,415 Equilibrium, 89 diagrams, 88-121 heterogeneous, 89 homogeneous, 89 liquid-liquid, 146-147, 223-230 ratio, 145... 

Phase equilibria for ternary mixtures are conventionally represented on equilateral triangular diagrams. Such diagrams provide a convenient way to present basic material balance relations these are reviewed in Appendix H. Triangular diagrams are T diagrams, and for C = 3 components, (9.1.12) gives... 

Figure 1.6.1. Compositions of a ternary system in equilateral triangular diagram.

Figure 4. Triangular phase diagram, showing partitions of R2ar. / gc, and at fixed Q > ab + bc + ca- Physically allowed combinations lie inside the circle, with the conical intersection, corresponding to equilateral triangular ABC, at the center.

Further use of graphical methods is discussed by Scheibel(8), though here attention is confined to the use of right-angled triangular diagrams. Equilateral triangles will also be used in liquid-liquid extraction, as illustrated in Chapter 13. 

Both equilateral and right triangular diagrams have the property that the compositions of mixtures of all proportions of two mixtures appear on the straight line connecting the original... 

All the solutions which are necessary to form an equilateral triangular llxllxll, 61-element ternary phase diagram were prepared automatically by a liquid dispensing machine. Mixtures with compositions of each component ranged from 0 to 100% in 10% increments. On the 3 in quartz wafer used, 144 wells form a 12 x 12 square grid for the catalyst spots. Each of these elements has a diameter of 3 mm. The whole array is calcined at 500 °C for 12 h and subsequently for an additional 12 h at 800 °C under a 6% H2 in argon atmosphere [80],... 

Figure 3.11 Summary diagrams in the manner of Fignre 3.10 identifying the group orbitals on the vertices of the equilateral triangular orbit in a C3V structure such as NF3 with N at the coordinate origin. Note, with reference, to the Character Table for C3V that Fz is Ai and Fg is A2.

Whenever the miscibility of the two phases varies and is dependent on concentration, a triangular diagram is employed (Fig. 2.5). Here the three comers of the equilateral triangle stand for the pure components, the solvent S, the carrier T and the solute C. Each side of the triangle represents binary mixtures, each point within the triangle a ternary mixture. Since the sum of the perpendicular lines of any point in the triangle... 

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