Triangular plot

Figure 3. Relaxed triangular plot [68] of the U3 ground-state potential energy surface using hyperspherical coordinates. Contours, are given by the expression (eV) — —0.56 -t- 0.045(n — 1) with n = 1,2,..,, where the dashed line indicates the level —0.565 eV. The dissociation limit indicated by the dense contouring implies Li2 X Sg ) -t- Li.

In the remainder of this section, we focus on the two lowest doublet states of Li3. Figures 3 and 4 show relaxed triangular plots [68] of the lower and upper sheets of the 03 DMBE III [69,70] potential energy surface using hyper-spherical coordinates. Each plot corresponds to a stereographic projection of the... 

Figure 11. Perspective view [60] of a relaxed triangular plot [68] for the two DMBE adiabatic potential energy surfaces of H3 using hyperspherical coordinates.

Because an N-component system has N — I independent concentrations, a three-component equilibrium can be plotted in a plane and a four-component equilibrium in a three-dimensional space. Figure 16-8 shows a triangular plot of c contours in equilibrium with the corresponding /I coordinates. 

For an N-species system, with N c"s (or n s) known, the N n°s (or c s) can be found by simultaneous solution of the N — 1 independent i.j combinations for Eq. (16-45) using Eq. (16-44a) one nj/cl is assumed, the other values can be calculated using Eq. (16-45), and the sum of the trial n s (or c s) is compared with Eq. (16-44h). Because an N-component system has N — 1 independent concentrations, a three-component equilibrium can be plotted in a plane and a four-component equilibrium in a three-dimensional space. Figure 16-8 shows a triangular plot of c contours in equilibrium with the corresponding n coordinates. Improved models for ion-exchange equilibria are in Smith and, SJk... 

Fig. 2. Triangular plot of Ca, Na, and A-site vacancies in pyrochlore from Vishnevogorskii calculated from structural formulae normalized to two B-site cations. Compositions of primary pyrochlore plot near the Ca-Na join (solid symbols). Compositions of the altered areas move toward the Ca-vacancy join, then along this join toward the top of the triangle.

Figure 14.1. Equilibria in a ternary system, type 1, with one pair of partially miscible liquids A = 1-hexene, B = tetramethylene sulfbne, C = benzene, at 5(TC (JR.M. De Fre, thesis, Gent, 1976). (a) Equilateral triangular plot point P is at 20% A, 10% B, and 70% C. (b) Right triangular plot with delines and tieline locus, the amount of A can be read off along the perpendicular to the hypotenuse or by difference, (c) Rectangular coordinate plot with tieline correlation below, also called Janecke and solvent-free coordinates.

If this activity coefLcient term is applied to Equation 2.41, the mole fraction solubility can be shown to reach a maximum wh00i equals5D2, < pi equals, and< m equals - Teas (1968) presented a triangular plot where the sides represent the three contributions to the solvent solubility parameter. For example, the dispersion force contribution would be... 

B, and C each represent 100% by weight of their respective components on the triangular plot. 

The question now is, how can a two-dimensional x-y rectangular plot represent a three-dimensional triangular plot In answer, the first criterion to explain is the equilibrium distribution coefficient ... 

Figure 19. Triangular plot of the H02(X2/4") DMBE potential141 with the molecular perimeter fixed at the equilibrium value 4 — 7.56a0 see Fig. 3).

Figure20. Triangular plot of the O iX 1 A,) DMBE potential159 with the molecular perimeter fixed at the average value of the perimeters for the C2l. equilibrium structure and the D h cyclic structure (4 = 8.52a0). Contours are equally spaced by 0.007E, starting at A = — 0.221...

The Salen-Soininen perspectively transformed chart is a triangular plot. It is tricky to plot and read, but covers a much wider range of humidity than do the other types of chart (up to 2 kg/kg) and is thus very effective for high-humidity mixtures and calculations near the... 

The composition of a typical system is satisfactorily presented in the form of a diagram. Those diagrams most frequently employed are a right-triangular plot of mass fraction of solvent against mass fraction of solute (Fig. 18-92(i) and a plot suggestive of a Ponchon-Savarit dia-... 

The average framework compositions of the four depositional sequences are reported in Table 1. The triangular plots of Fig. 4 show the composition of the total framework (Fig. 4A), the terrigenous framework (Fig. 4B) and the fine-grained rock fragments (Fig. 4C). 

Crude oils can be classified according to the relative amounts of acyclic alkanes, cycloalkanes and combined aromatic hydrocarbons plus NSO compounds present. This classification is represented by the ternary (triangular) plot in Fig. 4.22, and can be seen to distinguish between the main fields of marine and terrestrially sourced oils. The main classes of normal crudes resulting from this classification are ... 

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