Composition triangle

A convenient way of representing the T—x y phase diagram (Eig. 14b) is by projection onto the composition triangle at the base of the figure. It is understood that the temperature varies from point to point on the projected vapor line and on the projected boiling envelope. The latter looks like an isothermal Hquid—Hquid binodal envelope, but is not. Each tie line across the boiling envelope is associated with a different boiling temperature (Eig. 15). 

Depending on the required chemical properties of the enamel, the appropriate area of the composition triangle (Fig. 18.5) is chosen. 

Figure 4.15 Equilateral composition triangle for defining composition in a ternary system...

More complex situations were shown in Figs. 2.26 and 2.27, where some typical examples of isobarothermal sections of ternary alloy phase diagrams were presented. In the case of ternary systems, several binary and ternary stoichiometric (Fig. 2.28) phases and/or different types of variable composition phases (Fig. 2.29) may be found. We may differentiate between these phases by using terms such as point compounds (or point phases, that is, phases represented in the composition triangle, or more generally in the composition simplex by points), Tine phases , field phases , etc. 

Figure 5.32. In the composition triangle (mass%) of ternary Au-Ag-Cu alloys, colours are indicated. Constant mass% values of Au are identified by dotted lines for instance 22 carats = 91.7 mass% Au, etc.).

Figure 5.41. Schemes of ternary compound formation in ternary alloys. For a few metal pairs (Al-Cu, Al-Fe, etc.) the third elements are indicated (defined by their position in the Periodic Table) with which true ternary phases are formed that is, phases are formed which are homogeneous in internal regions of the composition triangle not connected with the corners or edges. Compare these data with those shown for the formation of binary compounds in the figures relevant to the involved metals.

Figure 7.2. Distribution of the more common ternary intermetallic phases according to their stoichiometry, (a) Shows the position of AxByC2 phases in a representative portion of a general composition triangle. The hatched region corresponds to composition values for which in general ternary compounds are very seldom observed, (b) An indication is given about the number of phases reported by Rodgers and Villars (1993) for different typical stoichiometries.

Figure 5. Calculated ternary phase diagram for EC/PC/ DMC as expressed in the form of a composition triangle plane. The dotted lines represent the isotherms with 10 K intervals with 300 K marked. (Reproduced with permission from ref 167 (Figure 12). Copyright 2003 The Electrochemical Society.)...

Figure 537 Locations of metamorphic amphiboles in compositional triangle Na -Ca-(Fe ++Mg+Mn) (atom proportions). Miscibility gaps are simplified. Solid lines are microprobe analyses dashed lines are wet chemical analyses. From Robinson et al. (1982). Reprinted with permission of The Mineralogical Society of America.

Let us now consider the crystallization process operating on a composition C2, initially poorer in component 1 this composition falls into the compositional triangle C -2-3. Crystallization begins in primary phase field y" (T = 1225 °C). Precipitation of y" crystals drives the residual liquid radially away from C2 along direction 2-C2. At T = 1100 °C, the composition of the liquid reaches cotectic line Ejii-P, where crystals y " begin to form together with y". At peritectic point P, crystals y" are partially resorbed by reaction with the liquid to form intermediate compound C . However, the peritectic reaction is not completed, because of ex-... 

There are a few other useful properties of the composition triangle which should be noted ... 

If two compositions on the composition triangle are mixed, the resulting composition lies on a line joining them. In this case the starting compositions lie at the endpoint of a binary tie-line and the mixture composition can be located using the lever principle. 

The liquidus isotherms and solid-solution isoconcentration lines over the entire Gibbs composition triangle are shown in Fig. 28. A point to be elaborated upon further below is that in the Hg-Cd rich half the solid-solution isoconcentration lines turn to the Hg corner even for very high x values. An expanded plot near the -rich corner is shown in Fig. 29. The liquidus isotherms match Harman s (1980) experimental values for Cd < 0.005 and are close to his for 550 and 600°C. However, his 450 and 500°C isotherms are displaced from the calculated lines towards higher xCd by about 0.003 in xCd-The calculated isoconcentration lines agree with the composition analysis of films grown epitaxially upon CdTe substrates by Harman (1980) for x = 0.2 and 550°C, x = 0.3 and 575°C, x = 0.4 and 580°C, and x = 0.5 and 580°C. 

Fig. 28. Liquid isotherms (solid lines) at high temperatures and solid-solution isoconcentration lines (dashed lines) plotted across the entire Gibbs composition triangle.

The temperature dependence of ternary phase behavior can be described by affixing a new axis perpendicular to the composition triangle to obtain a three-dimensional triangular prism ... 

Ternary systems contain three components. The composition of such a system cannot be represented on a line. For that reason an equilateral triangle is used. When the temperature is a variable, the composition triangle (figure 6.10) in a T,x diagram is the base on which three T axes are placed perpendicularly on the vertices of the triangle. In a system with the components A, B and C there are three mole fractions for which holds x(A) + x(B) + x(C) = 1. 

Three kinds of systems can be represented in the composition triangle 1. The vertices on the triangle represent the unary system with the pure components. 

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