Conjugate lines

Alkemade lines are also called in many different ways including conjugation lines and joins. Both Alkemade lines and Alkemade triangles (composition triangles produced by Alkemade lines) are of use in die understanding of ternary systems. They play an essential role in understanding crystallisation or heating paths ... 

Figure 3.11 Construction of a tie-line from the conjugate line.

Plot equilibrium data from previous example (plotting the conjugate line will be really helpful for drawing tie-lines in this case). 

Find the saturated extract, saturated raffinate, and conjugate lines on a right-triangular diagram. 

A polarity is a projective correlation of period 2. A polarity. Figure 3.20, dualizes incidences if A, correlated with a, lies on b, correlated with B, then a passes through B. A and B are conjugate points, while a and b are conjugate lines. Line a is called the polar of A and A is the pole of a. Where A and a coincide the line is self-conjugate. It can be shown that a polarity induces an involution on any line that is not self-conjugate. 

Figure 13-13. Construction of tie line using conjugate line...

Plot equilibrium data and construct conjugate line. 

CPD... Binodal curve CD Tie line PK1K2K3 Conjugation line... 

Figure 15 Conjugation lines and solidus isotherms in the system Mg0-Fe0-Si02 after Nafziger et al. (1967).

In comparison with the latter system there is a striking difference in the orientation of conjugation lines in the system FeO - Si02 - Ti02 (see Fig. 18). It appears that iron is preferentially bound in the oxide phases which are coexisting with un-combined Si02/ while magnesium prefers the silicate phases. 

At this stage we want to state immediately that in each FCD the layers are folded around two conjugated lines, viz., an ellipse E and one branch H of a hyperbola, in such a way that they are everywhere perpendicular to the straight lines joining any point M on the ellipse to any point M" on the hyperbola (fig.2). Any point M on the line M M" is the orthogonal... 

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