Composition X

Point X

The bulk composition of X can be determined by drawing three lines (the magenta lines) through X, parallel to each side of the large triangle Fo-An-Si. Using this method we get a compostions of 70% Fo, 18% Si and 12% An. For equilbrium crystallization the final product must have the same bulk composition as the initial starting composition.

Point X also lies in the small triangle Fo-En-An, therefore the final solid must be a mixture of the three phase that define this small triangle. The proportions of these three phases, present at X, can be determined again by drawing three lines (the dashed black lines) through X, but parallel to the sides of the Fo-An-En triangle. The final solid will be a mixture of 28% Fo, 60% En and 12% An. These three phase in the final solid coexist at P, the peritectic, so the last liquid will have a composition equivalent to that of the peritectic.

The path followed by the liquid is shown in red, with the sequence of events as follows:

1. Cool the liquid down until it reaches the liquidus.
2. At the liquidus Fo begins to crystallize and the Fo is in equilibrium with liquid. The liquid composition moves directly away from Fo, as it is being depleted in Fo.
3. From X to Y, Fo continues to crystallize and the liquid moves along the path, represented by the red line, constantly changing composition.
4. At Y, which lies on the boundary curve between the fields of En + L and Fo +L.
   This cotectic curve is a reaction curve denoted by the double arrow. The reaction taking place is
   Fo====> En + L At Y Fo is resorbed, melted back into the liquid and En begins to crystallize with both phases in equilibrium with liquid, represented by Y.
5. From Y to Point Q
   Fo continues to be resorbed, En crystallizes and both of these are in equilibrium with the liquid, the composition of which is moving down the boundary curve from Y to Q.
   
6. At Q
   Point Q lies along the cotectic curve separating the En + L field from the Fo + L field.
   At Q we can determine:
   1. The proportion of solid Fo + En to L.
      To do this we must draw a tie line from Q through X, back to the En-Fo join (Point A).
      • % Solid (Fo+En) = XQ/AQ * 100 = 64% We can also determine the ratio or Fo:En at Q
        • % Fo = AEn/FoEn * 100 = 52%
        • % En = FoA/FoEn *100 = 48%
      • % L = AX/AQ * 100 = 36%
   2. The proportion of F being melted and En crystallizing.
      To do this we must draw a line which is tangential to the cotectic curve from Q back to intersect the the extension of the Fo-En tie line - Line segment QC.
      • Ratio of Fo being resorbed: En crystallizing = EnC/FoC = 1:1.65.
        From this ratio it can be seen that much more En is forming than Fo being resorbed.
   3. The composition of all phases present.
      • Fo is Pure Fo (100% Fo, 0% Si, 0% An)
      • En is pure En (68% Fo, 32% Si, 0% An)
      • Liquid composition is represented by point Q - draw three lines through Q parallel to the outside edges of the large triangle and get a compostion in terms of the three end member components Fo, Si and An. I haven't done it, you know how to, give it a try!
7. From Q to the peritectic (P). Fo resorbtion continues as does En crystallization.
8. At the peritectic Fo continues to be resorbed, En continues to crystallize and An begins to crystallize.
   The liquid stays at the point represented by the peritectic until all the liquid has been used up, leaving a solid mixture of Fo + En + An, in the proportions 26:60:12 - the proportions we calculated above using the small Fo-En-An triangle.