Composition A

For an initial liquid of composition A the final solid after Equilibrium crystallization must be a mixture of Di and plagioclase of composition B (PlB), in the proportions determined above.

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

1. Above the liquidus surface we have 100% liquid.
2. Cool this liquid to the liquidus
3. At the liquidus, Di begins to crystallize and is in equilibrium with liquid. The liquid composition moves directly away from Di towards the boundary curve.
4. From A to C, Di contiunes to crystallize and the liquid moves along the path, constantly changing composition to remain in equilibrium with the Di forming.
5. At Point C, on the boundary curve
   Pl begins to crystallize along with the Di and these two solid phases are in equilibrium with Liquid.
   1. The composition of the Di is fixed.
   2. The composition of the Pl, represented by Point D, will have an An content greater than B (the final Pl composition in equilibrium with Di).
      The actual plagioclase composition, i.e. the position of Point D between Ab and An, forming here must be determined experimentally.
      However, intuitively, we know from our examination of the Ab-An binary system that at equilibrium, the liquid is always more Ab-rich than the coexisting Pl, so the plagioclase must lie on the An side of the final Pl composition.
   3. The composition of the Liquid is represented by Point C.
   Note that the three points above, Di, C and D, form a triangle (the purple lines). The bulk composition A, lies on or very close to the Di-C join, which lies directly opposite D (the Plagioclase apex), giving <<< 1% Pl in the proportions of the three phases which coexist for composition A at Point C.
   
6. As cooling continues, the liquid composition moves down the boundary curve from C to E.
7. At E, in equilibrium we have Di, Pl, represented by point F, and Liquid represented by point E.
   These three phases are linked by the green tie lines.
   Note that the position of the green triangle has shifted from that of the purple triangle by rotating about the Di apex, common to both, resulting in the shifting of both the liquid composition, from C to E, and the plagioclase composition, from D to F, to more Ab-rich/An-poor compositions.
8. As cooling continues, the liquid composition moves down the boundary curve from E to G.
9. At G, in equilibrium we have Di, Pl, represented by point H, and Liquid represented by point G.
   These three phases are linked by the red tie lines.
   Note that the position of the red triangle has shifted from that of the purple and green triangles, again by rotating about the Di apex, common to all three, resulting in the shifting of both the liquid composition, from E to G, and the plagioclase composition, from F to H, to more Ab-rich/An-poor compositions.
10. When the plagioclase has reached it's final composition (Point B), the last liquid is consumed.
    The composition of the last liquid given by I, expressed in terms of the three end member components Di, Ab and An, on the boundary curve. The cyan tie lines join the Di, the last Liquid composition - I, and the final plagioclase composition - B.
    Examining the cyan triangle shows that the initial bulk composition point A now lies along the Di-PlB edge of the triangle, representing <<< 1% liquid, telling us that crystallization has ceased. The final solid mixture present consists of % Di and % plagioclase of composition B.

The important things to remember about equilibrium crystallization in this system are:

1. Equilibrium between the plagioclase and the liquid must be maintained as:
   1. The liquid migrates down the boundary curve it continuously reacts with the previously formed plagioclase, causing the liquid to become more sodic, i.e. more Ab-rich;
   2. While at the same time the liquid continues to precipitate plagioclase with a higher soda content, i.e. more Ab-rich.
2. Tie lines which join liquid compositions along the boundary curve with plagioclase compositions along the Ab-An join must be determined experimentally.