Equilibrium Crystallization of Composition X

Bulk composition of X is 80% Fo and 20% Si. Since this is equilibrium crystallization the final solid must also have the same bulk composition as the staring liquid and will be a mixture of Fo+En. This can be determined by drawing the isopleth from the initial liquid composition to the base of the diagram, where it lies in the stability field of Fo+En.

1. To begin Composition X lies above the liquidus and is 100% liquid.
2. Drop the temperature to the liquidus, Point X1, where Fo begins to crystallize and is in equilibrium with Liquid of composition X1.
3. As the temperature drops from X1 to X2, Fo continues to crystallize. Since Fo is being removed from the liquid, the liquid is becoming depleted in the Fo component and enriched in the Si component, thus it's composition moves down the liquidus surface, towards P, in the direction of increasing Si component.
4. At X3, the temperature of the peritectic, a reaction occurs where:
   1. Fo, crystallized in the interval from X1 to X3, reacts with the liquid, of composition P, and is resorbed back into the liquid, and
   2. En begins to crystallize.
5. Fo must compose a portion of the final solid, i.e. the isopleth extends into the Fo + En field, the resorbtion of Fo is incomplete - there is not enough liquid to react with the Fo.
6. As the Fo is resorbed, En crystallizes until all the liquid is used up.
7. The final liquid has a composition equivalent to the composition of P (52% Si, 48% Fo).
8. The final solid must be a mixture of Fo and En. The proportions of which can be determined by applying the lever rule to point X4. (50:50 mix of Fo:En)
9. The final solid has the same bulk composition as the initial starting liquid composition.

Equilibrium Crystallization of Composition Y

Bulk composition of Y is 50% Fo and 50% Si. Since this is equilibrium crystallization the final solid must also have the same bulk composition as the starting liquid and will be a mixture of En + Qtz.

1. To begin Composition Y lies above the liquidus and is 100% liquid.
2. Drop the temperature to the liquidus, Point Y1, where Fo begins to crystallize and is in equilibrium with Liquid of composition Y1.
3. As the temperature drops from Y1 to Y2, Fo continues to crystallize. Since Fo is being removed from the liquid, the liquid is becoming depleted in the Fo component and enriched in the Si component, thus it's composition moves down the liquidus surface, towards P, in the direction of increasing Si component.
4. At Y2 the system consists of a mixture of Fo+L. Applying the lever rule at Y2 shows that the proportion of Fo: L is 98:2.
5. As the temperature continues to drop from Y2 to the temperature of the peritectic Fo continues to crystallize.
6. At the temperature of P, the peritectic reaction takes place, where Fo + L ===> En.
   • Fo is resorbed into the liquid and En begins to crystallize. Both of theses solid phases are in equilibrium with liquid of composition P. There is an excess of L over Fo for this composition, i.e. all the Fo is resorbed and there is still liquid available.
   • With no Fo remaining the peritectic reaction no longer takes place and with a drop in temperature En crystallizes and we move into the field of En + L.
7. At Y3 the system is a mixture of En + L (64% En, 34% L). The liquid composition is moving down the liquidus surface towards E, the eutectic.
8. At the temperature of the eutectic, En continues to crystallize, Qtz begins to crystallize and these are in equilibrium with a liquid of eutectic composition. The temperature remains constant at 1543°C, until all the liquid is used up crystallizing into En and Qtz. These two phases crystallize out in the proportions given by the eutectic 45% En and 55% Qtz.
9. When the last drop of liquid crystallizes in to the last grains of En and Qtz we are left with a solid mixture of En+Qtz, in the proportions En:Qtz = 84:16, given by point Y4, with a bulk composition of 50% Fo and 50% Si, the original starting bulk composition.

Equilibrium Crystallization of Composition Z

Composition Z has a bulk composition of 40% Si and 60% Fo, equivalent to pure En, so our final solid must be 100% En, with the same bulk composition as the starting liquid.

For this starting composition at the temperature of the peritectic the reaction

When the last grain of Fo is resorbed into the liquid the last droplet of liquid forms a grain of En, leaving a final solid of 100% En.

The En isopleth essentially divides this system into two parts:

1. On the Fo side of En, the last liquid will have a composition represented by P, and will form a final solid mixture of En + Fo.
2. On the Qtz side of En, the last liquid will have a composition represented by E, and will form a final solid mixture of En + Qtz.

In this type of system with a peritectic, there is also an incongruently melting compound, in this case En, which implies that a reaction relationship occurs between this compound the liquid and another solid phase.

In this specific system Fo and Qtz will not occur together, they react to form En. This can be seen in the diagram where there is nor primary phase field where Fo and Qtz coexist.