Answers for Chapter 7: Ternary Systems.
Ternary systems are, by definition, 3-component systems. The addition of another component to a 2-
component
... [Show More] system requires 3-dimensions to illustrate the T-X variables for an isobaric system, but we
cannot further simplify our diagrams by ignoring T or a component, so we construct isobaric T-X
diagrams by contouring the liquidus surface for temperature, as illustrated in the ternary Fo-An-Di
system below. The inset shows the system in 3-D perspective, showing the three binary eutectic systems.
1. Begin with composition a at 1800oC. What is the weight fraction of An in the liquid ( Liq XAn )? What
about Liq XDi ? Liq XFo ?
Liq XAn = ~ 0.21, Liq XDi = ~0.16, Liq XFo = ~0.63
2. What is the variance at 1800oC? Show your work. List the intensive variables that are relevant to this
diagram and could contribute to F. Which variables in your list, if any, are not independent?
Above the liquidus, so only liquid present. F = C – φ + 1 (isobaric) = 3 – 1 + 1 = 3.
3. What mineral begins to crystallize as a liquid of composition a is cooled to 1700oC? What is the
variance? Show your work.
Forsterite begins to crystallize. F = 3 – 2 + 1 = 2.
1
4
6
8
9: Bulk solid extract
c
d
e
f
4. Illustrate with a dashed line labeled “4” the “liquid line of descent” as the liquid continues to cool
below 1700oC. Why does it move in the direction you have indicated?
It must move directly away from Fo because forsterite is being extracted from it.
5. What is the “continuous reaction” involved that permits the liquid composition to change?
LiquidA = Forsterite + LiquidB
6. Indicate with an “6” the point along the liquid line of descent where a new phase begins to
crystallize. What phase is it?
Anorthite
7. Derive the variance at this point and show your work.
F = 3 – 3 + 1 = 1
8. Show with a heavy line and an “8” the liquid line of descent from the point at which the new phase
in part (6) formed. Write the new continuous reaction responsible for the change in liquid
composition.
LiquidA = Forsterite + Anorthite + LiquidB
9. Choose a point along the cotectic between (6) and point M and show how you derive the bulk solid
extract crystallized from the liquid at that point. How does that bulk solid extract differ from the
total amount of solid crystallized?
Extrapolate a tangent to the cotectic from the point in question and extend it back to the Fo – An
side of the triangle to get the bulk solid extract. This is the instantaneous solid proportions
crystallizing from the melt at any particular point, whereas the total amount crystallized must
include all the prior Fo and An that has crystallized since 1700oC.
10. Determine a general geometric rule relating the bulk composition to the compositions of the three
phases that compose it (liquid, forsterite, and anorthite).
Xbulk must lie within a triangle having the three phases as corners.
11. Will the liquid line of descent reach point M under equilibrium conditions? Why or why not?
Yes. As long as Xbulk lies within the Fo-An-Di triangle it must have some of each component in
it and must therefore reach the eutectic, the only melt composition in equilibrium with all three
phases [Show Less]