1. Readings: Winter Chapter 7
Ternary Systems
Readings:
Winter Chapter 7

2. C = 3: Ternary Systems: Example 1: Ternary Eutectic Di - An - Fo
Anorthite
Note three binary eutectics
No solid solution
Ternary eutectic = M
As add components, becomes increasingly difficult to dipict.
1-C: P - T diagrams easy
2-C: isobaric T-X, isothermal P-X…
3-C: ??
Still need T or P variable
Project? Hard to use as shown M T
Forsterite
Diopside

3. T - X Projection of Di - An - Fo
Isobaric diagram illustrating the liquidus temperatures in the Di-An-Fo system at atmospheric pressure (0.1 MPa). After Bowen (1915), A. J. Sci., and Morse (1994), Basalts and Phase Diagrams. Krieger Publishers.
X-X diagram with T contours (P constant)
Liquidus surface works like topographic map
Red lines are ternary cotectic troughs
Run from binary eutectics down T to ternary eutectic M
Separate fields labeled for liquidus phase in that field

4. Crystallization Relationships
Cool composition a from 2000oC
At 2000oC:
phi = ? (1 (liquid)
F = ? F = C - f = = 3
= T, X(An)Liq, X(Di)Liq, and X(Fo)Liq
only 2 of 3 X’s are independent
Next cool to 1700oC
Intersect liquidus surface
What happens??

5. Pure Fo forms Just as in binary f = ? F = ? a Liquid An An + Liq
Di + Liq
Di + An a An
Pure Fo forms
Just as in binary
f = ?
F = ?

6. f = 2 (Fo + Liq)
F = = 2
If on liquidus, need to specify
only 2 intensive variables
to determine the system
T and or
and
X of pure Fo is fixed X An
liq X An
liq X Fo
liq

7. Continue to cool; Fo crystallizes and liquid loses Fo component
Xliq moves directly away from Fo corner
“Liquid line of descent” is a -> b
Along this line liquid cools from 1700oC to about 1350oC with a continuous reaction:
LiqA -> LiqB + Fo

8. Lever principle ® relative proportions of liquid & Fo At 1500oC
Liq x + Fo = bulk a
x/Fo = a-Fo/x-a
At any point can use the lever principle to determine the relative proportions of liquid and Fo

9. Pure diopside joins olivine + liquid
What happens next at 1350oC ?
Pure diopside joins olivine + liquid
phi = 3
F = = 1 (univariant at constant P)
Xliq = F(T) only
Liquid line of descent follows cotectic -> M

10. New continuous reaction as liquid follows cotectic: Bulk solid extract
LiqA ® LiqB + Fo + Di
Bulk solid extract
Di/Fo in bulk solid extract using lever principle
1400
1300
1500
1274
1270
1392
Diopside
Di + Liq M b c
Fo + Liq
1387
Bulk solid extract crystallizing from the liquid at any point (T): draw tangent back to the Di-Fo join
At 1350oC that is point c
Use c and the lever principle to get the Di-Fo ratio crystallizing at that instant (not the total solid mass crystallized)

11. Liq/total solids = a-m/Liq-a total Di/Fo = m-Fo/Di-m
At 1300oC liquid = X
Imagine triangular plane X - Di - Fo balanced on bulk a
Liq x a Di m Fo
Liq/total solids = a-m/Liq-a
total Di/Fo = m-Fo/Di-m
Total amounts of three phases at any T can be determined by a modified lever principle:

12. At 1270oC reach M the ternary eutectic
anorthite joins liquid + forsterite + diopside
phi = 4
F = = 0 (invariant)
discontinuous reaction:
Liq = Di + An + Fo
stay at 1270oC until consume liq
Below 1270oC have all
solid Fo + Di + An
phi = 3
F = = 1

13. Similar process with bulk X in any other field
Cool d to 1400oC and anorthite forms first
Xliq -> directly away from An and reaches cotectic at point e at 1290oC when forsterite joins An + Liq
Now univariant and Xliq follows
the cotectic where Di forms at 1270oC and the last liquid is consumed
Can get any sequence of Di-An-Fo depending on bulk X
Eutectic is always the last liquid and first melt
Equilibrium Melting: the opposite of equilibrium crystallization
Fractional crystallization (remove crystals):
Same liquid line of descent (since no solid solution)
only difference is final rock = M not a

14. Partial Melting (remove melt):
Try bulk = a
First melt at M (1270oC)
Stay at M until consume one phase (An) Why An?
Only Di and Fo left
Jump to Di-Fo binary
No further melt until N at 1387oC
Stay at N until consume one phase (Di)
Only Fo left
No further melt until 1890oC

15. Ternary Peritectic Systems: Fo - An - SiO2 (at 0.1 MPa)
3 binary systems:
Fo-An eutectic
An-SiO2 eutectic
Fo-SiO2 peritectic
Isobaric diagram illustrating the cotectic and peritectic curves in the system forsterite-anorthite-silica at 0.1 MPa. After Anderson (1915) A. J. Sci., and Irvine (1975) CIW Yearb. 74.
Shown without liquidus contours to reduce clutter
Binary peritectic behavior extends into the ternary system
c = ternary peritectic
d = ternary eutectic
Liquid immiscibility extends slightly into ternary, then becomes miscible
Final mineral assemblage determined by sub-triangle (Fo-En-An) or (En-An-Qtz)

16. Begin with composition a
Fo crystallizes first phi = 2 F = = 2
Xliq -> b as cool
En now forms and F = 1
Xliq then follows peritectic curve toward c

17. Fo En
Forsterite + Liq
Enstatite + Liq a b y x
As Xliq follows peritectic can get bulk solid extract at any T by tangent method
example at point x the tangent -> y as bulk solid
We know Fo, En, and Liq are the three phases
since y = solids, it must be comprised of Fo and En
but y falls outside the Fo-En join
y = En + (-Fo)
the reaction must be: Liq + Fo -> En
which is a peritectic continuous reaction
If y fell between En and Fo it would be L = En + Fo
1890

18. Continue cooling with continuous reaction until Xliq reaches c at 1270oC
Now get An + En + Fo + Liq
phi = 4 F = = 0
stay here with discontinuous reaction:
Liq + Fo = En + An
until Liquid used up
Since a plots in the Fo - En - An triangle these must be the final phases

19. i k Works the same way as the Fo - En - SiO2 binary
1557
If the bulk X is between Fo and En the liquid disappears first at the
peritectic temperature and Fo + En remain as the final solids
If, on the other hand, the bulk X lies to the right of En, then Fo is consumed first and the liduid continues to evolve toward the eutectic

20. As a variation on this sequence: begin with e
Fo is first phase to crystallize. As it does so,
Xliq -> b where En also forms
As before get continuous reaction Liq + Fo = En
But, when Xliq reaches f the Xbulk (e) lies directly between En and Xliq

21. Fo En
Forsterite + Liq
Enstatite + Liq e b f
Whenever Xbulk lies directly between two phases, these two phases alone add to comprise the system: En + f = e
Thus En and liquid are all it takes, so the olivine must be consumed by the reaction at this point
phi = 2 and F = = 2
Xliq then leaves the peritectic curve -> En + Liq field (directly away from En)

22. Xliq -> g where An joins En + Liq
As before get continuous reaction Liq = An + En
Xliq -> d where Tridymite also forms
Again stay at d with discontinuous reaction:
Liq = An + En + S
until last liq gone
Since e lies in the triangle En - An - SiO2, that is the final mineral assemblage

23. Other areas are relatively simple Liq h
Fo first and Xliq ® i
An joins and Xliq ® c
F = 0 and stay at c until
liquid consumed
never leave c
You pick others?

24. Fractional crystallization
Only real difference on liq path is in the Fo field
Since lose Fo, it can’t react with the liquid to -> En
So cross peritectic curve at b where En begins to crystallize and head straight -> e
Here An forms and follow cotectic -> d
Tridymite forms
Final rock = d

25. Diopside-Albite-Anorthite
Isobaric diagram illustrating the liquidus temperatures in the system diopside-anorthite-albite at atmospheric pressure (0.1 MPa). After Morse (1994), Basalts and Phase Diagrams. Krieger Publushers
Oblique View
Cotectic trough slopes down continuously from Di - An (1274oC) to Di - Ab (1133oC)
Di - An Eutectic
Di - Ab Eutectic
Ab - An solid solution

26. Isobaric polythermal projection
Isobaric diagram illustrating the liquidus temperatures in the system diopside-anorthite-albite at atmospheric pressure (0.1 MPa). After Morse (1994), Basalts and Phase Diagrams. Krieger Publishers.
Isobaric polythermal projection
Isothermal contours on the liquidus only.
None on the solidus (so Xplag indefinite).
Cotectic in red.
Some tie-lines connecting plagioclase compositions with cotectic liquids shown in green
Let’s begin by cooling composition a

27. Above 1300oC phi = 1 so F = C - phi + 1 = 3 - 1 + 1 = 3
At 1300oC diopside forms at the liquidus temperature
F = = 2 (liquid is restricted to the liquidus surface)
As cool further get continuous reaction liqA -> Di + liqB
and Xliq moves directly away from Di

28. At 1230oC plagioclase joins diopside and liquid b
F = = 1
So Xliq now restricted to the cotectic curve
Xplag can now be found from tie-lines (since they apply to cotectic liquids)
Xplag = An80

29. Xliq follows cotectic as continuous reaction:
liqA -> Di + Plag + liqB proceeds
At any point the bulk composition a must be within the triangle Di - Plag - Liq which comprise it
When Xliq reaches c Xplag reaches An50
Now Di-a-Plag are colinear
Thus c is the last drop of liquid

30. Now we cool a liquid of composition d
First solid to form will be plagioclase BUT, we cannot tell what composition it will be
Plag forms at about 1420oC
Xplag is about An87
Must be higher than An75
Why?

31. Now follow continuous reaction of type: liqA + plagB ® liqC + plagD
Plagioclase follows path at base
Liquid follows curved path (since moves away from a moving plagioclase comp.)
At 1230oC liquid reaches e and diopside forms along with cotectic liquid and plag An75 (tie-line works now)

32. Continuous reaction: liqA + plagB -> Di + liqC + plagD
As liquid moves e -> f and plag moves -> An65
When Xplag ® An65 then Di - d - plag are colinear
Thus the last liquid = f

33. Binary character is usually maintained when a new component is added
Eutectic behavior remains eutectic
Peritectic behavior remains peritectic
Solid solutions remain so as well