1. C = 3: Ternary Systems: Example 1: Ternary Eutectic
Anorthite
Note three binary eutectics
No solid solution
Ternary eutectic = E
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 E T
Forsterite
Diopside

4. An-Ab-Kfsp Ternary - Flattened
An-Kfsp Binary
Ab-Kfsp Binary
An-Ab Binary
Nekvasil & Lindsley, 1990; Brown, 1993

5. Intersection of Liquidus Surfaces
Temperature falls
from E toward M
in Thermal Valley

15. T - X Projection of Di - An - Fo
Figure 7.2. 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

16. 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??

17. 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 = ?

18. 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

19. 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

20. 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

21. 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

22. 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)

23. 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:

24. 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

25. 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

31. Ternary Peritectic Systems: (at 0.1 MPa)
3 binary systems:
Fo-An eutectic
An-SiO2 eutectic
Fo-SiO2 peritectic
Figure 7.4. 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)

32. 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

33. 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

34. 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

35. 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?

36. 4 - Component Diagrams Add Fo to Ab - An - Di
Plag - Diopside cotectic curve becomes a surface
As do Di - An - Fo cotectics
Surfaces meet in 4-C univariant curves, which meet in 4-C invariant points.
Cannot visualize depth in diagram
(is point y in the Di-An-Fo face, the Di-Ab-Fo face, or between?)
Reaching the point where lose the advantage of model systems
Figure The system diopside-anorthite-albite-forsterite. After Yoder and Tilley (1962). J. Petrol.

37. > 4 Components May as well melt real rocks
On right is a P-T diagram for the melting of a Snake River basalt.
Each curve represents the loss of a phase as heat system.
- Compare to simpler systems
Note pressure effects
Ol - Plag - Cpx at low P
Garnet at high P (eclogite)
Figure Pressure-temperature phase diagram for the melting of a Snake River (Idaho, USA) tholeiitic basalt under anhydrous conditions. After Thompson (1972). Carnegie Inst. Wash Yb. 71