1. 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

2. 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

3. 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??

4. 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 = ?

5. 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

6. 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

7. 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

8. 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

9. 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)

10. 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:

11. 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

12. 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

13. 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)

14. 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

15. 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

16. 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

17. 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

18. 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

19. 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)

20. 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

21. 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?

22. Diopside-Albite-Anorthite
Figure 7-5. 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

23. Isobaric polythermal projection
Figure 7-5. 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

24. 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

25. 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

26. 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

27. 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?

28. 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)

29. 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

30. Note: 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

31. Oblique View Isothermal Section
Figure 7-8. Oblique view illustrating an isothermal section through the diopside-albite-anorthite system. Figure 7-9. Isothermal section at 1250oC (and 0.1 MPa) in the system Di-An-Ab. Both from Morse (1994), Basalts and Phase Diagrams. Krieger Publishers.

32. Ternary Feldspars
1118 Ab 20 40 60 80 An
1100
1200
1300
1400
1500
1557
T C o
Plagioclase
Liquid
plus L i q u d s S l
Weight % An Or Ab
Ab-rich feldspar
+ liquid
liquid
single feldspar
two feldspars
1200
1000
800
Temperature oC
Wt.% a c b d e f g h i j k s o l v u q
Or-rich feldspar
Figure Schematic oblique view of the ternary feldspar system vs. temperature
The ternary liquidus and solvus surfaces have the hatch pattern
The solidus is shaded
Purple line e-c is the cotectic minimum
The yellow curve from a to b is the trace of solids that coexist with the cotectic liquids
x-y-z = coexisting plag-Afs-liq at constant T
Figure After Carmichael et al. (1974), Igneous Petrology. McGraw Hill.

33. Ternary Feldspars Trace of solvus at three temperature intervals
Triangle shows coexisting
feldspars and liquid at
900oC
Solvus gets larger as T lowered
Figure Winter (2001) An Introduction to Igneous and Metamorphic Petrology. Prentice Hall.

34. 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.

35. > 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

36. Bowen’s Reaction Series
olivine
Calcic plagioclase
(Spinel)
Mg pyroxene
Calci-alkalic plagioclase
Continuous
Series
Mg-Ca pyroxene
alkali-calcic plagioclase
Discontinuous
Series
amphibole
alkalic plagioclase
biotite
Temperature
potash feldspar
muscovite
quartz

37. The Effect of Pressure Solid Liquid Pressure
Temperature
Solid P1 P2 T1 T2
~All solid - liquid (melting) reactions have a positive slope
Increasing pressure (P1 -> P2) thus raises the melting point (T1 -> T2) of a solid

38. The magnitude of the effect will vary for different minerals
Eutectic system
In a eutectic system increasing pressure will raise the melting point (as predicted)
The magnitude of the effect will vary for different minerals
Anorthite compresses less than Diopside
Thus the elevation of the m. p. is less for An than Di
The eutectic thus shifts toward An
Figure Effect of lithostatic pressure on the liquidus and eutectic composition in the diopside-anorthite system. 1 GPa data from Presnall et al. (1978). Contr. Min. Pet., 66,

39. The Effect of Water on Melting
Dry melting: solid ® liquid
Add water- water enters the melt
Reaction becomes:
solid + water = liq(aq)
Dry melt reaction: solid -> liquid
Add water- water enters the melt
So the reaction becomes:
solid + water = liq(aq)
Thus adding water drives the reaction to the right.
Liquid is stabilized at the expense of the solid.
The result is to lower the melting point.
Pressure is required to hold the water in the melt, so increased pressure allows more water to enter the melt and this increases the melting point depression
Figure The effect of H2O saturation on the melting of albite, from the experiments by Burnham and Davis (1974). A J Sci 274, The “dry” melting curve is from Boyd and England (1963). JGR 68,

40. Note the difference in the dry melting temperature and
the melting interval of a basalt as compared to the water-
saturated equivalents
The melting point
depression is quite
dramatic
Especially at low
to intermediate
pressures
Figure Experimentally determined melting intervals of gabbro under H2O-free (“dry”), and H2O-saturated conditions. After Lambert and Wyllie (1972). J. Geol., 80,

41. Dry and water-saturated solidi for some common rock types
The more mafic the rock
the higher the melting
point
All solidi are greatly
lowered by water
Granite is only a crustal rock (not found deeper than 1 GPa)
Figure H2O-saturated (solid) and H2O-free (dashed) solidi (beginning of melting) for granodiorite (Robertson and Wyllie, 1971), gabbro (Lambert and Wyllie, 1972) and peridotite (H2O-saturated: Kushiro et al., 1968; dry: Ito and Kennedy, 1967).

42. We know the behavior of water-free and water-saturated
melting by experiments, which are easy to control by
performing them in dry and wet sealed vessles
What about real rocks?
Some may be dry, some saturated, but most are more
likely to be in between these extremes
a fixed water content < saturation levels
a fixed water activity

43. The Albite-Water System
Red curves = melting for
a fixed mol % water in
the melt (Xw)
Blue curves tell the water
content of a water-
saturated melt m
Return to a simpler system that we know
Green curves = “dry” and water-saturated melting
Red curves = melting for a fixed mol % water in the melt (Xw)
Blue curves tell the water content of a water-saturated melt
Note that any curve for a fixed % water and a curve that is saturated with that same % intersect at the green saturated curve
Figure From Burnham and Davis (1974). A J Sci., 274,

44. Raise a melt with a ratio of albite:water = 1:1 (Xwater = 0.5)
from point a at 925oC and
1 GPa pressure, toward the
Earth’s surface under
isothermal conditions.
melt
At a it is above the water-sat. solidus, so it is at least partially melted.
If it had 0.52% water it would be completely molten (red curves).
With only 50% water it is nearly molten, but not entirely so.
When the melt rises to b it does become completely molten (liquidus for 50% water)
From b to c the melt becomes progressively more superheated
At c the melt reaches the point where it is now saturated with 50% water (blue curve) so free water phase released
From c to d the melt is saturated with progressively less water
Between c and d the water content of the saturated melt will be reduced from 50% to 30% (nearly halved)
Figure From Burnham and Davis (1974). A J Sci., 274,

45. Conclusions: A rising magma with a fixed % water will
progressively melt
At shallower levels it
will become saturated,
and expel water into
its surroundings
Figure From Burnham and Davis (1974). A J Sci., 274,

46. Another example: isobaric heating of albite with
10 mol % water at 0.6 GPa.
At e it is solid albite.
At f it would all melt if it had enough water (65%), but it has only 10% water
Thus only 10/65 or 15% will melt.
At g it would be completely molten if it were 50% water, but with 10% it will be 10/50 or 20% molten.
At h it will be 10/20 or 50% molten and at i it will finally be 100% molten.
Melting starts out very slowly, and accelerates near the appropriate liquidus curve (see blue % at top)
Figure From Burnham and Davis (1974). A J Sci., 274,

47. 15% % % 100%
Conclusion:
Although the addition of water can drastically reduce the melting point of rocks, the amount of melt produced at the lower temperature may be quite limited, depending on the amount of water available
Figure From Burnham and Davis (1974). A J Sci., 274,

48. Melting of Albite with a fixed activity of H2O
Fluid may be a CO2-H2O mixture with Pf = PTotal
Figure From Burnham and Davis (1974). A J Sci., 274,

49. Melting of Albite with a fixed activity of H2O
Fluid may be a CO2-H2O mixture with Pf = PTotal
Figure From Millhollen et al. (1974). J. Geol., 82,

50. The solubility of water in a melt depends on the structure of
the melt (which reflects the structure of the mineralogical
equivalent)
The solubility of water in a melt depends on the structure of the melt (which reflects the structure of the mineralogical equivalent)
Water dissolves more in polymerized melts (An > Di)
Thus the melting point depression effect is greater for An than Di
The eutectic moves toward An
Figure The effect of H2O on the diopside-anorthite liquidus. Dry and 1 atm from Figure 7-16, PH2O = Ptotal curve for 1 GPa from Yoder (1965). CIW Yb 64.

51. Effect of Pressure, Water, and CO2 on the position
of the eutectic in the basalt system
Increased pressure moves the
ternary eutectic (first melt) from
silica-saturated to highly undersat.
alkaline basalts
Water moves the (2 GPa) eutectic
toward higher silica, while CO2
moves it to more alkaline types Ne Fo En Ab
SiO2
Oversaturated
(quartz-bearing)
tholeiitic basalts
Highly undesaturated
(nepheline-bearing)
alkali olivine
basalts
Undersaturated
3GPa
2GPa
1GPa
1atm
Volatile-free Ne Fo En Ab
SiO2
Oversaturated
(quartz-bearing)
tholeiitic basalts
Highly undesaturated
(nepheline-bearing)
alkali olivine
basalts
Undersaturated
CO2
H2O
dry
P = 2 GPa
Left: Effect of pressure on the ternary eutectic (minimum melt composition) in the system Fo-Ne-SiO2 (base of the “basalt tetrahedron”). From Kushiro (1968). JGR 73,
Right: Figure Effect of volatiles on the ternary eutectic (minimum melt composition) in the system Fo-Ne-SiO2 (base of the “basalt tetrahedron”) at 2 GPa. Volatile-free from Kushiro (1968) JGR 73, , H2O-saturated curve from Kushiro (1972), J. Petrol., 13, , CO2–saturated curve from Eggler (1974) CIW Yb 74.