1. C = 3: Ternary Systems: Example 1: Ternary Eutectic Di - An - Fo
Note three binary eutectics
No solid solution
Ternary eutectic = M
Anorthite
As add components, becomes increasingly difficult to depict.
1-C: P - T diagrams easy
2-C: isobaric T-X, isothermal P-X…
3-C: ??
Still need T or P variable
Projection? Hard to use as shown
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 phases in that field
Cotectic:
multiple solid phases crystallize from a single liquid
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 Still liquid
At 2000oC: phi = 1 (liquid)
F = C - phi + 1
= = 3
= T, X(An)Liq, X(Di)Liq, and X(Fo)Liq
only 2 of 3 X’s
are independent
Next cool to 1700oC
Intersects liquidus surface
Solids form
Cool composition a from 2000oC
Still liquid
At 2000oC: phi = 1 (liquid)
F = C - phi + 1 = = 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
Solids form
Crystallization Relationships

4. Pressure fixed at 0.1 MPa
Pure Fo forms
Just as in binary
f = ?
F = ?

6. Lever principle ® relative proportions of liquid & Fo
At 1500oC
At any point can use the lever principle to determine the relative proportions of liquid and Fo

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

8. At 1300oC liquid = x
Imagine triangular plane X - Di - Fo balanced on bulk a
Draw a working line from x through a to the opposite side, m = total solids
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:
Total amounts of three phases at any T can be determined by a modified lever principle

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

10. Partial Melting (remove melt):
Suppose bulk = a
First melt at M (1270oC)
Stay at M until consume one phase (An)
Only Di and Fo left
Jump to Di-Fo binary
No further melt until at 1387oC mp of Diopside
Stay at 1387oC until consume one phase (Di)
Only Fo left
No further melt until 1890oC mp of Fo
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

11. The Effect of Pressure Solid Liquid Pressure
Temperature
Solid P1 P2 T1 T2
~All solid - liquid (melting) reactions have a positive slope
You recall the Clapeyron Equation
if dG =0,
then dP/dT = ΔS / ΔV
OR dP ΔV = dT ΔS
For dG to stay zero, higher pressure requires lower volume so dT ΔS stays constant which phase should be stable at high P? The one where volume decreases as pressure increases, a solid. Notice then that the melting point increases with temperature, i.e. solid is stable at higher temperatures.
~All solid - liquid (melting) reactions have a positive slope
Increasing pressure (P1 -> P2) thus raises the melting point (T1 -> T2) of a solid

12. The magnitude of the effect will vary for different minerals
Increasing pressure decreases volume, and the liquid state, which usually needs more volume, is less likely at high P, so the Melting Point occurs at Higher Temperature
For example, in a eutectic system, increasing pressure will raise the eutectic melting point
The magnitude of the effect will vary for different minerals
Anorthite compresses less than Diopside
Thus the elevation of the melting point is less for An than Di along the liquidus
The only way to do that is to move the eutectic toward An as the liquidi rise.
Change in An liquidus small
Change in Diopside liquidus large
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
Eutectic system
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,

13. The Effect of Water on Melting
Dry melting: solid ® liquid
Add water- some water enters the melt
Reaction becomes:
solid + water = melt + water (right side is an aqueous solution)
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,

14. The Effect of Water on Melting
The reaction was Solid => Liquid. Adding water “drives the reaction to the right”, in the sense that it melts (goes to liquid) at a lower temp than it would if dry
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
THE SLOPE CHANGES TO NEGATIVE
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,

15. 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 1 – 1.5 GPa
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,

16. Dry and water-saturated solids for some common rock types
Granite is only a crustal rock (not found deeper than 2.2 GPa) ~80km MAX cont. crust
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).

17. 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
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.

18. Two principal types of basalt in the ocean basins
Tholeiitic Basalt and Alkaline Basalt
Ocean Islands such as Hawaii have both Tholeitic AND Alkaline Basalts
Table 10-1
Common petrographic differences between tholeiitic and alkaline basalts
Subalkaline: Tholeiitic-type Basalt
Alkaline Basalt
Usually fine-grained, intergranular
Usually fairly coarse, intergranular to ophitic
Groundmass
No olivine
Olivine common
Clinopyroxene = augite (plus possibly pigeonite)
Titaniferous augite (reddish)
Orthopyroxene (hypersthene) common, may rim ol.
Orthopyroxene absent
(a third, minor, one is hi-Al, or calc-alk basalt & will be discussed later)
No alkali feldspar
Interstitial alkali feldspar or feldspathoid may occur
Interstitial glass and/or quartz common
Interstitial glass rare, and quartz absent
Olivine rare, unzoned, and may be partially resorbed
Olivine common and zoned
Phenocrysts
or show reaction rims of orthopyroxene
Orthopyroxene uncommon
Orthopyroxene absent
Early plagioclase common
Plagioclase later in sequence, uncommon
Clinopyroxene is pale brown augite
Clinopyroxene is titaniferous augite, reddish rims
after Hughes (1982) and McBirney (1993).
A third is hi-Al, or calc-alkaline basalt, usually continental

19. 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
Constant P
H2O down
CO2 up
Increasing pressure
From Tholeiitic to Alkaline
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.