Phase Equilibrium At a constant pressure simple compounds (like ice) melt at a single temperature More complex compounds (like silicate magmas) have very different melting behavior

Magma samples recovered from various depths beneath solid crust Makaopuhi Lava Lake Magma samples recovered from various depths beneath solid crust From Wright and Okamura, (1977) USGS Prof. Paper, 1004.

Makaopuhi Lava Lake Temperature of sample vs. Percent Glass 100 90 70 60 50 40 30 20 10 Percent Glass 900 950 1000 1050 1100 1150 1200 1250 Temperature oc 80 > 200 oC range for liquid -> solid Fig. 6-1. From Wright and Okamura, (1977) USGS Prof. Paper, 1004.

olivine decreases below 1175oC Makaopuhi Lava Lake Minerals that form during crystallization 1250 1200 1150 1100 1050 1000 950 10 20 30 40 50 Liquidus Melt Crust Solidus Olivine Clinopyroxene Plagioclase Opaque Temperature oC olivine decreases below 1175oC Fig. 6-2. From Wright and Okamura, (1977) USGS Prof. Paper, 1004.

Makaopuhi Lava Lake Mineral composition during crystallization 100 Olivine Augite Plagioclase 90 80 Weight % Glass 70 60 50 .9 .8 .7 .9 .8 .7 .6 80 70 60 Mg / (Mg + Fe) Mg / (Mg + Fe) An Fig. 6-3. From Wright and Okamura, (1977) USGS Prof. Paper, 1004.

Crystallization Behavior of Melts 1. Cooling melts crystallize from a liquid to a solid over a range of temperatures (and pressures) 2. Several minerals crystallize over this T range, and the number of minerals increases as T decreases 3. The minerals that form do so sequentially, with considerable overlap 4. Minerals that involve solid solution change composition as cooling progresses 5. The melt composition also changes during crystallization 6. The minerals that crystallize (as well as the sequence) depend on T and X of the melt 7. Pressure can affect the types of minerals that form and the sequence 8. The nature and pressure of the volatiles can also affect the minerals and their sequence

The Phase Rule F = C - f + 2 F = # degrees of freedom f = # of phases The number of intensive parameters that must be specified in order to completely determine the system f = # of phases Phases are mechanically separable constituents C = minimum # of components Chemical constituents that must be specified in order to define all phases 2 = 2 intensive parameters Usually temperature and pressure for geologists

One Component Systems SiO2 Fig. 6-6. After Swamy and Saxena (1994), J. Geophys. Res., 99, 11,787-11,794. AGU

Two Component Systems Systems with Complete Solid Solution Plagioclase Ab (NaAlSi3O8 ) - An (CaAl2Si2O8) T - X diagram at constant P = 0.1 MPa F = C - phi + 1 since P is constant: lose 1 F Fig. 6-8. Isobaric T-X phase diagram at atmospheric pressure. After Bowen (1913) Amer. J. Sci., 35, 577-599.

Bulk composition a = An60 = 60 g An + 40 g Ab XAn = 60/(60+40) = 0.60 Example of cooling with a specific bulk composition Point a: at 1560oC phi = ? (1) F = ? = C - phi + 1 = 2 - 1 + 1 = 2

A continuous reaction of the type: liquidB + solidC = liquidD + solidF As cool, Xliq follows the liquidus and Xsolid follows the solidus, in accordance with F = 1 At any T, X(An)Liq and X(An)Plag are dependent upon T We can use the lever principle to determine the proportions of liquid and solid at any T

The lever principle: = D Amount of liquid Amount of solid ef = Amount of solid de where d = the liquid composition, f = the solid composition and e = the bulk composition d e f D liquidus de ef solidus

Equilibrium Crystallization of the Plagioclase Feldspars 1. Liquid of composition X (An61) cools to the liquidus 2. Crystals of approximately An87 begin to form 3. Crystals have higher Ca/Na than liquid; ppt of crystals causes L composition to become more sodic. X 4. Ratio of Ca/Na in both crystals and liquid decrease with decreasing temperature; proportion of crystals increases as liquid decreases P=1 atm 5. Crystals of An61 cool without further change in composition Composition of 1st crystal Composition of last crystal PowerPoint® presentation by Kenneth E. Windom Composition of last liquid

1. The melt crystallized over a T range of 135oC * Note the following: 1. The melt crystallized over a T range of 135oC * 4. The composition of the liquid changed from b to g 5. The composition of the solid changed from c to h Numbers refer to the “behavior of melts” observations (several slides back) ** The actual temperatures and the range depend on the bulk composition **

Equilibrium melting is exactly the opposite Heat An60 and the first melt is g at An20 and 1340oC Continue heating: both melt and plagioclase change X Last plagioclase to melt is c (An87) at 1475oC

Fractional crystallization: Remove crystals as they form so they can’t undergo a continuous reaction with the melt At any T, Xbulk = Xliq due to the removal of the crystals Thus liquid and solid continue to follow liquidus and solidus toward low-T (albite) end of the system Get quite different final liquid (and hence mineral) composition

Remove first melt as it forms Melt Xbulk = 0.60, first liquid = g Partial Melting: Remove first melt as it forms Melt Xbulk = 0.60, first liquid = g remove and cool bulk = g ® final plagioclase = i Fractional crystallization and partial melting are important processes in that they can cause significant changes in the final rock that crystallizes beginning with the same source rock.

also a solid-solution series Two Component Systems Olivine Fo - Fa (Mg2SiO4 - Fe2SiO4) also a solid-solution series Fig. 6-10. Isobaric T-X phase diagram at atmospheric pressure After Bowen and Shairer (1932), Amer. J. Sci. 5th Ser., 24, 177-213.

2-C Eutectic Systems Example: Diopside - Anorthite No solid solution Fig. 6-11. Isobaric T-X phase diagram at atmospheric pressure. After Bowen (1915), Amer. J. Sci. 40, 161-185.

1. A bulk composition of X cools to the liquidus, at which point An crystallizes. 2. Continued crystallization of An causes liquid composition to move toward Di. 3. When T=1274°C, liquid has moved to eutectic; Di begins to crystallize. No change in temperature or composition of any of the 3 phases is permitted until the liquid has completely crystallized. 4. At temperatures below 1274°C, only crystals of An and Di are present. X

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

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

Crystallization Behavior of Melts 1. Cooling melts crystallize from a liquid to a solid over a range of temperatures (and pressures) 2. Several minerals crystallize over this T range, and the number of minerals increases as T decreases 3. The minerals that form do so sequentially, with considerable overlap 4. Minerals that involve solid solution change composition as cooling progresses 5. The melt composition also changes during crystallization 6. The minerals that crystallize (as well as the sequence) depend on T and X of the melt 7. Pressure can affect the types of minerals that form and the sequence 8. The nature and pressure of the volatiles can also affect the minerals and their sequence