Phase Diagrams Liquid a b Anorthite + Liquid T C Diopside + Anorthite 1274 Di 20 40 60 80 An 1200 1300 1400 1500 1600 T o C Anorthite + Liquid Liquid Liquidus Diopside + Liquid Diopside + Anorthite a b c 1553 1392 Wt.% Anorthite 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

Updates/questions Lab: Field trip on Saturday 18th, waivers in lab Topics: phase diagrams (today and Wednesday) Phase rule 1 component systems 2 component systems: Eutectic Solid solution Solvus

The Phase Rule F = C - f + 2

The Phase Rule F = C - f + 2

The Phase Rule F = C - f + 2

The Phase Rule F = C - f + 2

1 - Component Systems A B After Swamy and Saxena (1994), J. Geophys. Res., 99, 11,787-11,794. AGU

1 - C Systems Liquid log Pressure (MPa) Vapor Temperature oC 300 200 Ice VII Ice VI Ice II Ice I Ice V Ice III 300 200 100 -100 -3 -1 3 log Pressure (MPa) 400 -2 -4 1 2 Liquid Vapor 1 atm critical point 374oC & 21.8 MPa 0.01 o C & 0.0006 MPa 1 - C Systems Temperature oC After Bridgman (1911, Proc. Amer. Acad. Arts and Sci., 5, 441-513; 1936, J. Chem. Phys., 3, 597-605; 1937, J. Chem. Phys., 5, 964-966.

Binary Systems Liquid Anorthite + Liquid Diopside + Anorthite T C 1600 Liquid 1553 Liquidus 1500 T o C 1400 Anorthite + Liquid 1392 1300 Diopside + Liquid 1274 1200 Diopside + Anorthite Di 20 40 60 80 An Wt.% Anorthite Isobaric T-X phase diagram at atmospheric pressure (After Bowen (1915), Amer. J. Sci. 40, 161-185.

Crystallization in Binary Systems 1274 Di 20 40 60 80 An 1200 1300 1400 1500 1600 T o C Anorthite + Liquid Liquid Liquidus Diopside + Liquid Diopside + Anorthite a 1553 1392 Wt.% Anorthite

Crystallization: first crystals 1274 Di 20 40 60 80 An 1200 1300 1400 1500 1600 T o C Anorthite + Liquid Liquid Liquidus Diopside + Liquid Diopside + Anorthite a b c 1553 1392 Wt.% Anorthite

Crystallization: ongoing 1274 Di 20 40 60 80 An 1200 1300 1400 1500 1600 T o C Anorthite + Liquid Liquid Liquidus Diopside + Liquid Diopside + Anorthite a b c 1553 1392 Wt.% Anorthite

Crystallization: eutectic 1600 a Liquid 1553 Liquidus 1500 b c T o C 1400 Anorthite + Liquid 1392 d 1300 Diopside + Liquid g h 1274 1200 Diopside + Anorthite Di 20 40 60 80 An Wt.% Anorthite

Crystallization: levers The lever principle: fraction of melt vs. crystals d e f D Amount of liquid ef = de ef Amount of solid de An 1274 Di 20 40 60 80 An 1200 1300 1400 1500 1600 T o C Anorthite + Liquid Liquid Liquidus Diopside + Liquid Diopside + Anorthite a b c 1553 1392 Wt.% Anorthite } Crystals

Crystallization: left half 1274 Di 20 40 60 80 An 1200 1300 1400 1500 1600 T o C Anorthite + Liquid Liquid Liquidus Diopside + Liquid Diopside + Anorthite d e f 1553 1392 Wt.% Anorthite g h

Augite forms before plagioclase Gabbro of the Stillwater Complex, Montana This forms on the left side of the eutectic

Plagioclase forms before augite Ophitic texture Diabase dike This forms on the right side of the eutectic

Additional notes Liquid a b e Anorthite + Liquid d h 1274 Di 20 40 60 80 An 1200 1300 1400 1500 1600 T o C Anorthite + Liquid Liquid Liquidus Diopside + Liquid Diopside + Anorthite a b c d e f 1553 1392 Wt.% Anorthite g h

Fractional crystallization 1274 Di 20 40 60 80 An 1200 1300 1400 1500 1600 T o C Anorthite + Liquid Liquid Liquidus Diopside + Liquid Diopside + Anorthite 1553 1392 Wt.% Anorthite

Equilibrium melting Liquid Anorthite + Liquid d Diopside + Anorthite T 1274 Di 20 40 60 80 An 1200 1300 1400 1500 1600 T o C Anorthite + Liquid Liquid Liquidus Diopside + Liquid Diopside + Anorthite d 1553 1392 Wt.% Anorthite

Solid solutions T C Liquid Plagioclase Weight % An s d u L i q 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 Isobaric T-X phase diagram at atmospheric pressure (after Bowen 1913, Amer. J. Sci., 35, 577-599).

Feldspar composition a T C Liquid Plagioclase Weight % An (100 XAn) o 1118 Ab 20 40 60 80 An 1100 1200 1300 1400 1500 1557 T C o Plagioclase Liquid plus Weight % An (100 XAn) a

Solid solutions & phase rule 1118 Ab 20 40 60 80 An 1100 1200 1300 1400 1500 1557 T C o Plagioclase Liquid plus Weight % An a b

Crystallization b c Liquid Plagioclase T C Liquid Plagioclase a o 1557 1500 b c Liquid 1400 Plagioclase T C o + 1300 Liquid Plagioclase 1200 1118 1100 Ab 20 40 60 80 An

Crystallization & phase rule F = 2 - 2 + 1 = 1 (“univariant”) Must specify only one variable from among: T a 1557 1500 b Liquid c X An liq X Ab liq X An plag X Ab plag 1400 Plagioclase o T C and are dependent upon T The slope of the solidus and liquidus are the expressions of this relationship + X An liq X An plag 1300 Liquid Plagioclase 1200 1118 1100 Ab 20 40 60 80 An

Ongoing crystallization 1557 1500 Liquid b c d f 1400 Plagioclase T C o + 1300 Liquid Plagioclase 1200 1118 1100 Ab 20 40 60 80 An

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 a d b e f Liquid c d f D Plagioclase liquidus de ef + Liquid solidus Plagioclase Ab An

End of crystallization 1557 1500 Liquid b c d f 1400 Plagioclase T C o g h plus 1300 Liquid Plagioclase 1200 i 1118 1100 Ab 20 40 60 80 An Weight % An

of melts” observations Plagioclase 1557 1500 Liquid b Numbers refer to the “behavior of melts” observations c d f 1400 Plagioclase T C o g h plus 1300 Liquid * The actual temperatures and the range depend on the bulk composition Plagioclase 1200 i 1118 1100 Ab 20 40 60 80 An Weight % An

Melting--reverse of crystallization 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 a 1557 1500 Liquid b c d f 1400 Plagioclase T C o g h plus 1300 Liquid Plagioclase 1200 i 1118 1100 Ab 20 40 60 80 An Weight % An

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 a 1557 1500 Liquid b c d f 1400 Plagioclase o T C g h plus 1300 Liquid Plagioclase 1200 i 1118 1100 Ab 20 40 60 80 An Weight % An

Melting Liquid Plagioclase g T C h Liquid Plagioclase i Weight % An a 1557 1500 Liquid b c d f 1400 Plagioclase o T C g h plus 1300 Liquid Plagioclase 1200 i i 1118 1100 Ab 20 40 60 80 An Weight % An

Olivine System, another example Fo 20 40 60 80 Fa 1300 1500 1700 1890 1205 T oC Olivine Liquid plus 1900 a b c d Wt.% Forsterite Isobaric T-X phase diagram at atmospheric pressure (After Bowen and Shairer (1932), Amer. J. Sci. 5th Ser., 24, 177-213.

C. Binary Peritectic Systems 1557 Mg2SiO4 20 40 60 80 SiO2 1400 1600 1800 2000 1713 T oC MgSiO2 1543 1470 Enstatite Forsterite + Enstatite Liquid + 1695 Enstatite + Tridymite Enstatite + Cristobalite Cristobalite + Liquid Two Liquids Liquid Wt.% X2 b e a Figure 6-12. Isobaric T-X phase diagram of the system Fo-Silica at 0.1 MPa. After Bowen and Anderson (1914) and Grieg (1927). Amer. J. Sci.

Immiscible Liquids Cool X = n At 1960oC hit solvus exsolution ® 2 liquids o and p f = 2 F = 1 both liquids follow solvus 1557 Mg2SiO4 20 40 60 80 SiO2 1400 1600 1800 2000 1713 T oC MgSiO2 1543 1470 Forsterite + Enstatite Liquid + 1695 Enstatite + Tridymite Enstatite + Cristobalite Cristobalite + Liquid Two Liquids Liquid Wt.% X2 o n c p Mafic-rich liquid Silica-rich Crst 1695 Reaction? At 1695oC get Crst also

D. Solid Solution with Eutectic: Ab-Or (the alkali feldspars) Figure 6-16. T-X phase diagram of the system albite-orthoclase at 0.2 GPa H2O pressure. After Bowen and Tuttle (1950). J. Geology.

Effect of PH O on Ab-Or 2 Figure 6-17. The Albite-K-feldspar system at various H2O pressures. (a) and (b) after Bowen and Tuttle (1950), J. Geol, (c) after Morse (1970) J. Petrol.