G EOL 5310 A DVANCED I GNEOUS AND M ETAMORPHIC P ETROLOGY Phase Diagrams October 26, 2009

M AKAOPUHI L AVA L AKE, H AWAII W ATCHING A M AGMA C RYSTALLIZE From Wright and Okamura, (1977) USGS Prof. Paper, TIME TEMPERATURE

M AKAOPUHI L AVA L AKE, H AWAII Percent Glass Temperature o c 80 Winter (2001), Figs. 6-1 & 6-2. From Wright and Okamura (1977) USGS Prof. Paper, 1004.

AnMg / (Mg + Fe) Weight % Glass OlivineAugitePlagioclase Mg / (Mg + Fe) Winter (2001), Fig From Wright and Okamura, (1977) USGS Prof. Paper, M AKAOPUHI L AVA L AKE, H AWAII C OMPOSITIONAL C HANGES IN S OLID S OLUTION M INERALS

C RYSTALLIZATION B EHAVIOR OF M AGMAS FROM NATURAL AND EXPERIMENTAL OBSERVATIONS AND THERMODYMANIC PREDICTIONS Cooling melts crystallize from a liquid to a solid over a range of temperatures (and pressures) Several minerals crystallize over this T range, and the number of minerals increases as T decreases The minerals that form do so sequentially, generally with considerable overlap Minerals that involve solid solution change composition as cooling progresses The melt composition also changes during crystallization The minerals that crystallize (as well as the sequence) depend on T and X of the melt Pressure can affect the temperature range at which a melt crystallizes and the types of minerals that form The nature and pressure of volatiles can also affect the temperature range of xtallization and the mineral sequence

W HY DO M AGMAS C RYSTALLIZE T HIS W AY ? P REDICTED BY P HASE D IAGRAMS Although magmas (melts + crystals) are some of the most complex systems in nature, we can evaluate how they form and crystallize by simplifying them into their basic chemical constituent parts and empirically determine (observe) how these simple systems react to geologically important variables – temperature and pressure. We portray this behavior through the construction of PHASE DIAGRAMS

P HASE D IAGRAMS T ERMINOLOGY PHASE of a System A physically distinct part of a system that may be mechanically separated from other distinct parts. (e.g., in a glass of ice water (the system), ice and water are two phases mechanically distinct phases) COMPONENTS of a System NaAlSi 3 O 8 CaAl 2 Si 2 O 8 - The minimum number of chemical constituents that are necessary to define the complete composition of a system (e.g. for the plagioclase system, components are NaAlSi 3 O 8 – albite and CaAl 2 Si 2 O 8 - anorthite) VARIABLES that define the STATE of a System Extensive – dependent on the quantity of the system – volume, mass, moles,... Intensive – properties of the phases of a system that are independent of quantities (temperature, pressure, density, molecular proportions, elemental ratios,...) Note that ratios of extensive variables become intensive (V/m = density,  V/moles=molar volume)

G IBBS P HASE R ULE F = C -  + 2 F = # degrees of freedom The number of intensive parameters that must be specified in order to completely determine the system, or the number of variables that can be changed independently and still maintain equilibrium  = # of phases phases are mechanically separable constituents C = minimum # of components (chemical constituents that must be specified in order to define all phases) 2 = Two intensive parameters Usually = temperature and pressure ONLY APPLIES TO SYSTEMS IN CHEMICAL EQUILIBRIUM!!

PHASE RULE IN A ONE-COMPONENT SYSTEM F = C -  + 2 Divariant Field F2 F = 1 – = 2 Univariant Line F1 F = 1 – = 1 Invariant Point F0 F = 1 – = 0 SiO 2

PHASE RULE IN A ONE- COMPONENT SYSTEM H 2 O Fluid Sublimation Note that HEAT is different than TEMPERATURE. A boiling pot of water must be continuously heated to completely turn to steam, all the while sitting at 100 o C This heat is called the latent heat of vaporization The heat require to turn solid into liquid is the latent heat of fusion

T WO -C OMPONENT S YSTEM WITH S OLID S OLUTION COMPARE X AND T AT A CONSTANT P System – Plagioclase Phases – Liquid and Plagioclase mineral Components – NaAlSi 3 O 8 CaAl 2 Si 2 O 8 Ab (NaAlSi 3 O 8 ) An (CaAl 2 Si 2 O 8 ) coupled substitution! An content = An / (Ab + An) F = C -  + 1 (only 1 variable since P is constant) Divariant Field F2 F = 2 – = 2 Univariant Field F1 F = 2 – = 1 Phase Relationships determined by Experimental Data

T WO -C OMPONENT S YSTEM WITH S OLID S OLUTION E QUILIBRIUM C RYSTALLIZATION a – Starting bulk composition of melt = An60 b – Beginning of crystallization T= 1475 o C c – Composition of first plagioclase to crystallize = An87

T WO -C OMPONENT S YSTEM WITH S OLID S OLUTION E QUILIBRIUM C RYSTALLIZATION a – Starting bulk composition of melt = An60 b – Beginning of crystallization T= 1475 o C c – Composition of first plagioclase to crystallize at 1475 o C = An87 d – Melt composition at 1450 o C = An48 e – Bulk composition of Magma (Melt + Crystals = An60) f – Composition of Plagioclase at 1450 o C = An81

T WO -C OMPONENT S YSTEM WITH S OLID S OLUTION E QUILIBRIUM C RYSTALLIZATION U SING THE L EVER R ULE TO DETERMINE C RYSTAL :M ELT R ATIO 40%60% %Melt%Melt%Plag

T WO -C OMPONENT S YSTEM WITH S OLID S OLUTION E QUILIBRIUM C RYSTALLIZATION a – Starting bulk composition of melt = An60 b – Beginning of crystallization T= 1475 o C c – Composition of first plagioclase to crystallize at 1475 o C = An87 d – Melt composition at 1450 o C = An48 e – Bulk composition of Magma (Melt + Crystals = An60) f – Composition of Plagioclase at 1450 o C = An81 g – Last melt composition at 1340 o C = An18 h – Final composition of plagioclase at 1450 o C = An60 i – Subsolidus cooling of plagioclase

T WO -C OMPONENT S YSTEM WITH S OLID S OLUTION F RACTIONAL C RYSTALLIZATION As crystals form, they are removed (fractionated) from the system and thus are not allowed to reequilibrate with the cooling melt. This has the effect of incrementally resetting the bulk composition of the liquid to a lower An content with each crystallization step. Consequently, the final melt may have a composition of An0 (pure Ab end member)

T WO -C OMPONENT S YSTEM WITH S OLID S OLUTION F RACTIONAL C RYSTALLIZATION uts.cc.utexas.edu/~rmr/CLweb/volcanic.htm Because of coupled substitution of Ca-Na and Al-Si in plagioclase, reequilibration is difficult with T decrease, leading to chemically zoned crystals like this one. Avg. An=60

T WO -C OMPONENT S YSTEM WITH S OLID S OLUTION O LIVINE Sonju Lake Intrusion Fayalite Fe 2 SiO 4 Fosterite Fe 2 SiO 4

T WO -C OMPONENT S YSTEM WITH A E UTECTIC P YROXENE - P LAGIOCLASE Eutectic Point

T WO -C OMPONENT S YSTEM WITH A E UTECTIC P YROXENE - P LAGIOCLASE Eutectic Point a – bulk starting composition = An70

T WO -C OMPONENT S YSTEM WITH A E UTECTIC P YROXENE - P LAGIOCLASE Eutectic Point a – bulk starting composition = An70 b – crystallization begins at 1450 o C c - pure plagioclase (An) crystallizes

T WO -C OMPONENT S YSTEM WITH A E UTECTIC P YROXENE - P LAGIOCLASE Eutectic Point a – bulk starting composition = An70 b – crystallization begins at 1450 o C c - pure plagioclase (An) crystallizes b-d – magma composition changes as plagioclase crystallizes d – reaction stays at 1274 o C until liquid is consumed An 30% Liq 70% An 50% Liq 50% An 70% Di 30% LeverRule

T WO -C OMPONENT S YSTEM WITH A E UTECTIC P YROXENE – P LAGIOCLASE E VOLUTION OF L IQUID AND S OLID DURING C RYSTALLIZATION Eutectic Point Equilibrium vs. Fractional

T WO -C OMPONENT S YSTEM WITH A E UTECTIC P YROXENE – P LAGIOCLASE E QUILIBRIUM M ELTING

T WO -C OMPONENT S YSTEM WITH A E UTECTIC P YROXENE – P LAGIOCLASE F RACTIONAL ( OR B ATCH ) M ELTING

Three phases 2MgSiO 3 (Opx) = Mg 2 SiO 4 (Ol) + SiO 2 (Qtz) Si-rich magma (a) (eutectic relationship) Winter (2001) Figure 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. T WO -C OMPONENT S YSTEM WITH A P ERITECTIC O LIVINE -O RTHOPYROXENE -Q UARTZ

Mg-rich magma (f) i - Peritectic Point Winter (2001) Figure 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. T WO -C OMPONENT S YSTEM WITH A P ERITECTIC O LIVINE -O RTHOPYROXENE -Q UARTZ

i Fo En 1557 Bulk X T WO -C OMPONENT S YSTEM WITH A P ERITECTIC O LIVINE -O RTHOPYROXENE -Q UARTZ Liq 60% Ol 40% Opx 67% Ol 33% Proportional amount of Ol that must be converted to Opx Mg 2 SiO 4 (Ol) + SiO 2 (Liq) 2MgSiO 3 (Opx) Opx Ol Opx –reaction rim Ol

1543 c d i k m Fo En 1557 bulk X x y Cr T WO -C OMPONENT S YSTEM WITH A P ERITECTIC O LIVINE -O RTHOPYROXENE -Q UARTZ System at: - pertectic point 10%Ol +90%Liq  50%Opx+50%Liq i.e. all original Ol recrystallizes to Opx (if equilibrium is maintained) - 80% Opx + 20% Liq - eutectic point 90%Opx +10%Liq  94%Opx+6%Qtz i m c

Incongruent Melting of Enstatite F Melt of En does not  melt of same composition F Rather En  Fo + Liq i at the peritectic Partial Melting of Fo + En (harzburgite = mantle) F En + Fo also  first liq = i F Remove i and cool F Result = ? 1543 c d i Fo En 1557 Cr T WO -C OMPONENT S YSTEM WITH A P ERITECTIC O LIVINE -O RTHOPYROXENE -Q UARTZ

P RESSURE E FFECTS Different phases have different compressibilities Thus P will change Gibbs Free Energy differentially Raises melting point (lower volume (solid) phase is favored at higher P) Shifts from a peritectic relationship at low P to a dual eutectic relationship at high P with a thermal divide separating them. Figure The system Fo-SiO 2 at atmospheric pressure and 1.2 GPa. After Bowen and Schairer (1935), Am. J. Sci., Chen and Presnall (1975) Am. Min. T WO -C OMPONENT S YSTEM WITH A P ERITECTIC O LIVINE -O RTHOPYROXENE -Q UARTZ

L IQUID I MMISCIBILITY T WO -C OMPONENT S YSTEM WITH A S OLVUS O LIVINE -O RTHOPYROXENE -Q UARTZ Hyper-liquidus Solvus

S OLID S OLUTION WITH A E UTECTIC T WO -C OMPONENT S YSTEM WITH S OLID S OLUTION, A E UTECTIC AND A S OLVUS P LAGIOCLASE AND A LKALI F ELDSPAR Subsolidus Solvus  Perthitic Exsolution

T WO -C OMPONENT S YSTEM WITH A S OLVUS P RESSURE E FFECTS

T HREE C OMPONENT S YSTEM WITH E UTECTICS O LIVINE -P LAGIOCLASE -P YROXENE (F O -A N -D I ) Liquidus surface showing temperature contours F = 3 – = 2 (divariant field) Cotectic (or binary eutectic) F = 3 – = 1 (univariant line) Liquidus surface showing temperature contours F = 3 – = 2 Ternary eutectic F = 3 – = 0 (invariant point) Pressure = 0.1 MPa Winter (2001) 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.

T HREE C OMPONENT S YSTEM WITH E UTECTICS O LIVINE -P LAGIOCLASE -P YROXENE (F O -A N -D I ) Pressure = 0.1 MPa X S X – starting magma composition S – starting bulk solid composition X’ X’ – magma composition when plagioclase become saturated along with olivine S’ S’ – bulk solid composition when magma at X’ (olivine composes ~ 30% of system) X’ X’’ X S S’’ S’ X” X” – magma comp at 50% crystallized (based on lever rule of tie-line through X) S” S” – bulk solid comp when magma at X” (composed of 68%Ol & 32%Pl) X* S* X* X*=M – magma reached ternary eutectic at 65% crystallized S* S* – bulk solid comp when magma reaches ternary eutectic (composed of 60%Ol & 40%Pl) X* SfSfSfSf X* X*=M – magma comp fixed at ternary eutectic until 100% crystallized S f S f – final bulk solid = X-starting liquid comp Equilibrium Crystallization

T HREE C OMPONENT S YSTEM WITH E UTECTICS O LIVINE -P LAGIOCLASE -P YROXENE (F O -A N -D I ) Pressure = 0.1 MPa X’ X’’ X S S’’ S’ X* S* X* SfSfSfSf Fractional Crystallization O PO PCO

3 binary systems: Fo-An eutectic An-SiO 2 eutectic Fo-SiO 2 peritectic Pressure = 0.1 MPa T HREE C OMPONENT S YSTEM WITH A P ERITECTIC P LAGIOCLASE -O LIVINE -(O RTHOPYROXENE )-Q UARTZ (A N -F O -(E N -)S I O 2 ) Winter (2001) 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. Liquidus contours not shown to reduce clutter

T HREE C OMPONENT S YSTEM WITH A P ERITECTIC P LAGIOCLASE -O LIVINE -(O RTHOPYROXENE )-Q UARTZ (A N -F O -(E N -)S I O 2 ) a – Starting Liquid Comp a-b – liquid path due to Fo crystallization b- En crystallization (and partial replacement of Fo) begins partial replacement of Fo) begins b-c – liquid path due to Fo+En crystallization c – An joins En and Fo as crystallizing phases; last liquid comp for equilibrium crystallization AB C F AB – Fo only crystallization drives liquid from a  b AB-C – En crystallization (and replacement) enriches bulk solid in En to C (where liquid reaches c) (and replacement) enriches bulk solid in En to C (where liquid reaches c) C-F – when liquid reaches c, An is added to bulk solid and is 100% crystallized when reach starting composition F LIQUID PATH SOLID PATH

T HREE C OMPONENT S YSTEM WITH A P ERITECTIC P LAGIOCLASE -O LIVINE -(O RTHOPYROXENE )-Q UARTZ (A N -F O -(E N -)S I O 2 ) All Ol is consumed g-d leg only possible with fractional crystallization final rock is En + An under equilibrium crystallization

T HREE C OMPONENT S YSTEM WITH S OLID S OLUTION P LAGIOCLASE -P YROXENE (A N -A B -D I ) Liquid – An content Tie-lines Winter (2001) 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.

T HREE C OMPONENT S YSTEM WITH S OLID S OLUTION P LAGIOCLASE -P YROXENE (A N -A B -D I ) Last Liquid (EC) Final Plag (EC)First Plag Starting Liquid Composition

T HREE C OMPONENT S YSTEM WITH S OLID S OLUTION P LAGIOCLASE -P YROXENE (A N -A B -D I ) First Plag Starting Liquid Composition Liquid composition arcs due to decreasing An content of plagioclase Last Liquid (EC) Final Plag (EC)

F OUR C OMPONENT S YSTEMS F O -D I -A N -A B Winter (2001) Figure The system diopside- anorthite-albite-forsterite. After Yoder and Tilley (1962). J. Petrol. Becoming difficult to visualize Time to revert to multi- dimensional mathematical models

B ACK TO T HERMODYNAMICS Think about Gibbs Free Energy again dG = VdP – SdT at a given P (0.1 MPa) and T (1300ºC) Low Volume, trumps Entropy  Minerals more stable High Entropy trumps volume  Liquid more stable Liq