fase binaria

Phase EquilibriumPhase Equilibrium

Makaopuhi Lava LakeMakaopuhi Lava LakeMagma samples recovered from various Magma samples recovered from various

depths beneath solid crustdepths beneath solid crust

From Wright and Okamura, (1977) USGS Prof. Paper, 1004.

Thermocouple attached to sampler to Thermocouple attached to sampler to determine temperaturedetermine temperature

Makaopuhi Lava LakeMakaopuhi Lava Lake

From Wright and Okamura, (1977) USGS Prof. Paper, 1004.

Temperature of sample vs. Percent GlassTemperature of sample vs. Percent Glass

10090706050403020100

Percent Glass

900

950

1000

1050

1100

1150

1200

1250

Tem

pera

ture

o c

80

Makaopuhi Lava LakeMakaopuhi Lava Lake

Fig. 6-1. From Wright and Okamura, (1977) USGS Prof. Paper, 1004.

Minerals that form during crystallizationMinerals that form during crystallization1250

1200

1150

1100

1050

1000

9500 0 0 010 10 20 10 102030 40 3050 40 50

Liquidus

Melt

Crust

Solidus

Olivine Clinopyroxene Plagioclase OpaqueT

emp

erat

ure

oC

olivine decreases

below 1175oC

Makaopuhi Lava LakeMakaopuhi Lava Lake

Fig. 6-2. From Wright and Okamura, (1977) USGS Prof. Paper, 1004.

Mineral composition during crystallizationMineral composition during crystallization100

90

80

70

60

50.7.8.9 .9 .8 .7 .6 80 70 60

AnMg / (Mg + Fe)

We

igh

t %

Gla

ss

Olivine Augite Plagioclase

Mg / (Mg + Fe)

Makaopuhi Lava LakeMakaopuhi Lava Lake

Fig. 6-3. From Wright and Okamura, (1977) USGS Prof. Paper, 1004.

Crystallization Behavior of MeltsCrystallization Behavior of Melts1. Cooling melts crystallize from a liquid to a solid 1. Cooling melts crystallize from a liquid to a solid over a range of over a range of

temperatures (and pressures)temperatures (and pressures)

Crystallization Behavior of MeltsCrystallization Behavior of Melts1. Cooling melts crystallize from a liquid to a solid over a range of 1. Cooling melts crystallize from a liquid to a solid over a range of

temperatures (and pressures)temperatures (and pressures)

2. 2. Several minerals crystallizeSeveral minerals crystallize over this T range, and the number of over this T range, and the number of minerals increases as T decreasesminerals increases as T decreases

Crystallization Behavior of MeltsCrystallization Behavior of Melts1. Cooling melts crystallize from a liquid to a solid over a range of 1. Cooling melts crystallize from a liquid to a solid over a range of

temperatures (and pressures)temperatures (and pressures)

2. Several minerals crystallize over this T range, and the number of 2. Several minerals crystallize over this T range, and the number of minerals increases as T decreasesminerals increases as T decreases

3. The minerals that form do so 3. The minerals that form do so sequentiallysequentially, with consideral overlap, with consideral overlap

Crystallization Behavior of MeltsCrystallization Behavior of Melts1. Cooling melts crystallize from a liquid to a solid over a range of 1. Cooling melts crystallize from a liquid to a solid over a range of

temperatures (and pressures)temperatures (and pressures)

2. Several minerals crystallize over this T range, and the number of 2. Several minerals crystallize over this T range, and the number of minerals increases as T decreasesminerals increases as T decreases

3. The minerals that form do so sequentially, with consideral overlap3. The minerals that form do so sequentially, with consideral overlap

4. Minerals that involve solid solution 4. Minerals that involve solid solution change compositionchange composition as cooling as cooling progressesprogresses

Crystallization Behavior of MeltsCrystallization Behavior of Melts1. Cooling melts crystallize from a liquid to a solid over a range of 1. Cooling melts crystallize from a liquid to a solid over a range of

temperatures (and pressures)temperatures (and pressures)

2. Several minerals crystallize over this T range, and the number of 2. Several minerals crystallize over this T range, and the number of minerals increases as T decreasesminerals increases as T decreases

3. The minerals that form do so sequentially, with consideral overlap3. The minerals that form do so sequentially, with consideral overlap

4. Minerals that involve solid solution change composition as cooling 4. Minerals that involve solid solution change composition as cooling progressesprogresses

5. The 5. The melt compositionmelt composition also changes during crystallization also changes during crystallization

Crystallization Behavior of MeltsCrystallization Behavior of Melts1. Cooling melts crystallize from a liquid to a solid over a range of 1. Cooling melts crystallize from a liquid to a solid over a range of

temperatures (and pressures)temperatures (and pressures)

2. Several minerals crystallize over this T range, and the number of 2. Several minerals crystallize over this T range, and the number of minerals increases as T decreasesminerals increases as T decreases

3. The minerals that form do so sequentially, with consideral overlap3. The minerals that form do so sequentially, with consideral overlap

4. Minerals that involve solid solution change composition as cooling 4. Minerals that involve solid solution change composition as cooling progressesprogresses

5. The melt composition also changes during crystallization5. The melt composition also changes during crystallization

6. The minerals that crystallize (as well as the sequence) depend on T 6. The minerals that crystallize (as well as the sequence) depend on T and X of the meltand X of the melt

Crystallization Behavior of MeltsCrystallization Behavior of Melts1. Cooling melts crystallize from a liquid to a solid over a range of 1. Cooling melts crystallize from a liquid to a solid over a range of

temperatures (and pressures)temperatures (and pressures)

2. Several minerals crystallize over this T range, and the number of 2. Several minerals crystallize over this T range, and the number of minerals increases as T decreasesminerals increases as T decreases

3. The minerals that form do so sequentially, with consideral overlap3. The minerals that form do so sequentially, with consideral overlap

4. Minerals that involve solid solution change composition as cooling 4. Minerals that involve solid solution change composition as cooling progressesprogresses

5. The melt composition also changes during crystallization5. The melt composition also changes during crystallization

6. The minerals that crystallize (as well as the sequence) depend on T 6. The minerals that crystallize (as well as the sequence) depend on T and X of the meltand X of the melt

7. 7. PressurePressure can affect the types of minerals that form and the can affect the types of minerals that form and the sequencesequence

Crystallization Behavior of MeltsCrystallization Behavior of Melts1. Cooling melts crystallize from a liquid to a solid over a range of 1. Cooling melts crystallize from a liquid to a solid over a range of

temperatures (and pressures)temperatures (and pressures)

2. Several minerals crystallize over this T range, and the number of 2. Several minerals crystallize over this T range, and the number of minerals increases as T decreasesminerals increases as T decreases

3. The minerals that form do so sequentially, with consideral overlap3. The minerals that form do so sequentially, with consideral overlap

4. Minerals that involve solid solution change composition as cooling 4. Minerals that involve solid solution change composition as cooling progressesprogresses

5. The melt composition also changes during crystallization5. The melt composition also changes during crystallization

6. The minerals that crystallize (as well as the sequence) depend on T 6. The minerals that crystallize (as well as the sequence) depend on T and X of the meltand X of the melt

7. Pressure can affect the types of minerals that form and the 7. Pressure can affect the types of minerals that form and the sequencesequence

8. The nature and pressure of the 8. The nature and pressure of the volatilesvolatiles can also affect the minerals can also affect the minerals and their sequenceand their sequence

F F = C - = C - + 2 + 2F = # degrees of freedomF = # degrees of freedom

The number of The number of intensiveintensive parameters that must be specified in parameters that must be specified in order to completely determine the systemorder to completely determine the system

The Phase RuleThe Phase Rule

F = C - F = C - + 2+ 2F = # degrees of freedomF = # degrees of freedom

The number of intensive parameters that must be specified in The number of intensive parameters that must be specified in order to completely determine the system order to completely determine the system

= # of phases= # of phasesphases are phases are mechanically separablemechanically separable constituents constituents

The Phase RuleThe Phase Rule

F = F = CC - - + 2 + 2F = # degrees of freedomF = # degrees of freedom

The number of intensive parameters that must be specified in The number of intensive parameters that must be specified in order to completely determine the system order to completely determine the system

= # of phases= # of phases

phases are mechanically separable constituentsphases are mechanically separable constituents

C = C = minimum #minimum # of of componentscomponents (chemical constituents that must (chemical constituents that must be specified in order to define all phases)be specified in order to define all phases)

The Phase RuleThe Phase Rule

The Phase RuleThe Phase RuleF = C - F = C - + + 22

F = # degrees of freedomF = # degrees of freedomThe number of intensive parameters that must be specified in The number of intensive parameters that must be specified in

order to completely determine the system order to completely determine the system

= # of phases= # of phasesphases are mechanically separable constituentsphases are mechanically separable constituents

C = minimum # of components (chemical constituents C = minimum # of components (chemical constituents that must that must be specified in order to define all be specified in order to define all phases)phases)

2 = 2 2 = 2 intensiveintensive parameters parameters

Usually = Usually = temperaturetemperature and and pressurepressure for us geologists for us geologists

High Pressure Experimental FurnaceHigh Pressure Experimental Furnace

Cross section: sample in redCross section: sample in red

thethe samplesample!

Carbide Carbide Pressure Pressure VessleVessle

1 cm FurnaceFurnaceAssemblyAssembly

Ta

lcSAMPLE

Graphite Furnace

800 Ton Ram

Ta

lc

Fig. 6-5. After Boyd and England (1960), J. Geophys. Res., 65, 741-748. AGU

1 - C Systems1 - C Systems1. The system SiO1. The system SiO22

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

1 - C Systems1 - C Systems2. The system H2. The system H22OO

Fig. 6-7. 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.

2 - C Systems2 - C Systems

1. 1. PlagioclasePlagioclase (Ab-An, NaAlSi(Ab-An, NaAlSi33OO88 - CaAl - CaAl22SiSi22OO88))

A. Systems with A. Systems with Complete Solid SolutionComplete Solid Solution

Fig. 6-8. Isobaric T-X phase diagram at atmospheric pressure. After Bowen (1913) Amer. J. Sci., 35, 577-599.

Bulk composition Bulk composition aa = An = An6060

= 60 g An + 40 g Ab= 60 g An + 40 g Ab

XXAnAn = 60/(60+40) = 0.60 = 60/(60+40) = 0.60

F = 2F = 2

1. Must specify 1. Must specify 22 independent independent intensiveintensive variables in order to completely determine variables in order to completely determine the systemthe system

= a = a divariantdivariant situation situation

2. Can vary 2 intensive variables independently 2. Can vary 2 intensive variables independently without changing without changing , the number of phases, the number of phases

same as:same as:

Must specify Must specify TT and or can vary these and or can vary these withoutwithout

changing the number of phaseschanging the number of phases

XXAnAnliqliq

Now cool to 1475Now cool to 1475ooC (point C (point bb) ... ) ... what happenswhat happens??Get Get new phasenew phase joining liquid: joining liquid: first crystals of first crystals of plagioclase: plagioclase: = 0.87 (point = 0.87 (point cc))

F = ?F = ?

XXAnAnplagplag

Considering an isobarically Considering an isobarically cooling magma, cooling magma,

and and are are dependent upon Tdependent upon T

XXAnAnliqliq

XXAnAnplagplag

F = 2 - F = 2 - 22 + 1 = + 1 = 1 (“univariant”)1 (“univariant”)Must specify only Must specify only oneone variable from among: variable from among:

TT XXAnAnliqliq

XXAbAbliqliq XXAnAn

plagplagXXAbAb

plagplag (P constant)(P constant)

The slope of the solidus and liquidus are the expressions of this relationship

At 1450At 1450ooC, liquid C, liquid dd and plagioclase and plagioclase f f coexist at equilibriumcoexist at equilibrium

A A continuous reactioncontinuous reaction of the type:of the type:

liquidliquidBB + solid + solidCC = =

liquidliquidDD + solid + solidFF

fd e

dede efef

The lever principle:The lever principle:

Amount of liquidAmount of liquid

Amount of solidAmount of solid dede

efef==

where where dd = the = the liquidliquid composition, composition, ff = the = the solidsolid composition composition and and ee = the = the bulkbulk composition composition

liquidusliquidus

solidussolidus

When XWhen Xplagplag hh, then X, then Xplagplag = X = Xbulkbulk and, according to the and, according to the

lever principle, the amount of liquid lever principle, the amount of liquid 0 0

Thus Thus gg is the composition of the last liquid to crystallize at is the composition of the last liquid to crystallize at 13401340ooC for bulk X = 0.60C for bulk X = 0.60

Final plagioclase to form is Final plagioclase to form is ii when = 0.60 when = 0.60

NowNow = 1 = 1 so F = 2 - 1 + 1 = 2 so F = 2 - 1 + 1 = 2

XXAnAnplagplag

Note the following:Note the following:1.1. The melt crystallized over a T range of 135 The melt crystallized over a T range of 135ooC *C *4.4. The composition of the liquid changed from The composition of the liquid changed from bb to to gg5.5. The composition of the solid changed from The composition of the solid changed from cc to to hh

Numbers referNumbers referto the “behaviorto the “behaviorof melts” observationsof melts” observations

* The actual temperatures * The actual temperatures and the range depend on the and the range depend on the bulk compositionbulk composition

Equilibrium Equilibrium meltingmelting is exactly the opposite is exactly the opposite Heat AnHeat An6060 and the first melt is and the first melt is g at Ang at An20 20 and 1340and 1340ooCC Continue heating: both melt and plagioclase change XContinue heating: both melt and plagioclase change X Last plagioclase to melt is Last plagioclase to melt is c (Anc (An8787) at 1475) at 1475ooCC

Fractional crystallization:Fractional crystallization: Remove crystals as they form so they can’t Remove crystals as they form so they can’t undergo a continuous reaction with the meltundergo a continuous reaction with the melt

At any T At any T XXbulkbulk = X = Xliqliq due to the removal of the crystalsdue to the removal of the crystals

Partial Melting:Partial Melting:Remove first meltRemove first melt as forms as formsMelt XMelt Xbulkbulk = 0.60 first liquid = = 0.60 first liquid = gg

remove and cool bulk = g remove and cool bulk = g final plagioclase = final plagioclase = ii

PlagioclasePlagioclase

Liquid

LiquidLiquid

plus

Plagioclase

Note the difference between the two types of fieldsNote the difference between the two types of fields

The The blueblue fields are fields are oneone phase fields phase fields

Any point in these fields represents a true Any point in these fields represents a true phase compositionphase composition

The blank field is a The blank field is a twotwo phase field phase field

Any point in this fieldAny point in this field represents a bulk represents a bulk

composition composed of two phasescomposition composed of two phases at the at the edge of the blue fields and connected by a edge of the blue fields and connected by a

horizontal tie-linehorizontal tie-line

2. The Olivine System2. The Olivine SystemFo - FaFo - Fa (Mg (Mg22SiOSiO44 - Fe - Fe22SiOSiO44))

also a solid-solution seriesalso 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 Systems2-C Eutectic Systems Example: Diopside - AnorthiteExample: Diopside - Anorthite

No solid solutionNo solid solution

Fig. 6-11. Isobaric T-X phase diagram at atmospheric pressure. After Bowen (1915), Amer. J. Sci. 40, 161-185.

Cool composition Cool composition aa::bulk composition = bulk composition = AnAn7070

Cool to 1455Cool to 1455ooC (point C (point bb))

Continue cooling as XContinue cooling as Xliqliq varies along the liquidus varies along the liquidus

Continuous reactionContinuous reaction: liq: liqAA anorthite + liq anorthite + liqBB

at 1274at 1274ooC C = 3 = 3 so F = 2 - 3 + 1 = so F = 2 - 3 + 1 = 0 invariant0 invariant (P) T and the composition of all phases is fixed(P) T and the composition of all phases is fixed Must remain at 1274Must remain at 1274ooC as a C as a discontinuous discontinuous

reactionreaction proceeds until a phase is lost proceeds until a phase is lost

Discontinuous Reaction: Discontinuous Reaction: all at a single Tall at a single T Use Use geometrygeometry to determine to determine

Left of the eutecticLeft of the eutectic get a similar situation get a similar situation

Note the following:Note the following:

1.1. The melt crystallizes over a T range up to ~280 The melt crystallizes over a T range up to ~280ooCC

2.2. A sequence of minerals forms over this interval A sequence of minerals forms over this interval

- And the number of minerals increases as T drops- And the number of minerals increases as T drops

6.6. The minerals that crystallize depend upon T The minerals that crystallize depend upon T

- The sequence changes with the bulk composition- The sequence changes with the bulk composition

#s are listed#s are listedpoints in textpoints in text

Augite forms before plagioclaseAugite forms before plagioclase

This forms on the This forms on the leftleft side of the eutectic side of the eutectic

Gabbro of Gabbro of the the Stillwater Stillwater Complex, Complex, MontanaMontana

Plagioclase forms before augitePlagioclase forms before augite

This forms on the This forms on the rightright side of the eutectic side of the eutectic

OphiticOphitic texture texture

Diabase dikeDiabase dike

Also note:Also note:• The last melt to crystallize in any binary eutectic The last melt to crystallize in any binary eutectic

mixture is the mixture is the eutecticeutectic composition composition• Equilibrium Equilibrium meltingmelting is the opposite of equilibrium is the opposite of equilibrium

crystallizationcrystallization• Thus the Thus the first meltfirst melt of any mixture of Di and An of any mixture of Di and Anmust be the eutectic composition as wellmust be the eutectic composition as well

Fractional crystallization:Fractional crystallization:

Fig. 6-11. Isobaric T-X phase diagram at atmospheric pressure. After Bowen (1915), Amer. J. Sci. 40, 161-185.

Partial Melting:Partial Melting:

C. Binary Peritectic SystemsC. Binary Peritectic SystemsThreeThree phases phases enstatiteenstatite = = forsteriteforsterite + + SiOSiO22

Figure 6-12. Figure 6-12. Isobaric T-X Isobaric T-X phase diagram of the system phase diagram of the system Fo-Silica at 0.1 MPa. After Fo-Silica at 0.1 MPa. After Bowen and Anderson (1914) Bowen and Anderson (1914) and Grieg (1927).and Grieg (1927). Amer. J. Amer. J. Sci.Sci.

C. Binary Peritectic SystemsC. Binary Peritectic Systems

Figure 6-12. Figure 6-12. Isobaric T-X Isobaric T-X phase diagram of the system phase diagram of the system Fo-Silica at 0.1 MPa. After Fo-Silica at 0.1 MPa. After Bowen and Anderson (1914) Bowen and Anderson (1914) and Grieg (1927).and Grieg (1927). Amer. J. Amer. J. Sci.Sci.

Figure 6-12. Figure 6-12. Isobaric T-X Isobaric T-X phase diagram of the system phase diagram of the system Fo-Silica at 0.1 MPa. After Fo-Silica at 0.1 MPa. After Bowen and Anderson (1914) Bowen and Anderson (1914) and Grieg (1927).and Grieg (1927). Amer. J. Amer. J. Sci.Sci.

ii = = “peritectic”“peritectic” point point

15571557ooC have C have colinearcolinear Fo-En-liq Fo-En-liq geometry indicates a reaction: Fo + liq = Engeometry indicates a reaction: Fo + liq = En consumesconsumes olivine (and liquid) olivine (and liquid) resorbed textures resorbed textures

When is the reaction finished?When is the reaction finished?

ccdd

iikk mm

FoFo EnEn

15571557

Bulk X

15431543

ccdd

iikkmm

FoFo EnEn

15571557

bulk Xbulk X

xx

yy

CrCr

Incongruent Melting of EnstatiteIncongruent Melting of Enstatite Melt of En does not Melt of En does not melt of same composition melt of same composition Rather Rather En En Fo + Liq Fo + Liq ii at the peritectic at the peritectic

Partial Melting of Fo + En (harzburgite) mantlePartial Melting of Fo + En (harzburgite) mantle En + Fo also En + Fo also firsl liq = firsl liq = ii Remove Remove ii and cool and cool Result = Result = ??

15431543

ccdd

ii

FoFo EnEn

15571557

bulk Xbulk X

CrCr

Immiscible LiquidsImmiscible LiquidsCool X = nCool X = n At 1960At 1960ooC hit C hit solvussolvus

exsolutionexsolution

2 liquids2 liquids oo and and pp

= 2 F = 1= 2 F = 1both liquids follow solvusboth liquids follow solvus

Mafic-richMafic-rich liquidliquid

Silica-richSilica-rich liquidliquid

Crst1695

Reaction?Reaction?

At 1695At 1695ooC get Crst alsoC get Crst also

Pressure EffectsPressure EffectsDifferent phases have different compressibilitiesDifferent phases have different compressibilities

Thus P will change Gibbs Free Energy differentiallyThus P will change Gibbs Free Energy differentially Raises melting pointRaises melting point Shift eutectic positionShift eutectic position (and thus X of first melt, etc.) (and thus X of first melt, etc.)

Figure 6-15. The system Fo-SiO2 at atmospheric pressure

and 1.2 GPa. After Bowen and Schairer (1935), Am. J. Sci., Chen and Presnall (1975) Am. Min.

D. Solid Solution with Eutectic:D. Solid Solution with Eutectic:Ab-Or Ab-Or (the alkali feldspars)(the alkali feldspars)

Eutectic Eutectic liquidus liquidus

minimumminimum

Figure 6-16.Figure 6-16. T-X phase T-X phase diagram of the system albite-diagram of the system albite-orthoclase at 0.2 GPa Horthoclase at 0.2 GPa H

22O O

pressure. After Bowen and pressure. After Bowen and Tuttle (1950).Tuttle (1950). J. Geology. J. Geology.

Effect of PEffect of PH OH O on Ab-Or on Ab-Or22

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.