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.

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 Opaque

Tem

per

atu

re o

C

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 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 considerable 3. The minerals that form do so sequentially, with considerable overlapoverlap

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

The Phase RuleThe Phase RuleF = C - F = C - + 2 + 2

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 C = minimum # of components

Chemical constituents that must be specified in order to Chemical constituents that must be specified in order to define all phases define all phases

2 = 2 intensive parameters2 = 2 intensive parametersUsually temperature and pressure for geologistsUsually temperature and pressure for geologists

OneOneComponent Component

SystemsSystems

SiOSiO22

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

Two Component SystemsTwo Component Systems

PlagioclasePlagioclase Ab (NaAlSiAb (NaAlSi33OO8 8 ) - An (CaAl) - An (CaAl22SiSi22OO88))

Systems with 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

A A continuous reactioncontinuous reaction of the type: of the type:liquidliquidBB + solid + solidCC = liquid = liquidDD + 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

P=1 atm

Composition of 1st crystal

X

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.

4. Ratio of Ca/Na in both crystals and liquid decrease with decreasing temperature; proportion of crystals increases as liquid decreases

Composition of last crystal

Composition of last liquid

5. Crystals of An61 cool without further change in composition

PowerPoint® presentation by Kenneth E. Windom

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(several slides back)(several slides back)

** The actual temperatures ** The actual temperatures and the range depend on the and the range depend on the bulk composition **bulk 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 it forms as it forms

Melt 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

OlivineOlivineFo - 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.

Two Component SystemsTwo Component Systems

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.

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

TT

MM

AnorthiteAnorthite

ForsteriteForsterite

DiopsideDiopside

Note three binary Note three binary eutecticseutectics

No solid solutionNo solid solution

Ternary eutectic = MTernary eutectic = M

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 considerable 3. The minerals that form do so sequentially, with considerable overlapoverlap

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