Phase Equilibria. Olivine and Clinopyroxene (Augite) follow Bowen’s Reaction Series, Discontinuous...

Phase EquilibriaPhase Equilibria

Olivine and Clinopyroxene (Augite) follow Bowen’s Reaction Series, Discontinuous Side. Olivine appears first, then decreases as pyroxenes start. Olivine becomes embayed. Note also that, in this case, plagioclases start at cooler temperatures than pyroxenes.

Mineral Stability Phase Stability The stability of a phase is

determined by the Gibbs free energy, G.

A Mineral of constant composition is considered a solid phase

Mineral stability is commonly portrayed on a Phase Diagram

Components and Phases

Components are the chemical entities necessary to define all the potential phases in a system of interest

Here one Component, Al2SiO5

Phases: number of mineral species plus fluidsHere three Phases: Kyanite, Sillimanite, and Andalucite

And

Degrees of Freedom f by Examples

If T and P can change without changing the mineral assemblage, the system has two degrees of freedom f = 2

If neither T or P can change without changing the mineral assemblage, the system has zero degrees of freedom f = 0

If T and P must change together to maintain the same mineral, the system has one degree of freedom f = 1

Ky.

And.

Sill.

On a phase diagram f=0 corresponds to a point,

f = 1 to a reaction line,

f = 2 to a 1 phase area.

p + f = c + 2

The Phase Rule

The number of minerals (phases) that may stably coexist is limited by the number of chemical components

p + f = c + 2 OR f = c – p +2where P is the number of mineral phases, c

the number of chemical components, and f is the number of degrees of freedom.

Simple System: H20

In a one component system, for example H2O, phase changes occur at constant temperature until one phase is used up. We can use this, for example, to measure the true temperature of crystallization, seen here as the level 2, where liquid water turns to ice.

Note: Temperature versus Time plot, Pressure = 0.1 MPa (1 bar, atmospheric pressure)

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

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 = temperature and pressure,temperature and pressure,

or temperature and composition, or temperature and composition, for geologistsfor geologists

Here is an internally heated Here is an internally heated pressure vessel at the AMNHpressure vessel at the AMNH

With these you can study, for example:

1. the temperature and pressure conditions at which polymorphs change from one form to another.

2. The reactions of minerals with fluids (for example salty or alkaline water) at high temperatures and pressures. Dangerous, why?

3. The conditions necessary to change one assemblage of minerals to another

http://research.amnh.org/earthplan/research/Equipment/Petrology

Called BOMBS

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 - Component 1 - Component SystemsSystems

1. 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 2 components 2 components (Ab-An, i.e. NaSiAlSi(Ab-An, i.e. NaSiAlSi22OO88 - CaAlAlSi - CaAlAlSi22OO88))

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.

T - X diagram at constant P = 0.1 MPa

F = C - F = C - phi + + 1 1 since since Pressure is Pressure is constant: lose constant: lose 1 degree of 1 degree of FreedomFreedom

A solid solution is a mixture of one or more solutes in a solvent, where the crystal structure of the solvent remains unchanged by addition of the solutes. Typically the solutes are metal ions of similar ionic radii and having the same charge.

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

Example of cooling with a specific bulk composition

Point Point a:a: at 1560 at 1560ooCCPhases = 1 (liquid, X= AnPhases = 1 (liquid, X= An6060))

2 components An and Ab2 components An and Ab

Fixed pressure soFixed pressure so

Deg F = C – Deg F = C – phases phases + 1 + 1

F = 2 - 1 + 1 = 2F = 2 - 1 + 1 = 2

Considering an isobarically Considering an isobarically cooling magma, (constant cooling magma, (constant pressure)pressure)

and and are are dependent upon Tdependent upon T

XXAnAnliqliq

XXAnAnplagplag

At b –c: F = 2 - 2 + 1 = At b –c: F = 2 - 2 + 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

a “tie-line” connects coexisting phases b and ca “tie-line” connects coexisting phases b and c

When the temperature dropsto b, about 1475C, crystals of plagioclase form at composition c, about 87%An2 Components An and Ab2 phases liquid and solid

liqui

dus

solid

us

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

As the system cools, XAs the system cools, Xliqliq follows the liquidus and X follows the liquidus and Xsolidsolid follows the follows the solidus, in accordance with F = 1solidus, in accordance with F = 1

At any T, X(An)Liq and X(An)Plag are At any T, X(An)Liq and X(An)Plag are dependent upondependent upon T T

We can use the We can use the lever principlelever principle to determine the proportions of liquid and solid to determine the proportions of liquid and solid at any Tat any T

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

We can use the We can use the lever principlelever principle to to determine the proportions of liquid determine the proportions of liquid and solid at any Tand solid at any T

Notice these are reversedSolid distance det. Liq. amt.

The bulk composition is the pivot.

When XWhen Xplagplag h, then X h, 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 g is the composition of the last liquid to crystallize at Thus g is the composition of the last liquid to crystallize at 13401340ooC for bulk X = 0.60C for bulk X = 0.60

Final plagioclase (solid) to form is i when = 0.60Final plagioclase (solid) to form is i when = 0.60

NowNowphasesphases = 1 = 1 (all solid) so deg F = 2 - 1 + 1 = 2 (all solid) so deg F = 2 - 1 + 1 = 2

XXAnAnpla gpla g

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 b to g The composition of the liquid changed from b to g5.5. The composition of the solid changed from c to h The composition of the solid changed from c to h

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

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

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

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.

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))

Is also a solid-solution series MgIs also a solid-solution series Mg+2+2 to Fe to Fe+2+2

Fig. 6-10. Isobaric T-X phase diagram at atmospheric pressure After Bowen and Shairer (1932), Amer. J. Sci. 5th Ser., 24, 177-213.

Are Mg+2 and Fe+2 about the same size?

Early Olivines react with the melt much more than early Ca++ Plagioclases. Why?

2-Comp. Eutectic Systems2-Comp. 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.

Diopside is a pyroxene MgCaSi2O6

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

At a: phi = phases = 1 (all liquid)F = C - phi + 1 = 2 - 1 + 1 = 2Good choice for axes is T and X(An)Liq

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

What happens at b? Pure Anorthite forms (point c)phi = 2 liquid at b plus solid An at cF = 2 - 2 + 1 = 1

composition of all phases determined by T

Xliq is really the only compositional variable in this particular system

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

Continuous reactionContinuous reaction: liq: liqaa anorthite + liq anorthite + liqbb

Lever rule shows less liquid and more Anorthite as cooling progresses

At d, 1274At d, 1274ooC C = 3: = 3: Di, An, Liquid Di, An, Liquid

so F = 2 - 3 + 1 = so F = 2 - 3 + 1 = 0 invariant0 invariant– Pressure, Temp., and the composition of all Pressure, Temp., and the composition of all

phases is fixedphases is fixed– Must remain at 1274Must remain at 1274ooC until a phase is lostC until a phase is lost

Discontinuous Reaction: Discontinuous Reaction:

at d all at a single Tat d all at a single Td between g and h, so reaction must be:Liquid = Diopside + Anorthite must run right toward low entropy of solidstherefore first phase lost is liquid

Below 1274oC have pure Diopside + pure Anorthitephi = 2 and F = 2 - 2 + 1 = 1Only logical variable in this case is T (since the composition of both solids is fixed)

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

Pyroxene forms before plagioclasePyroxene 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 PyroxenePlagioclase forms before Pyroxene

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•The final rock composition for no solid solution is the The final rock composition for no solid solution is the bulk compositionbulk composition

•is the opposite of equilibrium crystallizationis the opposite of equilibrium crystallization• Thus the Thus the first melt first melt of any mixture of Di and An must be of any mixture of Di and An must be the eutectic composition as wellthe eutectic composition as well

Equilibrium Equilibrium melting melting

Fractional crystallization:Fractional crystallization:

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

If fractional crystallization is efficient, and earlier xtals are removed, the last layer to crystallize will be the eutectic composition, because the last liquid composition is the eutectic composition

Partial Melting:Partial Melting:if remove liquid perfectly as soon as it forms (must be rare)First melts of Di + An would be eutectic liquid composition d at 1274oC consume either Di or An first depending on bulk XThe melting solid would be either pure Di or An dep on bulk X After one solid consumed, the Temp would rise, with no further melting,until the melting point of the remainiing solid.New melt temp and composition would jump from 1274oC f to either 1392o for pure Diopside or to 1553 for pure Anorthite.Thus heat 118oC or 279oC before next melt

Binary Peritectic SystemBinary Peritectic System

It is possible to combine Forsterite, a Mg Olivine, with Cristobalite SiO2 to get the intermediate Mg-orthopyroxene Enstatite in the Fo-SiO2 system.

Mg2SiO4 +SiO2 = 2MgSiO3

Fo + Cr = En

Notice the is an extra inflection point, the Peritectic P

There are still only two components, Fo and Cr, but an intermediate phase, Enstatite, forms during cooling at and below 1557oC

This is called a Peritectic System

Crystallization of a mantle partial melt

Isopleth (the Isopleth (the vertical blue vertical blue line) a line of line) a line of constant constant compositioncomposition

Binary Partial MeltBinary Partial Melt

Isopleth (the Isopleth (the vertical blue vertical blue line) a line of line) a line of constant constant compositioncomposition

It shows the It shows the original bulk original bulk compositioncomposition

Binary Partial MeltBinary Partial Melt

Fractional crystallization of a mantle partial meltFractional crystallization of a mantle partial melt

Initially onlyInitially onlyOlivine freezes, Olivine freezes, settles, & is settles, & is removed. Bulk removed. Bulk composition in composition in liquid becomes liquid becomes more silica-rich. more silica-rich. Melt composition Melt composition (Liquidus) (Liquidus) approaches approaches Enstatite as Enstatite as Magnesium ions Magnesium ions are removedare removed


Melt changes Melt changes composition past composition past EnEn, Temp lowers to , Temp lowers to Peritectic P, then Peritectic P, then solids solids X changes X changes atatconstant T get constant T get Enstatite + Fo +LEnstatite + Fo +Lat the Peritectic at the Peritectic temperaturetemperature

Peritectic - a Peritectic - a low low temperature temperature inflection point inflection point on the liquidus on the liquidus at which a at which a liquid of liquid of specified specified composition is composition is in equilibrium in equilibrium with two or with two or more more crystalline crystalline phases.phases.


Between Between the the Peritectic Peritectic and and Eutectic E, Eutectic E, the crystals the crystals forming are forming are 100% 100% EnstatiteEnstatite

Eutectic - the T Eutectic - the T on a T-X on a T-X diagram where a diagram where a mixture of mixture of elements of a elements of a single chemical single chemical composition X composition X solidifies at a solidifies at a lower lower temperature temperature than any other than any other composition composition made up of the made up of the same same ingredients.ingredients.


At Eutectic, At Eutectic, Enstatite and Enstatite and SiOSiO22 crystallize crystallize at same time.at same time.New New composition is composition is much more much more silica rich. silica rich. Below Eutectic, Below Eutectic, solids are solids are Enstatite and Enstatite and Silica. At 100 Silica. At 100 MPa, the Silica MPa, the Silica mineral is mineral is CristobaliteCristobalite

Mantle Crust


Notice what Notice what happened, Initially, a happened, Initially, a partial melt of the partial melt of the mantle made of mantle made of Forsterite olivine, and Forsterite olivine, and below 1557C below 1557C Forsterite plus the Forsterite plus the pyroxene Enstatite. pyroxene Enstatite. This is an upper This is an upper mantle composition. mantle composition. These early crystals These early crystals are removed.are removed.

From the Peritectic From the Peritectic 1557C to the Eutectic 1557C to the Eutectic 1543C and below, the 1543C and below, the composition shifts to composition shifts to Enstatite plus silica, a Enstatite plus silica, a crust compositioncrust composition

Mantle Crust

Fractionation of a Mantle partial melt yields a silica rich crust composition


Notice what Notice what happened, Initially, a happened, Initially, a partial melt of the partial melt of the mantle made of mantle made of Forsterite olivine, and Forsterite olivine, and below 1557C below 1557C Forsterite plus the Forsterite plus the pyroxene Enstatite. pyroxene Enstatite. This is an upper This is an upper mantle composition. mantle composition. These early crystals These early crystals are removed.are removed.

From the Peritectic From the Peritectic 1557C to the Eutectic 1557C to the Eutectic 1543C and below, the 1543C and below, the composition shifts to composition shifts to Enstatite plus silica, a Enstatite plus silica, a crust compositioncrust composition

Mantle Crust



Original isopleth is mantle Original isopleth is mantle composition field. For 100 composition field. For 100 MPa, as the partial melt is MPa, as the partial melt is cooled, the first Olivine cooled, the first Olivine crystals are formed at crystals are formed at 1890°C. These crystals are 1890°C. These crystals are 100% Forsterite and are 100% Forsterite and are removed from the system, removed from the system, driving the bulk driving the bulk composition to a more composition to a more SiO2-rich or continental SiO2-rich or continental nature. Forsterite continues nature. Forsterite continues to be the only crystals to be the only crystals formed until the formed until the temperature reaches that temperature reaches that of the Peritectic. At the of the Peritectic. At the Peritectic, Enstatite begins Peritectic, Enstatite begins to crystallize. Between the to crystallize. Between the Peritectic and the Eutectic Peritectic and the Eutectic the crystals forming are the crystals forming are 100% Enstatite. At the 100% Enstatite. At the Eutectic the three phases of Eutectic the three phases of Enstatite, melt, and Silica Enstatite, melt, and Silica co-exist. The melt co-exist. The melt continues to cool, resulting continues to cool, resulting in two solid phases, in two solid phases, Enstatite and silica.Enstatite and silica.

Mantle Crust


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Phase Equilibria. Olivine and Clinopyroxene (Augite) follow Bowen’s Reaction Series, Discontinuous...

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