Metamorphic Petrology GLY 262Metamorphic reactions and isograds

What do we mean by “reaction”?

ReactionReaction:: change in the nature or types of change in the nature or types of phases in a phases in a systemsystem=> formation of new => formation of new mineral(smineral(s) which are stable under the new ) which are stable under the new conditions.conditions.Reactions are written in the form:Reactions are written in the form:

reactants = productsreactants = productsA + B = C + DA + B = C + D

Or A = B + C + DOr A = B + C + DAlAl--Silicates Silicates =>=> Quartz + Quartz + CorundumCorundum Al2O3 SiO2Al2O3 SiO2 =>=> SiO2SiO2 ++ Al2O3Al2O3

Stable under P1-T1 conditions Stable under P2-T2 conditions

= Equilibrium

What is an What is an EquilibriumEquilibrium??

••If we subject a If we subject a systemsystem to some specific conditions of to some specific conditions of PP--T, and maintain these conditions unchanged for a T, and maintain these conditions unchanged for a sufficiently long time (t), the atoms/minerals in the sufficiently long time (t), the atoms/minerals in the system will group themselves into the most system will group themselves into the most stablestable possible possible configurationconfiguration and the and the systemsystem is then said to is then said to be in be in equilibriumequilibrium. . ••The most stable configuration is the one with the The most stable configuration is the one with the least free energyleast free energy..

EquilibriumEquilibrium

Energy States: Stability and EquilibriumEnergy States: Stability and Equilibriumexampleexample

(A)(A)

(B)(B)

(C)(C)

Unstable: falling or rollingUnstable: falling or rolling

MetastableMetastable: in low: in low--energyenergy

Stable: at rest in lowest energy Stable: at rest in lowest energy statestate

••) A ) A systemsystem is said to be in is said to be in EquilibriumEquilibrium when when the result of forces acting on the system at rest the result of forces acting on the system at rest is zero. is zero. ••) Thus ) Thus equilibrium equilibrium is a state of no changeis a state of no change

The most stable state is the The most stable state is the one with lowest free one with lowest free

energy (G)energy (G)

SystemSystemis simply a group of atoms, minerals is simply a group of atoms, minerals ((phasesphases), or rocks which are under ), or rocks which are under consideration. consideration. A A systemsystem is made up of one or moreis made up of one or more phasesphasesEx:Ex:••) Quartzite = ) Quartzite = systemsystem, made of Quartz = , made of Quartz = phasephase••) Gneiss = System), made of ) Gneiss = System), made of BiotBiot, , QtzQtz, Sill, , Sill, KfsKfs = = phasesphases

Phase (P)Phase (P)

Each Each physically separablephysically separable part (constituent) of part (constituent) of the system. the system.

••a minerala mineral••a liquid/Melta liquid/Melt••a vapor/fluida vapor/fluid

If: If: systemsystem = = rockrock => => phasesphases = = mineralsminerals, , fluidsfluids, , meltmelt..Each phase is composed of a set of Each phase is composed of a set of chemical chemical component.component.

Chemical components (C)Chemical components (C)

Each Each phasephase in a in a systemsystem= =

one or more one or more componentscomponents

How many phases can coexist in equilibrium in a system? How many phases can coexist in equilibrium in a system?

-Willard Gibbs 1875-1876) => rule which determines the number of rule which determines the number of degrees of degrees of freedomfreedom for a heterogeneous system in equilibrium : for a heterogeneous system in equilibrium : Phase RulePhase Rule

The number of degrees of freedomThe number of degrees of freedom for a system is the number of intensive variables (often P, T, and X (composition)) that may be arbitrarily specified without

changing the

number of phases.

If a system in equilibriumequilibrium contains PP phasesphases and CC componentscomponents then the phase rulephase rule states that the number of degrees of freedom is given by :

F = C + n F = C + n -- Φ

F = number of variables that can change independently without destabilising the system (independent variables).C= number of component of the systemn = number of variables: P, TP= number of phases in the system that coexist at different topological locations in a phase diagram.

For an assemblage to be stable over a finite range of T and P:F ≥

2, so P ≤

C

Phase Rule and Topologic Features

Value of F Topologic feature

< 0 The system contains more than one invariant point and is a multisystemmultisystem0 Invariant Point - No intensive variables may be changed 1 Univariant Line (reaction) - One intensive variable may be changed independently 2 Divariant Field or Divariant Phase assemblage - Two intensive variables may be

changed independently 3 Trivariant field or Trivariant Phase Assemblage- Three intensive variables may be

changed independently

•

C = 1 Al2SiO5•

Φ

= 3 : Therefore F =

0, paragenesis is invariant: forms a point on ground surface and P-T plot.

Φ

= 2: Therefore F = 1, paragenesis is univariant: forms a line on the ground surface (isograd) and a line on the P-T plot.

Φ

= 1: Therefore F = 2, paragenesis is divariant: forms an

th

d

An isograd is a line in the field or on a map defined by the appearance or disappearance of a specific mineral, mineral composition or a group of minerals as a result of a specific reaction

Isograds are reactions therefore we can:Understand what physical variables might affect the

location of a particular isogradWe may also be able to estimate the P-T-X conditions

that an isograd

represents

Metamorphic reactions are just chemical reactionsTherefore we can use equilibrium thermodynamics to

investigate the P-T-X conditions of any given chemical reaction

Chemographics refers to the graphical representation of the chemistry of mineral assemblages

A simple example: the plagioclase system as a linear C = 2 plot:

= 100 An/(An+Ab)

Chemographic Diagrams3-C mineral compositions are plotted on a triangularchemographic

diagram.

They may form the hypothetical mineralsx, y, z, xz, xyz,

and

x2

z

Suppose that the rocks in our area have the following 5 assemblages:

X+xy+x2zXy+xyz+x2zXy+xyz+yXyz+z+x2zY+z+xyz

Three mineral phases stable together definea triangle

Equilibrium mineral assemblages are indicated by tie-lines whichconnect co-existing minerals.Minerals not directly connected by tie lines cannot stably coexist under P-T conditions represented by the diagram.

Note that this subdivides the chemographic

diagram into 5 sub-triangles, labeled (A)-(E)

X+xy+x2z = (A)Xy+xyz+x2z = (B)Xy+xyz+y = (C)Xyz+z+x2z = (D)Y+z+xyz = (E)

Each of these assemblages forms in rocks of different bulk composition,and they are called compatible assemblages.Any point within the diagram represents a rock of specific bulk composition.

We can use chemographics to infer reactions

MgO SiO2

Per Fo En Qtz

Fo + Qtz = EnEn + Per = FoPer + Qtz = FoPer + Qtz = EnIf we know the chemographics we can determine that a reaction is possible (and can dispense with balancing the reaction)

What reaction is possible between A-B-D-W?

A A chemographicchemographic diagram for some diagram for some

metamorphic zonemetamorphic zone

W

A + B + D = W

Chemographic Diagrams3-C X-Y-Z mineral compositions are plotted on a triangular or ternary diagram.

1.

2.

3.

Write reactions for theformation of minerals1-3 expressedin terms of xyz?

1. X + Y = XY2. 2X + Z = X2 Z3. X + Y + Z = XYZ

What reaction is possible between A-B-C-D?

A A chemographicchemographic diagram for some diagram for some

metamorphic zonemetamorphic zone

A + B = C + D

This is called a tie-line flip, and results in new groupings in the next metamorphic zone

At the isograd

Above the isograd

Below the isograd

Two kinds of isograds:

A) isograds caused by

discontinuous reactions

B) isograds caused by

continuous reactions

A) Isograds caused by discontinuous reactions

e.g. staurolite isograd

grt + chl + mu ----> staur + bt + qtz + H2 O

Phase Rule: Φ

+ F = C + 2

C = 6

Φ

= 7

∴

F = 1

discontinuous reaction forms a line on P-T graph

and a line in the field. Can be deduced by the breaking of a tie-line on a Δ diagram

F M

grt

staur

chlorite

biotite

A

+ muscovite + quartz + H2O

x y z

F M

grt

staur

chlorite

biotite

A

x y z

Discontinuous reaction

all rocks in grt-chl-bt Δ

show same reaction at same T regardless of small

F/M/A variations

B) Isograds caused by continuous reactions

e.g. garnet isograd

chl1 + mu + qtz ----> chl2 + grt + bt + H2 OFe-rich Mg-rich

Phase Rule: Φ

+ F = C + 2

C = 6

Φ

= 6

∴

F = 2

A continuous reaction forms an area on a P-T grid and area in the field.

In this example tie-lines migrate to more Mg-rich comps.

F M

grtchlorite

biotite

A

F M

grt chlorite

biotite

A

Continuous reactions e.g.

first appearance of garnet critically depends on the F/M ratio

Continuous reactions occur when F > 1, and the reactants and products coexist over a temperature interval

Schematic isobaric T-XMg diagram representing the simplified metamorphic reaction Chl + Qtz →

Grt + H2 O. From Winter (2001) An Introduction to Igneous and Metamorphic Petrology. Prentice Hall. Winter (2001) An Introduction to Igneous and Metamorphic Petrology. Prentice Hall.

Isobaric T-X phase diagram at atmospheric pressure After Bowen and Shairer (1932), Amer. J. Sci. 5th Ser., 24, 177- 213. Winter (2001) An Introduction to Igneous and Metamorphic Petrology. Prentice Hall.

Geologic map of a hypothetical field area in which metamorphosed pelitic sediments strike directly up metamorphic grade. Modified from Winter (2001) An Introduction to Igneous and Metamorphic Petrology. Prentice Hall.

600oC

550oC

Garnet appears at different grades in rocks of different

composition

WHY?

200m

Two possible reasons for variation across the map:

1. Such contrasting composition that the garnet reaction is different

Example: garnet in some pelites may be created by the reaction:

Chl + Ms + Qtz →

Grt + Bt + H2 OWhereas in more Fe-rich and K-poor pelites, garnet

might be generated by an (unbalanced) reaction involving chloritoid:

Chl + Ctd + Qtz →

Grt + H2 O2. The reaction on which the isograd is based is the

same in each unit but it is a continuous reaction

If Chl + Ms + Qtz →

Grt + Bt + H2 Owere a discontinuous reaction and is

responsible for the formation of garnet in the map, the reaction should run to completion

(when one of the reactants was consumed) at a single grade (P-T).

If Chl + Ms + Qtz →

Grt + Bt + H2 Owere a continuous reaction, then we would find chlorite, muscovite, quartz, biotite, and garnet

all together in the same rock over an interval of metamorphic grade above the garnet-in

isograd

• Reactions can be deduced from compatibility diagrams in 4 ways

A + B = C + D

1. Crossing tie-lines

W

2. Within a triangle

A + B + D = W

3. Along a binary join

A + B = C

A BC

A B C

D

E

F

1. A + E = D2. D + E + C = F3. A + C = B4. B + F = D + C5. B + E = D + C6. D + B = A + F7. E + B = F

Deduce at least 7 reactions that can occur between thesehypothetical minerals