Metamorphic Phase Diagrams

• Differ from Igneous Phase Diagrams

• Show a snapshot of all compositions at given T,P

• Rock remains at same point but diagram changes

Phase Diagram for Water

The Phase Rule (Gibbs, 1928)Phases (Distinct Materials or States)

+

Degrees of Freedom (Independent Variables)

=

Components

+

2

Phase Rule and Phase Diagrams

Phase Diagram for Al2SiO5

Phase Diagram for Ice

Phase Diagram of Silica

Degrees of Freedom

• Pressure

• Temperature

• PH2O

• PCO2

• pH

• Oxygen fugacity

• Eh

Simplifying Degrees of Freedom

• Generally ignore pH, Eh, Oxygen fugacity for most rocks– Important for sulfide systems

• Usually care about T,P– Assume PH2O = Ptotal for silicates, PCO2 = 0

– Assume PCO2 = Ptotal for carbonates, PH2O = 0

– Assume PH2O = 0 and PCO2 = 0 in some cases

Simplifying Degrees of Freedom

• P + F = C + 2

• If F = 2, then P = C

• Number of phases = number of components

• Components = SiO2, Al2O3, Fe2O3, FeO, CaO, MgO, Na2O, K2O, TiO2, Cr2O3, MnO, BaO, SrO, P2O5, H2O, CO2, F, Cl

Simplifying Components

• We can plot a maximum of three components using triangle diagrams

• Ignore SiO2(excess), H2O (excess or 0), CO2 (excess or 0)

• Assume P2O5 goes into apatite, Na2O into albite, TiO2 into rutile or ilmenite, Cr2O3, into chromite, F into fluorite or apatite, Cl into halite

• Include MnO with FeO, BaO and SrO with CaO, Fe2O3 with Al2O3 or FeO, Cl, F with OH

• Subtract major elements as necessary

Simplifying Components

• Components reduced to Al2O3, FeO, CaO, MgO, K2O

• ACF graphs Al2O3, CaO, (FeO+ MgO)• A’KF graphs Al2O3, (FeO + MgO), K2O• AFM graphs Al2O3, FeO, MgO, K2O in a

tetrahedron• SiO2 – CaO – MgO used for carbonate

systems• Plot Molar amounts, not weights

Metamorphic Phase Diagrams

• Tie lines denote two coexisting phases

• Triangular subfields denote three coexisting phases

• Phase Diagram is snapshot of mineral combinations under given T,P conditions

• Evolution tracked by changes in diagrams

• Not really interested in amounts

Carbonate Rocks at 450C

Metamorphic Phase Diagrams• Normally F = 2, C = 3, P = 3• On a reaction curve, F = 1, P = 4• How to get 4 Phases Together:

– New Phase Appears in Middle of Field– New Phase Appears on Tie Line– Tie Line Breaks and New One Forms

• Changes in Metamorphism– New Minerals Appear– Old Minerals Disappear– Compatibilities Shift

Carbonate Rocks at Low T

400 C: New Phase on Tie Line(Quartz + Brucite -> Talc)

450 C: One Tie Line Replaced by Another(Quartz + Dolomite -> Calcite + Talc)

500 C: New Phase in Middle of Field(Quartz + Talc + Calcite -> Tremolite)

ACF Diagram

• Probably most versatile and instructive diagram

• A = (Al2O3 + Fe2O3) – (Na2O, + K2O)

– Subtract Al2O3 in K-spar and albite

• C = CaO - 3.3 * P2O5

– Subtract Ca in apatite

• F = FeO + MgO + MnO

The ACF Diagram

A’KF Diagram

• A’ = (Al2O3 + Fe2O3) – (Na2O, + K2O) – variable Ca (epidote, garnet, anorthite)

• K = K2O

• F = FeO + MgO + MnO – amount in diopside or hornblende

• Distinguishes K-feldspar and micas

The A’KF Diagram

ACF and A’KF Diagrams are often paired

AFM Diagram

• Graphs Al2O3, FeO, MgO, K2O• Cross-section through a tetrahedron• Used where MgO and FeO don’t fully

substitute• Must include K2O because of micas• A = (Al2O3-3K2O)/(Al2O3-3K2O+FeO+MgO)• M = MgO/ (FeO + MgO)• F = FeO/ (FeO + MgO)

AFM Diagram

AFM Diagram

CaO-MgO-SiO2 Diagram