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**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

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**Phase Diagram for Water**

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

Degrees of Freedom (Independent Variables) = Components 2

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**Phase Rule and Phase Diagrams**

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**Phase Diagram for Al2SiO5**

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Phase Diagram for Ice

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**Phase Diagram of Silica**

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**Degrees of Freedom Pressure Temperature PH2O PCO2 pH Oxygen fugacity**

Eh

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**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

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**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

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**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

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**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

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**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

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Carbonate Rocks at 450C

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**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

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**Carbonate Rocks at Low T**

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

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

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

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**ACF Diagram Probably most versatile and instructive diagram**

A = (Al2O3 + Fe2O3) – (Na2O, + K2O) Subtract Al2O3 in K-spar and albite C = CaO * P2O5 Subtract Ca in apatite F = FeO + MgO + MnO

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The ACF Diagram

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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

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The A’KF Diagram

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**ACF and A’KF Diagrams are often paired**

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**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)

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AFM Diagram

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AFM Diagram

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CaO-MgO-SiO2 Diagram

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