Chemographic Analysis

(Net Transfer Reactions)

The Phase Rule in Metamorphic SystemsThe Phase Rule in Metamorphic Systems

F = C – P + 2 F – number of degrees of freedomC – minimum number of components needed to define systemP – number of phases

Mineralogical Phase Rule

F = C – PUniva

riantDivariant

Invariant

Pressure and temperature not specified

Divariant Mineral Assemblages in a Three Component System

Bulk rock composition (A, B, C, D, E)

A

B

C

DE

B, C, and E are compositionally degenerate

(Components in this representation are extensive parameters)

Implication of Solid Solution in a Three Component System

Bulk rock composition

A

B

C

D

E

J.B. Thompson’s A(K)FM Diagram for MetapelitesJ.B. Thompson’s A(K)FM Diagram for Metapelites

Most pelitic rocks can be described by the system K2O-Al2O3-FeO-MgO-SiO2-H2O

Quartz is an excess phase and buffers the activity of SiO2

Muscovite and K-feldspar are ubiquitous phases above and below the K-feldspar-aluminosilicate isograd, respectively

H2O is mobile and is therefore an intensive parameter of the system

The A(K)FM Projection

A = AlA = Al22OO33 - 3K - 3K22O (Ms projection)O (Ms projection)

A = AlA = Al22OO33 - K - K22O (Kfs projection) O (Kfs projection)

Pelitic minerals on an AFM Diagram

Projection from muscovite

Representation of a mineral assemblage on an AFM diagram

Mg-enrichment typically in the order: cordierite > chlorite > biotite > chloritoid > staurolite > garnet

A(K)FM Projection from Muscovite

The ACF DiagramThe ACF DiagramA,C, F are pseudo-components calculated on an atomic basis:A = Al2O3 + Fe2O3 – Na2O – K2O; C = CaO – 3.3 P2O5

F = FeO + MgO + MnO

Mineral Assemblages on an ACF Diagram

The AKF DiagramThe AKF DiagramA,K, F are pseudo-components calculated on an atomic basis:A = Al2O3 + Fe2O3 – Na2O – K2O - CaO; K = K2OF = FeO + MgO + MnO

Mineral Assemblages on an AKF Diagram

MgO SiO2

Per Fo En Qtz

Fo + Qtz = EnFo + Qtz = En Mg Mg22SiOSiO44 + SiO + SiO22 = Mg = Mg22SiSi22OO66

En + Per = FoEn + Per = Fo Mg Mg22SiSi22OO66 + 2 MgO = 2 Mg + 2 MgO = 2 Mg22SiOSiO44

Per + Qtz = Fo or EnPer + Qtz = Fo or En

Reactions in a 2-Component System

Above the isograd

Below the isograd

At the isograd

A + B = C + D

Crossing Tie-Line Reaction

Reactions in a 3-Component System

Biotite +Muscovite = Cordierite + K-feldspar + H2O

2 K(Fe,Mg)2 K(Fe,Mg)33AlSiAlSi33OO1010(OH)(OH)22 + 6 KAl + 6 KAl33SiSi33OO1010(OH)(OH)22 + 15 SiO + 15 SiO22

= 3 (FeMg)= 3 (FeMg)22AlAl44SiSi55OO1818 + 8 KAlSi + 8 KAlSi33OO88 + 8 H + 8 H22OO

The Cordierite-K-feldspar-in Reaction

Orijärvi: Orijärvi: Ms-Cd-Bt Ms-Cd-Bt Ms-Kf-BtMs-Kf-Bt

Oslo: Ms-Kf-Cd Kf-Bt-Cd

Above the isograd

E

E

Below the isograd

At theisograd

Above theisograd

Terminal Reaction

A + B + D = E

Bulk rock composition

Reactions in a 3-Component System

A

F M

St

Gt

Cld

Bt

Chl

Crd

AFM Potting positions

A

F M

St

Gt

Cld

Bt

Chl

Crd

Crossing Tie-Line Reaction

A

F M

St

Gt

Cld

Bt

Chl

Crd

Terminal Reaction