Chemographic Analysis (Net Transfer Reactions)

The Phase Rule in Metamorphic Systems F = C – P + 2 F – number of degrees of freedom C – minimum number of components needed to define system P – number of phases Divariant Mineralogical Phase Rule Univariant F = C – P Invariant Pressure and temperature not specified

Divariant Mineral Assemblages in a Three Component System (Components in this representation are extensive parameters) A B C D E Bulk rock composition (A, B, C, D, E) B, C, and E are compositionally degenerate

Implication of Solid Solution in a Three Component System Bulk rock composition B A C

J.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 = Al2O3 - 3K2O (Ms projection) A = Al2O3 - K2O (Kfs projection)

Projection from muscovite Pelitic minerals on an AFM Diagram Projection from muscovite

Representation of a mineral assemblage on an AFM diagram

A(K)FM Projection from Muscovite Mg-enrichment typically in the order: cordierite > chlorite > biotite > chloritoid > staurolite > garnet

The ACF Diagram A,C, F are pseudo-components calculated on an atomic basis: A = Al2O3 + Fe2O3 – Na2O – K2O; C = CaO – 3.3 P2O5 F = FeO + MgO + MnO To calculate A for a mineral, we combine the atomic proportions Al and Fe3+ in the mineral formula, and then subtract Na and K If you begin with an ideal mineral formula Fe3+ is rare, except in a few minerals In real mafic minerals, Fe is probably in both valence states, but generally is dominated by Fe2+ Microprobe analyses cannot distinguish Fe oxidation states, but you can often estimate the relative proportions of ferric and ferrous iron by calculating the charge balance

Mineral Assemblages on an ACF Diagram

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

Mineral Assemblages on an AKF Diagram

Reactions in a 2-Component System Fo + Qtz = En Mg2SiO4 + SiO2 = Mg2Si2O6 En + Per = Fo Mg2Si2O6 + 2 MgO = 2 Mg2SiO4 Per + Qtz = Fo or En

Reactions in a 3-Component System Below the isograd Crossing Tie-Line Reaction A + B = C + D At the isograd Above the isograd Note that phi = 4 at the isograd with crossing tie-lines Then have new groupings : A + C + D or B + C + D No new minerals become stable- simply different associations The groupings follow from the reaction: If A > B then B consumed first, and A remains with new C & D -> A + C + D C + D cannot coexist below the isograd, and A + B cannot coexist above it If a chemographic diagram is a projection, the approach still works, but you will have to balance the reaction with other components For example, if the previous diagram is projected from quartz, SiO2 will have to be added to one side of the A + B = C + D reaction to balance it properly

The Cordierite-K-feldspar-in Reaction Biotite +Muscovite = Cordierite + K-feldspar + H2O 2 K(Fe,Mg)3AlSi3O10(OH)2 + 6 KAl3Si3O10(OH)2 + 15 SiO2 = 3 (FeMg)2Al4Si5O18 + 8 KAlSi3O8 + 8 H2O Orijärvi: Ms-Cd-Bt Ms-Kf-Bt Oslo: Ms-Kf-Cd Kf-Bt-Cd

Reactions in a 3-Component System Terminal Reaction Below the isograd A + B + D = E At the isograd Above the isograd Above the isograd Note that phi = 4 at the isograd with crossing tie-lines Then have new groupings : A + C + D or B + C + D No new minerals become stable- simply different associations The groupings follow from the reaction: If A > B then B consumed first, and A remains with new C & D -> A + C + D C + D cannot coexist below the isograd, and A + B cannot coexist above it If a chemographic diagram is a projection, the approach still works, but you will have to balance the reaction with other components For example, if the previous diagram is projected from quartz, SiO2 will have to be added to one side of the A + B = C + D reaction to balance it properly E E Bulk rock composition

AFM Potting positions A St Crd Cld Gt Chl F M Bt

Crossing Tie-Line Reaction St Crd Cld Gt Chl F M Bt

Terminal Reaction A St Cld Crd Gt Chl F M Bt