The Phase Rule and Metamorphic Diagrams

See http://plate-tectonic.narod.ru/metpetrographylinks.html
C http://ijolite.geology.uiuc.edu/08SprgClass/geo436/lectures.html


I. The phase rule

A. Review

-F = C - p + 2

-C = components
-p = phases
-2 represents T and P

-Then F = degrees of freedom:

-Number of independent intensive variables that can be changed without changing the mineral assemblage.
-Applies to systems at equilibrium

-Evidence :

-Lack of reaction textures or relict textures
-Each mineral is in contact with all others, somewhere in sample
-Non-layered (layered ones may be in equilibrium within layers)
-Constant composition of mineral grains (from microprobe data)

B. Consider a metamorphic terrane

-Any one sample is more likely to be located within a zone than right on an isograd:

-Thus, F = 2: T and P may vary
-Composition may vary as well => F > 2

-Then C - p + 2 > 2, so p < C:

-If p = C, this is the usual divariant case.
-If p < C, this usually means some components form solid solutions.
-What if p > C? (Not an equilibrium assemblage/F < 2/Wrong value for C)

II. Triangular (chemographic) diagrams

A. ACF diagram

-Definitions:

-A = Al2O3 + Fe2O3 - Na2O - K2O
-C = CaO
-F = FeO + MgO + MnO

-Simplifying assumptions:H2O is perfectly mobile; Quartz, K-spar, plag are also part of the assemblage.

-Use this as a reference, along with A-C-F table from last week''s handout.
-If you''re not familiar with minerals, look them up.


-Mafic rx plot in Pl-Hb field or Pl-Hb-Al sub-triangle
-Rocks with higher Al plot above the Pl-Al tieline, so contain Ky or Ms and no Hb

-Note that most minerals plot in the lower half of the triangle. Some petrologists use different definitions of A, C, and F, which shift mineral positions closer to A apex.

B. AKF diagram - used for pelitic rocks with higher K and Al

-Definition:

-A = Al2O3 + Fe2O3 - Na2O - K2O - CaO
-K = K2O
-F as before

-mineral positions:

-Common minerals in pelites are Ms, And, Kfs - these plot as separate points in this diagram


-Al-poor rx contain Bio + Amph or Kfs, depending on K vs. Mg and Fe
-Al-rich rx have And + Cord

C. Projections

-Both ACF and AKF assemblages include quartz. Think of triangles as one side of a tetrahedron with SiO2 as other vertex. ACF is projected from SiO2.
-Detailed discussion of projection in text:

-From vertex of triangle to opposite side reduces a 2-D diagram to a 1-D one.
-From vertex of tetrahedron to opposite side reduces 3-D to 2-D.
-Note that it is also possible to project from a point other than a vertex.

D. AFM diagram
-More detailed than AKM diagram for pelites
-start with AKFM tetrahedron:

-A = Al2O3
-K = K2O
-F = FeO
-M = MgO

-This is already a projection from SiO2 (in 4-D), so quartz is a ubiquitous phase:

-Now project to AFM side to reduce it to 2-D.
-But don''t project from K vertex. Must project from a phase that''s present, i.e., muscovite (most common K-rich phase in pelites).
-Not every phase in the tetrahedron projects to AFM from Ms, e.g., biotite projects to a band beyond the FM side.
-Note: at higher grade, Ms may dehydrate and Kfs becomes the K phase => project from K vertex.

-Mathematics of projection :

-A = Al2O3 - 3K2O (projecting from Ms) or Al2O3 - K2O (projecting from Kfs)
-F = FeO
-M = MgO

- plot location of Bio KFe2MgAlSi3O10(OH)2 :

-A = 0.5 - 3(0.5) = -1
-F = 2
-M = 1
-Normalizing, A = -0.5, F = 1, M = 0.5. Plot.


-X represents location of a rock with Sil-St-Ms-Bt-Qtz-Pl. In AFM diagram, all phases shown except Pl.
- ACF diagram, only Sil-St-Pl plot:

- AKF diagram, Sil-Ms-Bi-St plot but tielines cross.
-Crossing tielines are an artifact of projecting. In the full tetrahedral diagram, they don''t cross.

-Choosing a diagram is an art!