Metamorphic Petrology GLY 262Petrogenetic grids and Schreinemakers

Petrogenetic grids•

P-T grids or petrogenetic grids illustrate the positions AND intersections of ALL the possible equilibria

(reactions) in a given chemical system

(e.g. KFMASH). •

The reactions can be determined experimentally in the lab or determined theoretically using thermodynamics.

•

A more powerful tool than compatibility diagrams as there are no problems with projection or being limited to 3 or 4 components on ternary diagram

Simplified KASH (K2

O-Al2

O3

-SiO2

-H2

O) grid from Spear (1999)

KFMASH from White et al. (2001)

Petrogenetic grids

•

Can be a useful tool in geothermobarometry – the science of estimating pressure and temperature via equilibrium thermodynamics

How?

Simplified KASH (K2

O-Al2

O3

-SiO2

-H2

O) grid from Spear (1999)

Suppose we had the following mineral assemblage: Qtz

+ Kfs

+ sill + H2

O (V)

Petrogenetic Grids• P-T diagrams for multicomponent systems that show a set of

reactions, generally for a specific rock type

Petrogenetic grid for mafic rocks

Simplified petrogenetic grid for metamorphosed mafic rocks showing the location of several determined univariant reactions in the CaO-MgO-Al2 O3 -SiO2 -H2 O-(Na2 O) system (“C(N)MASH”). Winter (2001) An Introduction to Igneous and Metamorphic Petrology. Prentice Hall.

Schreinemakers analysis

•

Is a geometric approach used to determine the relationships of reaction curves that intersect at an invariant point in multi-component systems

•

It can be used to constrain the ‘topology’

of a petrogenetic

grid if the compositions of the

phases are known•

Essentially the way in which the various univariant

equilibria

are connected.

•

The EXACT position(s) of the equilibria

in P-T space is determined later using equilibrium thermodynamics

Schreinemaker's Analysis - method used to work out the arrangement of the reactions in the phase diagram=> theoretical petrog. gridsuse of the geometrical constraints which are a consequence of the Phase Rule.

F = C + n - PF = 0 = invariant Point in P-T spaceF = 1 = Univariant Reaction in P-T spaceF = 2 = Divariant Reaction in P-T space

A

B

C

B

AC

P (kbar)

(C)

(A)(B)

Rules:•1) All reactions meet at invariant points.

•2) A univariant reaction (curve) which passes through an invariant point has two parts: a stable part and a metastable part. The stable and metastable parts of a reaction are on opposite sides of any invariant point the reaction passes through.

3) The stable part of a univariant reaction occurs on the opposite side of the stability field of the corresponding phase or assemblage.

•4) univariant reaction (curve) can be conveniently labelled by the name of the phase that is absent, placed in brackets.

•5) No divariant assemblage can be stable within a sector that makes an angle of more than 180 measured between any two univariant lines in the same bundle.

T(°C)

< 180 °

•

The number of points (or reactions), each involving Y phases, in a system containing X phases altogether, is given by the combinatorial equation

For example, suppose we wish to know how many invariant points there will be in a P-T grid of reactions involving a total of 8 phases whose compositions can be expressed in terms of 3-

components

)!(!!

YXYXN−

=

•

From the phase rule we know that an invariant point in a 3-component system contains 5 phases

F = C –

Φ

+ 20 = 3 –

5 + 2

Therefore

56)!58(!5

!8=

−=N

1.Quartz SiO22.Enstatite

Mg2

Si2

O63.Pyrope

Mg3

Al2

Si3

O124.Sapphirine

Mg4

Al8

Si2

O20

1.

Work out the ‘chemographic

relationships’

i.e. where the phases plot on the appropriate diagram

2.

Determine the number of univariant

equilibria

and invariant points in the system

3.

Deduce all the univariant

reactions

Schreinemakers

analysis class exercise

•

The example contains only 1 invariant point but we still need to establish the number of univariant

reactions and how many phases are

involved in each.•

Use the phase rule

F= C-Φ+21= 3-4+2

Use the combinatorial equation to determine thenumber of reactions or in this simple case just use the chemographics

as we need to determine the

reactions anyway

Univariant reactions

•

(En) Py

+ Sill = Sa + Qz•

(Py) En + Sill = Sa + Qz

•

(Sa) En + Sill = Py

+ Qz•

(Sill) Py

= En + Sa + Qz

•

(Qz) Py

= En + Sa + Sill

•

Choose any reaction e.g. (EN) Draw a solid line to represent the stable part of the equilibrium extending from the invariant point. Draw the metastable

extension as a

short dashed line. Arbitrarily label either side of the reaction with the appropriate assemblage

(EN)

PY+SILL

SA+QZ

The construction rule:The metastable

extension of an (X)

absent reaction must lie between two X producing reactions

•

Choose a second reaction e.g. (SILL). Use the construction rule to place this correctl

relative to the first one. The stable extension of (SILL) must fall somewhere on the opposite side (EN) from SILL

(EN)

PY+SILL

SA+QZ

(SILL)

(EN)

PY+SILL

SA+QZ

(SILL)

(EN)

PY+SILL

SA+QZ

(SILL)EN + SA + QZ

PY EN + SA + QZ

PY

X

(EN)

PY+SILL

SA+QZ

(SILL)EN + SA + QZ

PY

(SA)

PY + QZEN + SILL

(EN)

PY+SILL

SA+QZ

(SILL)EN + SA + QZ

PY

(SA)

PY + QZEN + SILL

(PY)

SA + QZ

EN + SILL

(EN)

PY+SILL

SA+QZ

(SILL)EN + SA + QZ

PY

(SA)

PY + QZEN + SILL

(PY)

SA + QZ

EN + SILL

(QZ) PYEN + SA + SILL

Limitations of using Schreinemakers

method

•

They yields the shape of the P-T grid but can not determine the exact slope or positions of equilibria

on a P-T plane

Slide Number 1Petrogenetic gridsSlide Number 3Slide Number 4Petrogenetic gridsHow?Slide Number 7Petrogenetic GridsSchreinemakers analysisSlide Number 10Slide Number 11Slide Number 12Slide Number 13Slide Number 14Slide Number 15Univariant reactionsSlide Number 17Slide Number 18Slide Number 19Slide Number 20Slide Number 21Slide Number 22Slide Number 23Limitations of using Schreinemakers method