Metamorphic Petrology GLY 262 Petrogenetic grids and Schreinemakers

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1 Metamorphic Petrology GLY 262 Petrogenetic grids and Schreinemakers

2 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

3 Simplified KASH (K 2 O-Al 2 O 3 -SiO 2 -H 2 O) grid from Spear (1999)

4 KFMASH from White et al. (2001)

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

6 How?

7 Suppose we had the following mineral assemblage: Qtz Kfs sill H 2 O (V) Simplified KASH (K 2 O-Al 2 O 3 -SiO 2 -H 2 O) grid from Spear (1999)

8 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-Al 2 O 3 -SiO 2 -H 2 O-(Na 2 O) system ( C(N)MASH ). Winter (2001) An Introduction to Igneous and Metamorphic Petrology. Prentice Hall.

9 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

10 Schreinemaker's Analysis - method used to work out the arrangement of the reactions in the phase diagram=> theoretical petrog. grids use of the geometrical constraints which are a consequence of the Phase Rule. F = C n - P F = 0 = invariant Point in P-T space F = 1 = Univariant Reaction in P-T space F = 2 = Divariant Reaction in P-T space P (kbar) A C A B C B (C) < 180 Rules: 1) All reactions meet at invariant points. (B) T( C) (A) 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.

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

12 From the phase rule we know that an invariant point in a 3-component system contains 5 phases Therefore F = C Φ 2 0 = N = 5!(8 8! 5)! = 56

13 Schreinemakers analysis class exercise 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 1.Quartz SiO 2 2.Enstatite Mg 2 Si 2 O 6 3.Pyrope Mg 3 Al 2 Si 3 O 12 4.Sapphirine Mg 4 Al 8 Si 2 O 20

14 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-Φ2 1= 3-42 Use the combinatorial equation to determine the number of reactions or in this simple case just use the chemographics as we need to determine the reactions anyway

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16 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

17 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) SILL SA QZ

18 The construction rule: The metastable extension of an (X) absent reaction must lie between two X producing reactions

19 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) SILL SA QZ (SILL)

20 (EN) (EN) SILL SA QZ X SILL SA QZ EN SA QZ (SILL) (SILL) EN SA QZ

21 (SA) QZ EN SILL (EN) SILL SA QZ EN SA QZ (SILL)

22 (SA) (EN) SILL SA QZ EN SA QZ (SILL) SA QZ EN SILL () QZ EN SILL

23 (EN) (SA) SILL SA QZ EN SA QZ (SILL) SA QZ EN SILL () QZ EN SILL EN SA SILL (QZ)

24 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