Chapter 24. Stable Mineral Assemblages in Metamorphic Rocks

Equilibrium Mineral Assemblages At equilibrium, the mineralogy (and the composition of each mineral) is determined by T, P, and X . “Mineral paragenesis” “Mineral assemblage” is used by some as a synonym for paragenesis, conventionally assuming equilibrium for the term Impossible to prove that a mineral assemblage now at the Earth’s surface represents thermodynamic (chemical) equilibrium at prior elevated metamorphic conditions Indirect textural and chemical support for such a conclusion is discussed in the text In short, it is typically easy to recognize non-equilibrium minerals (retrograde rims, reaction textures, etc.) We shall assume equilibrium mineral assemblages in the following discussion (will ignore retrograde…)

The Phase Rule in Metamorphic Systems at equilibrium: F = C - f + 2 the phase rule (6-1) f = #phases at a point C = # components: the minimum number of chemical constituents required to specify every phase in the system. Many poss. choices F = the number of degrees of freedom: the number of independently variable intensive parameters of state (such as temperature, pressure, the composition of each phase, etc.)

Goldschmidt’s Rule If F  2 (phase field) then F = C - f + 2  2 So f  C (24-1) Useful in evaluating whether or not a rock is at equilibrium http://serc.carleton.edu/research_education/equilibria/phaserule.html

Picking the Components C is the minimum number of chemical components required to constitute all the phases. Consider the reaction: CaMg(CO3)2 + 2 SiO2 = CaMgSi2O6 + 2 CO2 Dolomite + 2 Quartz = Diopside + 2 Carbon Dioxide Normally we would pick the 4 components: CaO, MgO, SiO2, and CO2 based on the simple oxides. However, because Ca and Mg are in a 1:1 ratio in both dolomite and diopside (and not present in quartz or carbon dioxide), we could choose a ternary system with components: CaMgO2, SiO2, and CO2 Easier to plot

The Phase Rule in Metamorphic Systems Suppose we have determined C for a rock Consider the following three scenarios: Case 1 f = C The rock probably represents an equilibrium mineral assemblage from within a metamorphic zone

The Phase Rule in Metamorphic Systems b) f < C Common with mineral systems that exhibit solid solution Plagioclase Liquid plus For example, in the plagioclase or the olivine system we can see that under metamorphic conditions (below the solidus) these 2-C systems consist of a single mineral phase F = 1 and C = 2 so F < C

Case 3: f > C Consider the following three scenarios: Subcase a: C = 1 f = 1 is common f = 2 Isograd less common f = 3 only at the specific P-T conditions of the invariant point (~ 0.37 GPa and 500oC) Figure 21-9. The P-T phase diagram for the system Al2SiO5 calculated using the program TWQ (Berman, 1988, 1990, 1991). Winter (2001) An Introduction to Igneous and Metamorphic Petrology. Prentice Hall.

Case 3 f > C Subcase b: Equilibrium has not been attained The phase rule applies only to systems at equilibrium, and there could be any number of minerals coexisting if equilibrium is not attained Relict inclusions in garnet http://serc.carleton.edu/research_education/equilibria/PTtPaths.html

Case 3 f > C Subcase 3:  We didn’t choose the # of components correctly Some guidelines for an appropriate choice of C Begin with a 1-component system such as CaAl2Si2O8 (anorthite), there are 3 common types of major/minor components that we can add: Case a)  Components that generate a new phase Adding a component such as CaMgSi2O6 (diopside), results in an additional phase: in the binary Di-An system diopside coexists with anorthite below the solidus If a component goes only into a single phase (for example, P2O5  apatite, or TiO2  ilmenite) we can effectively ignore both the component and the phase because the phase rule is unaffected by reducing f and C by the same amount As a result, many minor elements, such as P2O5 and TiO2, are often ignored along with the corresponding accessory phase so as to simplify the application of the phase rule Otherwise components that generate additional phases must be considered

Case 3 f > C Begin with a 1-component system, such as CaAl2Si2O8 (anorthite), there are 3 common types of major/minor components that we can add: Case b) Components that substitute for other components Adding a component such as NaAlSi3O8 (albite) to the CaAl2Si2O8 anorthite system. Albite would dissolve in the anorthite structure, resulting in a single solid- solution mineral (plagioclase) below the solidus Fe and Mn commonly substitute for Mg Al may substitute for Si Na may substitute for K

Case 3 f > C Begin with a 1-component system, such as CaAl2Si2O8 (anorthite), there are 3 common types of major/minor components that we can add: c) “Perfectly mobile” components, e.g. abundant H2O with excellent permeability These are components are either a freely mobile fluid or a component that dissolves readily in a fluid phase and can be transported easily (e.g. LILs)

Perfectly Mobile Components Consider the very simple metamorphic system, MgO- H2O Possible natural phases in this system are periclase (MgO), aqueous fluid (H2O), and brucite (Mg(OH)2) F > C How we deal with H2O depends upon whether water is perfectly mobile or not A reaction can occur between the potential phases in this system: MgO + H2O  Mg(OH)2 Per + Fluid = Bru BTW this is a retrograde reaction as written (occurs as the rock cools and hydrates)

If water is not abundant or perfectly mobile it may become a limiting factor in the reaction A reaction involving more than one reactant will proceed until any one of the reactants is consumed MgO + H2O  Mg(OH)2 Per + water = Bru The reaction will proceed until either periclase or water is consumed Periclase can react only with the quantity of water that can diffuse into the system If water is not perfectly mobile, and is limited in quantity, it will be consumed first Once the water is gone, the excess periclase remains stable as conditions change into the brucite stability field The reaction line is not the absolute stability boundary of periclase, or of water, because either can be stable across the boundary if the other reactant is absent Figure 24-1. P-T diagram for the reaction brucite = periclase + water. From Winter (2001). An Introduction to Igneous and Metamorphic Petrology. Prentice Hall.

Chemographic Diagrams Chemographics refers to the graphical representation of the chemistry of mineral assemblages A simple example: the plagioclase system as a linear C = 2 plot: Metamorphic components typically expressed as molar quantities, and not as weight % Any intermediate composition is simply plotted an appropriate distance along the line An50 would plot in the center, An25 would plot ¼ of the way from Ab to An, etc.

Chemographic Diagrams Suppose you had a small area of a metamorphic terrane in which the rocks correspond to a hypothetical 3-component system with variable proportions of the components x-y-z as shown in Fig. 24-2 The rocks in the area are found to contain 6 minerals with the fixed compositions x, y, z, xz, xyz, and yz2 Example: components x,y and z are MgO, FeO, and SiO2 respectively Actual choices more complex

Compatibility Diagram Suppose that the rocks in our area are found to have the following 5 assemblages: x-xy-x2z xy-xyz-x2z xy-xyz-y xyz-z-x2z y-z-xyz MgO, FeO, and SiO2 x2z = Mg2SiO4 Forsterite Figure 24-2 Phases that coexist at equilibrium in a rock are connected by tie-lines Compatibility Diagram

Note that this subdivides the chemographic diagram into 5 sub-triangles, labeled (A)-(E) A:x-xy-x2z B:xy-xyz-x2z C:xy-xyz-y D:xyz-z-x2z E:y-z-xyz Any point within the diagram represents a specific bulk rock composition The diagram determines the corresponding mineral assemblage that develops at equilibrium For example, a point within the sub-triangle (E), the corresponding mineral assemblage corresponds to the corners = y - z - xyz Any rock with a bulk composition plotting within triangle (E) will develop that same mineral assemblage

What happens if you find a place that falls directly on a tie-line, such as point (f)? In this case the mineral assemblage consists of xyz and z only (the ends of the tie-line), since by adding these two phases together in the proper proportion you can produce the bulk composition (f) In such a situation F= C = 2, as required at equilibrium

In the unlikely event that the bulk composition equals that of a single mineral, such as xyz, then f = 1, but C = 1 as well “compositionally degenerate” i.e “requiring fewer components than normal

Chemographic Diagrams for Metamorphic Rocks Most common natural rocks contain the major elements: SiO2, Al2O3, K2O, CaO, Na2O, FeO, MgO, MnO and H2O such that C = 9 Three components is the maximum number that we can easily deal with in two dimensions What is the “right” choice of components? Some simplifying choices:

The ACF Diagram Eskola (1915) proposed the ACF diagram as a way to illustrate metamorphic mineral assemblages in mafic rocks on a simplified 3-C triangular diagram He wanted to concentrate only on the minerals that appeared or disappeared during metamorphism, thus acting as indicators of metamorphic grade

Fig. 24-4 illustrates the positions of several common metamorphic minerals on the ACF diagram. Note: this diagram is presented only to show you where a number of important phases plot. It is not specific to a P-T range and therefore is not a true compatibility diagram, and has no petrological significance Figure 24-4. After Ehlers and Blatt (1982). Petrology. Freeman. And Miyashiro (1994) Metamorphic Petrology. Oxford.

The ACF Diagram The three pseudo-components are all calculated on an atomic basis: A = Al2O3 + Fe2O3 - Na2O - K2O C = CaO - 3.3 P2O5 F = FeO + MgO + MnO For A we are here interested only in the Al that occurs in excess of that combined with K and Na to make any feldspar 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

The ACF Diagram By creating these three pseudo-components, Eskola reduced the number of components in mafic rocks from 8 to 3 Water is omitted under the assumption that it is perfectly mobile Note that SiO2 is simply ignored We shall see that this is equivalent to projecting from quartz In order for a projected phase diagram to be truly valid, the phase from which it is projected must be present in the mineral assemblages represented WHERE DOES A MINERAL PLOT? HOW DO SOLID SOLUTIONS OR MIXTURES PLOT? Thus, to be valid, the ACF diagram must have both quartz, alkali feldspar, and plagioclase present It may work anyway when these phases are lacking, but the result may also violate the mineralogical phase rule on occasion

The ACF Diagram An example: Anorthite CaAl2Si2O8 A = Al2O3 + Fe2O3 - Na2O - K2O C = CaO - 3.3 P2O5 F = FeO + MgO + MnO An example: Anorthite CaAl2Si2O8 A = 1 + 0 - 0 - 0 = 1, C = 1 - 0 = 1, and F = 0 Provisional values sum to 2, so we can normalize to 1.0 by multiplying each value by ½, resulting in A = 0.5 C = 0.5 F = 0 X Anorthite thus plots half way between A and C on the side of the ACF triangle, as shown in Fig. 24-4

Example 1: Where does K-feldspar plot? For KAlSi3O8 A = 0.5 + 0 - 0.5 = 0, C = 0, and F = 0 Kspar doesn’t plot on the ACF diagram Example 2: If you try this for albite NaAlSi3O8 you will find that it doesn’t plot either A = Al2O3 + Fe2O3 - Na2O - K2O C = CaO - 3.3 P2O5 F = FeO + MgO + MnO For albite NaAlSi3O8 A = 0.5 + 0 - 0.5 -0 = 0 C = 0 + 0 F = 0 + 0 + 0 Figure 24-4. The ACF formula eliminates Na and K from the diagram (and thus these phases) without altering the remaining Al after the removal All Ca-bearing plagioclase feldspars, regardless of the K and Na content, plot at the anorthite point

A typical ACF compatibility diagram, referring to a specific range of P and T (the kyanite zone in the Scottish Highlands) Plot all phases and connect coexisting ones with tie-lines Field R: Mafic rocks in the hb-plag –gt (almandine) triangle, and thus most metabasaltic rocks occur as amphibolites or garnet amphibolites in this zone Field S: More aluminous rocks develop kyanite and/or muscovite and not hornblende Field T: More calcic rocks lose Ca-free garnet, and contain diopside, grossularite, or even calcite (if CO2 is present) The diagram allows us to interpret the relationship between the chemical composition of a rock and the equilibrium mineral assemblage S R T Figure 24-5. After Turner (1981). Metamorphic Petrology. McGraw Hill.

NEW for Pelitics:The AKF Diagram Because pelitic sediments are high in Al2O3 and K2O, and low in CaO, Eskola proposed a different diagram that included K2O to depict the mineral assemblages that develop in them In the AKF diagram, the pseudo- components are: A = Al2O3 + Fe2O3 - Na2O - K2O - CaO K = K2O F = FeO + MgO + MnO We are now interested only in the Al that occurs in excess of that combined with K, Na, and Ca to make any feldspar Pelite (Greek Pelos, Clay) is a descriptive name for a clastic rock with a grain size of less than 1/16mm.

Another figurative AKF to show where metapelitic minerals plot Figure 24-6. After Ehlers and Blatt (1982). Petrology. Freeman.

AKF compatibility diagram (Eskola, 1915) illustrating paragenesis of pelitic hornfelses, Orijärvi region Finland Figure 24-7. After Eskola (1915) and Turner (1981) Metamorphic Petrology. McGraw Hill. Region R: Al-poor rocks contain biotite K(Mg,Fe)2(AlSi3O10)(F,OH)2, and may contain an amphibole (e.g. Anthophyllite (Mg, Fe)7Si8O22(OH)2 ) if sufficiently rich in Mg and Fe, or microcline KAlSi3O8 if not. Region S: Rocks richer in Al contain andalusite Al2SiO5 ,cordierite (Mg,Fe)2Al4Si5O18 and Muscovite KAl2(AlSi3O10)(OH)2 S R

Three of the most common minerals in metapelites: andalusite, muscovite, and microcline, all plot as distinct points in the AKF diagram Figure 24-7. After Ehlers and Blatt (1982). Petrology. Freeman. And & Ms plot as the same point in the ACF diagram, and Micr doesn’t plot at all, so the ACF diagram is much less useful for pelitic rocks (rich in K and Al)

Projection from Apical Phases ACF and AKF diagrams eliminate SiO2 by projecting from quartz, so quartz MUST be present The shortcoming is that these projections compress the true relationships as a dimension is lost Let’s examine projections on another diagram, the A(K)FM of Thompson. To be properly applicable, quartz must therefore be present in every mineral assemblage on the ACF and AKF diagrams (or SiO2 must at least be present to the point of saturation) Why create projected pseudo- systems when they lead to such inconsistencies? 3-C -> 2-C does not provide much of a benefit, since both are easily illustrated in 2D diagrams When > 3 components, the systems are no longer so easily visualized Reducing the components from 8 or 9 to three provides a motivation to combine components As seen in the ACF and AKF diagrams, the ability to visualize the geometric relationships is often an advantage that outweighs the problems

J.B. Thompson’s A(K)FM Diagram An alternative to the AKF diagram for metamorphosed pelitic rocks Although the AKF is useful in this capacity, J.B. Thompson (1957) noted that Fe and Mg do not partition themselves equally between the various mafic minerals in most rocks Biotite is useful in assessing temperature histories of metamorphic rocks, because the partitioning of iron and magnesium between biotite and garnet is sensitive to temperature Pelites are sensitive to T & P, and undergo many mineralogical changes as grade increases Good to have a comprehensive diagram to display these changes

J.B. Thompson’s A(K)FM Diagram A = Al2O3 K = K2O F = FeO M = MgO In order to avoid dealing with a three-dimensional tetrahedron, Thompson projected the phases in the system to the AFM face, thereby eliminating K2O He recognized that projecting from K2O would not work, since no phase corresponds to this apical point, and projections would cross important tie-lines Four principal components thus remain (A = Al2O3, K = K2O, F = FeO, M = MgO)

J.B. Thompson’s A(K)FM Diagram Since muscovite is the most widespread K-rich phase in metapelites, he decided to project from muscovite (Mu) to the AFM base as shown Projecting from muscovite can lead to a strange looking AFM projections Note that Mu is still rather K-poor, and only mineral phases in the volume A-F-M-Mu in Fig. 24-18 will be projected to points within the AFM face of the AKFM tetrahedron Biotite is outside this volume, and projecting it from Mu causes it to plot as a band (of variable Fe/Mg) outside the AFM triangle Biotite is outside this volume, and projecting it from Mu causes it to plot as a band (of variable Fe/Mg) outside the AFM triangle

J.B. Thompson’s A(K)FM Diagram At high grades muscovite dehydrates to K-feldspar as the common high-K phase Then the AFM diagram should be projected from K- feldspar, because Muscovite IS NOT PRESENT When projected from Kfs, biotite projects within the F- M base of the AFM triangle Muscovite may be absent in some pelitic rocks, particularly at higher grades when it dehydrates, giving way to K-feldspar as the common high-K phase When this is the case, the AFM diagram should be projected from K-feldspar if the mineral assemblages of the diagram are to have significance When projected from Kfs, biotite projects within the F-M base of the AFM triangle Figure 24-18. AKFM Projection from Kfs. After Thompson (1957). Am. Min. 22, 842-858.