1. Quiz 2 is on Thursday, Nov. 14Quiz 2 is on Thursday, Nov. 14 Exam 2 is on Thursday, Nov. 21Exam 2 is on Thursday, Nov. 21 HW 2 is due on Tuesday, Nov. 26, 5PMHW 2 is due on Tuesday, Nov. 26, 5PM

2. Metamorphic Assemblages, Reactions, and Equilibrium MUST MUST MUST read Chapter 19MUST MUST MUST read Chapter 19

3. Stable Mineral Assemblages in Metamorphic Rocks What does equilibrium mean? Describe a system in a state of equilibrium.What does equilibrium mean? Describe a system in a state of equilibrium. How is equilibrium different? What are examples of metastable systems on Earth’s surface?How is equilibrium different? What are examples of metastable systems on Earth’s surface?

4. Equilibrium Mineral Assemblages At equilibrium, the mineralogy (and the composition of each mineral) is determined by T, P, and X (composition)At equilibrium, the mineralogy (and the composition of each mineral) is determined by T, P, and X (composition) Concept is important because many metamorphic mineral assemblages appear to be in equilibrium--so examining them can tell us about P-T (and possibly X).Concept is important because many metamorphic mineral assemblages appear to be in equilibrium--so examining them can tell us about P-T (and possibly X).

5. How Do We Evaluate Mineral Assemblages and Equilibrium?

6. Chemographic Diagrams Chemographics refers to the graphical representation of the chemistry of mineral assemblages A simple example: the MgO-SiO 2 system as a linear C = 2 plot: MgO SiO 2 Qtz EnFoPer MgSiO 3 Mg 2 SiO 4

7. Example: CaO-MgO-SiO2 diagram C =3 = ternary diagram!

8. Example: CaO-MgO-SiO2 diagram Additional Information: P, T fixed so this diagram is called isothermal, isobaric diagram. OR range of P, T small Now consider: Bulk composition (6 possible equilibrium mineral assemblages)

9. Types of Metamorphic Reactions A metamorphic reaction represents a change in mineral assemblage that is brought on by a change in pressure, temperature and/or composition. The easiest way to understand what reaction is occurring is to examine chemographic diagrams. We will examine two types of metamorphic reactions: tie-line switch, and terminal appearance/disappearance

10. Types of Metamorphic Reactions: Discontinuous or Univariant Reaction Discontinuous reactions are recognized by distinct changes in the field (in metamorphic zones) through the appearance and disappearance of minerals Two types of discontinuous reactions: 1.Terminal Reaction 2. Tie-Line Switch

11. Discontinuous Reaction: Terminal reaction Consider a metamorphic system of bulk composition a. For this system, H 2 O and CO 2 are part of the assemblage but not plotted on the diagram. The stable assemblage at the start of the reaction is: Quartz + Talc + Dolomite + H 2 O + CO 2 aa

12. Discontinuous Reaction: Terminal reaction At the end of the reaction, the mineral assemblage is: Quartz + Tremolite + Dolomite + H 2 O + CO 2 So the reaction is approximately: Quartz + Talc + Dolomite --> Tremolite aa

13. Discontinuous Reaction: Terminal reaction Note that you can determine the three mineral assemblage after the reaction is completed by examining where the bulk composition lies within the triangle. In this case, you know the assemblage includes quartz-dolomite-tremolite because the bulk composition, labeled “a”, sits inside that three phase or three mineral triangle. aa

14. Discontinuous Reaction: Terminal reaction Note that composition “a” contains more dolomite and quartz than talc. Once talc is consumed, the reaction stops, leaving newly formed tremolite, plus the left-over quartz and dolomite. Called a terminal reaction because this marks the terminal appearance (or disappearance) of tremolite for any bulk composition. It is discontinuous because a mineral disappears and a new one appears. aa

15. Discontinuous Reaction: Tie-line switch Type 2: A tie-line switch reaction involves changes in mineral compatibility. We will examine the same system as it is metamorphosed to higher temperature.

16. Discontinuous Reaction: Tie-Line Switch Now consider a metamorphic system of bulk composition x. H 2 O and CO 2 are part of the assemblage but not plotted on the diagram. The stable assemblage at the start of the reaction is: Quartz + Calcite + Dolomite + H 2 O + CO 2 xx

17. Discontinuous Reaction:Tie-Line Switch At the end of the reaction, the mineral assemblage is: Tremolite + Calcite + Dolomite + H 2 O + CO 2 So the reaction is approximately: Quartz + Dolomite --> Tremolite + Calcite xx

18. Discontinuous Reaction:Tie-Line Switch This reaction, which occurs when calcareous rocks are metamorphosed at low-medium grade, is thought to be responsible for the first appearance of tremolite in MgO-, SiO 2 -poor calcareous rocks. Called a tie-line switch because the tie line connecting dolomite and quartz switches to a tie-line connecting calcite and tremolite. It is discontinuous because a mineral disappears and a new one appears. xx

19. Discontinuous Reaction:Tie-Line Switch Finally, note that you can determine the three mineral assemblage by examining where the bulk composition lies within the triangle. In this case, you know the assemblage includes calcite-dolomite-tremolite because the bulk composition, labeled x, sits inside that three phase or three mineral triangle. xx

20. How can we tell if an assemblage is in equilibrium? Theoretical analysis of thermodynamicsTheoretical analysis of thermodynamics Textures--some textures reflect equilibrium statesTextures--some textures reflect equilibrium states ExperimentsExperiments

21. The Phase Rule in Metamorphic Systems Phase rule, as applied to systems at equilibrium: F = C -  + 2 the phase rule  = the number of phases in the system C = the number of components: the minimum number of chemical constituents required to specify every phase in the system 2 = typically represents P and T of system F = the number of degrees of freedom: the number of independently variable parameters of state

22. The Phase Rule in Metamorphic Systems s Think of components as ingredients (flour, sugar, butter) s Think of phases as products (different types of cookies) s So in a metamorphic system, components can be SiO 2, CaO, Al 2 SiO 5 s Phases are particular minerals like kyanite, quartz s Different F --> how many parameters can change?

23. Three Cases F = 2 is the most common situation; the phase rule tells us: F = C -  + 2; then  = C (case 1) Number of components and phases equal in a system where there are 2 degrees of freedom (typically P and T can vary)

24. The Phase Rule in Metamorphic Systems For case 1 (  = C) : F The standard divariant situation F The rock probably represents an equilibrium mineral assemblage from within a metamorphic zone F We will see what this means on a P-T diagram in a minute

25. The Phase Rule in Metamorphic Systems F =0 (case 3) The sample is collected from a location right on a invariant point (e.g., triple point). F =1 (case 2) The sample is collected from a location right on a univariant reaction curve (isograd).

26. The Phase Rule in Metamorphic Systems Consider the following three scenarios: C = 1   = 1 common   = 2 rare   = 3 only at the specific P-T conditions of the invariant point (~ 0.37 GPa and 500 o C) Figure 21-9. The P-T phase diagram for the system Al 2 SiO 5 calculated using the program TWQ (Berman, 1988, 1990, 1991). Winter (2001) An Introduction to Igneous and Metamorphic Petrology. Prentice Hall.

27. The Phase Rule in Metamorphic Systems 2) Equilibrium has not been attained s The phase rule applies only to systems at equilibrium, and there could be any number of minerals coexisting if equilibrium is not attained

28. Chemographic Diagrams for Metamorphic Rocks Most common natural rocks contain the major elements: SiO 2, Al 2 O 3, K 2 O, CaO, Na 2 O, FeO, MgO, MnO and H 2 O such that C = 9Most common natural rocks contain the major elements: SiO 2, Al 2 O 3, K 2 O, CaO, Na 2 O, FeO, MgO, MnO and H 2 O such that C = 9 Three components is the maximum number that we can easily deal with in two dimensionsThree components is the maximum number that we can easily deal with in two dimensions What is the “right” choice of components?What is the “right” choice of components? Several “standard” ternary diagrams applied to metamorphic rocks.Several “standard” ternary diagrams applied to metamorphic rocks. Goal is to understand these; you will not have to derive these…….but understand how to use them!Goal is to understand these; you will not have to derive these…….but understand how to use them!

29. The ACF Diagram Illustrate metamorphic mineral assemblages in mafic rocks on a simplified 3-C triangular diagramIllustrate metamorphic mineral assemblages in mafic rocks on a simplified 3-C triangular diagram Concentrate only on the minerals that appeared or disappeared during metamorphism, thus acting as indicators of metamorphic gradeConcentrate only on the minerals that appeared or disappeared during metamorphism, thus acting as indicators of metamorphic grade So SOME minerals are not shown, but are ASSUMED to be part of assemblage (e.g., quartz, muscovite). In these cases, mineral names will be provided.So SOME minerals are not shown, but are ASSUMED to be part of assemblage (e.g., quartz, muscovite). In these cases, mineral names will be provided.

30. Figure 24-4. After Ehlers and Blatt (1982). Petrology. Freeman. And Miyashiro (1994) Metamorphic Petrology. Oxford.

31. The ACF Diagram The points of ternary are defined as componentsThe points of ternary are defined as components Calculated on an atomic basis:Calculated on an atomic basis: A = Al 2 O 3 + Fe 2 O 3 - Na 2 O - K 2 O C = CaO - 3.3 P 2 O 5 F = FeO + MgO + MnO

32. The ACF Diagram A = Al 2 O 3 + Fe 2 O 3 - Na 2 O - K 2 O Why the subtraction? Na and K in the average mafic rock are typically combined with Al to produce Kfs and AlbiteNa and K in the average mafic rock are typically combined with Al to produce Kfs and Albite In the ACF diagram, we are interested only in the other K- bearing metamorphic minerals, and thus only in the amount of Al 2 O 3 that occurs in excess of that combined with Na 2 O and K 2 O (in albite and K-feldspar)In the ACF diagram, we are interested only in the other K- bearing metamorphic minerals, and thus only in the amount of Al 2 O 3 that occurs in excess of that combined with Na 2 O and K 2 O (in albite and K-feldspar) Because the ratio of Al 2 O 3 to Na 2 O or K 2 O in feldspars is 1:1, we subtract from Al 2 O 3 an amount equivalent to Na 2 O and K 2 O in the same 1:1 ratioBecause the ratio of Al 2 O 3 to Na 2 O or K 2 O in feldspars is 1:1, we subtract from Al 2 O 3 an amount equivalent to Na 2 O and K 2 O in the same 1:1 ratio

33. The ACF Diagram C = CaO - 3.3 P 2 O 5 C = CaO - 3.3 P 2 O 5 F = FeO + MgO + MnO

34. The ACF Diagram Water is omitted under the assumption that it is perfectly mobileWater is omitted under the assumption that it is perfectly mobile Note that SiO 2 is simply ignoredNote that SiO 2 is simply ignored F 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.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. What this means is that QUARTZ MUST BE PRESENT for use of the ACF diagram.What this means is that QUARTZ MUST BE PRESENT for use of the ACF diagram. By creating these “combined” components, Eskola reduced the number of components in mafic rocks from 8 to 3

35. How do we use this diagram? Figure 24-5. After Turner (1981). Metamorphic Petrology. McGraw Hill. Different bulk compositions: equilibrium assemblage or no? (Lab)

36. Choosing the Appropriate Chemographic Diagram Variations in metamorphic mineral assemblages result from: 1) Differences in bulk chemistry 2) differences in intensive variables, such as T, P, P H2O, etc (metamorphic grade) A good chemographic diagram permits easy visualization of the first situation The second can be determined by a balanced reaction in which one rock’s mineral assemblage contains the reactants and another the products These differences can often be visualized by comparing separate chemographic diagrams, one for each grade