Equilibrium assemblages and Phase Diagrams Christian de Capitani With the help of: (chronologically) Tom Brown Hugh Greenwood Rob Berman Marcus Kirschen Christian Meyre Thorsten Nagel Konstantin Petrakakis Philipp Hunziker Romain Bousquet Fred Gaidies Doug Tinkham  What is the Theriak-Domino Software?  Petrogenetic grid > < equilibrium assemblage diagram  Some applications It is with tremendous ill grace that I grudgingly acknowledge the contribution of a few other people. (Hugh Grant, 1995)

What is the Theriak-Domino Software? The THERIAK-DOMINO Software is a program collection to calculate and plot thermodynamic functions, equilibrium assemblages and equilibrium assemblage diagrams: Theriak: stable mineral assemblage and phase compositions for a given bulk composition at specified P,T conditions. Domino: - equilibrium assemblage diagrams (P, T, a, ln(a)) - Pseudo-binary or pseudo-ternary phase diagrams - isopleths, density, volume or modal distributions - and more Therbin,Therter: binary and ternary phase diagrams Thalia,Thermo: thermodynamic functions (T, P or composition) Guzzler, Explot, Makemap, Plotxy: transform graphics information to postscript files

What is the aim of thermodynamic modeling?

Nature Experiments, Theory

Nature Experiments, Theory

Nature Models, Software Experiments, Theory Database

Nature Experiments, Theory Models, Software Software Theriak-Domino Database Software Theriak-Domino

Nature Prediction Experiments, Theory Models, Software Software Database Software Theriak-Domino Prediction

Nature Prediction Experiments, Theory Models, Software Software Database Software Theriak-Domino Prediction

Petrogenetic grids: Focus on reactions 1. System (eg. K2O-MgO-Al2O3-SiO2-H2O) 2. Choose phases (eg. for pelites: Qz, Sil, And, Ky, Stau, Alm, Grs, Py, etc.) 3. Calculate all reactions 4. Schreinemakers

Petrogenetic grids: Focus on reactions P-T phase diagram showing the experimental results of Koziol and Newton (1988), and the equilibrium curve for reaction (27-37). Open triangles indicate runs in which An grew, closed triangles indicate runs in which Grs + Ky + Qtz grew, and half-filled triangles indicate no significant reaction. The univariant equilibrium curve is a best-fit regression of the data brackets. The line at 650oC is Koziol and Newton’s estimate of the reaction location based on reactions involving zoisite. The shaded area is the uncertainty envelope. After Koziol and Newton (1988) Amer. Mineral., 73, 216-233

Petrogenetic grids: Focus on reactions K2O-MgO-Al2O3-SiO2-H2O K2O-FeO-MgO-Al2O3-SiO2-H2O P-T grid for pelites, after Spear and Cheney (1989). (inF. Spear (1993): Metamorphic Phase Equilibria and Pressure-Temperature-Time Paths.

Petrogenetic grids: Focus on reactions K2O-Na2O-CaO-FeO-MgO-Al2O3-SiO2-H2O 85 possible phases: 1 AKERMANITE 2 ANTIGORITE 3 BRUCITE 4 CHRYSOTILE 5 DIASPORE 6 GEHLENITE 7 HEMATITE 8 HERCYNITE 9 KALSILITE 10 KAOLINITE 11 LAWSONITE 12 ALEUCITE 13 BLEUCITE 14 LIME 15 MAGNETITE 16 MERWINITE 17 MONTICELLITE 18 NEPHELINE 19 PERICLASE 20 PREHNITE 21 PYROPHYLLITE 22 SPINEL 23 TALC 24 WOLLASTONITE 25 PSEUDOWOLLASTONI 26 HEULANDITE 27 LAUMONTITE 28 STILBITE 29 WAIRAKITE 30 PUMPELLYITE2 31 A-QUARTZ 32 B-QUARTZ 33 COESITE 34 CORUNDUM 35 ALPHA CRISTOBALITE 36 BETA CRISTOBALITE 37 LOW TRIDYMITE 38 HIGH TRIDYMITE 39 ANDALUSITE 40 KYANITE 41 SILLIMANITE 42 FAYALITE 43 FORSTERITE 44 GROSSULAR 45 PYROPE 46 ALMANDINE 47 ALBITE 48 K-FELDSPAR 49 ANORTHITE 50 ANNITE 51 PHLOGOPITE 52 MARGARITE 53 MUSCOVITE 54 CELADONITE 55 FE-CELADONITE 56 PARAGONITE 57 FE-STAUROLITE 58 MG-STAUROLITE 59 ORTHOENSTATITE 60 PROTOENSTATITE 61 FERROSILITE 62 DIOPSIDE 63 JADEITE 64 HEDENBERGITE 65 CA-AL PYROXENE 66 CLINOCHLORE 67 DAPHNITE 68 AMESITE 69 CORDIERITE(DRY) 70 FE_CORDIERITE 71 MGCTD 72 FECTD 73 ZOISITE 74 CLINOZOISITE 75 EPIDOTE 76 ANTHOPHYLLITE 77 TREMOLITE 78 FETREMOLITE 79 TSCHERMAKITE 80 PARGASITE 81 FEPARGASITE 82 GLAUCOPHANE 83 STEAM 84 OXYGEN 85 HYDROGEN 4.117·1011 reactions(maximum)

Equilibrium assemblage diagrams: Focus on equilibria Temperature Composition Obere Tiefenstufe Untere Tiefenstufe Al allein . . . . Disthen Disthen, Sillimanit Fe + Al . . . . Chloritoid, Granat Almandin Mg allein . . . . Antigorit Rhomb. Pyroxene; bei Si-Mangel Olivin Mg + Al . . . . Chlorit Pyrop, Cordierit Mg + Ca . . . . Hornblende Diopsid, Omphacit Ca + Al . . . . Zoisit, Epidot Anorthitreicher Plagioklas Na + Al . . . . Albit, bei Si-Mangel Albitsubstanz im Plagioklas, bei Si-Mangel Glaukophan Na Al -Verbindung im Omphacit Na + Fe . . . . Na-Hornblenden Ägirin als Beimischung im Omphacit Ka + Al . . . . Muscovit Kalifeldspat K + Fe + Mg . . . Biotit Biotit Ti . . . . . . meist mit Ca und Rutil Si als Titanit F. Becke: Über Mineralbestand und Struktur der kristallinen Schiefer. Comptes Rendus IX. Congrès géol. internat. de Vienne 1903 Most people would sooner die than think; in fact, they do so. (Bertrand Russell)

Equilibrium assemblage diagrams: Focus on equilibria

Equilibrium assemblage diagrams: Focus on equilibria

Equilibrium assemblage diagrams: Focus on equilibria 1. Chemical composition, eg.: SiO2 59.58 Al2O3 12.16 FeO 4.87 MgO 2.79 CaO 0.53 Na2O 1.27 K2O 2.69 H2O 30.00 2. Choose phases (eg. for pelites: Qz, Sil, And, Ky, Stau, Alm, Grs, Py, etc.) 3. Calculate all reactions 4. Schreinemakers equilibrium assemblage diagram

Example of equilibrium calculation Equilibrium assemblage diagrams: Focus on equilibria Example of equilibrium calculation Input Output bulk composition mols SiO2 59.58 Al2O3 12.16 MgO 2.79 FeO 4.87 CaO 0.53 Na2O 1.27 K2O 2.69 H2O 30.00 (excess) mols phase composition 2.38 GARNET X(grossular) 0.038 X(pyrope) 0.310 X(almandine) 0.652 1.82 FSP X(albite) 0.836 X(K-feldspar) 0.022 X(anorthite) 0.142 6.35 wh_mica X(muscovite) 0.717 X( paragonite) 0.159 X( M-celadonite) 0.090 X( F-celadonite) 0.034 27.40 Quartz 23.65 Steam P and T T = 700 oC P = 10000 Bar

Equilibrium assemblage diagrams: Focus on equilibria T. Nagel, C. de Capitani and M. Frey, J. metamorphic Geol., 2002, 20, 309-324

Eqiulibrium assemblage Phase Diagrams

Equilibrium assemblage diagrams When are the results of a prediction useful? When you learn something Simple problems: Summarize what is known Plan experimental work Test data and solution models Complex problems: Calculations help understand nature Science is like sex: sometimes something useful comes out, but that is not the reason we are doing it. (Richard Feynman)

Equilibrium assemblage diagrams When are the results of a prediction useful? When you learn something Simple problems: Summarize what is known Plan experimental work Test data and solution models Complex problems: Calculations help understand nature When the results are unexpected Did we interpret our observations correctly? Is the thermodynamic data correct? Is the software calculating correctly? Science is like sex: sometimes something useful comes out, but that is not the reason we are doing it. (Richard Feynman)

Equilibrium assemblage diagrams When are the results of a prediction useful? When you learn something Simple problems: Summarize what is known Plan experimental work Test data and solution models Complex problems: Calculations help understand nature When the results are unexpected Did we interpret our observations correctly? Is the thermodynamic data correct? Is the software calculating correctly? When the results are oviously wrong Opportunity to improve the database Fix bugs in the software Science is like sex: sometimes something useful comes out, but that is not the reason we are doing it. (Richard Feynman)

Eqiulibrium assemblages and Phase Diagrams Petrogenetic grids > < equilibrium assemblage diagrams

Equilibrium assemblage diagrams: Simple problems Comparision Petrogenetic grid Equilibrium assemblage diagram focus reactions chemical equilibrium calculation input system and choice of phases bulk composition interpretation may be difficult very easy solution models only activities of some phases needed fixed compositions in input Thermodynamic properties and activities of all endmembers must be known compositions are calculated I don't necessarily agree with everything I say. (Marshall McLuhan)

Equilibrium assemblage diagrams: applications

Equilibrium assemblage diagrams: testing databases Bulk composition: SiO2 Diagram: stable assemblages Database from TWQ Database from THERMOCALC coesite coesite -quartz -quartz quartz cr cr melt tr tr

Equilibrium assemblage diagrams: testing databases Bulk composition: SiO2 Diagram: densities [ccm/mol] Database from TWQ Database from THERMOCALC coesite coesite -qtz quartz -qtz cr cr melt tr tr

Birch’s law (1964) extended Birch’s law Equilibrium assemblage diagrams: seismic velocities Physical properties of rocks use for seismic velocities Birch’s law (1964) extended Birch’s law Vp Vs 0.2 GPa 0.6 GPa 1.0 GPa Vp Vs Velocity (km.s-1) Velocity (km.s-1) Density (g.cm-3) V=aρ+b Density (g.cm-3) Ludwig et al., 1970 R. Bousquet, C. de Capitani, D. Arcay, Strasbourg 2006

Equilibrium assemblage diagrams: seismic velocities Physical properties of rocks use for seismic velocities Pelites density MORB density Gabbro density R. Bousquet, C. de Capitani, D. Arcay, Strasbourg 2006

Equilibrium assemblage diagrams: understanding rocks 1 mm T. Nagel, C. de Capitani and M. Frey, J. metamorphic Geol., 2002, 20, 309-324

Equilibrium assemblage diagrams: understanding rocks If you cannot convince them, confuse them. (Harry S Truman) T. Nagel, C. de Capitani and M. Frey, J. metamorphic Geol., 2002, 20, 309-324

Equilibrium assemblage diagrams: understanding rocks If you cannot convince them, confuse them. (Harry S Truman) T. Nagel, C. de Capitani and M. Frey, J. metamorphic Geol., 2002, 20, 309-324

Equilibrium assemblage diagrams: understanding rocks T. Nagel, C. de Capitani and M. Frey, J. metamorphic Geol., 2002, 20, 309-324

TWQ Equilibrium assemblage diagrams: understanding rocks GARNET (rim) GROSSULAR 0.061 PYROPE 0.209 ALMANDINE 0.730 TWQ PHLOGOPITE 0.617 ANNITE 0.383 BIOTITE PARAGONITE 0.128 MUSCOVITE 0.872 WHITE MICA ALBITE 0.760 K-FELDSPAR 0.018 ANORTHITE 0.222 FELDSPAR STAUROLITE FE-STAUROLITE 0.906 MG-STAUROLITE 0.094 T. Nagel, C. de Capitani and M. Frey, J. metamorphic Geol., 2002, 20, 309-324

Equilibrium assemblage diagrams: understanding rocks T. Nagel, C. de Capitani and M. Frey, J. metamorphic Geol., 2002, 20, 309-324

Equilibrium assemblage diagrams: understanding rocks T. Nagel, C. de Capitani and M. Frey, J. metamorphic Geol., 2002, 20, 309-324

Equilibrium assemblage diagrams: understanding rocks

Equilibrium assemblage diagrams: Final remarks Equilibrium calculations (THERIAK etc.) are powerful tools to • visualize the implications of databases • help understanding natural processes • help to develop new eqations of state and solution models • help planning experimental work A conclusion is simply the place where someone got tired of thinking. (Arthur Block)

Equilibrium assemblage diagrams: Final remarks Equilibrium calculations (THERIAK etc.) are powerful tools to • visualize the implications of databases • help understanding natural processes • help to develop new eqations of state and solution models • help planning experimental work Difficulties for beginners • software is a black box • low rate of succes (You get what you asked for but it may not what you wanted).