It is with tremendous ill grace that I grudgingly acknowledge the contribution of a few other people. (Hugh Grant, 1995) Christian de Capitani Equilibrium.

It is with tremendous ill grace that I grudgingly acknowledge the contribution of a few other people. (Hugh Grant, 1995)

Christian de Capitani

Equilibrium assemblagesand Phase Diagrams

What is the Theriak-Domino Software?

Some applications

Petrogenetic grid > < equilibrium assemblage diagram

With the help of:(chronologically)

Tom BrownHugh GreenwoodRob BermanMarcus KirschenChristian MeyreThorsten NagelKonstantin PetrakakisPhilipp HunzikerRomain BousquetFred GaidiesDoug Tinkham

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 bulkcomposition 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

Experiments, Theory

Models,Software

Database

Nature

Experiments, Theory

SoftwareTheriak-Domino

Models,Software

Database

Nature

Experiments, Theory

Prediction

Models,Software

Database


Nature

Experiments, Theory

Models,Software

Prediction

Database


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.)

4. Schreinemakers

3. Calculate all 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


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.


1 AKERMANITE2 ANTIGORITE3 BRUCITE4 CHRYSOTILE5 DIASPORE6 GEHLENITE7 HEMATITE8 HERCYNITE9 KALSILITE10 KAOLINITE11 LAWSONITE12 ALEUCITE13 BLEUCITE14 LIME15 MAGNETITE16 MERWINITE17 MONTICELLITE18 NEPHELINE19 PERICLASE20 PREHNITE21 PYROPHYLLITE22 SPINEL23 TALC24 WOLLASTONITE25 PSEUDOWOLLASTONI26 HEULANDITE27 LAUMONTITE28 STILBITE29 WAIRAKITE30 PUMPELLYITE231 A-QUARTZ32 B-QUARTZ

33 COESITE34 CORUNDUM35 ALPHA CRISTOBALITE36 BETA CRISTOBALITE37 LOW TRIDYMITE38 HIGH TRIDYMITE39 ANDALUSITE40 KYANITE41 SILLIMANITE42 FAYALITE43 FORSTERITE44 GROSSULAR45 PYROPE46 ALMANDINE47 ALBITE48 K-FELDSPAR49 ANORTHITE50 ANNITE51 PHLOGOPITE52 MARGARITE53 MUSCOVITE54 CELADONITE55 FE-CELADONITE56 PARAGONITE57 FE-STAUROLITE58 MG-STAUROLITE59 ORTHOENSTATITE60 PROTOENSTATITE61 FERROSILITE62 DIOPSIDE63 JADEITE64 HEDENBERGITE

65 CA-AL PYROXENE66 CLINOCHLORE67 DAPHNITE68 AMESITE69 CORDIERITE(DRY)70 FE_CORDIERITE71 MGCTD72 FECTD73 ZOISITE74 CLINOZOISITE75 EPIDOTE76 ANTHOPHYLLITE77 TREMOLITE78 FETREMOLITE79 TSCHERMAKITE80 PARGASITE81 FEPARGASITE82 GLAUCOPHANE83 STEAM84 OXYGEN85 HYDROGEN

85 possible phases:

K2O-Na2O-CaO-FeO-MgO-Al2O3-SiO2-H2O

4.117·1011 reactions(maximum)


Obere Tiefenstufe Untere Tiefenstufe

Al allein . . . . Disthen Disthen, SillimanitFe + Al . . . . Chloritoid, Granat AlmandinMg allein . . . . Antigorit Rhomb. Pyroxene; bei Si-Mangel OlivinMg + Al . . . . Chlorit Pyrop, CordieritMg + Ca . . . . Hornblende Diopsid, OmphacitCa + Al . . . . Zoisit, Epidot Anorthitreicher PlagioklasNa + Al . . . . Albit, bei Si-Mangel Albitsubstanz im Plagioklas, bei Si-Mangel

Glaukophan Na Al -Verbindung im OmphacitNa + Fe . . . . Na-Hornblenden Ägirin als Beimischung im OmphacitKa + Al . . . . Muscovit KalifeldspatK + Fe + Mg . . . Biotit BiotitTi . . . . . . 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

Temperature

Com

posi

tion

Equilibrium assemblage diagrams: Focus on equilibria

Most people would sooner die than think; in fact, they do so. (Bertrand Russell)



4. Schreinemakers

3. Calculate all reactions

equilibrium assemblage diagram

1. Chemical composition, eg.:

2. Choose phases (eg. for pelites: Qz,Sil, And, Ky, Stau, Alm, Grs, Py, etc.)

SiO2 59.58Al2O3 12.16FeO 4.87MgO 2.79CaO 0.53Na2O 1.27K2O 2.69H2O 30.00


Example of equilibrium calculation

Input Output

P and T

T = 700 oCP = 10000 Bar

bulk composition

molsSiO2 59.58Al2O3 12.16MgO 2.79FeO 4.87CaO 0.53Na2O 1.27K2O 2.69H2O 30.00 (excess)

mols phase composition

2.38 GARNET X(grossular) 0.038X(pyrope) 0.310X(almandine) 0.652

1.82 FSP X(albite) 0.836X(K-feldspar) 0.022 X(anorthite) 0.142

6.35 wh_mica X(muscovite) 0.717X( paragonite) 0.159X( M-celadonite) 0.090X( F-celadonite) 0.034

27.40 Quartz

23.65 Steam


T. Nagel, C. de Capitani and M. Frey, J. metamorphic Geol., 2002, 20, 309-324


Eqiulibrium assemblage Phase Diagrams

When are the results of a prediction useful?

When you learn something

Equilibrium assemblage diagrams

Simple problems: Summarize what is knownPlan experimental workTest 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)



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 unexpected

When the results are oviously wrong




Did we interpret our observations correctly?Is the thermodynamic data correct?Is the software calculating correctly?

Opportunity to improve the databaseFix bugs in the software


Eqiulibrium assemblages and Phase Diagrams

Petrogenetic grids equilibrium assemblage diagrams> <

Equilibrium assemblage diagrams: Simple problems

Equilibrium assemblage diagramPetrogenetic grid

Comparision

calculation input bulk compositionsystem and choice of phases

interpretation very easymay be difficult

solution models •Thermodynamic properties and activities of all endmembers must be known

• compositions are calculated

• only activities of some phasesneeded

• fixed compositions in input

focus chemical equilibriumreactions

I don't necessarily agree with everything I say. (Marshall McLuhan)

Equilibrium assemblage diagrams:

applications

coesite coesite

-quartz -quartzquartz

melttr tr

cr cr

Database from TWQ Database from THERMOCALC

Bulk composition: SiO2

Diagram: stable assemblages

Equilibrium assemblage diagrams: testing databases

coesitecoesite

-qtz

-qtzquartz

melttr tr

Database from TWQ Database from THERMOCALC

Bulk composition: SiO2

Diagram: densities [ccm/mol]

Equilibrium assemblage diagrams: testing databases

cr cr

Birch’s law (1964)

Vp

Vs

extended Birch’s law

Vp Vp

VsVs

V=aρ+b

Vel

ocity

(km

.s-1)

Density (g.cm-3)

Vel

ocity

(km

.s-1)

Density (g.cm-3)

0.2 GPa 0.6 GPa 1.0 GPa

Ludwig et al., 1970

Physical properties of rocks use for seismic velocities

R. Bousquet, C. de Capitani, D. Arcay, Strasbourg 2006

Equilibrium assemblage diagrams: seismic velocities

Pelites

density

MORB

density

Gabbro

density

Physical properties of rocks use for seismic velocities

R. Bousquet, C. de Capitani, D. Arcay, Strasbourg 2006

Equilibrium assemblage diagrams: seismic velocities

1 mm


Equilibrium assemblage diagrams: understanding rocks


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


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



Garnet


GARNET (rim)GROSSULAR 0.061PYROPE 0.209ALMANDINE 0.730

ALBITE 0.760K-FELDSPAR 0.018ANORTHITE 0.222

FELDSPAR

PARAGONITE 0.128 MUSCOVITE 0.872

WHITE MICA

PHLOGOPITE 0.617ANNITE 0.383

BIOTITE

STAUROLITEFE-STAUROLITE 0.906MG-STAUROLITE 0.094

TWQ







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

Equilibrium assemblage diagrams: Final remarks

A conclusion is simply the place where someone got tired of thinking. (Arthur Block)

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).

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

It is with tremendous ill grace that I grudgingly acknowledge the contribution of a few other people. (Hugh Grant, 1995) Christian de Capitani Equilibrium.

Documents

theriakdomino software

ternary phase diagrams

phase compositions

t grid

thermodynamic functions

reactionspt phase diagram

t conditions

univariant equilibrium