GibbsTut(Feb, 2001) Pt Aees2.geo.rpi.edu/.../Software/GibbsWeb/GibbsTut(Feb,2001)_Pt_A.pdf ·...

Program GibbsTutorial

by

Frank S. Spear

© 2001 by Frank S. Spear

F. S. Spear Program Gibbs Tutorial 2

Program Gibbs

Tutorial

February, 2001

Frank S. SpearDepartment of Geology, Rensselaer Polytechnic Institute, Troy, New York 12180

[email protected]

Table of Contents

Introduction to Program Gibbs .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3General program notes.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

Installation.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1The Macintosh Fortran interface .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

Program Gibbs Tutorial . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6General considerations.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6Starting the program... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6The Main menu ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

Program Gibbs exercises.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9Introduction .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9Exercise 1: Drawing a P-T univariant curve.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

Theory.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9Exercise 1.A. Drawing the univariant using integral

thermodynamics and the “Steps” menu ... . . . . . . . . . . . . . . . . . . 9Exercise 1.B. Drawing the univariant using integral

thermodynamics and the “Contour” menu ... . . . . . . . . . . . . . . . 12Exercise 1.C. Examine the change of mineral compositions

along a univariant curve.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13Exercise 2: Contouring divariant P-T space with

mineral composition and abundance.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14Exercise 2.A. Contouring divariant regions using integral

thermodynamics and no mass balance constraints. . . . . . . . . . . . . . . . . 14Exercise 2.B. Contouring divariant regions using integral

thermodynamics with mass balance constraints.. . . . . . . . . . . . . . . . . . . . 18Exercise 3: Saving text and graphics output .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23Exercise 3.A. Saving the text output .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23Exercise 3.B. Saving the graphics output .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23Exercise 3.C. Redrawing the plotting axes.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23Exercise 4: Petrogenetic grid routines.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24Exercise 4.A. AFM diagram routines .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24Exercise 4.B. T-X and P-X assemblage stability diagram routines .. . . . 27Exercise 4.C. P-T stability diagram routine .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31


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Setting Plotting Parameters .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186

Appendix 1. PostScript graphics files.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43


Introduction to Program Gibbs

Program GIBBS is a general algorithm to perform thermodynamic calculations ofheterogeneous phase equilibria. The program is designed to produce graphical output ofresults (phase diagrams, P-T diagrams, etc.) and there are several modules that permit thefollowing types of calculations

a) P-T path calculation (DT)b) Contour diagrams (P-T-X-M)(DT and IT)c) Petrogenetic grids/AFM diagrams (IT)d) Pseudosections (IT)e) ReNTRs and ReERsf) Forward modeling of reaction history (DT and IT)g) Forward modeling of garnet growth with or without diffusion (Garnet Grow/

DiffGibbs) (DT)h) Whole-rock reaction balancing (DT)i) Thermodynamic projections

The last “official” release of Program Gibbs was in 1997 (Gibbs 4.7). I supposethis version should be labeled “Gibbs 5.0” but I make so many changes to the code itdoesn’t seem worth the effort to keep track of version numbers. Rather, the programversion will be identified by a release date, in this case “Gibbs (Feb, 2001).

Thermodynamic background

The thermodynamic basis for the calculations are described in detail in Spear(1993). The user selects a chemical system and an assemblage of minerals. The programthen sets up a system of simultaneous equations that consists of the equilibrium relations(∆G = 0) for every independent reaction in a system and mass balance equations (ifdesired). The matrix is inverted and the Jacobian transformation matrix that relates a user-specified set of independent variables to the remaining dependent variables is calculated.There are two basic calculation modes in Program GIBBS: Integral thermodynamics mode(Newton’s method) and differential thermodynamics mode (Gibbs’ method). In IntegralThermodynamics mode the Jacobian transformation matrix is used to solve the system ofequations for the values of dependent variables (P, T, X or M) given the user-specifiedvalues of independent variables. In differential mode, the Jacobian transformation is usedto compute changes (i. e., finite differences) in a set of dependent thermodynamic variablesgiven the changes in a set of independent thermodynamic variables. The program isdesigned so that the choice of which thermodynamic variables are to be independent andwhich are to be dependent is arbitrary. Because of this, a variety of different types ofproblems can be addressed (and solved?) by this program. The tutorial of this manualcontains examples of several different types of problems that can be solved.


General Program Notes

Program Gibbs is coded in FORTRAN 77 and has been compiled using Absoft'sMacFortran II compiler v 4.5. The program requires approximately 8.0 Mb to run andrequires a Macintosh with a Power PC processor with Mac OS 7.5 or higher (the programwill not run on a 68k processor).

Installation

There is no special installation instructions. Just double-click the program icon tostart the program.

The Macintosh Fortran interface

An attempt has been made to make these programs as "user friendly" as possible, but Ihave chosen to use a more standard Fortran I/O in many cases where the Macintoshguidelines call for menus and dialog boxes.

Program Gibbs has a Command window, an Output window and one or moreGraphics windows. Here are some important considerations when running the programs1) Input of user responses can only take place in the Command window (or a dialog

box, if implemented). The Command window must be the front (active) window forkeyboard I/O to occur. The Command window can be made active in the standardMacintosh ways: clicking on the window, selecting it from the Windows menu, orusing the command-key equivalent (see menu). Also, the cursor must be at the end ofwhatever text there is in the Command window.

2) Text output is directed to the Output window, which may be scrolled, highlighted,copied, pasted, saved and printed. Note if you use the "Save" option from the "File"menu to save the contents of this window, the file name will be "Output". Use the"Saveas" option to set the file name.

3) Graphics output is directed to the Graphics window, which can be viewed while theprogram is running. Graphics output is also directed to a PostScript file in a formatcompatible with Adobe Illustrator (version 3.0, 5.0 and 6.0 compatible). ThePostScript file can be saved and opened in the Illustrator for enhancement and printing.a) Graphics output can also be saved as PICT files from several places in the program.a) Graphics output can also be obtained by screen dumps. In Mac OS 8 and above,

use the system command:shift 4

The cursor will turn into a + and you can select an area of the screen by clicking themouse and dragging. This command generates PICT file labeled “Picture 1” etc inyour startup disk.

How to use this manual

The tutorial part of this manual contains step-by-step instructions on the use of theprogram for specific purposes. It is recommended that new users begin with the tutorial.The reference section contains detailed information about each module as well as tidbitsabout program design and philosophy. For users who wish in-depth description of theprogram behavior, the reference section is provided as a resource. The appendix containsdetails about data file construction designed for individuals who wish to modify these files.


Program Gibbs TutorialThis section provides step-by-step instructions for the calculation of specific types

of diagrams. Each tutorial unit is designed to be self contained so one can go through thesein any order desired.

General considerations

It is essential to understand that there are two modes of calculation in ProgramGibbs: Integral mode (here called Newton’s method) and differential mode (the Gibbs’method). The user can select the calculation mode depending on the type of problem to besolved. For example, calculation of a petrogenetic grid, AFM diagrams and pseudosectionsfrom an internally consistent thermodynamic database uses the integral mode. Calculationof P-T paths from zoned garnet, whole-rock reaction balancing or forward modeling (e.g.DiffGibbs module) would use the differential mode.

The Gibbs Tutorial thermodynamic data file works only in differential modebecause the enthalpy data are not internally consistent. The Holland and Powell (1998),S&C and SPaC data bases work in both integral and differential mode.

Starting the program

When you start program Gibbs you will see a splash screen with an image of theprogram’s namesake. You will then be asked to select a thermodynamic data file from alist.

Thermodynamic data files in Gibbs.fig file:

1 Gibbs Tutorial Thermo.dat 2 HoPo Thermo (12/20/98) 3 S&C(03/2000) Thermo.dat 4 SPaC(4/2000)_Thermo.dat Pick thermodynamic data file to use in this session

Note that the Gibbs Tutorial Thermo.dat file can be used only in differentialthermodynamics mode. HoPo Thermo, S&C, and SPaC can be used in differential orintegral mode.


The Main menu

The main menu will then appear:

*********************************** Thermo file: Gibbs Tutorial Thermo.dat Gibbs' method *********************************** MAIN MENU OPTIONS: 1 = Begin/save problem ----------------------------- 2 = Single steps 3 = Contour X-Y diagrams 4 = Make my grid 5 = Grow Garnet 6 = DiffGibbs (Garnet growth with diffusion) 7 = Whole rock reaction balancing ----------------------------- 8 = Go to global menu 9 = Plotting menu 10 = Plot digitized reactions 11 = Thermodynamic data menu ----------------------------- CHOOSE OPTION

The thermodynamic data file name is listed at the top with the status of theGibbs/Newton switch (Differential/Integral thermodynamics). Then there are a list of themain menu options. Here is a short discussion of each option. More detailed discussionsare given in the reference manual.

(1) Begin/save a problem. This menu handles input of a new problem from a data file,creating a new input file from the console, saving the current problem in an input fileformat, opening a bulk composition, saving the graphics output to a postscript or a PICTfile and saving the window and graphics preferences. Note that you MUST open a newproblem here before using the Single Steps or Contour menu items. You do not need toopen an input file to use the “Make my grid” menu option.

(2) Single steps. This menu item contains the most generalized Gibbs Methodcomputational options. From here one can calculate P-T paths from garnet zoning (e.g.Spear and Selverstone, 1983), draw any type of P-T-X-M contour diagram and performany type of Jacobean transformation. However, if contour diagrams are to be drawn,menu option 3 streamlines many of the operations.

(3) Contour X-Y diagrams. A contour diagram is one in which isopleths of compositionor mineral modes (or any other dependent variable) is drawn on X-Y axes. This menustreamlines the drawing of contour diagrams by allowing the user to select the isopleths tobe drawn (the number depending on the variance), and the contour routine will draw theisopleth automatically within the X-Y plot bounds. (Contouring can also be done from theSingle Steps menu, but it takes more user input). Pseudosections can be created (manually)from this routine.

(4) Make my grid. This module contains a number of routines that relate to petrogeneticgrids. Grids have been created for several thermodynamic data sets and the user can viewthe grid, calculate and draw AFM diagrams at any P and T, examine assemblage stabilityregions, and construct pseudosections.


(5) Grow garnet. Garnet zoning profiles can be calculated for any assemblage and plottedas radius versus composition. New garnets can be nucleated at user specified intervals andthe effect of continuous nucleation and growth examined. This routine was designed to testdifferent kinetic (or, more accurately, geometric) models of garnet growth.

(6) DiffGibbs. This routine incorporates garnet diffusion into a garnet growth model. Asingle garnet is grown in a specified bulk composition over a specified P-T path. At eachtime step the zoning profile in the growing garnet is allowed to relax by volume diffusionso the final growth + diffusion profile can be examined. Formerly a stand alone program(called DiffGibbs) this routine is now incorporated as a module in Gibbs.

(7) Whole rock reaction modeling. The stoichiometric coefficients of a continuous reactionare only defined in a differential sense at the P, T, X and M of the assemblage. Thereaction coefficients are a function of the P-T vector (path) specified. This routinecalculates the Jacobian for the assemblage and then computes a balanced reaction amongphases along any user specified P-T path.

(8) Global menu (usually option 8 in all submenus as well). The global menu allows theuser to change global parameters of the problem.

(9) Plotting menu (usually option 9 in submenus as well). Contains options for the user tospecify the type of X-Y or triangular plot.

(10) Plot digitized reactions. Plots reaction curves from files containing X-Y coordinates(usually P and T) of reactions digitized from literature sources, or calculated from anotherprogram. Compatible with TWQ plot files. This routine is especially useful whencomparing results from different sources on the same P-T axes.

(11) Thermodynamic data menu. Contains routines for examining thermodynamic data forphases.


Program GIBBS exercisesIntroduction

This section contains several tutorial exercises that illustrate the major capabilities ofProgram Gibbs. It is important to note that there are often more than one way to achieve aparticular result with this program, and many options have been added over the years tostreamline certain operations. For example, it is possible to do most operations from withinthe “Steps” menu, but contouring operations are far easier using the “Contour” menu andcalculations for certain KFMASH grids are completely automated in the “MakeMyGrid”menu. To realize the diverse capabilities of the program, the reader is encouraged to executethe tutorial exercises in order.

The first several exercises will illustrate the operation of Program Gibbs in integralthermodynamic mode. Integral thermodynamic mode is used to explore mineral stabilitybased on an internally consistent thermodynamic data set. Differential mode is best suited toexamining the P-T-X-M behavior of a particular rock sample, and will be discussed in thecontext of several specific examples.

Exercise 1: Drawing a P-T univariant curveTheory

This exercise produces a simple result – the plot of a univariant curve on a P-Tdiagram – and is designed to show how to achieve this result using the Steps and Contourmenus

In this exercise we will calculate the reaction

garnet + chlorite + muscovite = staurolite + biotite + quartz + H2O

Drawing a univariant curve using the integral approach involves picking a T or P(depending on the slope of the curve) and solving for the other variable, in addition to all ofthe equilibrium compositions, by simultaneous solution of the linearly independentheterogeneous reactions. The equations are identical to those used in the differentialapproach, and the Jacobean is computed in exactly the same manner, except in the integralapproach the Jacobean is used to iterate to an exact (within tolerance) solution whereas inthe differential approach, the Jacobean is used to increment the dependent variable (P or Tand X).

Exercise 1.A. Drawing the univariant using integral thermodynamics andthe “Steps” menu

1) Start program Gibbs2) Choose the Holland and Powell thermodynamic data set.3) From the main menu, choose menu item 1 (Begin/save problem)4) From the Begin/Save menu, choose menu item 2 (Select assemblage from Master Input

Files)5) From the list, choose “KFMASH” system. The “Master Input file” for this system will

be read (and listed in the output window) and a dialog box will appear that allows youto choose the assemblage. Note that the compositions of the minerals in this input fileare NOT equilibrium compositions (although the partitioning is close to correct).


6) Select minerals for the assemblage garnet + chlorite + muscovite + biotite + staurolite +quartz + H2O and click “Done”.a) You will see the assemblage information scroll in the Output Window. Examine the

information to see that it is correct.b) Then return to the main menu (Begin/Save menu item 0).

7) Select menu item 2 (Single steps). You should now see the “Steps” menu.8) Be sure that it says “Newton’s method” in the Command window.

a) If not, then select “Steps” menu item 10 (Gibbs/Newton switch) and change to“Newton’s method”

b) Check the Steps menu to be sure Newton’s method is active.9) Select “Steps” menu item 2 (Choose monitors/set deltas). You will see a dialog box

listing the thermodynamic variables for the system.a) Hit the “Reset” button,b) Select “P” as the independent variablec) Type in “5000” for ∆Pd) Type in “10” for the number of finite difference steps. This will subdivide the 5000

bars into 10 steps (500 bars each).i) The size of the step is not important in integral mode (although it is very

important in differential mode). In general, the step size (in this case 500 bars)should be set at an interval appropriate for the spacing desired along the curve.

e) Click “Done”1) Select “Steps” menu item 4 (Compute one increment). The increment is ∆P = 5000 bars

in 50 steps of 100 bars each. You should see the curve being drawn on the screen.a) Select “Steps” menu item 4 again. This will draw the next 5000 bars.b) Select “Steps” menu item 4 again. This will draw the next 5000 bars.c) Select “Steps” menu item 4 again. This will draw the next 5000 bars.d) Before this last part of the line is drawn, the program will beep and display

information in the command window. This information says In subroutine Activity A cation on a site has a zero or negative value Chlorite

e) Look at the information in the command window. You will see that FeM1 andFeM23 are negative in chlorite. This signifies that you have hit the Fe = 0 limit ofthe reaction (the KMASH limit). So you are done with this part of the curve.

f) Hit return to continue11) Select steps menu option 6 (Reference points) and sub-menu option 3 (return to starting

conditions). This option resets the compositions, P and T to the starting conditions. Atriangle should appear on the plot at the starting conditions.

12) Select 2 (Choose monitors) from the Steps menu.13) We will now draw the second half of the curve.

a) Set ∆P = -5000b) Set NSTEP = 50

14) Choose Steps option 4. The P-T curve should be drawn to lower pressure at 100 barincrements.a) The program will beep when you hit the Mg = 0 limit of the reaction (KFASH

limit). Examine the information in the Command window to see that MgM1 isnegative.

b) Hit return to continue.15) The entire curve is now drawn.16) Select “Steps” menu item 0 and return to the main menu


Exercise 1.B. Drawing the univariant using integral thermodynamics andthe “Contour” menu

Now we will do the same exercise using the contour menu. The contour routineworks in much the same way that the Steps routine works, except that a number ofoperations are automated. In particular, the program knows which variables are the X andY axes, so you don’t need to specify these as monitor parameters. One of the axes isalways an independent variable and the other is a dependent variable.

1) Select menu item 3 (Contour X-Y diagrams) from the Gibbs main menu.2) To be sure we are at the starting conditions:

a) Select “Contour” menu item 6 (Reference points)b) Select 3 (Return to starting conditions). You should see a triangle plotted at the

starting conditions.3) For a univariant curve, no variables need to be held constant to draw a contour, so there

is no need for this example to use menu items 2 or 3 (if you do select one of these, analert will tell you that you don’t need to).

4) Select Contour menu item 4 (Plot a contour). You should see the entire contour beingdrawn. When the curve gets to the KMASH or KFASH limit, you will hear theprogram beep and you will need to hit return a couple of times.

5) Your plot should look like the one below. See how much easier that was?


Exercise 1.C. Examine the change of mineral compositions along aunivariant curve

Except in systems in which all phases are pure, the compositions of phasesgenerally change along univariant reaction curves. This change can readily be examinedusing Program Gibbs.

1) Select Contour menu item 7 (Print assemblage information to output window). Nowexamine the output window. You will see the following information, which are theequilibrium compositions at the P-T conditions listed as “Current” (600., 7878.7)

****************************************************************************** T P Pfluid START 600.0 6000.0 6000.0 CURRENT 600.0 7878.7 7878.7

--MONITOR PARAMETERS-- NSTEP= 1 IMASS= 0 1 T_ -12.000

System components Si.. Al.. Mg.. Fe.. K... H2O. Mass balance = OFF

# OF PHASES, NPH= 7 Mineral compositions PhCo X(i) dX(i) sumdX(i) 1001 Quartz(a-b) Quartz 1.0000 0.0000 0.0000 1002 Fluid(H2O-CO2) H2O 1.0000 0.0000 0.0000 1123 Chlorite Clinochl 0.4216 0.0000 0.0762 Mg-Amesi 0.0920 0.0000 -0.1275 Daphanit 0.4864 0.0000 0.0513 SiT1 SiT2 AlT2 AlM4 MgM4 FeM4 AlM1 MgM1 FeM1 MgM23 FeM232.0000 0.9080 1.0920 1.0000 0.0000 0.0000 0.0920 0.4216 0.4864 2.0545 1.9455 1030 garnet Pyrope 0.1328 0.0000 -0.0172 Almandin 0.8672 0.0000 0.0172 XMg XFe XMn XCa 0.1328 0.8672 0.0000 0.0000 1040 Staurolite Mg-Staur 0.1203 0.0000 -0.0121 Fe-Staur 0.8797 0.0000 0.0121 XMg XFe XMn 0.1203 0.8797 0.0000 1122 Biotite Phlogopi 0.0952 0.0000 0.0117 Eastonit 0.2993 0.0000 -0.1708 Annite 0.4301 0.0000 -0.0271 Ordered- 0.1754 0.0000 0.1862 SiT2 SiT1 AlT1 AlM1 MgM1 FeM1 MgM2 FeM2 K 2.0000 0.7007 1.2993 0.2993 0.0952 0.6055 1.1398 0.8602 1.0000 1017 Muscovite Celadoni 0.0386 0.0000 -0.0114 Fe-Celad 0.1540 0.0000 0.1040 Muscovit 0.8074 0.0000 -0.0926 SiT2 SiT1 AlT1 AlM2A MgM2A FeM2A AlM2B K Na 2.0000 1.1926 0.8074 0.8074 0.0386 0.1540 1.0000 1.0000 0.0000


Values of new variables__FeMg(Chlor) 0.4955 0.0000 0.0404__FeMg(Biot) 0.5427 0.0000 0.0048__Al(Biotite) 1.5985 0.0000 -0.3417

In this exercise, we will learn how to use mineral composition as independentvariables as we examine the change in composition along the univariant reaction.

2) Go to the “Steps” menu3) Select menu option 2 (Choose monitors/set deltas)

a) In the dialog boxHit “Reset”

b) Select XAlmandine as the monitorc) Type in –0.1 for the delta valued) Type in 10 for the number of finite difference iterationse) Click Done

4) Select Steps menu option 4 (Compute one increment). We are now using Xalmandineas an independent variable and T and P (and all the other compositions) are dependent.You will see the curve being drawn as Xalmandine is decreased by 0.1 in steps of 0.01per increment. You can examine the composition of other minerals at any point byselecting option 7 (Print assemblage informations).

5) Suppose you wanted to answer the question: “What are the composition of biotite andchlorite along this reaction when garnet has the composition of Xalmandine = 0.8?” Todo this, you would perform the following steps:a) Select option 2 from the Steps menu (Choose monitors/set deltas)b) Select Xalmandine as the monitor parameterc) Examine the current value of Xalmandine and compute the value of ∆Xalmandine

necessary to get to a value of 0.8. For example, if the current value is 0.85 (thestarting value), then ∆Xalmandine must be –0.05. Type this value into the text box.

d) You can set the number of finite difference steps to 1 if using Newton’s methode) Click donef) Select option 4 (Compute one increment). The program will calculate the

equilibrium compositions at Xalmandine = 0.8.g) Select Steps option 7 to examine the results. The Fe/(Fe+Mg) of biotite and chlorite

are 0.4293 and 0.3886, respectively.


Exercise 2: Contouring divariant P-T space withmineral composition and abundance

For the next exercise, we will generate a P-T diagram that is contoured for mineralcomposition and mineral abundance. P-T-X contour diagrams contain identical informationas P-X and T-X diagrams. P-T-M (mineral abundance) contour diagrams display P-Tregions over which minerals grow and are consumed. These types of diagrams aretremendously useful in interpreting reaction textures, mineral zoning and compositionaltrends in mineral inclusion suites.

We will do this exercise in two parts to illustrate the different types of contouroptions in Gibbs. In the first section (Exercise 2.A) we will use integrated thermodynamicsmode (Newton’s method) to generate contours of Xalmandine in the KFMASH systemacross the univariant reaction garnet + chlorite + muscovite = staurolite + biotite + quartz +H2O. In the second section (Exercise 2.B) we will add mass balance equations to thesystem of thermodynamic equations and construct contours of mineral abundance.Contouring using differential thermodynamics (the Gibbs method) using a naturalassemblage as a starting point (reference assemblage) will be done in a later exercise.

Exercise 2.A. Contouring divariant regions using integral thermodynamicsand no mass balance constraints.

1) From the Gibbs Program main menu, select 1 (Begin/Save problem)2) Select menu item 2 (Select assemblage from MIF)

a) Choose KFMASH system from listb) Select the assemblage Grt + Chl + Bt + Ms + Qtz + H2Oc) Click Doned) Select 0 (Return)

3) From the Gibbs main menu, select 3 (Contour X-Y diagrams)4) Select Contour menu option 2 (Absolute contour routine)

You are presented with a list of the thermodynamic variables for this assemblage. Inthis dialog, you are to specify the absolute value of the variable you want to contour.Note that this differs from the dialog box in the Steps menu, which asks for the changein the variable selected (∆ value).a) Click Resetb) Select Xalmandinec) Set the contour value to 0.8d) Click Compute Contoure) You should see the contour being drawn on the plot.f) Repeat c-e drawing contours for Xalmandine = 0.9, 0.99, 0.7, 0.6, 0.5.g) Click Cancel when done

5) Go back to the Begin/Save menu and select a new assemblage in the KFMASH system(as in 2 above). This time, select the assemblage Grt + St + Bt + Ms + Qtz + H2O.

6) Repeat number 4, contouring the P-T diagram for this new assemblage.7) Go back to the Begin/Save menu and select the univariant assemblage Grt + Chl + St +

Bt + Ms + Qtz + H2O (same as exercise 1).8) Go to the contour menu and select option 4 (Plot a contour). No need to hold any

variables constant, because this is a univariant assemblage. Your plot should look likethis:


I saved this figure as a PostScript file (Begin/Save menu option 6) and cleaned it up inAdobe Illustrator. After editing out the metastable contours and adding some labels, thefigure looks like this:


Discussion:This diagram shows how Xalmandine changes as a function of P and T for two

assemblages in the KFMASH system, and across the univariant reaction that relates theassemblages. Note that the contours must intersect at the univariant.

This diagram can be used to infer changes in P and T from a zoned garnet. Forexample, a decrease in Fe/(Fe+Mg) in the assemblage Grt + St + Bt + Ms + Qtz can onlybe achieved by P-T trajectories that cross Xalmandine contours to lower values.

Note, however, that this diagram is valid for the KFMASH system, but we couldhave drawn a similar diagram in a system that contained additional components. Forexample, if Mn is added to the system, the variance of each assemblage increases by 1. Thediagram could still be drawn, however, if we held Xspessartine constant and would lookquite similar. However, one must be careful when interpreting contour diagrams becausesometimes the addition of a component or a phase can change the contours dramatically.This is especially true when contour diagrams are constructed using mass balanceconstraints (see below).

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20

T (C)

P k

bar

Contours of X(almandine) in KFMASH

0

.800

0

.700

0

.600

0

.500

0

.900

0

.990

0.900

0.800

0.700

0.600

0.500

0.990

�

Grt

+ C

hl +

Ms�

St +

Bt

Grt + Chl + Bt

Grt + St + Bt


Exercise 2.B. Contouring divariant regions using integral thermodynamics(Newton’s method) with mass balance constraints

In this exercise we will add mass balance equations to the system of thermodynamicequations so that we can compute the amounts of phases in the assemblage, in addition tophase composition. Duhem’s theorem states that for a thermodynamic system of fixed bulkcomposition, there are only two degrees of freedom. That is, every rock of fixed bulkcomposition is effectively divariant. This is a powerful result and is the reason why themineral facies concept works. It also predicts that the composition and amounts of phasesin a rock are a function of P and T only.

There are two ways to add mass balance constraints in Program Gibbs. From theBegin/Save menu, option 4 (Select bulk composition from disk file) lets the user pick abulk composition from a list that is stored in a text file in the Gibbs_Essentials folder (FileName = BulkRockAnalyses). The user can edit and add to this list as desired. In general,this is the preferred mode of adding mass constraints when using Newton’s method.

The second way is used when reading input files with natural assemblage data.Mass balance constraints are implemented by setting a switch variable called imass in theinput file. The bulk rock composition is specified by giving the mode (volume percent) ofeach phase in the assemblage. The program then calculates the bulk composition using themolar volume and composition of each phase.

1) From the main menu, select 1 (Begin/Save)2) From the Begin/Save menu, select 4 (Select bulk composition).

You will see the list of bulk compositions that are stored in the BulkRockAnalyses file.The analyses stored in the file are only for the KFMASH system, but other bulkcompositions can easily be added.a) Select the bulk composition titled

“KFMASH AFM example Al'= 0.0 Fe/(Fe+Mg) = .75”b) Select 0 to return to the main menu

3) Select 3 to go to the contour menu4) From the Macintosh menubar, select the Plot menu and choose Red for the line color.

This will help distinguish the molar isopleths from the composition isopleths drawn inthe last exercise. Alternatively, if your graphics window is too messy, go to the Plottermenu (option 9) and redraw the X-Y axes.

5) In the contour menu, select 2 (Absolute contour routine).Note that the list of thermodynamic variables now includes the moles of each phase(i.e. Mphase). These can be selected as variables to contour.


a) Click Resetb) Select Mgarnetc) Set the value to contour to be 0.0 moles of garnetd) Click Compute contour. You will see the contour being drawne) Now Click Reset, Select Mchlorite, Set the value to 0.0, and click Compute

contour. A contour at 0.0 moles of chlorite will be drawn.

The diagram should look something like this:


DiscussionThe two curves define the stability limit of the assemblage Grt + Chl + Bt + Ms +

Qtz + H2O for the bulk composition specified. A bulk composition with a higherFe/(Fe+Mg) would have two similar curves at lower temperature (this bulk compositionhas an Fe/(Fe+Mg) = 0.75). At temperatures lower than Mgarnet = 0, the assemblagewould be Chl + Bt + Ms + Qtz + H2O and at temperatures above Mchlorite = 0, theassemblage would be Grt + Bt + Ms + Qtz + H2O.

Note that the P-T region we contoured in Exercise 1 was much wider than thestability region for any specific bulk composition in the KFMASH system.

Also note that addition of Mn to the bulk composition will expand the stability limitof garnet to lower T (i.e. Mgarnet will shift to lower T).

It is possible to draw stability regions for other assemblages so that the entire P-Tdiagram is contoured with stability regions for every possible phase assemblage. One coulddo this by the method used in this exercise (the brute force approach) but it would requiresome knowledge of the stable univariant reactions through which mineral assemblageschange discontinuously. This information is inherent in a petrogenetic grid, and we will usethe petrogenetic grid routines below to construct such a diagram.


Examining phase abundance when mass balance is active

It is often useful to examine the amounts of phases in an assemblage. This is thelink between the calculations and the petrographic observation of mineral modes.

From the contour menu, select 7 (Print assemblage information). The information willscroll into the Output window. The composition information is the same as discussedearlier. The mass balance information is at the bottom:

****************************************************************************** T P Pfluid START 600.0 6000.0 6000.0 CURRENT 563.0 5999.9 5999.9..[composition information omitted].. Moles and volumes of phases switch Volumes Mineral mMoles fXliz Mode V0 V1 V21001 Quartz(a-b) 812.763 0 46.177 0.19093E+02 0.19093E+02 0.19093E+021002 Fluid(H2O-CO2) 285.215 0 14.103 0.58314E+01 0.58314E+01 0.58314E+011123 Chlorite 25.331 0 12.987 0.53698E+01 0.53698E+01 0.53698E+011030 garnet 0.000 0 0.000 0.00000E+00 0.00000E+00 0.00000E+001017 Muscovite 71.858 0 24.652 0.10193E+02 0.10193E+02 0.10193E+021122 Biotite 5.637 0 2.081 0.86047E+00 0.86047E+00 0.86047E+00

Bulk composition - calculated from mineral composition and moles Si.. Al.. Mg.. Fe.. K... H2O. dm(i) 0.000 0.000 0.000 0.000 0.000 0.000 mMoles 1131.6 251.1 38.4 115.5 77.5 464.0 Wt % 69.050 12.998 1.574 8.428 3.706 4.245

Bulk composition - input wt% and moles Si.. Al.. Mg.. Fe.. K... H2O. mMoles 1131.6 251.1 38.4 115.5 77.5 464.0 Wt % 68.000 12.800 1.550 8.300 3.650 4.180

The last several lines give the mineral moles (units are mmoles), volumes, and bulkcomposition information. Of particular interest is the Mode, which is the number of modesconverted to volume units, normalized to 100%. The columns labeled V0, V1 and V2 arethe mineral volumes (unnormalized) (moles*molar volume) in cm3. In this example, at thegarnet isograd (Mgarnet = 0), the mode of chlorite is 12.98 %. Of course, the modes canbe examined at any P and T desired.

Note that the input bulk composition is not exactly the same as the calculated bulkcomposition. This is because the input bulk composition is not necessarily normalized to100%, whereas the calculated bulk composition is normalized. The moles of each systemcomponent are, however, identical.

Note also that negative amounts of phases are perfectly OK in a thermodynamicsense, but are obviously impossible in a physical sense. The mass balance equations do notcare whether a phase has a positive or negative abundance, so it is good to check to see thatall phases have non-negative amounts.


Exercise 3: Saving text and graphics outputExercise 3.A. Saving the text output

Any text output (in the Command window or the Output window) can be saved as atext file. Here is the procedure:

1) Highlight (bring to the front) the window you want to save2) Select “SaveAs” from the “File” menu in the Macintosh menu bar3) Type in a file name and click Save

Note that only 32K of information is saved in these text windows. If you wish to generatemore text output, you may have to save more than once.

Exercise 3.B. Saving the graphics output

Fancy plots are of little use if you can’t save them. There are several ways thatgraphics can be saved in Program Gibbs.1) Use the Macintosh system function to save the screen as a PICT file.

a) Arrange the graphics window so that it shows what you wish to save as a PICT fileb) On the keyboard, press Command+Shift+3. The cursor should turn into a + signc) Click the mouse and drag the cursor across the area you want to save. When you

release the mouse, you will hear a noise (supposedly the sound of a camerashutter). The image you selected will be saved on the root director of your startupdisk with a name like “Picture 1”. These images can be viewed in SimpleText or inPhotoshop.

2) Use the “Save Picture” option in Gibbsa) Select Begin/Save problem from the Main menub) Select option 7 (Save Picture as PICT file).c) You will be presented with a list of graphics windows. Type in the number of the

graphics window you want to save.d) You will now be requested to input a file name for the image. Choose any name

you like.e) The image will be saved as a PICT file. These files can be viewed in Photoshop or

SimpleText. They can also be opened in Adobe Illustrator and Illustrator willvectorize the image so that you can edit it.

3) Use the “Save as PostScript file” option in Gibbsa) From the Begin/Save menu select option 6 (Save as Postscript File)b) You will be prompted for a file name.c) This file can be opened in Adobe Illustrator. Note, however, that only the primary

graphics window can currently be saved in this way. To save an editable version ofan AFM diagram, you must use the “Save Picture” option.

Exercise 3.C. Redrawing the plotting axes

Many different types of diagrams can be drawn in Program Gibbs. Any twovariables from the list of thermodynamic variables in an assemblage can be plotted as X-Ydiagrams. So far, we have only plotted P-T diagrams, but T-X, P-X, X-X, T-M, P-M, X-M and M-M diagrams can also be plotted. Several different types of plots types areavailable from the plotting menu, and others can be added to the text file namedGibbs.PlotDefinitions in the Gibbs_Essential folder. Tie lines can be drawn betweenphases, if desired. Ternary diagrams can also be drawn using any of the systemcomponents, plus some simple projections. Coordinates of projection points are in the first


few rows of the thermodynamic data file and can be augmented by the user (see GibbsReference manual for details).

A common need is to redraw the same set of axes to create a new plot. To redrawthe axes, do the following:9) From the main menu (or the Contour or Steps menu) select 9 (Go to plotter menu)10) In the plotter menu, select 2 (Draw axes for X-Y diagrams).

a) You will see a dialog box that will enable you to change the range on the X and Yaxes, if desired.

b) Click OKc) You will see a dialog box asking if you want to save the PostScript file (of the plot

just drawn). Click NO.d) The new axes will be drawn in the graphics window.

It is also possible to change the color of lines plotted. Simply choose the desiredcolor from the Macintosh menu named Plot.


Exercise 4: Petrogenetic grid routinesFeatures of petrogenetic grid routines

The MakeMyGrid module in Program Gibbs is a collection of routines to facilitatecalculation a number of operations on an internally consistent thermodynamic data set. Theprogram has options to perform the following types of calculations:1) Plotting a petrogenetic grid for the defined system (KFMASH in this release).2) Calculation of quantitative AFM diagrams for any P and T. Several options are

available for specification of the desired P-T conditions:a) Input T and P from a dialog box.b) Click the mouse on the grid to specify P and T.c) Read T and P from an input file that contains a list of P-T conditions along any P-T

path.3) Outline on the grid the stability region for any divariant AFM assemblage.4) Construction of P-T, T-X and P-X assemblage stability diagrams.5) Contouring P-T regions with mineral composition and abundance.

Currently, there are two data sets supported by the program:1) Spear, Pattison and Cheney (2000, unpublished) thermodynamic data set.2) Holland and Powell (1998, Journal of Metamorphic Geology) data set.

Exercise 4.A. AFM diagram routines

1) From the Gibbs main menu, select option ???? (MakeMyGrid)2) You will see a list of thermodynamic data sets for which grids have been constructed.

a) Select Holland and Powell (1998) KFMASH

The petrogenetic grid is automatically plotted when you start up this routine. The grid is notlabeled, so it is not possible to tell by inspection what each reaction is. A labeled version ofeach grid is included as PDF files on the disk and can be viewed by clicking these links:1) Holland & Powell (1998) grid (labeled – pdf version)2) Spear, Pattison & Cheney (2000) + Cld (labeled – pdf version)3) Spear, Pattison & Cheney (2000) no Cld (labeled – pdf version)

4) From the Make My Grid menu, select option 1 (AFM diagram routines). The list ofKFMASH assemblages will scroll in the command window and you will be presentedwith a sub-menu:

AFM diagram menu 0 = return --------------------------- Pick P and T for AFM diagram 1 = P&T dialog box 2 = Point and click on grid for T and P 3 = Open file with P&T --------------------------- Options 4 = Set scale for AFM triangle 5 = AFM diagram options --------------------------- Other AFM routines 6 = Plot region outlines on P-T diagram 7 = AFM diagrams for individual assemblages (ignores absolute stability of assemblage)


8 = Hints on making a movie

There are three ways to specify P-T conditions for drawing AFM diagrams.Option 1 presents the user with a dialog box:

If you specify only a start T and P, and click “Calculate AFM” a single AFM diagram willbe drawn. If you specify Start, End and ∆ values and click “Animate”, a series of AFMdiagrams will be drawn at intervals specified by the Start and delta values along a linear P-Tpath. For example, clicking “Animate” with the values specified above will result in 50AFM diagrams being drawn along an isobaric heating path from 500 to 600 ˚C at 2˚Cintervals (500, 502, 504, etc.).

Option 3 requests the name of a TEXT file with values of T and P along a P-T path. AFMdiagrams will be drawn at each P-T condition in the file.

Options 1 and 3 are most useful when creating sequences of AFM diagrams to convert intomovies.

Option 2 is the most fun:4) Select option 2 (Point and click on grid for T and P

a) The Grid graphics window will become active.b) Click on the grid and the AFM diagram at the indicated P-T conditions will be

drawn in the AFM diagram window.c) Click anywhere you want to draw new AFM diagramsd) When you’ve seen enough, hit “esc” to exit from this routine.

5) Select option 6 (Plot region outlines on P-T diagram). You will be presented with thelist of all stable 3-phase assemblages. Select one (any one) and the stability region forthis assemblage will be illustrated on the grid. The magenta dots are places at the P-Tlocations that define the assemblage stability region.

Option 5 (AFM diagram options) provides means for modifying the appearance of the AFMdiagram:


6) The color of the 3-phase triangle and 2-phase tie lines can be set with the pull-downmenus.

7) Erase old AFM, if unchecked, will overprint one diagram with another8) Plot small grid will plot a small version of the grid and the P-T point in the AFM

window9) PT path or point will erase (or not) old P-T points from the grid in the AFM window.10) Save AFM as PICT file will request the user for a “base” file name. All AFM diagrams

calculated until this switch is turned off will be saved with this base name, the P&T anda PICT number (user specified in the text box). These PICT files can be opened inAdobe Illustrator and drafted, or imported into NIH image, converted into a stack, andsaved as a Quicktime movie.

DiscussionConstruction of an AFM diagram takes a large number of calculations. First, the

program must determine which AFM assemblages are stable at the P and T specified. Itdoes this by comparing the specified P and T with the P-T region defined by each mineralassemblage in the grid. The Macintosh toolbox PtInRgn (Point-in-region) is used for thispurpose. Then the assemblage is loaded into the Gibbs Program and the stablecompositions calculated at the P and T specified. This is done for each stable assemblage.Then the 2-phase tie lines are calculated and drawn by first determining which 3-phaseassemblages form upper or lower bounds for the 2-phase assemblage.


People have asked me after seeing this routine “What is there left to ask the studentsto do?” and I have thought of some exercises that can be integrated into a petrology classwith this routine.(1) Determination of grid reactions by comparing AFM topologies on either side of the

reaction. The grids are unlabeled, but the AFM diagrams are. (Labeled versions of thegrids are available in PDF format on the disk). Students can be asked to label the gridreactions by seeing how the AFM diagram changes. This is an excellent way to reinforcethe relationship between AFM topology and univariant reactions.

(2) Determination of sequence of mineral assemblages for a specified bulk composition.Students can create movie showing the sequence of AFM diagrams along a specified P-T path. Then, using the frames of the movie, they can determine the sequence of mineralassemblages and reactions encountered for a bulk composition that plots on the AFMdiagram. The easiest way to do this is to simply put a dot on the computer monitor witha water-based felt pen, then step through the sequence of AFM diagrams and see whichassemblages intersect the bulk composition. This is an excellent way for students tograsp the relationship between bulk composition, phase diagrams and mineralassemblages. It also illustrates how some isograds are discontinuous reactions whereasothers are continuous reactions.

(3) Students can be given a set of mineral assemblages found in rocks of different bulkcompositions at an outcrop and asked to find the P-T region where these assemblageswould all be stable. This can easily be done using option 6 (Plot region outlines on P-Tdiagram) for each assemblage. A good example to try is the two assemblages Staurolite+ garnet + biotite (+muscovite + quartz) and Cordierite + biotite + sillimanite (+quartz +muscovite).

Exercise 4.B. T-X and P-X assemblage stability diagram routines

Program Gibbs has the capability of drawing P-T, T-X, and P-X mineral stabilitydiagrams. One can do this for any system with any thermodynamic database using theSteps and Contour menus. For thermodynamic databases for which there is a petrogeneticgrid, the program can perform many of the required operations automatically.

In this exercise, we will draw a T-X diagram along an isobaric heating pathshowing the assemblage stabilities and the Fe/(Fe+Mg) of each phase.

1) From the Gibbs program main menu, select option ???? (Make My Grid).2) Select the Holland and Powell (1998) thermodynamic data set.3) From the Make My Grid menu, select option 3 (Stability diagrams)4) Select option 2 (T-X or P-X diagram)

a) Click OK to select the default plotting parameters. A window should open with theT-X diagram plotted. The X-axis is scaled from 0 to 1 Mg/(Mg+Fe) and the Y axisis scaled from 0 to 1 but is unlabeled. The scaling of the Y axis is determined in thedialog box below.

5) Select option 1 (P&T dialog box). Enter values in the appropriate places so that it lookslike this:


This routine can construct a PT-X section along any linear P-T path. The values in the boxshown above will generate a section along an isobaric heating path at 5000 bars between500 and 700 ˚C, divided into 200 steps or 1 ˚C/step. The section will be drawn at an Alcontent of 0.1 (the Al’ coordinate on the AFM diagram).

Two diagrams are possible. One can plot the Fe/(Fe+Mg) of each Fe-Mg solutionphase (the option highlighted above), or one can plot a pseudosection projection. Apseudosection projection defines the stability limit for each assemblage, and is defined bythe region bounded by lines in which the abundance of one phase is zero. One way tounderstand the difference between an Fe/(Fe+Mg) plot and an assemblage stability diagram(pseudosection projection) is to consider the two AFM diagrams below:


Fe Mg

Al'(Ms)

TC = 560.0 PB = 9000.0

Ky

Chl Grt

St

Cld

Bt

+ Qtz+ H2O+ Ms

Fe Mg

Al'(Ms)

TC = 587.0 PB = 9000.0

Ky

Chl Grt

St

Bt

+ Qtz+ H2O+ Ms

Below 560 ˚C, the assemblage in the rock represented by the magenta dot is Chl + Bt + Ms+ Qtz + H2O. At 560 ˚C, garnet joins the assemblage (the garnet isograd). As temperatureincreases from 560 to 587 ˚C, the assemblage is Grt + Bt + Chl + Ms + Qtz + H2O, garnetincreases in amount at the expense of chlorite (the continuous reaction Chl + Qtz = Grt +H2O) and garnet, chlorite, and biotite become increasingly Mg-rich. At 587 ˚C, chloriteleaves the assemblage and above 587 ˚C, the assemblage is Grt + Bt + Ms + Qtz + H2O.

The Fe/(Fe+Mg) and assemblage stability diagrams for Al’ = 0.1 are shown belowwith the temperature window 560-587 ˚C and the Fe/(Fe+Mg) of the magenta dot rockindicated. At all temperatures, the Fe/(Fe+Mg) plot correctly depicts the Fe/(Fe+Mg) ofgarnet, chlorite, and biotite. However, note that at 560 ˚C, the magenta dot plots inside ofthe T-X loop describing the Fe/(Fe+Mg) of the assemblage, giving the impression that thegarnet isograd in this rock would be at approximately 550 ˚C, rather than at 560 ˚C.

The assemblage stability diagram, on the other hand, does not show the correctFe/(Fe+Mg) of any phase, but rather shows the Fe/(Fe+Mg) of where the magenta dotintersects the 3-phase triangle Grt + Chl + Bt on the AFM diagram. This diagram does,however, show the correct temperature of the garnet-in and chlorite-out isograds. Theassemblage stability diagram for XAl’ = 0.1 for this assemblage is thus defined as theregion bounded by the curves where MGrt = 0 and MChl = 0.


Fe/(Fe+Mg)�

T C

�Fe/(Fe+Mg) plot�

P = 6 kbar�

1.0� 0.8� 0.6� 0.4� 0.2� 0.0�500�

540�

580�

620�

660�

700�

740�

780�

Grt�

Chl�

Bt�

560�

587�

Fe/(Fe+Mg)�

T C

�

Stability Diagram�

P = 6 kbar�

1.0� 0.8� 0.6� 0.4� 0.2� 0.0500�

540�

580�

620�

660�

700�

740�

780�

Grt + Bt�

Chl + Bt�

Grt +

Chl +

Bt�

560�

587�

6) Click “Calculate PTX diagram”. You should see the diagram being drawn in thegraphics window.a) If you hear a beep, look at the command window and you will likely see a message

that says that a component has a zero or negative value. This usually is causedwhen the Newton-Rapheson routine doesn’t find a solution. It also means that aspecific mineral stability region won’t be calculated and plotted. Generally, it is asmall, skinny one, but it is important to take note of this when you are trying tolabel the fields on the diagram.

7) Now repeat numbers 5 and 6, but this time draw a stability diagram (pseudosection).Your final plots should look like this (cleaned up and labeled in Adobe Illustrator):


0.0 0.2 0.4 0.6 0.8 1.00.0

0.2

0.4

0.6

0.8

1.0

Mg/(Mg+Fe)

�T

or

P

vector

(0-1)

Stability diagram

Chl + Bt

St + Bt

Sil + Bt

Grt + Bt

Grt + Bt

Crd + Bt

Grt+

Sil +

Bt

Grt+St+Bt

Grt Chl

Bt

Sil St

BtSil

Chl Bt

Crd Sil Bt

St Chl

Bt

500

600

700

P = 5000 bars

0.0 0.2 0.4 0.6 0.8 1.00.0

0.2

0.4

0.6

0.8

1.0

Mg/(Mg+Fe)

�T

or

P

vector

(0-1)

Fe/(Fe+Mg) plot

Chl + Bt

St + Bt

Sil + Bt

Grt + Bt

Crd + Bt

Bt

Chl

Bt

Crd

Grt

Grt

St

Bt

DiscussionThe two diagrams are drawn along the same P-T trajectory (500-700 ˚C, 5 kbar)

but they show different information. The diagram on the left (th Fe/(Fe+Mg) plot) depictsthe Fe/(Fe+Mg) of each phase at the indicated temperature. The diagram on the right showsthe P-T regions in which different assemblages will actually be stable.

The Fe/(Fe+Mg) plot is an excellent aid to help interpret chemical zoning in phases.For example, the diagram reveals that staurolite becomes more Mg-rich with increasing T inthe assemblage St + Chl + Bt but becomes more Fe-rich with increasing T in theassemblage Grt + St + Bt.

The Assemblage stability diagram is very useful for interpreting reaction textures.For example, a rock with a Fe/(Fe+Mg) of 0.75 (Mg/(Fe+Mg) = 0.25) will have theassemblage Chl + Bt (+ Ms + Qtz) up to approximately 560 ˚C at which point staurolitewill enter the assemblage by continuous reaction. At approximately 565 ˚C, chlorite willleave the assemblage, again by continuous decrease. Between 565 and 610 ˚C, theassemblage will be St + Bt, at which point sillimanite will appear. Staurolite will react outby 615 ˚C, leaving the assemblage Sil + Bt (+ Ms + Qtz). Note that all of these changestake place by continuous reaction and not one of the univariant reactions shown on thepetrogenetic grid is encountered by this bulk composition.

Exercise 4.C. P-T stability diagram routine

P-T stability diagrams are very much like T-X or P-X stability diagrams except thatthey are plotted on a P-T diagram and they are only valid for a single bulk composition. Wewill create a P-T stability diagram for the same bulk composition examined in Exercise 2,except that this time we will take advantage of the capabilities of the assemblage regiondefinitions to simplify our task.


1) From the Make My Grid menu, select option 3 (Pseudosections)2) Select option 1 (P-T pseudosection (stable assemblage for a fixed bulk composition))3) From the Pseudosection menu, select 1 (Pick a bulk composition)

a) Select the bulk composition Al’=0.056, Fe/(Fe+Mg) = 0.754) From the Macintosh menu bar, select Plot > Magenta. This will make the lines we are

to draw a different color from the lines on the grid.5) From the Pseudosection menu, select 2 (Construct pseudosection)

The routine to construct P-T pseudosections is not extensively automated, and theprocedure is very much like the one we used in Exercise 2 when we constructed thecontour diagram. I may try to automate this a bit more in the future.

6) Select the assemblage Chl + Grt + Bt from the list.7) You will now be in the Contour dialog box

a) Click Resetb) Select Mgarnetc) Set the value to contour to 0.0d) Be sure the interval is set to 1%e) Click Compute Contourf) The contour will be calculated and plotted (the same as with the Contour menu)g) After the contour is drawn, the program asks if you want to clip the curve in the

stability region. Click “Yes”. This will remove the parts of the curve that are notstable.

h) Type 1 to continue contouring with this assemblagei) Repeat (a) – (g) for Mchlorite.j) Type 0 to return (you are done contouring this assemblage).

8) Repeat 5, 6 and 7, drawing contours for Mphase = 0 for the following assemblagesa) Grt + St + Bt (contour MGrt and MSt)b) Chl + St + Bt (contour MChl and MSt)c) Sil + Grt + Bt (contour MSil and MGrt)d) Sil + St + Bt (contour MSil and MSt)e) And + St + Bt (contour MAnd and MSt)f) Sil + Grt + Bt + Kfs (contour MGrt – MSil is off the diagram)g) Grt + Crd + Bt + Kfs (contour MGrt)h) Sil + Crd + Bt + Kfs (contour MCrd and MSil)i) And + Crd + Bt + Kfs (contour MCrd and MAnd)j) And + Crd + Bt + Ms (contour MCrd and MAnd)k) And + Chl + Bt (contour MAnd and MChl)

9) Return to the Begin/Save menu and save your graphic (as a PICT file or a PostScriptfile)

When done, the P-T diagram looks like this (after some editing in Adobe Illustrator)


Grt + Bt

Grt + Sil +

Bt

Crd +

Als +

Bt

Grt+St+ Bt

Chl + Bt

Als + Bt

Crd + Bt

St+Bt

Grt+Bt+

Chl

Grt+

Crd+

BtSt+Als+Bt

Chl+St+Bt

Chl+Als+Bt

400 500 600 700 8000

2

4

6

8

10

12

14

16

18

20

T (C)

P k

bar

Stability diagramAl' = 0.1; Fe/(Fe+Mg) = 0.75H&P (98) data set; KFMASH

DiscussionThe P-T stability diagram depicts the phase assemblages that will appear at different

P-T conditions for the bulk composition we specified. The diagram is most useful forpredicting and interpreting reaction textures. For example, a clockwise P-T path such as theone shown by the large arrow will generate the assemblage sequenceChl + Bt > Grt + Chl + Bt > Grt + Bt > Grt + Sil + Bt > Sil + Bt

It is interesting to note that there is no staurolite zone in this sequence. It is alsointeresting that not one of the “isograds” experienced by this rock is the result of adiscontinuous reaction; rather all appearances and disappearances of phases are the result ofcontinuous reactions.

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